BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

Temperature is one of the most significant environmental factors that affects germination of grass seeds. Reliable prediction of the optimal temperature for seed germination is crucial for determining the suitable regions and favorable sowing timing for turf grass cultivation. In this study, a back-propagation-artificial-neural-network-aided dual quintic equation (BP-ANN-QE) model was developed to improve the prediction of the optimal temperature for seed germination. This BP-ANN-QE model was used to determine optimal sowing times and suitable regions for three Cynodon dactylon cultivars (C. dactylon, ‘Savannah’ and ‘Princess VII’). Prediction of the optimal temperature for these seeds was based on comprehensive germination tests using 36 day/night (high/low) temperature regimes (both ranging from 5/5 to 40/40°C with 5°C increments). Seed germination data from these temperature regimes were used to construct temperature-germination correlation models for estimating germination percentage with confidence intervals. Our tests revealed that the optimal high/low temperature regimes required for all the three bermudagrass cultivars are 30/5, 30/10, 35/5, 35/10, 35/15, 35/20, 40/15 and 40/20°C; constant temperatures ranging from 5 to 40°C inhibited the germination of all three cultivars. While comparing different simulating methods, including DQEM, Bisquare ANN-QE, and BP-ANN-QE in establishing temperature based germination percentage rules, we found that the R2 values of germination prediction function could be significantly improved from about 0.6940–0.8177 (DQEM approach) to 0.9439–0.9813 (BP-ANN-QE). These results indicated that our BP-ANN-QE model has better performance than the rests of the compared models. Furthermore, data of the national temperature grids generated from monthly-average temperature for 25 years were fit into these functions and we were able to map the germination percentage of these C. dactylon cultivars in the national scale of China, and suggested the optimum sowing regions and times for them.

Seed germination percentage is a major criterion used for evaluating suitability of an environment for grass cultivation. Previous studies showed that extreme temperatures could lead to seed dormancy and significantly decreased germination percentage [24][25][26]. Constructing a precise mathematical model that correlates the germination percentage with temperature may avoid failure of plantation due to inappropriate sowing timing or mismatch between the grass species and climate zone. Hence it would be very helpful for decision-makers to select grass species and sowing time for lawn, erosion control and forage cultivation. Using thermal time approach, Bradford [27] constructed temperature/water potential based seed germination and dormancy models. This study showed that germination experiments under temperature regime with discrete (stepwise) changes could also be used to accurately predict thermal responses of seeds in field environment with continuously changing temperature. Hardegree and Van Vactor [28,29] used the Piece-wise linear (PWL) regression equations to confirms that constant-temperature experimental results derived mathematical models could be used to predict the germination/growth responses to the combined effects of multiple environmental factors in the field. Although various experimental procedures have been established to generate data for the development and validation of reliable prediction models [30][31][32][33][34][35], the R 2 values of temperature-germination percentage functions in some of the previous studies were relatively low (0.61-0.80) [34,36] and more accurate predictions are desired.
Recently, the Geographic Information System (GIS) based spatial prediction approach was introduced for the creation of quantitative and accurate grass suitability maps [36]. The grid data of mean minimum and maximum temperatures [37] were used for calculating suitability values of regions via the temperature-germination percentage functions. Therefore, the suitability of grass for different regions could be appropriately visualized on the map. However, the visualization of time scale (season) of these maps remains to be streamlined for readability to facilitate their practical application.
The objectives of this research were to: (i) explain the correlation error between temperature and seed germination percentage caused by selection of functions (ii) provide a new program for optimizing the temperature-germination function, (iii) use temperature-based seed germination percentage function in combination with national temperature grids in China for predicting the suitability of three bermudagrass cultivars, C. dactylon, 'Savannah' and 'Princess VII'.

Germination response to Diurnal Fluctuations of Temperature
The germination response of the three bermudagrass cultivars was similar (Tables 1-3). All the three cultivars were capable of germinating in warm-period temperature (T 2 ) from 25 to 35uC and cool-period temperature (T 1 ) ranging from 5-40uC. The optimal temperature for seed germination is defined as that which is not lower than the maximum germination minus one-half of its confidence interval (P = 0.05). For example, the maximum germination percentage (the optimal temperature for seed germination) of C. dactylon was 87.3% at 15/35uC (Table 1); and the germination percentage at 5/30uC was only 80.7%, but it was still accepted as the optimal temperature for seed germination since the one-half of its confidence interval was 7.0% and 80.7%.(87.3%-7.0%). Fluctuating between 5-25uC cool-period temperature and 30-40uC warm-period temperature gave rise to the optimal temperature for seed germination. On the other hand, germination percentage was usually lower than 50% at constant temperature ranging from 20 to 40uC (except the ''Savannah'' at constant 25/25uC in Table 2), for example the germination percentages of ''Princess VII'' (Table 1)

Performance of Different Regression Models
All the regression equations of temperature treatments that assess the germination suitability of the three bermudagrass cultivars are summarized in Table 5. Quadratic and quintic general equations were used for data simulation. The bisquare and BP-ANN approaches ( Fig. 1) were utilized for optimizing these equation coefficients. There was no significant difference between the quintic functions and bisquare optimized quintic functions. Bisquare quintic functions of cultivars C. dactylon, 'Savannah' and 'Princess VII' showed lower R 2 than quintic functions (data not shown). Similar optimization results were observed for all the cultivars tested. Generally, quintic equations performed better than quadratic equations (Fig. 2, Table 5). The highest R 2 values were generated by the back propagation artificial neural networks aided dual quintic equation (BP-ANN-QE) model (0.9439 to 0.9813). In contrast, the dual quadratic equation model (DQEM) generated the lowest R 2 values (0.6940 to 0.8177). Contour plot maps were then used to visualize the prediction errors generated from different simulation functions (Fig. 2). The blue spot represents the experimental germination percentage associated with particular fluctuating temperature combinations. Obviously, DQEM is the one most prone to produce prediction errors among the compared models ( Fig. 2A, D and G). However, some weakness in functional convergence of quintic equations was observed, a small portion of observed temperature-germination spots were still out of their equation derived surfaces ( Fig. 2B, C, E, F, H and I).

Spatial Mapping of Optimal Planting Times
The temperature-germination functions derived from our experimental data were used to predict germination percentage for various regions in China in different seasons using the 25 years mean minimum and mean maximum earth surface temperature grids as input. The percentage reflected the likelihood of germination suitability at each grid cell of the maps via FreeMicaps ( Fig. 3-5). The results reveal that most of the Chinese regions are not suitable for seed germination of all the tested bermudagrass cultivars from November to March. Although 'Savannah' has the Table 2. Quadratic response surface based on estimated percent germination with the confidence interval at the 0.05 probability level for seeds of the cultivar 'Savannah'.  narrowest geographic range of germination with percentages arranging from above 0 to 100%, it was predicted to have optimal temperatures for germination in widest geographic range in China (Fig. 4). In contrast, C. dactylon had the narrowest range for the optimal temperatures for seed germination (Fig. 3). For both C. dactylon and 'Princess VII', the widest range with the optimal temperatures for seed germination was in the month of June, whilst for 'Savannah' it was in May (Fig. 3-5).

Discussion
Simulation models have been widely used to correlate cultivation conditions and plant germination/growth [38][39][40]. These regression models were generally used to predict the plant suitability to particular regions where climate and soil environment information is available. These mathematical models could help grass cultivation in three major aspects. First, these functions combined with a visual suitability map may help decision makers in selecting a grass species and planning its seeding timing [36,41]. Second, they may serve as useful tools for identifying and evaluating desirable quantitative characteristics for specific grass breeding objectives [42], which is helpful in coupling genotype and phenotype of a target cultivar, a technology with significant application value in the rapidly expanding turf industry [43]. Third, these grass-condition models may improve our understanding of how changes in agricultural systems would quantitatively influence grass germination/growth [44].

Comparison of Regressions Using Quadratic and Quintic Equations
The quadratic equation was broadly accepted as an effective statistical tool for simulating continuous variable-response relationship, and quadratic response surface has been a predominant method to analyze germination performance of grass seeds under various temperature regimes, especially to test the seed germination affected by diurnal temperature treatments [36,41]. However, the weakness of quadratic equation is also obvious. Since the twodimensional quadratic response surface cannot display some errors in the global fitting between quadratic function and experimental data [36], the weakness of low R 2 values (0.61-0.80) was ignored. In this study, quintic equation was employed for regression to simulate diurnal temperature-germination responses of three bermudagrass cultivars. Compared to quadratic surfaces, quintic approaches had significantly lower fitting errors and higher confidence ( Fig. 2 and Table 5). This may be due to the nonlinear temperature-germination correlation. Hence these quintic equation models could provide more reliable predictions for field performance of grasses, further improving the reliability of the suitability map of grasses tinted with different color based on predicted germination percentage data.

BP-ANN and Bisquare for Intercept and Coefficients Fitting
Artificial Neural Network (ANN), an algorithm for simulating the thinking processes of the human brain which usually have multiple networks that are logically arranged as fundamental units [45]. The information of any unit can be learnt, recalled, concluded and speculated. Hence, the ANN has many advantages such as distributed storage of information, self-adaptability, selforganization and fault-tolerance properties [40]. As a computer based program, it could be used to perform large-scale parallel calculations to simulate nonlinear correlation [46]. Therefore, ANN is broadly used in various of fields including biomedical research [47,48], optimization of soil nutrient distribution coefficient [43,49,50], forecasting of microorganism community assemblages [51], prediction of animal metabolism and diets correlation [52], and simulation of fruit post-ripening process [53][54][55].
Currently, there are tens of ANN models. Amongst them, the back propagation (BP) network is the most widely used one for simulation of nonlinear relationship [56]. The BP-ANN model belongs to supervised study and its training process has two phases, forward propagation and backward propagation [57]. In the forward propagation, the weighted value and threshold value of each layer is calculated by iteration and passed into the BP threelayer network. Subsequently, the backward propagation uses the weighted value and threshold values for revision [58]. These two phases commonly occur repeatedly for about 10, 000 times, and the weighted value and threshold values alternate until they converge. The target of these training processes is to generate a function that can globally 'distinguish' and 'remember' all the input raw data [59]. Therefore, the simulated BP-ANN functions could be used to predict proposed parameter with appropriate input variables.
The robust bisquare estimator, also known as Tukey's bi-weight function, was a popular choice for nonlinear function fitting [60]. This estimator was often used for smoothing the nonlinear response surface [61,62]. It was reported that bisquare estimator could be adapted to process noisy data with outliers [63].
In our study, both BP-ANN and bisquare methods were used to optimize the temperature-germination functions for three bermudagrass cultivars. We did not find significant difference between general quintic functions and bisquare fitted quintic functions. Furthermore, most bisquare quintic functions in this study had slightly lower R 2 values than the quintic functions. Therefore, the BP-ANN optimized quintic equations were found to be the best option for fitting temperature-germination functions of the tested bermudagrass cultivars.
To some degree, the BP-ANN based temperature-germination functions could be evaluated by the visualized suitability map (Figs. [3][4][5] and the observed temperature-germination results (Tables 1-3). Generally, the cultivar ''Savannah'' could germinate under the widest temperature regimes (Tables 1-3), from about 20/5uC to 40/40uC, it also present the highest suitability with widest geographic regions in China (eg. Fig. 4D-I). On the other hand, the predicted suitability map worked in concert with the observations that all the three cultivars preferred warm temperature above 15/15uC (Tables 1-3), and little germination could be found during the cool seasons in China (eg. Fig. 4A-C).
To simulate the grass germination-temperature response function, both quadratic and quintic equations were employed. Quintic functions performed significantly better (R 2 were around 0.9439) than the quadratic ones (R 2 ranging from 0.6940,0.8177) for the tested cultivars. The main objective of this study was to test the nonlinear fittin\g approaches, bisquare and BP-ANN, for optimizing the regression functions. Our results suggested that BP-ANN has significant advantages over bisquare for fitting the intercept and coefficients of the temperature-germination functions.
Based on the experimentally derived BP-ANN functions and available climate data, we prepared a seed suitability map of three bermudagrass cultivars for cultivation in the People's Republic of China. We observed that most of the regions in China are not suitable for bermudagrass seed germination from November to March. The cultivar 'Savannah' had the widest geographic range of the optimal temperature for seed germination, whilst C. dactylon had the narrowest range of the optimal temperature for seed germination percentage. The month with widest range of the optimal temperature for seed germination for C. dactylon and 'Princess VII' is June, whilst for 'Savannah', it is May.

Seeds and Conditioning
The bermudagrass cultivars (C. dactylon, 'Savannah' and 'Princess VII') were planted widely in China. All the grass seeds were purchased from Shanghai Chunyin Turf Inc., (Shanghai, China) and stored at room temperature until use. Seed viability was tested on sterilized wet filter paper at 25uC in darkness [36].
Briefly, seeds were surface sterilized in 0.01% HgCl 2 for 1 min followed by four rinses with distilled water. The seeds were subsequently placed on wet filter papers in Petri dishes. The Petri dishes were placed in incubators set up for 36 different regimes of diurnal fluctuations of temperature treatments: 16 h at temperature T 1 and 8 h at temperature T 2 . The T 1 and T 2 ranged from 5 to 40uC with 5uC increments [36]. Germinated seeds were counted daily until no further germination occurred (about 15-20 days) for viability analysis (Supplementary file Tables 1-3). For each experiment, three replications of 50 seeds were used in a randomized block design.

Statistical Analysis
In this study, quadratic and quintic response surfaces were constructed with estimated means and confidence intervals [64]. Table 5. Equations and R 2 values for predicting germination as a function of cool (T 1 ) and warm (T 2 ) temperature treatments for the three C. dactylon cultivars tested.   The quadratic equations were first used for estimating germination percentages. The generalized equation was [36]: where Y 1 : predicted germination percentage, A 0 : intercept, A 1 through A 5 : coefficients, T 1 and T 2 : two temperature in the diurnal regime.
Meanwhile, quintic equations with the following generalized equation were also used to simulate the temperature-germination : intercept, f(A): coefficient function. Temperature inputs were normalized by dividing the maximum value. Subsequently, the intercept and coefficients were optimized using Bisquare, a default curve fitting method of MATLAB 7.9-R2009b software and back propagation artificial neural networks (BP-ANN) approach described in Fig. 1, respectively. The BP-ANN (or feed-forward network) has the capability to learn arbitrary nonlinearity and great potential for adaptive control applications [46]. In the BP-ANN, the correlations among the input variables do not need to be specified. Instead, they learn from the examples fed to them (Fig. 1). In addition, they can generalize correct responses that only broadly resemble the data in the learning phase [56,65,66].

Spatial Mapping
The suitability of a grass is represented by seed germination percentage. The grass suitability maps were created using the FreeMicaps software (http://bbs.121323.com/guojf/ FreeMicaps20111001.rar). Like the Surfer software [67], FreeMicaps also uses grid data at selected points (station) that is compatible with GIS. The temperature data of adjacent regions around the station are generated using regression functions. The data used to construct the temperature grid are curated in the database in National Aeronautics and Space Administration (NASA, http://power.larc.nasa.gov/cgi-bin/cgiwrap/solar/sse. cgi?grid@larc.nasa.gov#s11) which are composed of minimum and maximum daily temperature of earth surface from 313 Chinese weather stations for a period of 25 years (from 1983 to 2007). These mean values of minimum and maximum daily temperatures were used as the T 1 and T 2 variables, respectively in the BP-ANN-Quintic functions for calculating germination percentages (grass suitability).