Bagworm census data.

The census data were collected biweekly over the period of 2014 and 2015, resulting in 24 census cycles annually. The census was conducted according to the standard practice of the plantation management where for each cycle, 25 random palms were selected: 5 palms from each cardinal direction i.e. the north, south, east, west and center of the block. Frond number 17 was destructively pruned for each of the chosen palm as it is considered to represent oil palm crown as a whole [33] and bagworm larvae of instar 1, 2, 3, and 4 from this frond were collected and counted. Only bagworm of these instar level were considered in this study due to the fact that bagworm larvae at these stages bring the most destruction to oil palm owing to the high level of leaf consumption [34]. The total bagworm counts in these 25 palms were then averaged to obtain an average bagworm number per palm per block.

Remotely sensed derived relative humidity.

The computation of RH was performed according to algorithm described and modified for Malaysia’s utilization by Peng et al. [35]. RH is the ratio of vapour pressure (e) and saturation vapour pressure (e_s) and can be computed according to Eq 1A, 1B, and 1C: (1A) Where (1B) (1C)

Where, RH stands for relative humidity, e stands for vapour pressure, e_s represents saturation vapour pressure, Ta denotes surface air temperature, Pa signifies air pressure and Q represents specific humidity.

The estimation of vapour pressure (e) was dependent on air pressure (Pa) and specific humidity (Q) that was computed from precipitable water vapour (PW). Their relationship is described in Eq 2A and 2B. The computation of saturation vapour pressure (e_s), on the other hand was dependent on surface air temperature (Ta) (2A) While (2B)

Where, the acquisition of precipitable water vapour (PW) was done through the retrieval of atmospheric water content by channel ratio technique that utilizes near infrared (NIR) channels using NIR bands. Among 36 bands of MODIS platform, 5 of them are NIR bands: 2 (0.865μm), 5 (1.24μm), 17 (0.905μm), 18 (0.936μm), and 19 (0.940μm) in which band 2 and 5 are atmosphere window bands while band 17, 18, and 19 are absorption bands that were represented as observed transmittance (Tobs) in Eq 2B. The algorithm of the computation of Tobs was provided by Kaufman and Gao [36] as the following (Eq 3A, 3B and 3C): (3A) (3B) (3C)

Where Tobs B17, Tobs B18, and Tobs B19 stands for the observed transmittance for band 17, band 18, and band 19, respectively (Eq 4A, 4B, 4C). α and β were the observed transmittance coefficients that was different for each Tobs and was provided for Malaysia region by Peng et al. [34] as follows: (4A) (4B) (4C)

It is also worth noting that ρ * represents the apparent reflectance which is a ratio between the radiance at the sensor and solar radiance at the top of atmosphere for the specified channel: C1 = 0.8 and C2 = 0.2 [27].

Since derived water vapour (PW) values were different for all three channels, a mean water vapour was obtained using Eq 5.

(5)

Where, PW1, PW2, PW3 are water vapour derived from channel 0.905μm, 0.936μm, 0.940μm or band 17, 18, and 19, respectively. f is the corresponding weight of water vapour values of each channels for Malaysia region: f1 = 0.36, f2 = 0.24, and f3 = 0.40.

Finally, the air pressure (Pa) used in Eq 1B was obtained using algorithm provided by Peng et al. [35] as shown below (Eq 6): (6)

Where H stands for elevation obtained from data provided by shuttle Radar Topography Mission (SRTM) version 3.0 Global 1 arc second Data.

According to Eqs 1 to 6, two sets of MODIS images observed from the Terra and Aqua satellites were required. The first image was MOD07 for the acquisition of surface air temperature (Ta) data used in Eq 1C, while the second image was MOD021KM for the acquisition of 5 NIR bands used to compute precipitable water vapour (PW). Both of their temporal resolutions were 1 day with spatial resolution of the first product being 5 km and second product being 1 km.

Hence, a total of 444 and 443 of the images for 2014 and 2015, respectively, were utilized in performing the RH derivation. The images were first downloaded from the United States Geological Survey (USGS) Global Visualization Viewer (GloVis) website (https://glovis.usgs.gov/). Further, the required band layers were extracted from each images; surface air temperature layers from the MOD07 images, while layers of NIR bands from the MOD021KM images. All of the layer spatial projections were set to WGS 1984 UTM Zone 47 N and the algorithm was applied to the layers to compute RH images. Finally, all of the images were subset according to the study area.

Data extraction.

Prior to data extraction, the RH layers pixel size were resampled by nearest neighbour from 1 km to 250 m. The area-weighted mean of RH values for each blocks were then calculated according to Eq 7. Next, the RH values were extracted and paired with the average number of bagworms per palm for each block of each census cycle at 6 different time lags; 1 week (T1), 2 weeks (T2), 3 week (T3), 4 weeks (T4), 5 week (T5) and 6 weeks (T6) prior to the census date. The time lag analysis was carried out based on the hypothesis that the response of insect population towards the effect of abiotic factors in some cases may not be immediate as demonstrated by Wood and Foot [17], Karpakakunjaram et al. [18] and Intachat et al. [19]. Besides, the knowledge of insects responding towards the environmental fluctuation ahead of time is also important in developing a forewarning system of insect outbreak and provide the opportunity for a better and more efficient mitigation program.

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Regression analysis.

The relationship between the average bagworm per palm per block with the area-weighted mean of RH of each block at time lag T1, T2, T3, T4, T5, and T6 was determined by Pearson’s correlation coefficient (r). The analysis was later followed by single and multiple regression analyses, linear or polynomial, to measure the magnitude of influence that RH possessed over the M. plana number. In order to determine the best time lags to be used as the model input, the RH dataset was tested according to these different configurations as follows: (i) individual time-lags i.e. T1, T2, T3, T4, T5 or T6, (ii) divided into two classes of multiple time lags: week 1, 2 and 3 (T1, T2 and T3) or week 4, 5 and 6 (T4, T5 and T6), and (iii) individual time-lags as selected through stepwise selection criteria method. For configuration (iii), among all the time lags analysed, T3, T4 and T5 and T6 were selected for linear regression while T1 and T6 were chosen for polynomial regression. All the statistical analysis was carried out by using statistical analysis software SAS version 9.2 (SAS Institute Inc., Cary, North Carolina, USA).

Artificial neural network (ANN).

Three main layers characterize the architecture of neural network: the input, output, and hidden layers. The input layer represents the independent variables, the output layer represents the dependent variables, and the hidden layer represents the relationship developed between input and output variables. The relationship between the input and the output variables will be established by the hidden layers through the adjustment of weightage that is performed iteratively by the training network. In each training, an estimated output will be generated and compared to the actual output values to produce an error term. This error will be used in the network training and the iterative process will be conducted until the minimum error is achieved [37].

In this study, multilayer perceptron ANN was used to further analyse the relationship between dependent and independent parameters to construct the prediction model for the outbreak of Metisa plana. The analysis was conducted by using the Alyuda Neurointelligence 2.2 (Alyuda Research LLC, Cupertino, CA). Datasets containing missing values, as well as data anomalies and outliers were excluded before the neural network analysis. All data were then divided into 3 datasets; i) network training dataset which accounted for 60% of the data, i.e. n = 170 ii) network testing dataset which accounted for 20% of the data, i.e. n = 56 and iii) network validation dataset which accounted for remaining dataset, i.e. n = 56. All of the input data were scaled into numbers between -1 to 1 prior to the ANN processing in the next step.

Further, the RH dataset was tested according to the same configurations as in the regression analysis. However, for configuration (iii), forward stepwise feature selection method was conducted where the feature mask with the best fitness value was chosen. Through the feature selection procedure, four time lags were chosen as the input layer i.e. T1, T3, T4 and T6. Prior to the training of the data, network architecture for each input layer was determined as follows: for the (i) input layer, the network architecture was 1-x-1, while for the (ii) input layers, a different architecture was assigned i.e. 3-x-1 and finally, the (iii) input layer was represented by 4-x-1 architecture. The number of hidden layers or x for the different input layers were later determined through the best fitness value of the network architecture. The logistic (sigmoid) function was selected as the activation function connecting the hidden and output layers. Network trainings were then performed upon the training dataset using the quick propagation (QP) algorithm. This ANN algorithm was selected since QP is a modification of back-propagation algorithm making it faster than the standard incremental back-propagation, which would be efficient in processing large amount of data in this study [38]. In the training process, the data fed to the network was analyzed and the weights were adjusted according to their influence towards the dependent variables in a series of iterations. The weights were fine-tuned through the validation process of neural network where the number of hidden units were determined and the declination of predictive ability of the neural network was detected. Finally, the output were back transformed to the input data scale prior to the evaluation metrics.

Evaluation metrics.

The accuracy of predictions for the regression and ANN models were then evaluated and compared by using the adjusted R² values between the actual and predicted M. plana number. In evaluating the quality of the ANN predictions, two methods were employed in this study which were the absolute error (Eq 8) [39] and testing accuracy (Eq 9) of the training models. The absolute error is the average value of the absolute difference between the predicted and original or actual values, whereby smaller error values indicate a better trained network. On the other hand, the accuracy of prediction models in this study used the min-max accuracy by dividing the minimum average value with the maximum average value among the averaged prediction and actual values and multiplying it by 100 [40]. The minimum-maximum accuracy indicates the deviation of the predicted values from the actual values where the perfect accuracy is 100%. (8) Where absolute error represents absolute error for training, validation and testing datasets.

(9)

Regression versus ANN.

The fact that the ANN models was found to produce higher adjusted R² values than the regression models suggest that the former caters non-linearly and non-normally distributed datasets as opposed to the latter. The regression analysis, for instance, essentially predicts the relationship between dependent (y) and independent (X₁, X₂… X_k) variables by assuming that their associations are linear (Eq 10). This include the polynomial regression; the model still assumes the linearity of the relationships when predicting the associations of dependent and independent variables despite it being used to fit a non-linear data into least squares regression (Eq 11). (10) (11) Whereas y represents dependent variables i.e. bagworm numbers and X represents independent variables i.e. RH, a represents initial intercepts and β represents partial regression coefficients of variableX.

As a result, this principle limits the ability of regression analysis, either linear or polynomial, to predict non-linear relationships efficiently. The ANN, in contrast, is more superior in assessing large datasets with multivariate interactions and complex patterns [41, 42]. This can be attributed to its ability to self-learn the data and produce models through weight adjustment without preliminary assumptions of the datasets linearity.

In comparing among the ANN architectures, the 3-8-1 architecture with RH T1, T2 and T3 input layer was found to be able to predict the presence of Metisa plana with high accuracy and the highest adjusted R² value. Despite the lowest error and highest accuracy terms were produced with the RH at T2 layer with 1-5-1 network architecture, the adjusted R² value for this model was too low i.e. 0.11. A close inspection found that the model failed to predict extreme values of M. plana at both ends and hence implies a low reliability. Finally, it was noticeable that the absolute error of the best training models utilizing multiple time lags portrayed an almost one-fold increase during the validation and testing phases (from 0.56 to 1.14 and 1.06, and from 0.94 to 1.35 and 1.54, respectively). The amplification of the absolute error was contributed by the overfitting of the training model; likely from the combination of high iteration number and small size of training datasets [43]. Nonetheless, evaluating from the magnitude of the errors, the overfitting could be considered inconsequential and thus, the prediction model was stable and reliable.

Time lag effects on modelling algorithms.

The effects of time lag was pronounced during the ANN analyses, which generally suggested that multiple time lags could produce high adjusted R² values and acceptable testing accuracies (more than 79%). Individual time lags, on the other hand, resulted in models with unacceptable values of adjusted R² and relatively higher errors than the multiple time lags, despite high overall accuracies. This suggests that, a duration of a week, regardless at any time lags, was insufficient to evaluate the impacts of RH on Metisa plana’s population dynamic. In contrast, better accuracies of the multiple time lags models signified the importance to consider the continuity of the RH fluctuations over a longer period towards insects’ population, especially in the more recent weeks. This was manifested through the datasets from the T1, T2 and T3 time lags that were able to generate the highest adjusted R² value and accuracies i.e. above 95%. The results suggest RH fluctuations at the time lag T1, T2 and T3 are more influencing to the insect’s life cycle than at any other time lags. Given the focus of this study that was to predict Metisa plana’s larvae of instar level one to four, one to three weeks prior to these stages marks the reproductive stages of Metisa plana. This is in alignment with the importance of RH in regulating the efficiency of insects’ reproduction. The optimum level of RH for eggs hatchability is crucial due to the need of lubrication and soft cuticle tissues for eggs to be successfully hatched [8]. Nevertheless, high level RH has been associated with the increase of pathogens and fungi attack [44]. This is further supported by Sajap and Siburat [15], where 90% of fungal infected of Pteroma pendula was found on the bottom and middle of tree canopies where the RH was higher than the top canopies. RH, on both extreme ends, could hinder this process through desiccation or drowning of insect eggs [8–11]. Since RH been associated in successfully assisting the breed, grow, and dispersion of certain insects, having the right level of humidity is vital for their survivability. However, as the relationship between the presence of bagworm and RH is nonlinear, the optimum RH values for infestations to occur could not be determined. Over and above that, there has been no study conducted specifically to determine the optimum values of relative humidity for Metisa plana.

Despite the other multiple time lags models especially T4, T5 and T6 being lower in accuracies in comparison to the T1, T2 and T3 model, the adjusted R² and error terms were comparable between those two. This observation suggests that this model could be used to predict possible outbreak in an earlier manner so that proper mitigation actions could be taken and the risk could be reduced.