The Walloon farmers position differently their ideal dairy production system between a global-based intensive and a local-based extensive model of farm

Dairy farming systems are evolving. This study presents dairy producers’ perceptions of their ideal future farm (IFF) to ensure revenue, and attempts to determine the reasons for this choice, the environmental aspects related to this choice, the proximity between the current farm and the IFF and the requirements for reaching this IFF. Just before the end of the European milk quota, a total of 245 Walloon dairy producers answered a survey about the characteristics of their IFF and other socio-environmental-economic information. A multiple correspondence analysis (MCA) was carried out using seven characteristics of the IFF (intensive vs. extensive, specialised vs. diversified, strongly vs. weakly based on new technologies, managed by a group of managers vs. an independent farmer, employed vs. familial workforce, local vs. global market, standard vs. quality-differentiated production) to observe the relationships between them. Based on the main contributors to the second dimension of the MCA, this axis was defined as an IFF gradient between the local-based extensive (LBE) producers (26%) and the global-based intensive (GBI) producers (46%). The differences of IFF gradient between modalities of categorical variables were estimated using generalised linear models. Pearson correlations were calculated between the scores on the IFF gradient and quantitative variables. Finally, frequencies of IFF characteristics and the corresponding characteristic for the current situation were calculated to determine the percentages of “unhappy” producers. Some reasons for the choice of IFF by the producers have been highlighted in this study. Environmental initiatives were more valued by LBE than GBI producers. Low similarity was observed between the current farm situation of the respondents and their IFF choice. LBE and GBI producers differed significantly regarding domains of formation (technical and bureaucratic vs. transformation and diversification respectively) and paths of formation (non-market vs. market respectively). Two kinds of farming systems were considered by dairy producers and some socioeconomic and environmental components differed between them.

academic editor and one remark of the reviewer). The second part concerns the specific answers to the specific remarks formulated by the reviewers. Sincerely, Anne-Catherine Dalcq 1/ Methodology Please read carefully the propositions of reviewer #2 especially about the recommendations you did not took into account in your revision. I am afraid the reviewer is right about the interest of LCA vs MCA, as we expect a characterization of different profiles of dairy farmers. But my proposition is that instead of LCA, you use HCPC (Hierarchical Clustering on Principal Components) which a natural and standard extension of MCA (see Arguelles et al. 2014, Kassambara 2017 or the following technical report http://factominer.free.fr/more/HCPC_husson_josse.pdf). H. Soyeurt : Dear Editor, Dear Reviewers, Instead of my PhD student, Miss Anne-Catherine Dalcq, I would like to answer to the question related to the methodology used in this study. I am Professor Hélène Soyeurt and I teach courses related to Data Mining and Machine Learning at Gembloux Agro-Bio Tech (University of Liège). Therefore, I have an experience in the use of multivariate analysis. It is why I would like to answer by myself to the question related to the method used in this article. Before starting an explanation, I would like to precise that we have not really understood the comments of the reviewer about Latent Class Analysis (LCA) because the objective was not to create groups of farmers. Indeed, and this is the innovative aspect of this paper, a gradient between two quite different models of farms was studied. The gradient is really important because it appears to us simplistic to classify farmers in only 2 groups, working with a gradient allowed us to nuance the position of the dairy producers and to analyze more precisely the link between this position and other characteristics. The use of the gradient allows studying the trend of a farmer. It is why in this paper, we always mention "tend towards" to make a reference to the position on the gradient and not a binary choice of a model. As we did not want to create farmer's clusters, LCA was not appropriate as well as HCPC. However, as asked by the second reviewer to prove the robustness of our approach, we have decided to show you the similarities and the extended work that it is possible to do using Multiple Correspondence Analysis (MCA) and LCA. Indeed, it is also possible to use LCA to create a gradient instead of using the clusters. So, I would like to remind the methodology that we have proposed in this study (see the figure below, Fig 1)). Again, MCA was used to observe the relationships between the seven studied variables. Based on the interpretation of MCA dimensions, we have observed that the second dimension represented the positioning between the two models for a dairy farm. Therefore, the score for this dimension for a specific producer allows to know its perception of ideal future farm between the two extreme models. This gradient allows avoiding to limit the farm typology to 2 clusters. This is interesting because many farmers combined some approaches specific to one model of farms (no more intensification but extensification, local-based market) or another one (globalbased market, continuously improvement of the productivity thanks to, notably, intensification, …). Therefore, wishing to split the dairy farmers into 2 groups is too limitative. Some farmers remain between these two models (Fig 2), some farmers are more convinced than others by a model. Farmers showing higher scores are really convinced by GBI model, farmers showing lower but positive scores choose GBI model but are not 100% in this way of farm development. Negatives scores express the position of farms in favor of LBE model, the lowest scores reflected pronounced adhesion to this model. It is why the gradient as proposed in this paper was useful and seem to us the most interesting tool to represent dairy producers. Distribution of the producers (the "with an opinion" ones) along the second dimension of the MCA Similarly, we have done this job using LCA methodology as requested by the reviewer#2. LCA allows defining clusters from the dataset. In this case and to be in line with the study objective, we have decided to create 3 clusters. Moreover, based on the AIC and BIC values, it was also the best model (Fig 3). LCA allows us to create those 3 clusters. After the interpretation of defined clusters, it appeared that we have a cluster representing "No opinion" responders, one cluster representing "global-based intensive" (GBI) farmers and one cluster representing "local-based extensive" (LBE) farmers (Fig 4). Therefore, those clusters were similar to the ones obtained by combining MCA and Ward clustering (=HCPC method) as done to clean the dataset (i.e., extract responders with "no opinion" behavior). Again, we did not want to use those clusters to make our analysis. But, using this methodology, it is possible to obtain a probability to belong to a specific cluster. Therefore, we have decided to compare the gradient as defined in the current study to the probability to belong to the LBE or GBI clusters defined using the LCA method. So, now, it is time to present you the results. I will not present you the results about MCA as those results are reported in the article. In this paragraph, we will focus on the LCA results. As we used categorical variables which are not ordinal, we have decided to use the polytomous latent class analysis. The variables used, called manifest variables, were the same than the one used for MCA. The modalities for each variable were recoded from 1 to 3 As this clustering is very sensitive to the prior values used to start the iteration, 10 repetitions were used to provide you the final results for all models. All calculations were done with R software and more specifically the package poLCA. First, we have run different LCA models using a different number of classes (clusters). We have tested models from 1 to 10 classes and then we have estimated the AIC and BIC criteria to observe which model allowed the best fitting. The results of AIC and BIC for all models are presented in the figure below (Fig 3). From this figure, we can conclude that the model allowing the creation of 3 classes is a good comprise between BIC and AIC (i.e., the lowest BIC and AIC values).

Figure 3 AIC & BIC criteria values
The figure below shows you the clusters defining by the model allowing a discrimination of the data into 3 clusters (Fig 4). This figure represents the probability to have a specific modality for each cluster. So, based on those results, we can conclude that the first clustering (class 1) is related to GBI dairy producers, the second cluster (class 2) is related to LBE dairy producers and the last cluster (class 3) is related to the dairy producers with "no opinion". Figure 4Description of the three clusters obtained by LCA method Therefore, in order to clean the dataset (i.e., delete records from farmers having many "no opinion" views), we can use the clustering 3. This process is similar to the MCA + Ward clustering (HCPC) proposed in the manuscript. Again, we did not want to use clusters but we want to use a gradient. For MCA, this gradient was the second MCA dimension. In the context of LCA, this gradient can be derived from the probability to belong to class 1 ("GBI producer") or class 2 ("LBE producer"). So, to show the robustness of the MCA approach used, we calculated the correlation between those probabilities and the score of the second MCA dimension (called gradient in the manuscript). The correlation between the probability to belong to class 1 and the gradient was equal to 0.83. The correlation between the probability to belong to class 2 and the intensification gradient was equal to -0.87. The correlation between the 2 probabilities was equal to -0.97. From all of those results, you can see that the relationship is strong between MCA and LCA using an innovative approach focusing on the score/probability of an individual and not directly to a cluster. Using only the second dimension of MCA, we can reflect both clusters (class 1 and class 2) simultaneously. Indeed, the second dimension is a gradient "GBI-LBE" and included both. This is really interesting to observe the relationships between this gradient and other quantitative or qualitative variables as now the studied trait is quantitative. It allows to see if a modality of a categorical variable is the choice of really convinced GBI dairy producers or dairy producers only sticking out of the GBI model. I hope that this demonstration illustrates well the relevancy of the approach proposed in our paper. A sentence will be added in the materials and methods section to explain why LCA was not used. Moreover, some articles exist also in the literature to prove the mathematical relationships between MCA and LCA (e.g., Lautsch and Plichta, Psychology Science 2003:298-323 as well as Van der Heijden, et al., Sociological methodology 1999). The fact that the two dimensions explained almost 95% of the variability and that all the modalities representing an opinion positioning themselves along the second dimension support us to take the second dimension as gradient, after deletion of the No-opinion producers which were discriminated by the first dimension. Finally, I would like to acknowledge you for the great job done in the review of this paper. The manuscript was improved a lot. Sincerely, Prof Hélène Soyeurt PS : The answers to all other comments were done by Anne-Catherine Dalcq. 2/ Others comments Reviewer #2: In this revision, the authors have significantly improved the English language translation and clarified their research questions, but they have failed to address the shared concerns of reviewers regarding methods and clarity of writing. They have not adequately addressed the substance of the comments from reviewers. Regarding methods, the reviewers still do not offer a compelling and clear justification for why MCA is appropriate for their goals and they do not offer the latent class analysis that I suggested or the hierarchical clustering (related) suggested by reviewer 3 as alternatives or robustness checks. MCA, while performed adequately, is not well suited to the way they discuss their results. They continually refer to "types" of respondents, which is what latent class analysis is for. MCA is about identifying clustering of variables, not clusters of respondents. All of their interpretation of results is about clustering and patterns of PEOPLE, not variables. This indicates a significant misalignment between the method and the research goals. A-C Dalcq: First, we would like to thank you for the deep reading done on this article and for your formulated comments. We missed your request to test the robustness of our method with other ones. We apologize for this mistake. You will find our work of comparison with LCA method in the first part of this letter. In the article, we speak about producers tending towards "GBI" or "LBE" models to express the results coming from the use of our gradient. Indeed, MCA is a method to identify relationships between variables but is also suitable to make groups of individuals thanks to the use of its extension HCPC, as proposed by the academic editor. A detailed information about the comparison of MCA and LCA is now given in the first part of this letter.
The authors do not adequately discuss the two dimensions of the MCA (figure 1) and the axes are not adequately labeled. It is not made clear why the second dimension is retained. A-C Dalcq: We added some information. The updated explanations of the two dimensions are taken up just after . Do you need more information? If it is the case, could you guide us? Remark : Lines specified throughout this letter are those of the revised manuscript with track changes. The axes are labeled as the figure is provided by SAS 9.4. We precised its meaning thanks to the caption and the following interpretation. Explanations of the two dimensions: Lines 254-261: "The first dimension of MCA showed positive relationships with the modalities no opinion of each characteristic and negative relationships with all the modalities representing an opinion. Thus, the first dimension of the MCA allowed permitted differentiation between the producers who did not give their opinion concerning characteristics of IFF and the producers who did (Fig 1). Cluster analysis was used to isolate the group of producers with a lot of 'no opinion' answers to the seven questions: this formed the first separation of classes of the analysis, dividing the "no-opinion" producers (15%) from the others (85%)." Lines 286-306: "The second dimension of the MCA showed positive relationships with some modalities of the IFF characteristic and negative relationships with their opposite. Thus, this dimension seems was the most interesting for highlighting to highlight the wishes of dairy farmers about their IFF, for those who took a position on this question.
More precisely, this axis showed a gradation of question modalities and proximity between several characteristics. This dimension led to the identification of two extreme tendencies (Fig 1); the modalities of familial workforce, independent farmer management and management by a group of farmers were near to zero on this axis (Fig 1). This means that the small proportion of producers supporting group management was distributed between the two extreme tendencies observed. The position of the modalities of familial workforce and independent farmer at the middle of the second dimension illustrated the fact that these modalities were chosen by producers from the two tendencies identified. The small proportion of producers choosing an employed workforce was positioned at the top of the second dimension (Fig 1)." "The first tendency, related to high scores on the second MCA dimension, corresponds to IFF with the following characteristics: global market, standard milk, intensive system, employed workforce, specialised and strongly based on new technologies." Lines 339-343: "The second tendency, contrary to the first tendency, was characterised by negative scores on the second MCA dimension. This axis was represented by the following modalities: weakly based on new technologies, diversified, differentiated quality milk, local market and extensive system (Fig 1). This reflects another form of dairy farming. » Reason of the use of the second dimension: Lines 379-384: "To study the relationships between the different IFF, the reasons for these and other interesting technico-economic information, the second dimension was considered as a gradient (IFFg) interpreted at the extremities as global-based intensive producers (GBI: high positive scores) and local-based extensive producers (LBE: high negative scores). The choice to work with a gradient rather than a clear separation of the two tendencies was motivated by the will to not put dairy producers into boxes pigeonholes" While the authors have provided a link to the survey online, that link is only in French and requires registration with an email address before it can be viewed, so that is not adequate. The authors still have not addressed the real concern that I raised in my previous review: they need to be clear about how they measured their concepts (intensive/extensive, etc.), what specific survey questions were used, and how those variables were coded. A clear list of questions for each concept and the coding for each is needed. For instance, in Table 2, it is not clear what specific survey questions or variables represent these concepts and how those variables were actually coded. A-C Dalcq: In the current version, we have added an annex (Appendix 1) with the translation of the questions mobilized in the paper. Given the length of the survey, we provided only the questions raised in the present paper. Some information are mentioned at lines 129-136 about the questions related to the ideal future farm characteristics (intensive vs. extensive,…), the way of measurement for our developed concepts. If you need more information, could you precise them to us explicitly ? Lines 129-136: "The entire survey was composed of 127 questions where the answers were decomposed into 498 categorical and 44 quantitative variables. The question 'Without taking into account your current farm, what is, according to you, the ideal future farm to ensure a revenue?" was proposed to the producers and they must could choose between short propositions on seven items: 1) intensive or extensive production; 2) specialised or. diversified activity (or activities); 3) farming strongly or weakly based on new technologies; 4) farm managed by an independent farmer or a group of managers; 5) family or employed workforce; 6) providing production for local or global markets; 7)providing standard or differentiated quality production. The modality "no opinion" was available for each IFF question." The authors still do not address response rate for the survey. They do now address representativeness of their respondents for this specific region, but they have not addressed the bigger questions of representativeness: how does this one region in one nation represent that nation, Europe, and/or agriculture broadly? A-C Dalcq: The response rate of 6,1% was already precised in the past manuscript. You can find it at lines 200-201 of the current text. Lines 200-201 : "The sample set of 245 producers represented 6.1% of the dairy producers in Wallonia (about 4,000 dairy producers in 2015 and 3,500 in 2017 (STATBEL, 2019))." For the second part of your comment, do you want that we precise that the Walloon Region is one of the two regions of Belgium, which is one of the 27 members countries of the European Union? If yes, the proposal could be : "The Walloon Region is one of the two regions of Belgium, which is one of the 27 members countries of the European Union". Or do you want that we precise the number of dairy producers in Belgium and in the European Union? The International Dairy Federation mentions 9,674 dairy farms in Belgium and 1,130,700 farms with a dairy activity in the European Union (Confédération Belge de l'Industrie Laitière, 2020). The number of Walloon dairy farms is obviously low amongst all of these countries. We do not know if all this information is relevant to be written in the manuscript. Complete reference: Confédération Belge de l'Industrie Laitière. 2020. Rapport Annuel 2020. The goal of this paper is to inform about the position of dairy producers of a region, which is moreover quite heterogeneous regarding the geopedologic conditions (lines 205-206), this one can represent the context and the resources of other producers in Europe. The goal was not to give a complete vision of all the European producers, which needs higher means.
In all tables the n, or respondent totals, should be clear. A-C Dalcq: We added a sentence at lines 395-396 :"These analysis were conducted on the producers who have an opinion (N = 207)." And the N was precised and added in each table. Thanks for this remark which brings clarity throughout all the paper.
For Table 5 there are subscripts/footnotes that are never defined or labeled. A-C Dalcq: The subscripts are now precised in each table. "Means with different letters are significantly different.". Thanks for this remark.
For Tables 3 and 4, no significance tests are reported. A-C Dalcq: Indeed, the goal was not to test the differences between the no-opinion producers and all the sample but to give an idea of the characteristics of the Noopinion producers. Reviewer#3 asked us to give all of this information also for producers with an opinion. We realized ANOVA tests between the no-opinion producers and the producers with an opinion (lines 280-284) The interpretation of the MCA results is circular logic. They define the clusters based on variables such as the attitude toward technology and then present a finding that people who are in the "pro-technology" GBI cluster have more positive attitudes towards technology. Of course, that is how you defined the scale in the first place. A-C Dalcq: The variable "technology" is "Mechanisation and robotisation : help for workload and administrative aspects " and is present in the part "Reasons". This result is presented to explain one reason of the producers tending towards "GBI-model" to tend to this model and one of its component, the technology. We have better precised our idea by adding the sentence: "We observed that the wish of technology of producers tending towards GBI model can be explained by the fact that they considered it as help for workload." at lines 534-536.
Regarding writing, the presentations of results and its mixing with discussion of existing literature is still extremely unclear and difficult to follow. Both reviewer 1 and myself raised this critique: presenting your results intermingled with other literature is difficult to read and makes it unclear what your key findings are. This is not about the technical requirements of the journal. In its current presentation, readers cannot easily identify what your key findings are in each subsection and it is very difficult to read. For instance, in the section on pages 15-16, the authors spend substantially more time discussing other studies than they do their own results. A-C Dalcq: As already mentioned and visible at lines 304-364 in the revised paper, the explanations based on the findings of other past studies help to explain the relationships observed between the modalities of the seven ideal future farm characteristics.
The introduction is improved, but still weak. The first paragraph is overly general and does nothing to build the focus of the paper. The authors also spend too much time asserting the contribution of their study before they have even reviewed the literature or told us what their analysis will be. A-C Dalcq: What could be your expectations about the structure of this introduction? As the reviewer#3 did not make comments about the redaction of this part and without deeper expectations from your, the structure of the introduction was not changed.
The attempts to incorporate new literature are cursory. A-C Dalcq: The work of Mr Mooney was consulted and two references was added to the paper (lines 236-238, lines 577-580). Did you expect references to more elements of his work? Could you precise which ones? Moreover, we also investigated the phenomenon of bifurcation. Literature about bifurcation was mainly found for the organic activity. We consulted a Professor with skills in sociology, Prof Kevin Maréchal, of Gembloux Agro-Bio Tech-University of Liège (Belgium), who provided us also this literature reference. Do you have other literature to advice to me?
The paper is not appropriately written for a general audience. They assume too much prior knowledge from readers regarding methods both methods and the case. A-C Dalcq: We have now added information about the choice of the method between MCA and LCA, and about the method WARD (regarding a following remark). We hope that it brings the missing information. If this information is not complete for you, could you precise us explicitly the requested information? Lines 165-170: "This method was chosen instead of the creation of classes, possible with the Latent Class Analysis method or the Numerical Classification on the scores of MCA (Hierarchical Clustering on Principal Components). This choice was motivated by the wish to not put the producers in boxes but study their position on a gradient between potential extreme models identified along the dimension." Lines 153-156 : "The WARD method is a hierarchical agglomerative method (Everitt et al., 2011). The principle of this kind of method is to put initially the n individuals in n groups and then to agglomerate the groups. The algorithm of WARD makes it in such a way that the gatherings induce the lowest decrease of R2 at each step." Overall, the authors have inadequately addressed the careful feedback of the reviewers and made inadequate improvements. Throughout the response to reviewers they reject several important critiques with no justification of their rejection. A-C Dalcq: We recognized that we do not explain the choice of the method and we do not test its robustness with statistic treatments. We apologized for that. We missed this request. We realized this analysis at this time.
A number of specific points are highlighted below: Line 79-How was that ensured (respondent producers were asked not to take into account their current farm when considering their IFF)? A-C Dalcq: It is now precised in the Materials and methods section (Lines 131-134). Thanks for your remark. Lines 131-134 : The question 'Without taking into account your current farm, what is, according to you, the ideal future farm to ensure a revenue?" was proposed to the producers and they must choose between short propositions on seven items: 1) intensive or extensive production; 2)[…]" Line 121-survey link not accessible without registering. Include in appendix? A-C Dalcq: The appendix is realized and available in the new submission.
Line 146-What is WARD? A-C Dalcq: We added sentences of explanation about the Ward method at lines 153-156. It is a hierarchical agglomerative method of Numerical classification. Lines 153-156: "The WARD method is a hierarchical agglomerative method (19). The principle of this kind of method is to put initially the n individuals in n groups and then to agglomerate the groups. The algorithm of WARD makes it in such a way that the gatherings induce the lowest decrease of R2 at each step." Line 145-What are "particular characteristics" beyond no-opinion profiles? A-C Dalcq: We replaced particular by "some" (Lines 151). We hope it makes it clearer.
Line 157-What? A-C Dalcq: This sentence is a part of the method. As explained and precised before, we realized a MCA on the seven ideal future farm questions. We observed that the modalities "no-opinion" of the seven questions gathered and were positively related with the first dimension of the MCA. All the modalities reflecting an opinion were negatively related to the first dimension. Thus, the first dimension allowed to differentiate the producers with an opinion or not. The modalities "intensive", "global-market", "specialized", "standard quality milk", "employed workforce" and "strongly based on new technologies" gathered and were positively related to the second dimension. The modalities "extensive", "local-market", "diversified", "quality differentiated milk" and "lowly based on new technologies" gathered and were negatively related to the second dimension. The second dimension appeared to us as a gradient between the two extreme models of ideal future farm "Global-based intensive" and "Local-based extensive". The two dimensions explained almost 95% of the variability of the dataset. Therefore, the study of only these two dimensions appeared to us relevant. Then, we realized a numerical classification on the scores on the two dimensions of the MCA (statistic treatment equivalent to HCPC-Hierarchical Clustering on Principal Components). The first two groups created were the "no-opinion" producers and the producers "with an opinion". This allowed us to exclude the "no-opinion" producers and to study the producers with an opinion thanks to the second dimension, this one had at its extremities the "Local-based extensive model" and the "Global-based intensive model". But the producers with an opinion distributed themselves along this dimension. Thus, we decide to work with the second dimension, as a gradient of ideal future farm (Fig 5).
Then we want to study the relationships between this ideal future farm gradient and the other information present in the survey. The relationships between the ideal future farm gradient and the categorical variables of the survey were studied thanks to generalized linear models. The gradient was the y, the variable to explain. The modalities of the categorical variables were the fixed effect of the generalized linear model, the factors explaining. y = effect + residual Where y was a vector contained the score on the ideal future farm gradient (the second dimension of MCA); effect was the qualitative variables of the survey. In other words, the model was : Ideal future farm gradient = categorical variable + e To study the relationships between the gradient and the quantitative variables of the survey, correlation coefficients and their level of significance were calculated.
Line 160-What are the quantitative variables? A-C Dalcq: Quantitative is a statistical term defining a continuous numerical variable. Do you want that we use the term « numerical » ? But this term is less precise as it does not reflect the continuous dimension of the variable. Table 1-What are the ns? Maybe a total figure? Percentages? A-C Dalcq: Absolute frequencies named counts. We precised at lines 186 and 194: "Absolute frequencies (counts)". How many questions in each dimension? A-C Dalcq: One question. We have now mentioned that in the Materials and methods section at Lines 187-188: "and of the answer to the question which corresponds to this corresponding characteristic for the current situation".
Line 180-specifics of response rate still missing. A-C Dalcq: The response rate is 6,1% (Line 200). Which supplementary indication do you need? We gave you numbers of farms with a dairy activity in Belgium and in European Union in this letter. We give also more information about the conditions where the survey was communicated to the producers to give you an idea of the way of proceeding. More information is given at lines 120-126. Lines 120-126: "We communicated with Walloon dairy producers about the goals of the survey and its access broadly via all communication ways towards them : specialised press, agricultural internet websites, Unions and also advertisements through the milk payment letter which is sent to all the Walloon dairy producers once a month. The survey written in French can be viewed at the following internet link: https://www.gembloux.ulg.ac.be/enquete/index.php/219425?lang=fr and its English translation is viewable in the Appendix"  The percentages in the axes labels are the inertia but these ones underestimated the part of information explained by the dimensions. The corrected inertia values were calculated. This is explained in the Materials and methods section at lines 142-146: "For a MCA, the eigenvalue of the dimensions generated, named principal inertia, is a biased measure of the amount of information presented by a dimension (Palm, 2007). Corrected inertia rates were calculated, as described by Benzécri (Benzécri, 1979), to quantify the correct proportion of information of a dimension." The corrected values of inertia are presented at lines 248-250. The nature of the values are precised in the caption of the figure (lines 251-253). "The percentage of principal inertia of the dimensions 1 and 2 of MCA were 16.75% and 12.38%, respectively (Fig 1). The value of corrected inertia for the two first dimensions reached 72.7% and 21.5% respectively, gathering almost 95% of the information. Fig 1. Representation of the modalities in the multiple correspondence analysis first factorial plan. Values of principal inertia reached 16.75% and 12.38%. Values of corrected inertia reached 72.7% and 21.5%." The correction of Benzécri is made following this calculation: corrected inertia=〖(s/(s-1))〗^2*(µ_k-1/s)^2 with µ_k> 1/s s = number of categorical variables in the MCA µk= eigenvalue of the dimension (0.33508 and 0.2475, eigenvalues of respectively the first and second dimension of the present MCA) The corrected inertia gives a better appreciation of the amount of information explained by each dimension (Benzécri, 1979), than the inertia automatically provided by the software. We did not think necessary to precise this in the paper but we provide the reference where this calculation is presented.
Line 335-where is this figure reference from A-C Dalcq : We did not provide a representation of the distribution of the producers along the second dimension, we did not think it was necessary as we provided the percentages and this figure would lengthen the paper. But following your request, we have now added this figure in the present manuscript (Lines 376-377).
Fig 2. Distribution of the producers along the second dimension (the dotted line represents the mean score on the second dimension of the producers)(N = 207) Table 5-footnotes? Which is LBI and which GBI A-C Dalcq : We were not sure about the goal of your question. We precised the function of the letters a and b. Concerning your request about the LBE and GBI, as explained with more details in the point 1/, the analysis is not done between groups LBE or GBI and the variables present in the survey but between an ideal future farm gradient and the variables present in the survey. The means presented in the tables 5, 7 and 8 are the mean value of this gradient for the different modalities of the categorical variables. We explained this at lines 390-395. Lines 390-395: "Tables 5, 7 and 8 give the results of generalised linear models where the categorical variables were introduced separately as a fixed effect in the model. Significantly lower estimates of IFFg for a specific modality of the considered categorical variable depicts a tendency of producers desiring a LBE model to choose this modality, while significantly higher estimates of IFFg means a tendency of producers wanting a GBI model to choose this modality." What test is used here? A-C Dalcq: Generalised linear models were used to study the level of significance of the differences between the means values of the gradient of the modalities of categorical variables: y was the ideal future farm gradient and the effect included in the model was the categorical variable. We explained this part of the method in the Materials and methods section at lines 178-184. Lines 178-184: "For categorical variables, the scores of MCA dimensions were modelled using these variables as a fixed effect in a generalised linear model. Least squares means were estimated for the two-by-two comparisons using the Tukey test. The level of significance of those differences was assessed based on the P-value of the test. For quantitative variables, Pearson correlation coefficients were calculated between the scores of MCA dimensions and these variables. Their corresponding Pvalues were estimated to observe if the correlation values were significantly different from 0." Line 356 explain what they mean by introduced as fixed effect A-C Dalcq: As explained in the point 1/ of this letter, the gradient was used as y (variable to be explained) of the generalized linear models and the fixed effect introduced in the generalized linear model was the categorical variables. See the previous answer related to the same topic for more details.
Line 620-What is SFI A-C Dalcq : We precised this at line 661. "SFI = study, formation and information ». It is after the table. We have now added an asterisk to highlight the explanation of this abbreviation.
Reviewer #3: Thanks to the authors, ho made significant improvements to the paper. The full potential of the data is now revealed in the analysis. I particularly appreciate the improvements on the description of the « no-opinion » farmers, as suggested in my first review. A-C Dalcq: Thank you for the interest given to this study.
Specific comments: 84: add references to « This change implied the disappearance of regulation of dairy supplies and caused volatility and decrease in the milk price » A-C Dalcq: We added a reference and precised our purpose (Lines 83-84). Thanks for your remark. Lines 83-84: "This change implied the disappearance of regulation of dairy supplies and was bringing uncertainty about the milk price (16). caused volatility and decrease in the milk price. " Reference 16: Salou, T., H.M.G. van der Werf, F. Levert, A. Forslund, J. Hercule, and C. Le Mouël. 2017. Could EU dairy quota removal favour some dairy production systems over others? The case of French dairy production systems. Agric. Syst. 153:1-10. doi:10.1016/j.agsy.2017.01.004. 99-100: the question #2 is unclear. « What is the proportion of producers desiring the different IFF? » should be rephrased a bit maybe. The expression « the different IFF » will be vague for the readers. Is the IFF always different from the current farm ? And I guess « their IFF » is more thuitable thant « the IFF » as each respondent will provide a personal definition of their IFF. A-C Dalcq: We understand your will to make this question clearer. We have replaced it by « How the dairy producers distribute themselves between IFF highlighted ?" (Lines 100-101, lines 365-366).
122: you do not answer to another reviewer's comment, who wanted to know the response rate to the interview. To how many farmers was this survey submitted ? e.g. number of farmers buying the « specialised press », number of advertisements sent with the milk payment letter etc. A-C Dalcq: We precised in the text that all the Walloon dairy producers received this payment letter: +/-4,000 producers. Therefore, the 245 respondents correspond to 6,1% of the population, i.e. the response rate. We added information at lines 120-126 & 200-201. We do not know if the information number of farmers buying the « specialised press », number of advertisements sent with the milk payment letter are necessary in this paper but we added information to give an idea of the conditions in which the survey was communicated. Lines 120-126: "We communicated with Walloon dairy producers about the goals of the survey and its access broadly via all communication ways towards them : specialised press, agricultural internet websites, Unions and also advertisements through the milk payment letter which is sent to all the Walloon dairy producers once a month. The survey written in French can be viewed at the following internet link: https://www.gembloux.ulg.ac.be/enquete/index.php/219425?lang=fr and its English translation is viewable in the Appendix. A total of 245 producers completed our survey between November 2014 and January 2015." Lines 200-201: "The sample set of 245 producers represented 6.1% of the dairy producers in Wallonia (about 4,000 dairy producers in 2015 and 3,500 in 2017 (STATBEL, 2019)." 240:253 : the description of the no-opinion farmers adds value to the data analysis. However I am not sure that the last sentence is useful. This is your personal interpretation, but the data do not permit to reveal it. A-C Dalcq: Indeed, this sentence was deleted (Line 279). Thanks for your remark.
Tables 3 and 4: you have two columns, which are « complete sample » and « noopinion farmers ». A third column which reflects the sample excluding the no-opinion farmers will permit the reader to compare the no-opinion ones with the others. A-C Dalcq: Indeed, this column was added (Lines 280, 283). And, as asked by reviewer#2, we realized (1) generalized linear models to compare the means of the quantitative variables between the no-opinion producers and producers with an opinion and (2) tests of proportion to compare the proportion of each modalities of the categorical variables between the no-opinion producers and producers with an opinion. We added description of these statistical treatments in the Materials and Methods section (Lines 157-160). 333 : as already said, I think this title is not well written and could be more explicit. A-C Dalcq: It was changed at lines 365-366. See also the answer to your previous comment related to the same topic.
350 : pigeonholes. Could you be more precise? A-C Dalcq: As it caused doubt in your comprehension of this idea, we replaced by boxes (Line 384). Put people (here dairy producers) in boxes. It was used to explain the fact to put a label of someone. But in this paper, we want to nuance the position of the producer regarding its ideal future farm. Ideal future dairy farms to ensure revenue 10 Abstract 11 Dairy farming systems are evolving. This study presents dairy producers' perceptions 12 of their ideal future farm (IFF) to ensure revenue, and attempts to determine the 13 reasons for this choice, the environmental aspects related to this choice, the proximity 14 between the current farm and the IFF and the requirements for reaching this IFF. Just 15 before the end of the European milk quota, a total of 245 Walloon dairy producers 16 answered a survey about the characteristics of their IFF and other socio-17 environmental-economic information. A multiple correspondence analysis (MCA) was 18 carried out using seven characteristics of the IFF (intensive vs. extensive, specialised 19

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vs. diversified, strongly vs. weakly based on new technologies, managed by a group 20 of managers vs. an independent farmer, employed vs. familial workforce, local vs. 21 global market, standard vs. quality-differentiated production) to observe the 22 relationships between them. Based on the main contributors to the second dimension 23 of the MCA, this axis was defined as an IFF gradient between the local-based 24 extensive (LBE) producers (26%) and the global-based intensive (GBI) producers 25 (46%). The differences of IFF gradient between modalities of categorical variables 26 were estimated using generalised linear models. Pearson correlations were calculated 27 between the scores on the IFF gradient and quantitative variables. Finally, frequencies 28 of IFF characteristics and the corresponding characteristic for the current situation 29 were calculated to determine the percentages of "unhappy" producers. Some reasons 30 for the choice of IFF by the producers have been highlighted in this study. 31 Environmental initiatives were more valued by LBE than GBI producers. Low similarity 32 was observed between the current farm situation of the respondents and their IFF 33 choice. LBE and GBI producers differed significantly regarding domains of formation 34 (technical and bureaucratic vs. transformation and diversification respectively) and 35 paths of formation (non-market vs. market respectively). Two kinds of farming systems 36 were considered by dairy producers and some socioeconomic and environmental 37 components differed between them. 38 39 Introduction 40 Food is a basic need. Working to provide food for themselves and their family 41 was the task of everyone at the dawn of humanity. The progressive organisation of 42 society during the Neolithic period has led to the appearance of "producers" who are 43 responsible for producing food for more than just themselves and their family (1,2). 44 Since World War II, public policies have been set up to increase food production (3). 45 These policies impacted the development of producers and their farms in the European 46 Union. In the southern part of Belgium, the mean number of cows and the mean 47 agricultural area per producer increased between 1980 and 2017 from 20 to 66 heads 48 and from 25 to 71 hectares, respectively (4). 49 Producers are now facing great challenges to stay profitable. The price of the 50 inputs (e.g. buildings, agricultural machinery, installations, feeding, veterinary care) of 51 dairy production (DP) are increasing while the milk price shows great variability and its 52 inflation is not similar to that observed for the inputs (5,6). Moreover, the European 53 Union has decreased financial support to farmers (7). On 1 st April 2015, the European 54 Union removed the quota system which had managed the supply of DP (8). This led to 55 greater milk price volatility. Additionally, sanitary crises such as mad cow disease 56 (bovine spongiform encephalopathy (BSE)) and the dioxine crisis, among others, have 57 shocked consumers and led to new rules and regulations at European level and to the 58 creation of food security agencies in its countries. Moreover, these episodes modified 59 consumers' behaviours regarding their food purchases, they asked for more 60 transparency and directed themselves towards organic food or local chains (9). Moreover, the present study explored the environmental and training aspects linked to 90 this IFF vision. The environmental aspect is of high importance at a time of increasing 91 awareness of the impacts of agriculture and breeding on the environment such as 92 carbon footprints, biodiversity, etc. The topic of trainings for dairy producers was 93 studied to orientate universities and other stakeholders of breeding improvement 94 towards the domains needed and desired by dairy producers. A comparison between 95 the current farm and the IFF of the respondent was realised, and permitted the 96 difference between the reality and the aspiration of the producers to be studied. More 97 specifically, the goals of this study were to answer the following questions: (1)  Belgium will react to this change. We created a survey using LimeSurvey software 113 (version 3.15.1+181017, LimeSurvey GmbH, Hamburg, Germany), which provides an 114 internet link to get access and to complete the survey. The survey was first pre-tested 115 orally with two dairy producers to estimate its duration and its clarity. The Board of 116 Ethics and Scientific Integrity of the University of Liege waives the need for ethical 117 approval. We communicated with Walloon dairy producers about the goals of the 118 survey and its access broadly via all communication ways towards them : specialised 119 press, agricultural internet websites, Unions and also advertisements through the milk 120 payment letter which is sent to all the Walloon dairy producers once a month. The 121 survey written in French can be viewed at the following internet link: 122 https://www.gembloux.ulg.ac.be/enquete/index.php/219425?lang=fr and its English 123 translation is viewable in the Appendix. 124 A total of 245 producers completed our survey between November 2014 and January 125

126
The entire survey was composed of 127 questions where the answers were 127 decomposed into 498 categorical and 44 quantitative variables. 128 The question 'Without taking into account your current farm, what is, according to you, 129 the ideal future farm to ensure a revenue?" was proposed to the producers and they 130 must choose between short propositions on seven items: 1) intensive or extensive 131 production; 2) specialised or. diversified activity (or activities); 3) farming strongly or 132 weakly based on new technologies; 4) farm managed by an independent farmer or a 133 group of managers; 5) family or employed workforce; 6) providing production for local 134 or global markets; 7) providing standard or differentiated quality production. The 135 modality "no opinion" was available for each IFF question. Counts were calculated for 136 all modalities of these seven sub-questions. 137 The first step was to study if there were relationships between all modalities derived 138 from the seven sub-questions asked. To achieve this objective, a multiple 139 correspondence analysis (MCA) was carried out as the variables were categorical. For 140 a MCA, the eigenvalue of the dimensions generated, named principal inertia, is a 141 biased measure of the amount of information presented by a dimension (17). Corrected 142 inertia rates were calculated, as described by Benzécri (18), to quantify the correct 143 proportion of information of a dimension. 144 Classes were established to study the distribution of producers along the dimensions 145 of the MCA. The interval between the 1% percentile and the 99% percentile of each 146 dimension was divided equally into five classes. Then, the individuals per class were 147 counted. 148 To exclude a group of producers with some characteristics if necessary, cluster 149 analysis with the WARD method was used on the scores of the individuals on each 150 dimension of the MCA. The WARD method is a hierarchical agglomerative method 151 (19). The principle of this kind of method is to put initially the n individuals in n groups 152 and then to agglomerate the groups. The algorithm of WARD makes it in such a way 153 that the gatherings induce the lowest decrease of R 2 at each step. 154 If a group of producers was excluded, its characteristics were previously studied 155 against the remaining producers. The level of significance of the difference of the 156 quantitative characteristics between the excluded and the remaining producers was 157 studied thanks to general linear models. The level of significance of the difference of 158 the proportions for each modalities of the qualitative characteristics between the 159 excluded and the remaining producers was studied thanks to tests of proportions. 160 To observe if dairy producers presented the farming characteristics they considered to 183 be ideal at the moment of survey, absolute frequencies (counts) were calculated as a 184 function of each ideal future farm characteristic and of the answer to the question which 185 corresponds to this characteristic for the current situation (Table 1). Moreover, the 186 percentage of "unhappy" producers was calculated as the ratio between the producers 187 not currently in the situation that they consider as ideal and the total number of 188 producers. 189

Characterisation of IFF choice
All editing and statistical analyses were carried out using SAS software (version 190 9.4., SAS Inst. Inc., Cary, NC, USA). 191 192 Table 1

. Absolute frequencies (counts) of producers as a function of their answer to the ideal future farm characteristic and 193
the corresponding characteristic for the current situation and percentage of "unhappy" producers (i.e., percentage of 194 producers not currently in the situation that they consider to be ideal) (N = 245) 195 1 Frequency in grey box corresponds to producers not currently in the situation that they consider as ideal regarding this characteristic 196 Corresponding characteristic for the current situation % of "unhappy" producers >2 cows per hectare of grass <2 cows per hectare of grass  As mentioned previously, the first aim of this study was to highlight the perceptions of 218 Walloon dairy producers of their ideal farm, just before the end of the milk quota. This 219 was done through the answers to 7 sub-questions. Table 2 shows the frequency for 220 each modality of those questions. 221 Contrasting opinions of dairy farmers were observed for almost all questions except 225 for the type of management and the kind of workforce: 71.84% of the respondents 226 wanted an independent farmer management, and 86.53% focused on a family 227 workforce (Table 2). These results highlight a will in the southern part of Belgium to 228 maintain the traditional structure of work organisation in the future, with family 229 workforce and one director of operations. More globally in the world, dairy farms are 230 still mostly owned and managed by a family structure, whatever the degree of 231 development of the country (22,23). The choice of producers to work by themselves 232 and not to deal with workers (i.e., an external person to the family employed on the 233 farm) was noted in other studies. For example in Spain Gonzalez and Gomez (24)  234 observed, when asking 3,370 farmers for their definition of a farmer, that more than 235 half of them chose labourer and 12% chose businessman. In the USA in 1988, Mooney 236 presented the fact that farmers had a particular status, being workers and employing 237 other workers (25). 238 From Table 2, it is interesting to note that the highest percentages of abstention were 239 observed for the questions about intensive vs. extensive, strongly vs. weakly based on 240 new technologies, and providing DP for local vs. global markets. These results show 241 that a quite significant proportion of the respondents did not take a position on these 242 directions for the evolution of dairy farms. 243

244
To study the relationships between the answers given by the respondents to all 245 questions about IFF, a MCA was performed as the related variables were categorical 246 (Table 2). The percentage of principal inertia of the dimensions 1 and 2 of MCA were 247 16.75% and 12.38%, respectively (Fig 1). The value of corrected inertia for the two first 248 dimensions reached 72.7% and 21.5% respectively, gathering almost 95% of the 249 information. 250 The first dimension of MCA showed positive relationships with the modalities no 254 opinion of each characteristic and negative relationships with all the modalities with an 255 opinion. Thus, the first dimension of the MCA allowed differentiation between the 256 producers who did not give their opinion concerning characteristics of IFF and the 257 producers who did (Fig 1). Cluster analysis was used to isolate the group of producers 258 with a lot of 'no opinion' answers to the seven questions: this formed the first separation 259 of classes of the analysis, dividing the "no-opinion" producers (15%) from the others 260 (85%). The no opinion producers cluster (N = 38) was removed from the analysis to 261 avoid potential bias coming from farmers who did not have a clear vision of their IFF. 262 Detailed information about this group is available in Tables 3 and 4. They tended to be 263 older farmers (45-54 years), who came from Liège, which is a historic dairy region 264 (Table 3). Even if it is not significant (P = 0.27), they are less likely to have other animal 265 production on the farm (Table 3). Percentages of grass and corn silage observed for 266 this group highlighted a same way of feeding as the complete sample (Table 4). Even 267 if these differences are not significantly different (P = 0.20, P = 0.59, P = 0.33), the 268 more represented single breed and the lower number of cows but with the higher milk 269 delivery quota of the no-opinion producers tended to express quite technical and high 270 performing producers in this group. They were more, even if not significant, to plan not 271 to keep constant their production (Table 3). Even if not significant (P = 0.32), they 272 declared more investment in the next five years than the complete sample, but no 273 difference of investment was observed since 2009. They seemed to be people who 274 have been dairy producers for a long time. We could assume that their farms had good 275 economic performances and did not lead them to think about evolution in response to 276 a great change (i.e. the quota removal). 277  The second dimension of the MCA showed positive relationships with some modalities 284 of the IFF characteristic and negative relationships with their opposite. Thus, this 285 dimension seems to highlight the wishes of dairy farmers about their IFF, for those who 286 took a position on this question. More precisely, this axis showed a gradation of 287 question modalities and proximity between several characteristics. The second 288 dimension of the MCA was the most interesting for highlighting the wishes of dairy 289 farmers about their IFF, for those who took a position on this question. This axis 290 showed a gradation of question modalities and proximity between several 291 characteristics. This dimension led to the identification of two extreme tendencies 292 (Fig 1); the modalities of familial workforce, independent farmer management and 293 management by a group of farmers were near to zero on this axis (Fig 1). This means 294 that the small proportion of producers supporting group management was distributed 295 between the two extreme tendencies observed. The position of the modalities of 296 familial workforce and independent farmer at the middle of the second dimension 297 illustrated the fact that these modalities were chosen by producers from the two 298 tendencies identified. The small proportion of producers choosing an employed 299 workforce was positioned at the top of the second dimension (Fig 1). 300 The first tendency, related to high scores on the second MCA dimension, corresponds 301 to IFF with the following characteristics: global market, standard milk, intensive system, 302 supermarket) led to the concentration of dairy processing in a few big firms (11). These 314 firms were better placed to develop because they could control their collection costs, 315 benefit from scale economies and were able to deliver to supermarkets with regularity 316 in quantity and with a standard quality (9). This state and the world market have 317 conditioned milk prices for the producers. Increasing production, thanks to more cows 318 or higher productivity, is a possible way to stay profitable, considering the undergone 319 milk price (5,11). To achieve profitability, an elevated production of milk per cow and 320 an increase of cows on the farm are reached (11). Moreover, this increase in milk 321 production at farm level was also forced by the orientated production Common 322 Agricultural Policy (CAP) primes, although CAP has limited help for the dairy sector. 323 Therefore, all of these characteristics intensify the dairy farming system. Intensification 324 was defined by  as the maximisation of the rarest factor, 325 traditionally the agricultural area. The increase in DP per unit of agricultural area was 326 possible thanks to intensive production of forage and purchase of inputs that are 327 produced where production costs were the lowest, to balance the ration and to increase 328 the production per cow, or the number of cows reared on a hectare of agricultural area 329 and therefore DP per unit of agricultural area at the level of the farm (9,11). This 330 intensification led to more specialised farms with more dairy cows and their entire 331 workforce directed to this specialisation (9). The enlargement of farms required a 332 higher work rate; this was surmounted thanks to equipment and new technologies and 333 to increased human workforce: collective organisation, subcontracting to private firms 334 and employment of workers (9). 335 The second tendency, contrary to the first tendency, was characterised by high 336 negative scores on the second MCA dimension. This axis was represented by the 337 following modalities: weakly based on new technologies, diversified, differentiated 338 quality milk, local market and extensive system (Fig 1). This reflects another form of 339 dairy farming. This form is favoured by a constant increase in input prices, combined 340 with a growing demand from consumers for high quality and local-based products (9). 341 These dairy producers choose to work with greater self-sufficiency to be less 342 dependent on the undergone input prices (9). The "localisation" of the production 343 demanded by consumers was executed thanks to this more locally-produced forage 344 and fewer inputs from outside (5). This return to self-sufficiency led to more extensive 345 farming (5). The production induced was also often quality-differentiated and dedicated 346 to local markets (9). Cournut et al. (9) showed in their study that this kind of dairy 347 farming is chosen by a minority of farms, which are still diversified. 348 This gradation with two kinds of models at the extremities of the second MCA 349 dimension was also described in other studies (5,6,9,11,(29)(30)(31). They were named 350 globalisation vs. territorialisation by Cournut et al. (9) To study the relationships between the different IFF, the reasons for these and other 375 interesting technico-economic information, the second dimension was considered as 376 a gradient (IFFg) interpreted at the extremities as global-based intensive producers 377 (GBI: high positive scores) and local-based extensive producers (LBE: high negative 378 scores). The choice to work with a gradient rather than a clear separation of the two 379 tendencies was motivated by the will to not put dairy producers into boxes. 380 The mean of the scores of the second MCA dimension was -0.012 with a SD of 0.053. 381 Minimal and maximal values were -1.09 and 0.92, respectively. 382 Based on the interpretation of IFFg, a significant negative correlation indicates a higher 383 relationship with the dairy producers desiring a LBE model. By opposition, a significant 384 positive correlation means a higher link with the dairy producers desiring a GBI model. 385 Tables 5, 7 and 8 give the results of generalised linear models where the categorical 386 variables were introduced separately as a fixed effect in the model. Significantly lower 387 estimates of IFFg for a specific modality of the considered categorical variable depicts 388 a tendency of producers desiring a LBE model to choose this modality, while 389 significantly higher estimates of IFFg means a tendency of producers wanting a GBI 390 model to choose this modality. These analyses were conducted on the producers who 391 have an opinion (N = 207). The following paragraphs will summarise the potential 392 reasons driving the choice of IFF made by the Walloon dairy farmers. 393

Effect of past crisis on perceptions of the ideal future farm The producers that 394
were impacted by past crises wished more for a LBE model (estimate = -0.17, Table  395 5). This could be related to the suffering involved in the crisis and the wish to apply 396 solutions in order to not repeat this situation: revenue from diversified activities, other 397 outlets for the milk production sold (i.e. local market characteristic) and/or self-398 sufficiency to be less dependent on purchased feed (i.e. extensive farm characteristic). 399 This is in agreement with a past finding (35). We observed a decrease in intensification 400 in 2012 which was the year of a dairy economic crisis mainly related to an increase in 401 the price of inputs. 402  Table 5; R workforce constraint = 0.22, P = 0.002). Producers wishing for a 408 GBI model were also more likely to be members of an agricultural replacement service 409 (estimate = 0.058, Table 5) and showed a tendency to be more interested in 410 employment of workers (estimate = 0.13, P worker engagement to implement vs. not interested= 0.11, 411 Table 5). The choice of GBI model could be explained by this current workload, 412 involving the need for an increase of revenue. So, the solution considered could be 413 higher milk production and the breeding of more cows rather than diversification of 414 activities and self-valorisation activity, the development of which requires a lot of time. 415 Samson et al. (36) confirmed this in the Netherlands by highlighting a nearly significant 416 effect of labour productivity on the DP increase strategy. 417 In contrast, producers with lower production factors can consider rarely more 436 enlargement and therefore think differently about the enhancement of their revenue: 437 better valorisation of quality differentiated milk, other activities on the farm, self 438 valorisation, the LBE model. Samson et al. (36) showed that lower stable capacity 439 varies inversely to a DP increase strategy, which is rather a GBI tendency. 440

Production factors
The findings of the current study, as confirmed by previous researchers, showed that 441 producers work within a tightly constrained and regulated environment limiting their 442 ability to determine the future of their farm according to their personal desires. This 443 statement was also concluded by Mc Elwee et al. (37) and Methorst et al. (38). In the 444 Netherlands, Keizer and Emvalomatis (39) and Groeneveld et al. (40) showed that 445 bigger farms are more likely to increase than other farms. 446 However, based on the quite low values of the correlations obtained between the 447 agricultural area and the number of cows, we can consider that this situation must be 448 nuanced and that the IFF chosen also depends on the opinions of the dairy producer, 449 not taking into account the current situation of his farm. This statement is reinforced by 450 the fact that the correlation of percentage of meadow with IFFg was not significantly 451 different to 0 (R = -0.097, P > 0.1). Also, the impact of the provinces of the Walloon 452 Region, which present different geographical and soil characteristics, on IFFg were not 453 significantly different (P = 0.51, Table 5). 454 Moreover the significant relations between IFFg and milk production evolution for five 455 years ( Table 5; R quantity of milk variation= 0.30, P < 0.001), investment for and in five years 456 (Table 5) support the assumption that the IFF chosen depends greatly on the mentality 457 of the producers. 458 In their study, Methorst et al. (13)  which are economics where psychology and biology, which explain human behaviours, 466 are added to better explain the development of enterprises. The consideration of more 467 than just economic aspects permits them to reduce the error of their model for 468 predicting DP increase strategies (36). 469 Age Age of the producer seems not to condition the desired IFF (Table 5). An IFF 470 could be chosen because of either the new ideas of young producers or the experience 471 of older producers. If mentality seems to influence IFF choice, it is not linked to age. 472 The two kinds of IFF could be an answer to both innovation and problems encountered 473 during a long career. Samson et al. (36) also studied age as a reflection of the farmers' 474 values, goals and strategies, and showed no relationship with DP increase, which is 475 rather a GBI characteristic. On the contrary, on the basis of data from 11 countries of 476 the European Union, Weltin et al. (42) observed an effect of age on the tendency 477 towards diversification, which is rather a LBE tendency. 478

Diversification and alternative valorisation
The results obtained in this study 479 showed a link between the diversification mentality and the choice of LBE model. 480 Significant negative estimates or correlations were observed for the following variables 481 related to diversification: the presence of other animal production (estimate = -0.093, 482 Table 5); the direct selling milk quota (R = -0.17, P = 0.016); dairy or no dairy 483 processing and direct sales (estimates = -0.33 and -0.39, Table 5); the development 484 of HORECA activities, tourism and teaching (estimate = -0.18, Table 5); the concern 485 for diversification (estimate = -0.23, Table 5); alternative chain for milk and other than 486 milk production valorisation (estimates = -0.49 and -0.56, Table 5) and the increase 487 of "other than dairy" activity without investment (estimate = -0.42, Table 5). 488 Conversely, producers desiring a GBI model were more likely to choose the item "no 489 activity to develop if supported", suggesting the unique principal activity way of thinking 490 of producers aiming for a GBI model (estimate = 0.27, Table 5). Samson et al. (36) 491 confirmed this tendency and showed that the presence of diversified activities evolved 492 inversely to the increase of milk production. In this study, we observed potential 493 explanations to support to this fact. Producers wishing for a LBE model considered 494 self-valorisation and diversification as solutions to the current situation to enhance 495 revenue due to the creation of added value (estimate = -0.097, Table 5). They thought 496 that diversification and transformation allowed financial, decisional and technical 497 autonomy (estimate = -0.27, Table 5) and were confident in consumer loyalty (estimate 498 = -0.047, Table 5). They considered relations with consumers as an opportunity and 499 not a threat, unlike producers desiring a GBI model (estimate = 0.17, Table 5). One 500 reason GBI model producers gave against self-valorisation and diversification seemed 501 to be the lack of trust in consumers and therefore the outlets. They frequently saw no 502 advantage to self-valorisation and diversification (estimate = 0.27, Table 5). The 503 relation to the consumer was also studied by Verhees et al. (15). They observed that 504 consumer orientation was more often declared as an opportunity by the profiles of 505 producers considering strategies similar to LBE. The positive impact of diversified 506 activities on autonomy was also shown by Bergevoet et al. (12). They mentioned that 507 proponents of the "extra source of income" model (closest to the LBE model) were 508 more able to declare that they can increase the sales-price of their milk. Producers 509 wishing for a LBE model were also likely to find no constraints to transformation and 510 diversification (estimate = -0.093, Table 5). The only limits to diversification and 511 transformation highlighted by producers wanting a LBE model were regulatory 512 constraints (estimate = -0.080, Table 5) and the size of investments (estimate = -0.14, 513 Table 5). As a consequence of these considerations, producers wanting a LBE model 514 felt that they were more able to meet society's expectations regarding local and 515 artisanal products (R = -0.22, P = 0.0016) and the desire for a familial structure (R = 516 -0.12; P = 0.084). 517 Breed to produce milk Producers wanting a LBE model are more open to breeding a 518 dual-purpose herd (estimate = -0.19, Table 5), which permits them to diversify their 519 production: milk and meat. Producers wishing for a GBI model target a single, more 520 specialised breed (estimate = 0.18, Table 5) which could offer more homogeneous 521 management of the herd. The link between mentality, observed through the choice of 522 breed(s), and the choice of IFF is once more highlighted. 523 Regrouping Producers tending towards the LBE model were more likely to promote 524 regrouping for its advantages regarding fiscal and administrative aspects, the 525 development of a joint project and the marketing of the products (estimates = -0.16; -526 0.15; -0.38, Table 5). The importance of mentality for the choice of IFF has been 527 shown. A mentality of cooperation, as a solution to enhance their quality of life and 528 revenue, tends to be shared between producers desiring a LBE model. 529

Mechanisation and robotisation
We observed that the wish of technology of 530 producers tending towards GBI model can be explained by the fact that they 531 considered it as help for workload (estimate = 0.12, Table 5). It can be assumed that 532 the solution considered by them is to keep the same activity or increase it with help 533 from machines. In southern France,Dufour et al. (43) observed the propensity of 534 farmers with workers, close to the GBI model, to prioritise investment in equipment. 535 Verhees et al. (15) observed that better management, including new technologies, was 536 more cited as an objective for producers whose strategy profiles were more similar to 537 the GBI than LBE models. 538 Reaction to external factors Reactions of dairy producers to factors external to their 539 decision-making power tend to be different as a function of their choice of IFF, showing 540 once more a different mentality of the producers. Producers wanting a LBE model tend 541 to show themselves to be more independent from the external economic actors: from 542 the input producing companies (estimate = -0.19, Table 5) and from the market and 543 factories, rejecting contracts which would link them to it (R = -0.13, Table 6). When 544 their opinion about dairy factories was surveyed, producers desiring a LBE model 545 preferred small or medium units with production limits (estimates = -0.52; -0.11; -546 0.23, Table 5), as before, which means regulation of the dairy offerings on the market. 547 Producers wishing for a GBI model direct themselves to big units of processing without 548 production limits (estimates = 0.42; 0.25, Table 5) and so more turned towards world 549 markets. They recognise the freedom in regarding DP as an asset of quota removal (R 550 = 0.23, Table 6). The reaction regarding the quantity of production was not similar 551 during a crisis, producers wanting a LBE model tended to maintain or decrease their 552 production (estimates = -0.17; -0.092, Table 5), whereas producers desiring a GBI 553 model tended to increase production (estimate = 0.21, Table 5). The latter wanted to 554 keep revenues constant with more litres produced when the price decreased, while the 555 others controlled or decreased production when the gross margin per litre decreased. 556 This can be due to a deliberate choice to decrease milk production or a decision to 557 decrease the variable costs causing a decrease in milk production. These results can 558 express a fear of producers tending toward the LBE model in considering world 559 markets, contrary to producers tending towards the GBI model who have decided to 560 work with this kind of market. Verhees et al. (15) observed that producers projecting 561 strategies similar to the LBE model consider the market more as a threat than 562 producers projecting strategies similar to the GBI model. Hansson et al. (44) and Weltin 563 et al. (14) explained that this uncertainty and risk perception can explain the choice of 564 diversification, which is a part of the strategy of the LBE model. 565 Couzy and Dockès (7)  How do environmental aspects factor into IFF decisions?

589
The environmental aspects related to the desired IFF were studied as awareness of 590 the environmental impact of breeding has become an important issue of our time. 591 Producers tending toward the GBI model seemed to work with a higher livestock 592 manure application pressure (R = 0.16, Table 6) and therefore are already more likely 593 to work in an intensified dairy system, which can have a greater impact on the 594 environment. Samson et al. (36) showed a tendency toward manure production surplus 595 by producers with increasing DP, which is rather a GBI characteristic. 596 Results of practices that are in accordance with the environment: measurement of the 597 grass height, forage mixture with leguminous plants, use of a field notebook (estimates 598 = -0.27; -0.11; -0.074,  Besides these, all the significant negative correlations between IFFg and the levels of 605 agreement with an agricultural area are important for the rurality of villages (R = -0.23, 606 Table 6), for conservation of permanent grasslands (R = -0.27, Table 6), for 607 biodiversity (R = -0.18, Table 6) and for hedges (R = -0.28, Table 6) showed the 608 importance of the environment in the dairy activity of producers wanting a LBE model. 609 It can be assumed that both LBE producers and GBI producers have concerns for the 610 environment but in different ways. These results showed that LBE producers are more 611 willing to employ the benefits of ecosystem services, which is observable in this 612 database. Moreover, they found it easy to realise environmentally friendly agricultural 613 practices, as asked for by society (R = -0.15, Table 6) and which are important to 614 answer to society's expectations to guarantee their revenue (R = -0.11, Table 6). to declare that in their decision-making they take the environment into consideration, 618 even if it lowers profit. The "large and modern farm" profile producers do not mention 619 their will to adopt these initiatives. 620 Climatic hazard Facing feed shortages due to unfavourable climatic conditions, 621 producers tending toward GBI and LBE seem not to have the same way of thinking; 622 GBI producers intend to buy high nutritional feed to balance shortages (estimate = 623 0.22, Table 7) and LBE producers are going to decrease the number of cows (estimate 624 = -0.25, Table 7) and ensure their feed autonomy (estimate = -0.17, Table 7). 625 How do farmers' ideal future farm compare to their current 626 farming systems?

627
The current situation of dairy producers was compared to their preferred IFF (Table 1). 628 Except for the type of workforce, quite high percentages of "unhappy" producers were 629 observed for the farm characteristics, between 37 to 50%. This suggested that not all 630 producers work as they would like to. The same comparison was not found in the 631 literature, to our knowledge. 632 As dairy producers do not work in a way that they consider to be ideal, it is interesting 633 to study the gaps to fill in order to reach their ideal system and so, amongst others, 634 their needs. The study of the requirements to reach the IFF, including ways to meet 635 these needs and the area of the needs, can inform the stakeholders of the dairy sector 636 about what must be developed to evolve into IFF. 637

Which paths and themes of training do dairy producers want
638 in order to reach their desired ideal future farm?

639
Paths to formation As way to improve their skills, producers wanting GBI tended to 640 favour consultancy (estimate = 0.17, Table 8) and commercial companies (estimate = 641 0.16, Table 8) and not days of study on other farms (estimate = 0.082, Table 8), 642 meanwhile producers wanting LBE supported this latter possibility (estimate = -0.088, 643 and producers' technical groups to implement in the future (estimate = -0.20, Table 8). 647 The choices presented confirm the will for a non-market way to learn for producers 648 wanting LBE, contrary to producers wishing for GBI. 649 As an information source, the agricultural press was commonly cited (N = 161, i.e. 78% 650 of respondents), but producers desiring LBE tend to not want to inform themselves in 651 this conventional way (estimate =-0.14, Table 8). 652 Producers wanting a GBI model tend to need more help to free them from their work 653 in order to follow a formation (R = 0.21, Table 6) 654

658
**producers declaring no will of formation were removed from this analysis 659 *** producers declaring no agricultural press as an information source were removed from this analysis 660 661

Formation domains The formation domains reflected the direction chosen by 662
producers looking for LBE and the ways to reach it. They tend to want skills related to 663 processing and diversification (estimate = -0.18, Table 8) and were likely to reject 664 finance, management (estimate = -0.24, Table 8), administrative (estimate = -0.11, 665 Table 8) and legal framework skills (estimate = -0.083, Table 8). For financial aspects 666 producers wanting LBE tend to favour requests for advice from experts rather than 667 self-formation (estimate = -0.15, P to implement vs. not interested = 0.12, Table 8). They do not 668 choose animal feeding (estimate = -0.14, Table 8) and selection formations (estimates 669 = -0.053; -0.082, Table 8). This could suggest the will of the producers not to change 670 their way of management and the level of quality of their herd but the method of 671 valorisation of their production. 672 In contrast, producers desiring GBI tend to want to continue to enhance their vegetal 673 and animal production (estimates = 0.083; 0.08, Table 8), to become more efficient 674 and enhance their revenue. Moreover they are more interested in legal aspects 675 (estimate = 0.14, Table 8). Expansion and complexification of the GBI model of dairy 676 farms wished for by these producers could be an explanation. Bergevoet et al. (12) 677 also observed a will to be well informed about the legislation for the "modern and large 678 farm" profile. This is not noted in their profile, which is close to the LBE model. 679 Two kinds of formation were identified and preferred by producers wanting LBE or GBI 680 models. Bergevoet et al. (12) observed the will to innovate for the two profiles closest 681 to LBE and GBI profiles of this study. Verhees et al. (15)  In conclusion, the GBI tendency is two times more represented than the LBE tendency. 691 Many reasons explain this choice of ideal farm. Past crises seem to cause farmers to 692 desire the LBE model. A high workload seems to orientate respondents to the GBI 693 model. The wish for the IFF is influenced by the current framework but is also a 694 question of mentality. Production factors reached, breeds chosen for the herd, ways to 695 react to factors external to the farm, consideration of diversification and alternative 696 valorisation, regrouping and mechanisation and robotisation describe the producers' 697 mentality and showed different relations with the IFF chosen. Moreover LBE and GBI 698 producers may both have concern for the environment, but the approach to act for the 699 environment by LBE producers, through concern for ecosystem services, is clearly 700 highlighted in this study. These producers found it important to answer to society's 701 expectations. Finally, as the current situation of farming is quite different to the ideal 702 one, the learning needs were studied and two types of customer appeared in relation 703 to their formation. We conclude that two kinds of dairy producers seem to appear, for 704 different reasons, with different relations to the environment and asking for different  Ideal future dairy farms to ensure revenue 10 Abstract 11 Dairy farming systems are evolving. This study presents dairy producers' perceptions 12 of their ideal future farm (IFF) to ensure revenue, and attempts to determine the 13 reasons for this choice, the environmental aspects related to this choice, the proximity 14 between the current farm and the IFF and the requirements for reaching this IFF. Just 15 before the end of the European milk quota, a total of 245 Walloon dairy producers 16 answered a survey about the characteristics of their IFF and other socio-17 environmental-economic information. A multiple correspondence analysis (MCA) was 18 carried out using seven characteristics of the IFF (intensive vs. extensive, specialised 19 vs. diversified, strongly vs. weakly based on new technologies, managed by a group 20 of managers vs. an independent farmer, employed vs. familial workforce, local vs. 21 global market, standard vs. quality-differentiated production) to observe the 22 relationships between them. Based on the main contributors to the second dimension 23 of the MCA, this axis was defined as an IFF gradient between the local-based 24 extensive (LBE) producers (26%) and the global-based intensive (GBI) producers 25 (46%). The differences of IFF gradient between modalities of categorical variables 26 were estimated using generalised linear models. Pearson correlations were calculated 27 between the scores on the IFF gradient and quantitative variables. Finally, frequencies 28 of IFF characteristics and the corresponding characteristic for the current situation 29 were calculated to determine the percentages of "unhappy" producers. Some reasons 30 for the choice of IFF by the producers have been highlighted in this study. 31 Environmental initiatives were more valued by LBE than GBI producers. Low similarity 32 was observed between the current farm situation of the respondents and their IFF 33 choice. LBE and GBI producers differed significantly regarding domains of formation 34 (technical and bureaucratic vs. transformation and diversification respectively) and 35 paths of formation (non-market vs. market respectively). Two kinds of farming systems 36 were considered by dairy producers and some socioeconomic and environmental 37 components differed between them. 38 39 Introduction 40 Food is a basic need. Working to provide food for themselves and their family 41 was the task of everyone at the dawn of humanity. The progressive organisation of 42 society during the Neolithic period has led to the appearance of "producers" who are 43 responsible for producing food for more than just themselves and their family (1,2). 44 Since World War II, public policies have been set up to increase food production (3). 45 These policies impacted the development of producers and their farms in the European 46 Union. In the southern part of Belgium, the mean number of cows and the mean 47 agricultural area per producer increased between 1980 and 2017 from 20 to 66 heads 48 and from 25 to 71 hectares, respectively (4). 49 Producers are now facing great challenges to stay profitable. The price of the 50 inputs (e.g. buildings, agricultural machinery, installations, feeding, veterinary care) of 51 dairy production (DP) are increasing while the milk price shows great variability and its 52 inflation is not similar to that observed for the inputs (5,6). Moreover, the European 53 Union has decreased financial support to farmers (7). On 1 st April 2015, the European 54 Union removed the quota system which had managed the supply of DP (8). This led to 55 greater milk price volatility. Additionally, sanitary crises such as mad cow disease 56 (bovine spongiform encephalopathy (BSE)) and the dioxine crisis, among others, have 57 shocked consumers and led to new rules and regulations at European level and to the 58 creation of food security agencies in its countries. Moreover, these episodes modified 59 consumers' behaviours regarding their food purchases, they asked for more 60 transparency and directed themselves towards organic food or local chains (9). The question 'Without taking into account your current farm, what is, according to you, 131 the ideal future farm to ensure a revenue?" was proposed to the producers and they 132 must could choose between short propositions on seven items: 1) intensive or 133 extensive production; 2) specialised or. diversified activity (or activities); 3) farming 134 strongly or weakly based on new technologies; 4) farm managed by an independent 135 farmer or a group of managers; 5) family or employed workforce; 6) providing 136 production for local or global markets; 7) providing standard or differentiated quality 137 production. The modality "no opinion" was available for each IFF question. Counts 138 were calculated for all modalities of these seven sub-questions. 139 The first step was to study if there were relationships between all modalities derived 140 from the seven sub-questions asked. To achieve this objective, a multiple 141 correspondence analysis (MCA) was carried out as the variables were categorical. For 142 a MCA, the eigenvalue of the dimensions generated, named principal inertia, is a 143 biased measure of the amount of information presented by a dimension (17). Corrected 144 inertia rates were calculated, as described by Benzécri (18), to quantify the correct 145 proportion of information of a dimension. 146 Classes were established to study the distribution of producers along the dimensions 147 of the MCA. The interval between the 1% percentile and the 99% percentile of each 148 dimension was divided equally into five classes. Then, the individuals per class were 149 counted. 150 To exclude a group of producers with some particular characteristics if necessary, 151 cluster analysis with the WARD method was used on the scores of the individuals on 152 each dimension of the MCA. The WARD method is a hierarchical agglomerative 153 method (19). The principle of this kind of method is to put initially the n individuals in n 154 groups and then to agglomerate the groups. The algorithm of WARD makes it in such 155 a way that the gatherings induce the lowest decrease of R 2 at each step. 156 If a group of producers was excluded, its characteristics were previously studied 157 against the remaining producers. The level of significance of the difference of the 158 quantitative characteristics between the excluded and the remaining producers was 159 studied thanks to general linear models. The level of significance of the difference of 160 the proportions for each modalities of the qualitative characteristics between the 161 excluded and the remaining producers was studied thanks to tests of proportions. 162 To observe if dairy producers presented the farming characteristics they considered to 185 be ideal at the moment of survey, absolute frequencies (counts) were calculated as a 186 function of each ideal future farm characteristic and of the answer to the question which 187 corresponds to this corresponding characteristic for the current situation (Table 1). 188

Characterisation of IFF choice
Moreover, the percentage of "unhappy" producers was calculated as the ratio between 189 the producers not currently in the situation that they consider as ideal and the total 190 number of producers. 191 All editing and statistical analyses were carried out using SAS software (version 192 9.4., SAS Inst. Inc., Cary, NC, USA). 193

Table 1. Absolute frequencies (counts) of producers as a function of their answer to the ideal future farm characteristic and 194
the corresponding characteristic for the current situation and percentage of "unhappy" producers (i.e., percentage of 195 producers not currently in the situation that they consider to be ideal) (N = 245) 196 1 Frequency in grey box corresponds to producers not currently in the situation that they consider as ideal regarding this characteristic 197 Corresponding characteristic for the current situation % of "unhappy" producers >2 cows per hectare of grass <2 cows per hectare of grass  As mentioned previously, the first aim of this study was to highlight the perceptions of 218 Walloon dairy producers of their ideal farm, just before the end of the milk quota. This 219 was done through the answers to 7 sub-questions. Table 2 shows the frequency for 220 each modality of those questions. 221 Contrasting opinions of dairy farmers were observed for almost all questions except 225 for the type of management and the kind of workforce: 71.84% of the respondents 226 wanted an independent farmer management, and 86.53% focused on a family 227 workforce (Table 2). These results highlight a will in the southern part of Belgium to 228 maintain the traditional structure of work organisation in the future, with family 229 workforce and one director of operations. More globally in the world, dairy farms are 230 still mostly owned and managed by a family structure, whatever the degree of 231 development of the country (22,23). The choice of producers to work by themselves 232 and not to deal with workers (i.e., an external person to the family employed on the 233 farm) was noted in other studies. For example in Spain Gonzalez and Gomez (24)  234 observed, when asking 3,370 farmers for their definition of a farmer, that more than 235 half of them chose labourer and 12% chose businessman. In the USA in 1988, Mooney 236 presented the fact that farmers had a particular status, being workers and employing 237 other workers (25). 238 From Table 2, it is interesting to note that the highest percentages of abstention were 239 observed for the questions about intensive vs. extensive, strongly vs. weakly based on 240 new technologies, and providing DP for local vs. global markets. These results show 241 that a quite significant proportion of the respondents did not take a position on these 242 directions for the evolution of dairy farms. 243

244
To study the relationships between the answers given by the respondents to all 245 questions about IFF, a MCA was performed as the related variables were categorical 246 (Table 2). The percentage of principal inertia of the dimensions 1 and 2 of MCA were 247 16.75% and 12.38%, respectively (Fig 1). The value of corrected inertia for the two first 248 dimensions reached 72.7% and 21.5% respectively, gathering almost 95% of the 249 information. 250 opinion. Thus, the first dimension of the MCA allowed permitted differentiation between 256 the producers who did not give their opinion concerning characteristics of IFF and the 257 producers who did (Fig 1). Cluster analysis was used to isolate the group of producers 258 with a lot of 'no opinion' answers to the seven questions : this formed the first 259 separation of classes of the analysis, dividing the "no-opinion" producers (15%) from 260 the others (85%). The no opinion producers cluster (N = 38) was removed from the 261 analysis to avoid potential bias coming from farmers who did not have a clear vision of 262 their IFF. 263 Detailed information about this group is available in Tables 3 and 4. They tended to be 264 older farmers (45-54 years), who came from Liège, which is a historic dairy region 265 (Table 3). Even if it is not significant (P = 0.27), they are less likely to have other animal 266 production on the farm (Table 3). Percentages of grass and corn silage observed for 267 this group highlighted a same way means of feeding as the complete sample (Table  268 4). Even if these differences are not significantly different (P = 0.20, P = 0.59, P = 0.33), 269 the more represented single breed and the lower number of cows but with the higher 270 milk delivery quota of the no-opinion producers tended to express quite technical and 271 high performing producers in this the no-opinion group. They were more less, even if 272 not significant, to plan not projecting to keep constant increase their production (Table  273 3). Even if not significant (P = 0.32), they declared more investment in the next five 274 years than the complete sample, but even if no difference of investment was observed 275 since 2009. They seemed to be people who have been dairy producers for a long time. 276 We could assume that their farms had good economic performances and did not lead 277 them to think about evolution in response to a great change (i.e. the quota removal). 278 Maybe they could also be 'asleep' in their old dairy traditions. 279  The second dimension of the MCA showed positive relationships with some modalities 286 of the IFF characteristic and negative relationships with their opposite. Thus, this 287 dimension seems was the most interesting for highlighting to highlight the wishes of 288 dairy farmers about their IFF, for those who took a position on this question. More 289 precisely, this axis showed a gradation of question modalities and proximity between 290 several characteristics. The second dimension of the MCA was the most interesting for 291 highlighting the wishes of dairy farmers about their IFF, for those who took a position 292 on this question. This axis showed a gradation of question modalities and proximity 293 between several characteristics. This dimension led to the identification of two extreme 294 tendencies (Fig 1); the modalities of familial workforce, independent farmer 295 management and management by a group of farmers were near to zero on this axis 296 (Fig 1). This means that the small proportion of producers supporting group 297 management was distributed between the two extreme tendencies observed. The 298 position of the modalities of familial workforce and independent farmer at the middle of 299 the second dimension illustrated the fact that these modalities were chosen by 300 producers from the two tendencies identified. The small proportion of producers 301 choosing an employed workforce was positioned at the top of the second dimension 302 (Fig 1). 303 The first tendency, related to high scores on the second MCA dimension, corresponds 304 to IFF with the following characteristics: global market, standard milk, intensive system, 305 supermarket) led to the concentration of dairy processing in a few big firms (11). These 317 firms were better placed to develop because they could control their collection costs, 318 benefit from scale economies and were able to deliver to supermarkets with regularity 319 in quantity and with a standard quality (9). This state and the world market have 320 conditioned milk prices for the producers. Increasing production, thanks to more cows 321 or higher productivity, is a possible way to stay profitable, considering the undergone 322 milk price (5,11). To achieve profitability, an elevated production of milk per cow and 323 an increase of cows on the farm are reached (11). Moreover, this increase in milk 324 production at farm level was also forced by the orientated production Common 325 Agricultural Policy (CAP) primes, although CAP has limited help for the dairy sector. 326 Therefore, all of these characteristics intensify the dairy farming system. Intensification 327 was defined by  as the maximisation of the rarest factor, 328 traditionally the agricultural area. The increase in DP per unit of agricultural area was 329 possible thanks to intensive production of forage and purchase of inputs that are 330 produced where production costs were the lowest, to balance the ration and to increase 331 the production per cow, or the number of cows reared on a hectare of agricultural area 332 and therefore DP per unit of agricultural area at the level of the farm (9,11). This 333 intensification led to more specialised farms with more dairy cows and their entire 334 workforce directed to this specialisation (9). The enlargement of farms required a 335 higher work rate; this was surmounted thanks to equipment and new technologies and 336 to increased human workforce: collective organisation, subcontracting to private firms 337 and employment of workers (9). 338 The second tendency, contrary to the first tendency, was characterised by high 339 negative scores on the second MCA dimension. This axis was represented by the 340 following modalities: weakly based on new technologies, diversified, differentiated 341 quality milk, local market and extensive system (Fig 1). This reflects another form of 342 dairy farming. This form is favoured by a constant increase in input prices, combined 343 with a growing demand from consumers for high quality and local-based products (9). 344 These dairy producers choose to work with greater self-sufficiency to be less 345 dependent on the undergone input prices (9). The "localisation" of the production 346 demanded by consumers was executed thanks to this more locally-produced forage 347 and fewer inputs from outside (5). This return to self-sufficiency led to more extensive 348 farming (5). The production induced was also often quality-differentiated and dedicated 349 to local markets (9). Cournut et al. (9) showed in their study that this kind of dairy 350 farming is chosen by a minority of farms, which are still diversified. 351 This gradation with two kinds of models at the extremities of the second MCA 352 dimension was also described in other studies (5,6,9,11,(29)(30)(31). They were named 353 The present study showed a bifurcation and quantified two ways: 46% vs. 26% of 368 producers having high positive and high negative scores respectively on the second 369 dimension (Fig 2). Verhees et al. (15) quantified producers as a function of their 370 strategies of development, but solely regarding specialisation vs. diversification of their 371 activity, 54.3% vs 15.1% respectively. The bifurcation phenomenon is also observed 372 in the organic sector. Two models appeared: organic agriculture realised by historic 373 actors and the other driven by the agribusiness to answer to a increasing organic 374 demand (32-34). 375 To study the relationships between the different IFF, the reasons for these and other 379 interesting technico-economic information, the second dimension was considered as 380 a gradient (IFFg) interpreted at the extremities as global-based intensive producers 381 (GBI: high positive scores) and local-based extensive producers (LBE: high negative 382 scores). The choice to work with a gradient rather than a clear separation of the two 383 tendencies was motivated by the will to not put dairy producers into boxes pigeonholes. 384 The mean of the scores of the second MCA dimension was -0.012 with a SD of 0.053. 385 Minimal and maximal values were -1.09 and 0.92, respectively. 386 Based on the interpretation of IFFg, a significant negative correlation indicates a higher 387 relationship with the dairy producers desiring a LBE model. By opposition, a significant 388 positive correlation means a higher link with the dairy producers desiring a GBI model. 389 Tables 5, 7 and 8 give the results of generalised linear models where the categorical 390 variables were introduced separately as a fixed effect in the model. Significantly lower 391 estimates of IFFg for a specific modality of the considered categorical variable depicts 392 a tendency of producers desiring a LBE model to choose this modality, while 393 significantly higher estimates of IFFg means a tendency of producers wanting a GBI 394 model to choose this modality. These analyses were conducted on the producers who 395 have an opinion (N = 207). The following paragraphs will summarise the potential 396 reasons driving the choice of IFF made by the Walloon dairy farmers. 397

Effect of past crisis on perceptions of the ideal future farm The producers that 398
were impacted by past crises wished more for a LBE model (estimate = -0.17, Table  399 5). This could be related to the suffering involved in the crisis and the wish to apply 400 solutions in order to not repeat this situation: revenue from diversified activities, other 401 outlets for the milk production sold (i.e. local market characteristic) and/or self-402 sufficiency to be less dependent on purchased feed (i.e. extensive farm characteristic). 403 This is in agreement with a past finding (35). We observed a decrease in intensification 404 in 2012 which was the year of a dairy economic crisis mainly related to an increase in 405 the price of inputs. 406 GBI model were also more likely to be members of an agricultural replacement service 413 (estimate = 0.058, Table 5) and showed a tendency to be more interested in 414 employment of workers (estimate = 0.13, P worker engagement to implement vs. not interested= 0.11, 415 Table 5). The choice of GBI model could be explained by this current workload, 416 involving the need for an increase of revenue. So, the solution considered could be 417 higher milk production and the breeding of more cows rather than diversification of 418 419 Samson et al. (36) confirmed this in the Netherlands by highlighting a nearly significant 420 effect of labour productivity on the DP increase strategy. 421  Verhees et al. (15) showed that 432 land was the most important factor in developing a specific farming strategy. In France,433 Hostiou et al. (26) observed that intensified farms with higher technology equipment 434 sometimes employed more workers, and were the farms with significantly higher 435 agricultural area, percentage of corn silage, number of cows and milk quota. In the 436 Netherlands,Samson et al. (36) showed that production intensity, number of cows, 437 modernity of technology and availability of land were important factors in DP increase 438 strategies. 439

Production factors
In contrast, producers with lower production factors can consider rarely more 440 enlargement and therefore think differently about the enhancement of their revenue: 441 better valorisation of quality differentiated milk, other activities on the farm, self 442 valorisation, the LBE model. Samson et al. (36) showed that lower stable capacity 443 varies inversely to a DP increase strategy, which is rather a GBI tendency. 444 The findings of the current study, as confirmed by previous researchers, showed that 445 producers work within a tightly constrained and regulated environment limiting their 446 ability to determine the future of their farm according to their personal desires. This 447 statement was also concluded by Mc Elwee et al. (37) and Methorst et al. (38). In the 448 Netherlands,Keizer and Emvalomatis (39) and Groeneveld et al. (40) showed that 449 bigger farms are more likely to increase than other farms. 450 However, based on the quite low values of the correlations obtained between the 451 agricultural area and the number of cows, we can consider that this situation must be 452 nuanced and that the IFF chosen also depends on the opinions of the dairy producer, 453 not taking into account the current situation of his farm. This statement is reinforced by 454 the fact that the correlation of percentage of meadow with IFFg was not significantly 455 different to 0 (R = -0.097, P > 0.1). Also, the impact of the provinces of the Walloon 456 Region, which present different geographical and soil characteristics, on IFFg were not 457 significantly different (P = 0.51, Table 5). 458 Moreover the significant relations between IFFg and milk production evolution for five 459 years ( Table 5; R quantity of milk variation= 0.30, P < 0.001), investment for and in five years 460 (Table 5) support the assumption that the IFF chosen depends greatly on the mentality 461 of the producers. 462 In their study, Methorst et al. (13)  norms, ways they see themselves or would like to be seen by producers, views, 466 capacities and their perceptions of opportunities and any room for manoeuvre, skills, 467 motives, entrepreneurship, goals and strategies (12,13,36,38,41) as factors which 468 influence farm development. Samson et al. (36) discussed experimental economics,469 which are economics where psychology and biology, which explain human behaviours, 470 are added to better explain the development of enterprises. The consideration of more 471 than just economic aspects permits them to reduce the error of their model for 472 predicting DP increase strategies (36). 473 Age Age of the producer seems not to condition the desired IFF (Table 5). An IFF 474 could be chosen because of either the new ideas of young producers or the experience 475 of older producers. If mentality seems to influence IFF choice, it is not linked to age. 476 The two kinds of IFF could be an answer to both innovation and problems encountered 477 during a long career. Samson et al. (36) also studied age as a reflection of the farmers' 478 values, goals and strategies, and showed no relationship with DP increase, which is 479 rather a GBI characteristic. On the contrary, on the basis of data from 11 countries of 480 the European Union, Weltin et al. (42) observed an effect of age on the tendency 481 towards diversification, which is rather a LBE tendency. 482

Diversification and alternative valorisation
The results obtained in this study 483 showed a link between the diversification mentality and the choice of LBE model. 484 Significant negative estimates or correlations were observed for the following variables 485 related to diversification: the presence of other animal production (estimate = -0.093, 486 Table 5); the direct selling milk quota (R = -0.17, P = 0.016); dairy or no dairy 487 processing and direct sales (estimates = -0.33 and -0.39, Table 5); the development 488 of HORECA activities, tourism and teaching (estimate = -0.18, Table 5); the concern 489 for diversification (estimate = -0.23, Table 5); alternative chain for milk and other than 490 milk production valorisation (estimates = -0.49 and -0.56, Table 5) and the increase 491 of "other than dairy" activity without investment (estimate = -0.42, Table 5). 492 Conversely, producers desiring a GBI model were more likely to choose the item "no 493 activity to develop if supported", suggesting the unique principal activity way of thinking 494 of producers aiming for a GBI model (estimate = 0.27, Table 5). Samson et al. (36) 495 confirmed this tendency and showed that the presence of diversified activities evolved 496 inversely to the increase of milk production. In this study, we observed potential 497 explanations to support to this fact. Producers wishing for a LBE model considered 498 self-valorisation and diversification as solutions to the current situation to enhance 499 revenue due to the creation of added value (estimate = -0.097, Table 5). They thought 500 that diversification and transformation allowed financial, decisional and technical 501 autonomy (estimate = -0.27, Table 5) and were confident in consumer loyalty (estimate 502 = -0.047, Table 5). They considered relations with consumers as an opportunity and 503 not a threat, unlike producers desiring a GBI model (estimate = 0.17, Table 5). One 504 reason GBI model producers gave against self-valorisation and diversification seemed 505 to be the lack of trust in consumers and therefore the outlets. They frequently saw no 506 advantage to self-valorisation and diversification (estimate = 0.27, Table 5). The 507 relation to the consumer was also studied by Verhees et al. (15). They observed that 508 consumer orientation was more often declared as an opportunity by the profiles of 509 producers considering strategies similar to LBE. The positive impact of diversified 510 activities on autonomy was also shown by Bergevoet et al. (12). They mentioned that 511 proponents of the "extra source of income" model (closest to the LBE model) were 512 more able to declare that they can increase the sales-price of their milk. Producers 513 wishing for a LBE model were also likely to find no constraints to transformation and 514 diversification (estimate = -0.093, Table 5). The only limits to diversification and 515 transformation highlighted by producers wanting a LBE model were regulatory 516 constraints (estimate = -0.080, Table 5) and the size of investments (estimate = -0.14, 517 Table 5). As a consequence of these considerations, producers wanting a LBE model 518 felt that they were more able to meet society's expectations regarding local and 519 artisanal products (R = -0.22, P = 0.0016) and the desire for a familial structure (R = 520 -0.12; P = 0.084). 521 Breed to produce milk Producers wanting a LBE model are more open to breeding a 522 dual-purpose herd (estimate = -0.19, Table 5), which permits them to diversify their 523 production: milk and meat. Producers wishing for a GBI model target a single, more 524 specialised breed (estimate = 0.18, Table 5) which could offer more homogeneous 525 management of the herd. The link between mentality, observed through the choice of 526 breed(s), and the choice of IFF is once more highlighted. 527 Regrouping Producers tending towards the LBE model were more likely to promote 528 regrouping for its advantages regarding fiscal and administrative aspects, the 529 development of a joint project and the marketing of the products (estimates = -0.16; -530 0.15; -0.38, Table 5). The importance of mentality for the choice of IFF has been 531 shown. A mentality of cooperation, as a solution to enhance their quality of life and 532 revenue, tends to be shared between producers desiring a LBE model. 533

Mechanisation and robotisation
We observed that the wish of technology of 534 producers tending towards GBI model can be explained by the fact that they 535 considered it as help for workload. A "pro-technology" mentality of the producers 536 tending towards the GBI model was observed (estimate = 0.12, Table 5). It can be 537 assumed that the solution considered by them is to keep the same activity or increase 538 it with help from machines. In southern France,Dufour et al. (43) observed the 539 propensity of farmers with workers, close to the GBI model, to prioritise investment in 540 equipment. Verhees et al. (15) observed that better management, including new 541 technologies, was more cited as an objective for producers whose strategy profiles 542 were more similar to the GBI than LBE models. 543 Reaction to external factors Reactions of dairy producers to factors external to their 544 decision-making power tend to be different as a function of their choice of IFF, showing 545 once more a different mentality of the producers. Producers wanting a LBE model tend 546 to show themselves to be more independent from the external economic actors: from 547 the input producing companies (estimate = -0.19, Table 5) and from the market and 548 factories, rejecting contracts which would link them to it (R = -0.13, Table 6). When 549 their opinion about dairy factories was surveyed, producers desiring a LBE model 550 preferred small or medium units with production limits (estimates = -0.52; -0.11; -551 0.23, Table 5), as before, which means regulation of the dairy offerings on the market. 552 Producers wishing for a GBI model direct themselves to big units of processing without 553 production limits (estimates = 0.42; 0.25, Table 5) and so more turned towards world 554 markets. They recognise the freedom in regarding DP as an asset of quota removal (R 555 = 0.23, Table 6). The reaction regarding the quantity of production was not similar 556 during a crisis, producers wanting a LBE model tended to maintain or decrease their 557 production (estimates = -0.17; -0.092, Table 5), whereas producers desiring a GBI 558 model tended to increase production (estimate = 0.21, Table 5). The latter wanted to 559 keep revenues constant with more litres produced when the price decreased, while the 560 others controlled or decreased production when the gross margin per litre decreased. 561 This can be due to a deliberate choice to decrease milk production or a decision to 562 decrease the variable costs causing a decrease in milk production. These results can 563 express a fear of producers tending toward the LBE model in considering world 564 markets, contrary to producers tending towards the GBI model who have decided to 565 work with this kind of market. Verhees et al. (15) observed that producers projecting 566 strategies similar to the LBE model consider the market more as a threat than 567 producers projecting strategies similar to the GBI model. Hansson et al. (44) and Weltin 568 et al. (14) explained that this uncertainty and risk perception can explain the choice of 569 diversification, which is a part of the strategy of the LBE model. 570 Couzy and Dockès (7) demonstrated different profiles of farmers and observed the 571 entrepreneurship mentality of each one, which highlights similar tendencies to those 572 presented here. Several profiles showed strong entrepreneurship but which was 573 expressed differently to here. A category of farmers showed entrepreneurship by their 574 wish for autonomy of decision in their management; they will keep a working approach 575 close to the conventional one but with a modernist vision, always adapting to the 576 market. They want to keep freedom in the classical framework. In 1988, Mooney 577 described the split personality of producers: they are independent people, making their 578 own decisions regarding their way of working and their investments but at the same 579 time are people dependent on different processing actors and banks (45). Another 580 category of farmers showed entrepreneurship by their wish to develop an original idea, 581 away from preexisting systems, a project in line with their conviction to be freer from 582 the existing system [5]. 583 Samson et al. (36) and Methorst et al. (13) reported that decisions of producers cannot 584 be reduced to only economic aspects: this includes policies and market conditions but 585 also their way of thinking about them. 586 Table 6 Correlations (R) between the ideal future farm gradient and quantitative 587 variables (N = 207) 588 *producers declaring no calling of replacement services were removed from this analysis 589 590 591 How do environmental aspects factor into IFF decisions?

592
The environmental aspects related to the desired IFF were studied as awareness of 593 the environmental impact of breeding has become an important issue of our time. 594 Producers tending toward the GBI model seemed to work with a higher livestock 595 manure application pressure (R = 0.16, Table 6) and therefore are already more likely 596 to work in an intensified dairy system, which can have a greater impact on the 597 environment. Samson et al. (36) showed a tendency toward manure production surplus 598 by producers with increasing DP, which is rather a GBI characteristic. 599 Results of practices that are in accordance with the environment: measurement of the 600 grass height, forage mixture with leguminous plants, use of a field notebook (estimates 601 = -0.27; -0.11; -0.074, Table 7) showed a stronger interest from producers wanting a 602 LBE model. 603 Besides these, all the significant negative correlations between IFFg and the levels of 608 agreement with an agricultural area are important for the rurality of villages (R = -0.23, 609 Table 6), for conservation of permanent grasslands (R = -0.27, Table 6), for 610 biodiversity (R = -0.18, Table 6) and for hedges (R = -0.28, Table 6) showed the 611 importance of the environment in the dairy activity of producers wanting a LBE model. 612 It can be assumed that both LBE producers and GBI producers have concerns for the 613 environment but in different ways. These results showed that LBE producers are more 614 willing to employ the benefits of ecosystem services, which is observable in this 615 database. Moreover, they found it easy to realise environmentally friendly agricultural 616 practices, as asked for by society (R = -0.15, Table 6) and which are important to 617 answer to society's expectations to guarantee their revenue (R = -0.11, Table 6). 618 Bergevoet et al. (12) had a considerably more consistent opinion. The "extra-source of 619 income" profile producers (showing similarities with the LBE model) were more likely 620 to declare that in their decision-making they take the environment into consideration, 621 even if it lowers profit. The "large and modern farm" profile producers do not mention 622 their will to adopt these initiatives. 623 Climatic hazard Facing feed shortages due to unfavourable climatic conditions, 624 producers tending toward GBI and LBE seem not to have the same way of thinking; 625 GBI producers intend to buy high nutritional feed to balance shortages (estimate = 626 0.22, Table 7) and LBE producers are going to decrease the number of cows (estimate 627 = -0.25, Table 7) and ensure their feed autonomy (estimate = -0.17, Table 7). 628 How do farmers' ideal future farm compare to their current 629 farming systems?

630
The current situation of dairy producers was compared to their preferred IFF (Table 1). 631 Except for the type of workforce, quite high percentages of "unhappy" producers were 632 observed for the farm characteristics, between 37 to 50%. This suggested that not all 633 producers work as they would like to. The same comparison was not found in the 634 literature, to our knowledge. 635 As dairy producers do not work in a way that they consider to be ideal, it is interesting 636 to study the gaps to fill in order to reach their ideal system and so, amongst others, 637 their needs. The study of the requirements to reach the IFF, including ways to meet 638 these needs and the area of the needs, can inform the stakeholders of the dairy sector 639 about what must be developed to evolve into IFF. 640 Which paths and themes of training do dairy producers want 641 in order to reach their desired ideal future farm?  and producers' technical groups to implement in the future (estimate = -0.20, Table 8). 650 The choices presented confirm the will for a non-market way to learn for producers 651 wanting LBE, contrary to producers wishing for GBI. 652 As an information source, the agricultural press was commonly cited (N = 161, i.e. 78% 653 of respondents), but producers desiring LBE tend to not want to inform themselves in 654 this conventional way (estimate =-0.14, Table 8). 655 Producers wanting a GBI model tend to need more help to free them from their work 656 in order to follow a formation (R = 0.21, Table 6) 657  Table 8) and legal framework skills (estimate = -0.083, Table 8). For financial aspects 669 producers wanting LBE tend to favour requests for advice from experts rather than 670 self-formation (estimate = -0.15, P to implement vs. not interested = 0.12, Table 8). They do not 671 choose animal feeding (estimate = -0.14, Table 8) and selection formations (estimates 672 = -0.053; -0.082, Table 8). This could suggest the will of the producers not to change 673 their way of management and the level of quality of their herd but the method of 674 valorisation of their production. 675 In contrast, producers desiring GBI tend to want to continue to enhance their vegetal 676 and animal production (estimates = 0.083; 0.08, Table 8), to become more efficient 677 and enhance their revenue. Moreover they are more interested in legal aspects 678 (estimate = 0.14, Table 8). Expansion and complexification of the GBI model of dairy 679 farms wished for by these producers could be an explanation. Bergevoet et al. (12) 680 also observed a will to be well informed about the legislation for the "modern and large 681 farm" profile. This is not noted in their profile, which is close to the LBE model. 682 Two kinds of formation were identified and preferred by producers wanting LBE or GBI 683 models. Bergevoet et al. (12) observed the will to innovate for the two profiles closest 684 to LBE and GBI profiles of this study. Verhees et al. (15)  In conclusion, the GBI tendency is two times more represented than the LBE tendency. 694 Many reasons explain this choice of ideal farm. Past crises seem to cause farmers to 695 desire the LBE model. A high workload seems to orientate respondents to the GBI 696 model. The wish for the IFF is influenced by the current framework but is also a 697 question of mentality. Production factors reached, breeds chosen for the herd, ways to 698 react to factors external to the farm, consideration of diversification and alternative 699 valorisation, regrouping and mechanisation and robotisation describe the producers' 700 mentality and showed different relations with the IFF chosen. Moreover LBE and GBI 701 producers may both have concern for the environment, but the approach to act for the 702 environment by LBE producers, through concern for ecosystem services, is clearly 703 highlighted in this study. These producers found it important to answer to society's 704 expectations. Finally, as the current situation of farming is quite different to the ideal 705 one, the learning needs were studied and two types of customer appeared in relation 706 to their formation. We conclude that two kinds of dairy producers seem to appear, for 707 different reasons, with different relations to the environment and asking for different 708 formations. 709 Acknowledgments 710 I want to thank the organising committee of "Carrefour des Productions animales" for 711 the supply of the data. 712 713 Dear Academic Editor, dear Reviewers, First, I would like to thank you for the time spent to improve the understanding of this manuscript. This letter is organized in two parts. The first part deals with the main issue of the review (i.e., the method mobilized, which corresponds to the point raised by the academic editor and one remark of the reviewer). The second part concerns the specific answers to the specific remarks formulated by the reviewers.

H. Soyeurt :
Dear Editor, Dear Reviewers, Instead of my PhD student, Miss Anne-Catherine Dalcq, I would like to answer to the question related to the methodology used in this study. I am Professor Hélène Soyeurt and I teach courses related to Data Mining and Machine Learning at Gembloux Agro-Bio Tech (University of Liège). Therefore, I have an experience in the use of multivariate analysis. It is why I would like to answer by myself to the question related to the method used in this article.
Before starting an explanation, I would like to precise that we have not really understood the comments of the reviewer about Latent Class Analysis (LCA) because the objective was not to create groups of farmers. Indeed, and this is the innovative aspect of this paper, a gradient between two quite different models of farms was studied. The gradient is really important because it appears to us simplistic to classify farmers in only 2 groups, working with a gradient allowed us to nuance the position of the dairy producers and to analyze more precisely the link between this position and other characteristics. The use of the gradient allows studying the trend of a farmer. It is why in this paper, we always mention "tend towards" to make a reference to the position on the gradient and not a binary choice of a model.
As we did not want to create farmer's clusters, LCA was not appropriate as well as HCPC. However, as asked by the second reviewer to prove the robustness of our approach, we have decided to show you the similarities and the extended work that it is possible to do using Multiple Correspondence Analysis (MCA) and LCA. Indeed, it is also possible to use LCA to create a gradient instead of using the clusters.
So, I would like to remind the methodology that we have proposed in this study (see the figure below, Fig 1)). Again, MCA was used to observe the relationships between the seven studied variables. Based on the interpretation of MCA dimensions, we have observed that the second dimension represented the positioning between the two models for a dairy farm. Therefore, the score for this dimension for a specific producer allows to know its perception of ideal future farm between the two extreme models. This gradient allows avoiding to limit the farm typology to 2 clusters. This is interesting because many farmers combined some approaches specific to one model of farms (no more intensification but extensification, local-based market) or another one (global-based market, continuously improvement of the productivity thanks to, notably, intensification, …). Therefore, wishing to split the dairy farmers into 2 groups is too limitative. Some farmers remain between these two models (Fig 2), some farmers are more convinced than others by a model. Farmers showing higher scores are really convinced by GBI model, farmers showing lower but positive scores choose GBI model but are not 100% in this way of farm development. Negatives scores express the position of farms in favor of LBE model, the lowest scores reflected pronounced adhesion to this model. It is why the gradient as proposed in this paper was useful and seem to us the most interesting tool to represent dairy producers. Similarly, we have done this job using LCA methodology as requested by the reviewer#2. LCA allows defining clusters from the dataset. In this case and to be in line with the study objective, we have decided to create 3 clusters. Moreover, based on the AIC and BIC values, it was also the best model (Fig 3). LCA allows us to create those 3 clusters. After the interpretation of defined clusters, it appeared that we have a cluster representing "No opinion" responders, one cluster representing "global-based intensive" (GBI) farmers and one cluster representing "local-based extensive" (LBE) farmers (Fig 4). Therefore, those clusters were similar to the ones obtained by combining MCA and Ward clustering (=HCPC method) as done to clean the dataset (i.e., extract responders with "no opinion" behavior). Again, we did not want to use those clusters to make our analysis. But, using this methodology, it is possible to obtain a probability to belong to a specific cluster. Therefore, we have decided to compare the gradient as defined in the current study to the probability to belong to the LBE or GBI clusters defined using the LCA method.
So, now, it is time to present you the results. I will not present you the results about MCA as those results are reported in the article. In this paragraph, we will focus on the LCA results. As we used categorical variables which are not ordinal, we have decided to use the polytomous latent class analysis. The variables used, called manifest variables, were the same than the one used for MCA. The modalities for each variable were recoded from 1 to 3: No opinion  Workforce: 1. Familial workforce, 2. Employed workforce, 3. No opinion  Kind of management: 1. Group of farmers management, 2. Independent farmer management, 3. No opinion  Market: 1. Global market, 2. Local market, 3. No opinion  Milk quality: 1. Standard quality milk, 2. Differentiated quality milk, 3. No opinion As this clustering is very sensitive to the prior values used to start the iteration, 10 repetitions were used to provide you the final results for all models. All calculations were done with R software and more specifically the package poLCA. First, we have run different LCA models using a different number of classes (clusters). We have tested models from 1 to 10 classes and then we have estimated the AIC and BIC criteria to observe which model allowed the best fitting. The results of AIC and BIC for all models are presented in the figure below (Fig 3). From this figure, we can conclude that the model allowing the creation of 3 classes is a good comprise between BIC and AIC (i.e., the lowest BIC and AIC values).

Figure 3 AIC & BIC criteria values
The figure below shows you the clusters defining by the model allowing a discrimination of the data into 3 clusters (Fig 4). This figure represents the probability to have a specific modality for each cluster. So, based on those results, we can conclude that the first clustering (class 1) is related to GBI dairy producers, the second cluster (class 2) is related to LBE dairy producers and the last cluster (class 3) is related to the dairy producers with "no opinion".

Figure 4Description of the three clusters obtained by LCA method
Therefore, in order to clean the dataset (i.e., delete records from farmers having many "no opinion" views), we can use the clustering 3. This process is similar to the MCA + Ward clustering (HCPC) proposed in the manuscript. Again, we did not want to use clusters but we want to use a gradient. For MCA, this gradient was the second MCA dimension. In the context of LCA, this gradient can be derived from the probability to belong to class 1 ("GBI producer") or class 2 ("LBE producer"). So, to show the robustness of the MCA approach used, we calculated the correlation between those probabilities and the score of the second MCA dimension (called gradient in the manuscript). The correlation between the probability to belong to class 1 and the gradient was equal to 0.83. The correlation between the probability to belong to class 2 and the intensification gradient was equal to -0.87. The correlation between the 2 probabilities was equal to -0.97. From all of those results, you can see that the relationship is strong between MCA and LCA using an innovative approach focusing on the score/probability of an individual and not directly to a cluster. Using only the second dimension of MCA, we can reflect both clusters (class 1 and class 2) simultaneously. Indeed, the second dimension is a gradient "GBI-LBE" and included both. This is really interesting to observe the relationships between this gradient and other quantitative or qualitative variables as now the studied trait is quantitative. It allows to see if a modality of a categorical variable is the choice of really convinced GBI dairy producers or dairy producers only sticking out of the GBI model. I hope that this demonstration illustrates well the relevancy of the approach proposed in our paper. A sentence will be added in the materials and methods section to explain why LCA was not used. Moreover, some articles exist also in the literature to prove the mathematical relationships between MCA and LCA (e.g., Lautsch and Plichta, Psychology Science 2003:298-323 as well as Van der Heijden, et al., Sociological methodology 1999).
The fact that the two dimensions explained almost 95% of the variability and that all the modalities representing an opinion positioning themselves along the second dimension support us to take the second dimension as gradient, after deletion of the No-opinion producers which were discriminated by the first dimension.
Finally, I would like to acknowledge you for the great job done in the review of this paper. The manuscript was improved a lot.
Sincerely, Prof Hélène Soyeurt PS : The answers to all other comments were done by Anne-Catherine Dalcq.

2/ Others comments
Reviewer #2: In this revision, the authors have significantly improved the English language translation and clarified their research questions, but they have failed to address the shared concerns of reviewers regarding methods and clarity of writing. They have not adequately addressed the substance of the comments from reviewers.
Regarding methods, the reviewers still do not offer a compelling and clear justification for why MCA is appropriate for their goals and they do not offer the latent class analysis that I suggested or the hierarchical clustering (related) suggested by reviewer 3 as alternatives or robustness checks. MCA, while performed adequately, is not well suited to the way they discuss their results. They continually refer to "types" of respondents, which is what latent class analysis is for. MCA is about identifying clustering of variables, not clusters of respondents. All of their interpretation of results is about clustering and patterns of PEOPLE, not variables. This indicates a significant misalignment between the method and the research goals.
Then we want to study the relationships between this ideal future farm gradient and the other information present in the survey.
The relationships between the ideal future farm gradient and the categorical variables of the survey were studied thanks to generalized linear models.
The gradient was the y, the variable to explain. The modalities of the categorical variables were the fixed effect of the generalized linear model, the factors explaining. y = effect + residual Where y was a vector contained the score on the ideal future farm gradient (the second dimension of MCA); effect was the qualitative variables of the survey. In other words, the model was : Ideal future farm gradient = categorical variable + e To study the relationships between the gradient and the quantitative variables of the survey, correlation coefficients and their level of significance were calculated.

Line 160-What are the quantitative variables?
A-C Dalcq: Quantitative is a statistical term defining a continuous numerical variable. Do you want that we use the term « numerical » ? But this term is less precise as it does not reflect the continuous dimension of the variable. A-C Dalcq: Absolute frequencies named counts. We precised at lines 186 and 194: "Absolute frequencies (counts)".

How many questions in each dimension?
A-C Dalcq: One question. We have now mentioned that in the Materials and methods section at Lines 187-188: "and of the answer to the question which corresponds to this corresponding characteristic for the current situation".
Line 180-specifics of response rate still missing.
A-C Dalcq: The response rate is 6,1% (Line 200). Which supplementary indication do you need? We gave you numbers of farms with a dairy activity in Belgium and in European Union in this letter. We give also more information about the conditions where the survey was communicated to the producers to give you an idea of the way of proceeding. More information is given at lines 120-126.
Lines 120-126: "We communicated with Walloon dairy producers about the goals of the survey and its access broadly via all communication ways towards them : specialised press, agricultural internet websites, Unions and also advertisements through the milk payment letter which is sent to all the Walloon dairy producers once a month. The survey written in French can be viewed at the following internet link: https://www.gembloux.ulg.ac.be/enquete/index.php/219425?lang=fr and its English translation is viewable in the Appendix"  A-C Dalcq: The percentages in the axes labels are the inertia but these ones underestimated the part of information explained by the dimensions. The corrected inertia values were calculated. This is explained in the Materials and methods section at lines 142-146: "For a MCA, the eigenvalue of the dimensions generated, named principal inertia, is a biased measure of the amount of information presented by a dimension (Palm, 2007). Corrected inertia rates were calculated, as described by Benzécri (Benzécri, 1979), to quantify the correct proportion of information of a dimension." The "The percentage of principal inertia of the dimensions 1 and 2 of MCA were 16.75% and 12.38%, respectively (Fig 1). The value of corrected inertia for the two first dimensions reached 72.7% and 21.5% respectively, gathering almost 95% of the information. The corrected inertia gives a better appreciation of the amount of information explained by each dimension (Benzécri, 1979), than the inertia automatically provided by the software.
We did not think necessary to precise this in the paper but we provide the reference where this calculation is presented.

Line 335-where is this figure reference from
A-C Dalcq : We did not provide a representation of the distribution of the producers along the second dimension, we did not think it was necessary as we provided the percentages and this figure would lengthen the paper. But following your request, we have now added this figure in the present manuscript (Lines 376-377).