Potentials and Limitations of a Growing Degree Day Approach to Predict the Phenology of Cereal Leaf Beetles

Potentials and Limitations of a Growing Degree Day Approach to Predict the Phenology of Cereal... Abstract Cereal leaf beetles (CLBs) are described as an invasive pest of small grain cereals in many regions worldwide. Prediction models aimed to prevent yield losses caused by these feeding insects have been developed by researchers all over the world. As a foundation for many of these prediction models, it is known that a specific number of heat units, or growing degree days (GDDs), is required for an insect to complete a certain physiological process. In this paper, we overview the existing GDD models for CLBs. Furthermore, we used our Belgian input data to compare model predictions with our own observations. Though, the existing models were not able to predict the seasonal trends present in our data: the occurrence of various life stages were monitored earlier then the model predicted. Hence, a weighted GDD model was tested on the data as well: the accumulated GDDs during certain periods were balanced according to the significance of this period for the insect. Rainfall and/or relative humidity were included as well. Based on these selected variables, multiple linear regression models, ridge regression models, and regression trees were fitted. This approach performed considerably better compared to the simple accumulation of GDD. However, based on cross-year cross-location validation method, to gain insight in the future performance of the models, the accuracy was still too low to serve as an accurate warning tool. cereal leaf beetle, growing degree day, modeling, winter wheat Wheat (Triticum aestivium L.) is a main agricultural crop grown worldwide (Food and Agriculture Organization of the United Nations 2017). During some years cereal leaf beetles (CLBs; composite of species, Coleoptera: Chrysomelidae) can be a problematic pest in winter wheat, imposing significant yield and quality losses, both directly and indirectly. Direct feeding damage, due to the removal of plant tissue, occurs when larvae develop on stems, leaves, and heads, from the stem elongation stage through to head filling stage. Furthermore, these insects cause indirect damage since they are vectors of a number of viruses (e.g., barley yellow dwarf virus and phleum mottle virus) (Nault et al. 1978). Flag leaf defoliation causes more damage and yield loss than injury to lower leaves, since the flag leaf photosynthesis contributes significantly more to grain yield (Zhang et al. 2006). Furthermore, the flag leaf stage often appears together with the fourth and last larval stage of CLBs. Larvae in this stage are most active and are known to cause major feeding damage to the plants: 70% of total plant damage caused by CLBs is linked with this stage (Kher et al. 2011). Yield losses associated with the presence of CLBs can regionally go up to 30% (Van Duyn et al. 1997, Ihrig et al. 2001, Kher et al. 2011). CLBs are a complex of several species belonging to the genus Oulema. In Western Europe, next to most common species O. melanopus (Linnaeus) (Coleoptera: Chrysomelidae) and O. gallaecianna (Heyden) (Coleoptera: Chrysomelidae), the species O. duftschmidi (Redtenbacher) (Coleoptera: Chrysomelidae), O. Septentrionis (Weise) (Coleoptera: Chrysomelidae), and O. rufocyanea (Suffrian) (Coleoptera: Chrysomelidae) occur (Bezdek and Baselga 2015). During the period April–May (2016 and 2017) more than 800 Oulema adults were sampled in Belgian wheat fields (2016: 28 fields; 2017: 23 fields) for species identification We found that next to the widespread species O. melanopus, also O. duftschmidi and O. gallaecianna frequently occurred in Belgian wheat fields (Elias Van De Vijver, unpublished data). The population size of CLBs, determined by the population growth rate, growth period, and mortality, fluctuates in time and space due to a variety of reasons, such as fluctuations in environmental conditions, availability of resources, host crop quality, and impact of antagonistic species (Philips et al. 2011). With the green revolution, new pesticides and chemical fertilizers were introduced, decreasing the need for integrated pest management (IPM; Tummala et al. 1975). Still today, a wide range of chemicals is available to prevent or to reduce the impact of pests. However, in order to arrive at a more sustainable agricultural system, a combined approach of cultural and chemical-based control methods is essential. Decision support systems (DSS) are increasingly important to achieve a more rational use of insecticides. These systems are based on predictive models simulating the outbreak and severity of pests. The output of these systems, in combination with appropriate economic thresholds, can then be used to evaluate the necessity to apply chemicals together with a correct timing and dosage of the application (Le Cointe et al. 2016). There is a more than 40-yr tradition of modeling wheat, CLB, and natural enemy interactions (Coulman et al. 1972, Casagrande and Haynes 1976, Guppy and Harcourt 1978, Philips et al. 2012). However, the use of such prediction models in plant protection is scarce, mainly because of their insufficient forecast accuracy. The most important problems in modeling CLBs and antagonist population dynamics have to do with describing the inter-field dynamics, estimation of mortality rates, and survival, which are influenced by several variables (Helgesen and Haynes 1972). In order to develop more accurate prediction models, a good understanding of the population dynamics, both spatially and temporally, is critically important. Weather conditions, crop husbandry practices, and landscape management (e.g., surrounding vegetation) are important factors affecting the tri-trophic interactions between plants, CLBs, and their natural enemies (Haynes and Gage 1981). A wide range of modeling approaches has been used to predict insect development, ranging from simple growing degree day (GDD) models (Evans et al. 2006; Philips et al. 2012) to more complex mechanistic models (Helgesen and Haynes 1972, Tummala et al. 1975, Lee and Barr 1976). Mechanistic models adopt a bottom-up approach to understanding system dynamics, and in case the life cycle of the various organisms is not completely described, these models will often not fit data as well as empirical models that use statistically derived functions. Detailed population models tend to be very complex, because it is often believed that higher complexity leads to higher accuracy. However, it is overlooked that such multiple input models are also very sensitive to measurement errors rising with each parameter, and can hence result in highly variable predictions (Klüken 2008). For this reason, in this research we will focus on the relatively simple GDD models. Although GDD models have a long history of use in predicting plant and insect phenology, this modeling approach is still amended in recent warning systems (Cayton et al. 2015, Akyuz et al. 2017, Calero et al. 2017) and offers, with appropriate thresholds, certainly opportunities. Since insects are poikilothermic, temperature is the major driver of phenology. Indeed, there exists a profound correlation between temperature and the phenology of insects. Therefore, insect phenology is often predicted via the calculation of heat units, or GDD. GDD accrual is typically initiated after a discrete biological event, referred to as a ‘biofix’, or a calendar date (e.g., 1 January). A GDD model can be represented according to (1). GDD=[Tmax+ Tmin2]−Tbase (1) where Tmax is the maximum daily temperature, Tmin is the minimum daily temperature, and Tbase is the lower threshold for development. In case the average temperature is lower than Tbase, no degree days are accumulated and 0 is recorded for that day, since no insect growth or development occurs. Since each developmental stage has its own total heat requirement, insect development can be estimated by accumulating GDD throughout the season until a certain GDD threshold is reached (Wilson and Barnett 1983, Zalom et al. 1983). The warmer the weather, the faster GDD accumulates and the faster the GDD threshold is reached. To predict the date of the various life cycle stages of CLBs, numerous GDD models have been developed, each with its specific GDD threshold and base temperature. In Table 1, an overview of the GDDs necessary to reach a certain life cycle stage of CLBs is given. All models start to accumulate GDD on the biofix date of 1 January. These data were based on field trials and in some cases supported by data retrieved from laboratory trials. It can be seen that the observations of the various researchers at different locations led to a wide range of base temperatures and GDD thresholds. Therefore, based on the thresholds set by Gage and Haynes (1975), Guppy and Harcourt (1978), Kidd (2002), Blodgett et al. (2004), Evans et al. (2006), and Hoffman and Rao (2010), a combined GDD model was developed and implemented on http://uspest.org/wea, a webserver of the Oregon State University on which GDD models for several organisms can be accessed. The suggested combined CLB model uses a base temperature of 9°C and the first egg, egg peak, first larvae, and larvae peak can be expected at 80, 150, 180, and 360 GDD, respectively. Furthermore, note that Philips et al. (2012) did not use a fixed base temperature and GDD threshold to predict the larvae peak. According to these authors, the larvae peak is expected to occur in average 17.5 d (within a range of 7–35 d) after the egg peak. Additionally, it can be seen that Evans et al. (2014) considered a variable threshold to predict the date of CLB egg peaks in Utah. Based on data from 2001 until 2011, these authors concluded that there was a considerable variation among years in the number of GDD associated with the occurrence of the CLB egg peak (ranging from 145 to 325 GDD). Much of this variability could be accounted for by considering early spring warmth. Indeed, there was a positive linear relationship between the GDD for egg peaks and the accumulated heat during spring, the higher the temperatures in spring the higher the GDD threshold. Thus, instead of using a fixed GDD threshold, these authors suggest that the GDD threshold should take into account early spring warmth. For instance, the threshold for egg peak (y) can be calculated according to y = 67.45 + 1.41x, with x the accumulated degree days from 1 January until 21 April. Table 1. Summary of the GDDs necessary to reach a certain life cycle stage of CLBs, between brackets the minimum development threshold is mentioned Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) View Large Table 1. Summary of the GDDs necessary to reach a certain life cycle stage of CLBs, between brackets the minimum development threshold is mentioned Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) View Large All the approaches mentioned in Table 1 studied the relationship between GDD and a certain life cycle stage. However, for practical insight into the phenology of the pest insect, predicting pest incidence on field level is important as well. Therefore, Ihrig et al. (2001) studied the relationship between CLB egg counts and the number of insects in the fourth-instar stage and the impact of fourth-instar population on winter wheat. A significant linear relationship was found between the 50th percentile of the number of eggs (x) and the density of the fourth-instar population (y) (y = 0.36x − 0.01; R2 = 0.79). Potentially detrimental larval infestations were forecast from egg populations present during the stem elongation to flag leaf emergence developmental stages. A significant positive linear relationship between total fourth-instar larvae stem population estimates (x) and percent flag leaf defoliation (y) was detected (y = 20.29x + 1.34; R2 = 0.60). Furthermore, a weaker, but still significant linear relationship between the total fourth-instar population estimates (x) and percent yield loss (y) was found (y = 11.74x + 6.51; R2 = 0.26), indicating that factors in addition to flag leaf injury, primarily by fourth instars, also contributed to reduced yields. Materials and Methods During the wheat growing seasons 2014–2015, 2015–2016, and 2016–2017, respectively, 29, 33, and 32 winter wheat fields throughout Flanders (Belgium) were monitored for the presence of CLBs and natural enemies. Starting from the end of April, when the plants reached growth stage BBCH 32 (stem elongation), until the beginning of July, when plants reached plant growth stage BBCH 87 (hard dough stage), the number of insects was counted weekly. These fields were selected in areas with significant wheat cultivation (Polders, Schelde Polders, Zuid-Vlaanderen, Vlaams-Brabant, and Haspengouw). All monitored fields were managed according to common crop husbandry practices. Densities of CLBs were registered on 30 stems, selected randomly, per plot. Plots lay in four replicates along the border of the field and in the middle of the fields and occupied 16 m2 per plot. In total, 240 plants per field were monitored (8 plots × 30 plants) on a weekly basis. At each monitoring time, eggs, larvae, and pupae of CLB were counted. Dates of first and peak occurrence of CLB larvae and eggs were determined based on the field monitoring of the 94 locations. Daily weather data (maximum, minimum, and mean temperatures were used for the construction of the GDD models, and precipitation and/or relative humidity for the regression models) were monitored using the automated weather stations across Flanders (distance < 5 km from the fields), directed from the Agricultural Centre for Potato Research (Kruishoutem). To predict the different growth stages of CLBs, the various GDD models, mentioned above, have been developed each having its own base temperature and GDD threshold. To determine the applicability of these thresholds for predicting CLB phenology in Belgian wheat fields, these models were validated using the field data collected in Belgium. Belgium is a Western European country with a temperate sea-climate with mild winters and cool summers. In the summer it can be rainy, humid, and cloudy. The annual average temperature is 10°C, with July being the hottest month (18°C) and February the coldest (3°C). The wettest month is June with an average total rainfall of 90 mm. To determine the length and starting time of the periods in which environmental variables were associated with annual fluctuations of CLB eggs and larvae, the window-pane methodology was adopted. The concept underlying window-pane analysis is the specification of a time window of predefined length or duration and the construction of summary environmental variables (e.g., means) for the specified window. This time window is moved along the total time frame of interest (e.g., a year or a growing season) in daily increments, so that the environmental data from the entire time frame are ultimately considered in the data analysis (Kriss et al. 2010). For this study, a window length of 25 d was chosen. The first window began on 1 January (time 0) and ended on 25 January, the second window began on 2 January and ended on 26 January, etc. until the end of June. So, two successive windows share all but 1 d of data. For each 25-d window, summary variables of temperature (sum), rainfall (sum), and relative humidity (mean) were calculated and the correlation with the date of the first CLB egg or larvae and the peak dates were calculated. Based on this window-pane methodology, the variables with the highest correlation with a certain life stage and with a low mutual correlation (i.e., a low correlation between the predictor variables) were chosen. So, the variable selection was based on the correlation analysis. To construct prediction models for the occurrence of CLB eggs and larvae, we used an ordinary multiple linear regression approach and a ridge regression approach. Ordinary multiple linear regression is the simplest and best-known metric regression model. This modeling approach involves a minimization of the residual sum of squares. Yet, it is known that least-squares minimization in multiple linear regression may not always provide accurate predictions for a number of reasons, such as a lack of robustness to outliers and missing mechanisms for handling multicollinearity and controlling the complexity in the presence of many predictor variables. Ridge regression offers a solution to the last two problems by shrinking the regression coefficients toward 0. As such, a penalized residual sum of squares is minimized (Hastie et al. 2008). Regression trees were used as a third type of prediction model, which allows for the construction of nonlinear functions, unlike the two former regression techniques. Trees are built using a process known as binary recursive partitioning. The algorithm recursively splits the data into two groups based on a splitting rule. The split that maximizes the reduction in impurity is chosen, the data set split and the process repeated. Splitting continues until the terminal nodes are too small or too few to be split. The partitioning intends to increase the homogeneity of the two resulting subsets or nodes, based on the response variable. The partitioning stops when no splitting rule can improve the homogeneity of the nodes significantly (Hastie et al. 2008). To validate the models, two versions of cross-validation (CV) were considered. The first version involved a standard random 10-fold CV for which the data were randomly subdivided into 10 parts. Subsequently, 10 iterations of model calibration and validation were performed, also known as training and testing, leaving out one particular fold for testing in each iteration, while using the remaining nine folds for training. The second evaluation strategy was a more specific cross-year cross-location (CYCL) validation strategy proposed in Landschoot et al. (2012). This strategy allows to obtain an unbiased estimate of the model performance for future years and new locations. Results Evaluation of the GDD Models In Fig. 1, the variability of predicted dates for the first CLB egg, the first CLB larvae, the egg, and larvae peak are shown together with the dates on which the first eggs, first larvae, or larvae peak were observed. These boxplots give a first indication of the model performance. It is clear that some models from literature do not succeed in predicting the various life stages within an acceptable margin of error (clearly different boxes), necessary for being suitable as a tool for growers. However, even if two boxes are similar this does not guarantee that the observations are correctly predicted. To gain insight in the predictive performance, the mean absolute errors (MAEs) were calculated. Furthermore, based on these observations and temperature data, similar to literature, the base temperatures and GDD thresholds resulting in the best fit for our data were determined. So, for a set of base temperatures, ranging from 0°C until 10°C, the average GDD threshold was determined. In a next step, the predictive performance of the thresholds associated with each base temperature was calculated. The GDD thresholds and base temperatures listed in Tables 2–5 are the values resulting in the lowest MAE. On average, the first eggs in Belgium occurred at 624 GDD (with a base temperature of 1°C) and the egg peak occurred at 924 GDD (with a base temperature of 0°C). However, the MAEs were still 8 and 6 d, respectively (Tables 2 and 3). The best prediction for the first and peak larvae were obtained for a 85 GGD threshold and a base temperature of 10°C and a 245 GDD threshold and a base temperature of 8.7°C, respectively. The MAEs were 6 and 5 d, respectively (Tables 4 and 5). The predicted dates versus the observed dates of the first egg, peak egg, first larvae, and peak larvae are represented in Supp Fig. S1 [online only]. The dots are scattered randomly around the line x = y and do not follow an increasing trend illustrating the poor predictive power of the models. Supp Table S1 [online only] lists the correlations between the predicted and observed values. None of these correlations appears to be significant. Furthermore, note that the SDs of the date of the first egg, egg peak, first larvae, and peak larvae are 9.21, 6.18, 5.74, and 5.58 d, respectively. These values are in line with the MAEs, and for a good model we expected MAEs to be considerably lower than the SD. So, it turned out that a GDD approach alone is not sufficient to predict CLB populations in Flanders. A more detailed study is necessary to map the driving factors determining the CLB populations. Fig. 1. View largeDownload slide View largeDownload slide Variation in predicted (gray) and observed (white) dates of the first CLB eggs (A–C), first larvae (D–F), egg peak (G–I), and peak larvae (J–L) in the monitored fields. The dark gray box represents the variation of the predicted dates using a GDD threshold of 624 and a Tbase of 1°C for the first egg, a GDD threshold of 85 and a Tbase of 10°C for the first larvae, a GDD threshold of 924 and a Tbase of 0°C for the egg peak, and a GDD threshold of 245 and a Tbase of 8.7°C for the peak larvae. Fig. 1. View largeDownload slide View largeDownload slide Variation in predicted (gray) and observed (white) dates of the first CLB eggs (A–C), first larvae (D–F), egg peak (G–I), and peak larvae (J–L) in the monitored fields. The dark gray box represents the variation of the predicted dates using a GDD threshold of 624 and a Tbase of 1°C for the first egg, a GDD threshold of 85 and a Tbase of 10°C for the first larvae, a GDD threshold of 924 and a Tbase of 0°C for the egg peak, and a GDD threshold of 245 and a Tbase of 8.7°C for the peak larvae. Table 2. MAE of the different GDD models predicting the date of the first eggs Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 View Large Table 2. MAE of the different GDD models predicting the date of the first eggs Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 View Large Table 3. MAE of the different GDD models predicting the date of the first larvae Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 View Large Table 3. MAE of the different GDD models predicting the date of the first larvae Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 View Large Table 4. MAE of the different GDD models predicting the date of the egg peak Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 View Large Table 4. MAE of the different GDD models predicting the date of the egg peak Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 View Large Table 5. MAE of the different GDD models predicting the date of the larvae peak Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 View Large Table 5. MAE of the different GDD models predicting the date of the larvae peak Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 View Large Development of a Prediction Model As mentioned above, a window-pane analysis was carried out to find the periods during which the weather conditions have the highest influence on the development of CLBs. For each independent variable (day number of the first egg, egg peak, first larvae, and larvae peak), six variables were selected as predictor variables (Table 6). As temperature is the main factor influencing the growth and development, most predictor variables are temperature based. Furthermore, it can be seen that for the first egg and egg peak, the correlations with the temperature for the selected periods were negative indicating that in case temperatures are lower, the first egg and egg peak come earlier. Furthermore, the correlation with rainfall during spring was positive indicating that the first egg and egg peak occur later in case of a lot of rainfall during that period. For the larvae the correlations with temperature are sometimes positive and sometimes negative, meaning that during some periods higher temperatures fasten development, while during other ones they delay development. Table 6. Periods during which weather variables were significantly correlated with the first egg, egg peak, first larvae, and peak larvae of monitored CLBs (based on the data from 2014 until 2017) No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 View Large Table 6. Periods during which weather variables were significantly correlated with the first egg, egg peak, first larvae, and peak larvae of monitored CLBs (based on the data from 2014 until 2017) No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 View Large These variables were used as predictors to construct multiple linear regression models, ridge regression models, and regression trees. The coefficients of the resulting models are listed in Table 7; it can be seen that the absolute values of the coefficients of the ridge regression model are smaller compared to the coefficients of the linear regression model since ridge regression puts constraints on the coefficients to avoid overfitting. The MAE of each model, validated without CV, with random CV, and with CYCL validation are represented in Table 8. Without validation, the regression tree model performed best (lowest MAE), followed by the ridge regression model and the linear regression model. In case random CV was applied, the ridge regression model performed better than the linear regression model. The CYCL validation led to the highest MAE for each modeling approach. Furthermore, the regression trees outperformed the other models. Table 7. Coefficients associated with the different variables included in the multiple linear regression model and the ridge regression model No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 View Large Table 7. Coefficients associated with the different variables included in the multiple linear regression model and the ridge regression model No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 View Large Table 8. Performance (MAE) of the multiple linear regression models, ridge regression models, and regression trees predicting the day number of the first egg, egg peak, first larvae, and larvae peak, without CV, with random 10-fpm CVa, and with CYCL validation Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 a10-fold cross-validation. bCYCL validation. View Large Table 8. Performance (MAE) of the multiple linear regression models, ridge regression models, and regression trees predicting the day number of the first egg, egg peak, first larvae, and larvae peak, without CV, with random 10-fpm CVa, and with CYCL validation Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 a10-fold cross-validation. bCYCL validation. View Large In the previous section, the optimal GDD thresholds and optimal base temperatures for our data were based on the entire data set, so the data were not split into a test and training set. In a next step, the applicability of these thresholds and base temperatures to predict the first egg, first larvae, larvae peak, and peak was determined. Since no test-train splitting was done to determine the optimal thresholds and base temperatures, the MAE of the GDD models should be compared with the MAE of the regression models without CV. It can be seen in Table 8 that the MAE of the GDD models is always higher compared to the MAE of the models without CV. So, our proposed models perform better compared to the GDD approach. However, it can be argued that an MAE of 3–4.88 d is still too high for an accurate prediction model to be used in practice. Discussion During seasons with a high insect pressure, CLBs can cause significant yield losses in winter wheat. To avoid potential economic damages, unwarranted calendar-based insecticide sprays are applied. Since the population size of these organisms fluctuates greatly from year to year and from location to location, the need and optimal timing of an insecticide application varies from year to year and from location to location. To avoid unnecessary insecticide treatments in view of IPM, models predicting the timing and magnitude of CLBs infestation are critically important. The different aspects of the CLB life cycle are mainly estimated using simple GDD models. The main differences between the various models are the accumulated GDD threshold and base temperature. The available GDD models from literature were subjected to an evaluation on our data; however, it turned out that none of the previously established thresholds was appropriate for our data. Literature shows that with decreasing latitude, the base temperature will be higher and the sum of effective temperatures will be lower (Honek 1996). This suggests that development will be slower at lower altitudes, which is in agreement that the American models predict specific life stages too late for our CLB population. Even in case we reparametrized the models with the optimal GDD threshold and base temperature for our data, the mean absolute errors were too high, in general as high as the SD of our data. So, these GDD models have little predictive value. It can be concluded that models based on accumulated temperature (from 1 January) are not appropriate to predict CLB populations under the prevailing Belgian weather conditions. The low predictive power can be explained by several factors. Firstly, in contrast to regions for which the GDD models were developed, the CLB incidence in the monitored fields was very low. Secondly, the CLB population in Belgium is a composite of several species, all with a similar, though slightly different temperature-based phenology (Ali et al. 1977, 1979; Morlacchi et al. 2007), which makes it more difficult to set a general temperature-based threshold. In addition, Guppy (1979) proved that there exist slight differences in optimum temperatures between European species and CLBs found in North America. For GDD models, it is assumed that a temperature increase influences the insect in exactly the same way whether it comes 1 d before the start of the season or a couple of months before the season starts. However, that might not be a correct assumption. Keeping this in mind, we performed a window-pane correlation analysis to reveal the periods during which weather conditions are most influential. Based on this information, various modeling approaches were explored to predict the date of the first egg, first larvae, egg peak, and larvae peak. These models performed considerably better compared to the common GDD models. Based on our correlation analysis, it was seen that for the larvae the correlations with temperature are sometimes positive and sometimes negative, meaning that during some periods higher temperatures fasten development, while during others they delay development. Based on the results gathered during 3 yr, we found that CLB larvae occurred earlier in the years with, e.g., a ‘colder’ winter. This seems at first sight biologically irrelevant; however, it has to be added that Flanders has a mild climate, e.g., the average temperatures in February 2015, 2016, and 2017 were, respectively, 6.3, 4.5, and 6.1°C. It seems that temperatures during winter were not really a limiting factor in delaying development. In addition, temperature fluctuations, cold periods during winter followed by warmer periods can accelerate the termination of the diapause resulting in an earlier CLB development. Furthermore, negative correlations between winter temperatures and CLBs have also been found in literature. Daamen and Stol (1993) found that in the Netherlands, the phenology and crop injury due to CLB to be negatively correlated with mean temperatures of winter months December, January, and February. Correspondingly, Ali et al. (1979) proved that mortality of overwintering beetles severely increases above 10°C. Concerning the different modeling approaches, multiple linear regression, ridge regression, and regression trees, it was concluded that regression trees outperformed linear regression and ridge regression. In case CV was applied, the multiple linear regression performed worst, since linear regression is prone to overfitting, whereas ridge regression and regression trees are more robust toward overfitting. Ridge regression puts constraints on the model coefficients by adding a penalty term to the loss function. Minimizing loss with this penalty term means we tend to avoid very large coefficient values, which ensures that the coefficients are not skewed due to outliers. Furthermore, the performance based on CYCL validation is the worst, but also the most realistic, as this is the performance that can be expected for new years and new locations. In conclusion, this analysis shows that GDD models, even with optimized thresholds for our data, have little predictive value to predict CLBs. Linear regression, ridge regression, and regression trees performed considerably better. However, in case CV was applied, to gain insight in the future predictive value, the MAEs were too high. As crop husbandry practices also influence CLB occurrence, these can be included as additional variables. It is indeed the intention to refine these models by incorporating additional data on crop husbandry practices (e.g., sowing density and date, crop rotation, fertilization application), natural enemies, etc., which should improve the efficacy of the models. In a last phase we intend to implement these models in a decision support system. Supplementary Data Supplementary data are available at Environmental Entomology online. Acknowledgments This work was financially supported by the agency Flanders Innovation & Entrepreneurship, VLAIO (Brussels, Belgium). Furthermore, we are grateful to the staff of the Bottelare Research Farm, Ghent University, University College Ghent, Inagro, and the Soil Service of Belgium for the participation in the field monitoring. References Cited Akyuz , F. A. , H. Kandel , and D. Morlock . 2017 . Developing a growing degree day model for North Dakota and Northern Minnesota soybean . Agr. Forest Meteorol . 239 : 134 – 140 . 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This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Environmental Entomology Oxford University Press

Potentials and Limitations of a Growing Degree Day Approach to Predict the Phenology of Cereal Leaf Beetles

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Abstract

Abstract Cereal leaf beetles (CLBs) are described as an invasive pest of small grain cereals in many regions worldwide. Prediction models aimed to prevent yield losses caused by these feeding insects have been developed by researchers all over the world. As a foundation for many of these prediction models, it is known that a specific number of heat units, or growing degree days (GDDs), is required for an insect to complete a certain physiological process. In this paper, we overview the existing GDD models for CLBs. Furthermore, we used our Belgian input data to compare model predictions with our own observations. Though, the existing models were not able to predict the seasonal trends present in our data: the occurrence of various life stages were monitored earlier then the model predicted. Hence, a weighted GDD model was tested on the data as well: the accumulated GDDs during certain periods were balanced according to the significance of this period for the insect. Rainfall and/or relative humidity were included as well. Based on these selected variables, multiple linear regression models, ridge regression models, and regression trees were fitted. This approach performed considerably better compared to the simple accumulation of GDD. However, based on cross-year cross-location validation method, to gain insight in the future performance of the models, the accuracy was still too low to serve as an accurate warning tool. cereal leaf beetle, growing degree day, modeling, winter wheat Wheat (Triticum aestivium L.) is a main agricultural crop grown worldwide (Food and Agriculture Organization of the United Nations 2017). During some years cereal leaf beetles (CLBs; composite of species, Coleoptera: Chrysomelidae) can be a problematic pest in winter wheat, imposing significant yield and quality losses, both directly and indirectly. Direct feeding damage, due to the removal of plant tissue, occurs when larvae develop on stems, leaves, and heads, from the stem elongation stage through to head filling stage. Furthermore, these insects cause indirect damage since they are vectors of a number of viruses (e.g., barley yellow dwarf virus and phleum mottle virus) (Nault et al. 1978). Flag leaf defoliation causes more damage and yield loss than injury to lower leaves, since the flag leaf photosynthesis contributes significantly more to grain yield (Zhang et al. 2006). Furthermore, the flag leaf stage often appears together with the fourth and last larval stage of CLBs. Larvae in this stage are most active and are known to cause major feeding damage to the plants: 70% of total plant damage caused by CLBs is linked with this stage (Kher et al. 2011). Yield losses associated with the presence of CLBs can regionally go up to 30% (Van Duyn et al. 1997, Ihrig et al. 2001, Kher et al. 2011). CLBs are a complex of several species belonging to the genus Oulema. In Western Europe, next to most common species O. melanopus (Linnaeus) (Coleoptera: Chrysomelidae) and O. gallaecianna (Heyden) (Coleoptera: Chrysomelidae), the species O. duftschmidi (Redtenbacher) (Coleoptera: Chrysomelidae), O. Septentrionis (Weise) (Coleoptera: Chrysomelidae), and O. rufocyanea (Suffrian) (Coleoptera: Chrysomelidae) occur (Bezdek and Baselga 2015). During the period April–May (2016 and 2017) more than 800 Oulema adults were sampled in Belgian wheat fields (2016: 28 fields; 2017: 23 fields) for species identification We found that next to the widespread species O. melanopus, also O. duftschmidi and O. gallaecianna frequently occurred in Belgian wheat fields (Elias Van De Vijver, unpublished data). The population size of CLBs, determined by the population growth rate, growth period, and mortality, fluctuates in time and space due to a variety of reasons, such as fluctuations in environmental conditions, availability of resources, host crop quality, and impact of antagonistic species (Philips et al. 2011). With the green revolution, new pesticides and chemical fertilizers were introduced, decreasing the need for integrated pest management (IPM; Tummala et al. 1975). Still today, a wide range of chemicals is available to prevent or to reduce the impact of pests. However, in order to arrive at a more sustainable agricultural system, a combined approach of cultural and chemical-based control methods is essential. Decision support systems (DSS) are increasingly important to achieve a more rational use of insecticides. These systems are based on predictive models simulating the outbreak and severity of pests. The output of these systems, in combination with appropriate economic thresholds, can then be used to evaluate the necessity to apply chemicals together with a correct timing and dosage of the application (Le Cointe et al. 2016). There is a more than 40-yr tradition of modeling wheat, CLB, and natural enemy interactions (Coulman et al. 1972, Casagrande and Haynes 1976, Guppy and Harcourt 1978, Philips et al. 2012). However, the use of such prediction models in plant protection is scarce, mainly because of their insufficient forecast accuracy. The most important problems in modeling CLBs and antagonist population dynamics have to do with describing the inter-field dynamics, estimation of mortality rates, and survival, which are influenced by several variables (Helgesen and Haynes 1972). In order to develop more accurate prediction models, a good understanding of the population dynamics, both spatially and temporally, is critically important. Weather conditions, crop husbandry practices, and landscape management (e.g., surrounding vegetation) are important factors affecting the tri-trophic interactions between plants, CLBs, and their natural enemies (Haynes and Gage 1981). A wide range of modeling approaches has been used to predict insect development, ranging from simple growing degree day (GDD) models (Evans et al. 2006; Philips et al. 2012) to more complex mechanistic models (Helgesen and Haynes 1972, Tummala et al. 1975, Lee and Barr 1976). Mechanistic models adopt a bottom-up approach to understanding system dynamics, and in case the life cycle of the various organisms is not completely described, these models will often not fit data as well as empirical models that use statistically derived functions. Detailed population models tend to be very complex, because it is often believed that higher complexity leads to higher accuracy. However, it is overlooked that such multiple input models are also very sensitive to measurement errors rising with each parameter, and can hence result in highly variable predictions (Klüken 2008). For this reason, in this research we will focus on the relatively simple GDD models. Although GDD models have a long history of use in predicting plant and insect phenology, this modeling approach is still amended in recent warning systems (Cayton et al. 2015, Akyuz et al. 2017, Calero et al. 2017) and offers, with appropriate thresholds, certainly opportunities. Since insects are poikilothermic, temperature is the major driver of phenology. Indeed, there exists a profound correlation between temperature and the phenology of insects. Therefore, insect phenology is often predicted via the calculation of heat units, or GDD. GDD accrual is typically initiated after a discrete biological event, referred to as a ‘biofix’, or a calendar date (e.g., 1 January). A GDD model can be represented according to (1). GDD=[Tmax+ Tmin2]−Tbase (1) where Tmax is the maximum daily temperature, Tmin is the minimum daily temperature, and Tbase is the lower threshold for development. In case the average temperature is lower than Tbase, no degree days are accumulated and 0 is recorded for that day, since no insect growth or development occurs. Since each developmental stage has its own total heat requirement, insect development can be estimated by accumulating GDD throughout the season until a certain GDD threshold is reached (Wilson and Barnett 1983, Zalom et al. 1983). The warmer the weather, the faster GDD accumulates and the faster the GDD threshold is reached. To predict the date of the various life cycle stages of CLBs, numerous GDD models have been developed, each with its specific GDD threshold and base temperature. In Table 1, an overview of the GDDs necessary to reach a certain life cycle stage of CLBs is given. All models start to accumulate GDD on the biofix date of 1 January. These data were based on field trials and in some cases supported by data retrieved from laboratory trials. It can be seen that the observations of the various researchers at different locations led to a wide range of base temperatures and GDD thresholds. Therefore, based on the thresholds set by Gage and Haynes (1975), Guppy and Harcourt (1978), Kidd (2002), Blodgett et al. (2004), Evans et al. (2006), and Hoffman and Rao (2010), a combined GDD model was developed and implemented on http://uspest.org/wea, a webserver of the Oregon State University on which GDD models for several organisms can be accessed. The suggested combined CLB model uses a base temperature of 9°C and the first egg, egg peak, first larvae, and larvae peak can be expected at 80, 150, 180, and 360 GDD, respectively. Furthermore, note that Philips et al. (2012) did not use a fixed base temperature and GDD threshold to predict the larvae peak. According to these authors, the larvae peak is expected to occur in average 17.5 d (within a range of 7–35 d) after the egg peak. Additionally, it can be seen that Evans et al. (2014) considered a variable threshold to predict the date of CLB egg peaks in Utah. Based on data from 2001 until 2011, these authors concluded that there was a considerable variation among years in the number of GDD associated with the occurrence of the CLB egg peak (ranging from 145 to 325 GDD). Much of this variability could be accounted for by considering early spring warmth. Indeed, there was a positive linear relationship between the GDD for egg peaks and the accumulated heat during spring, the higher the temperatures in spring the higher the GDD threshold. Thus, instead of using a fixed GDD threshold, these authors suggest that the GDD threshold should take into account early spring warmth. For instance, the threshold for egg peak (y) can be calculated according to y = 67.45 + 1.41x, with x the accumulated degree days from 1 January until 21 April. Table 1. Summary of the GDDs necessary to reach a certain life cycle stage of CLBs, between brackets the minimum development threshold is mentioned Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) View Large Table 1. Summary of the GDDs necessary to reach a certain life cycle stage of CLBs, between brackets the minimum development threshold is mentioned Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) Source Location First egg Egg peak First larvae Larvae peak Gage and Haynes (1975) North America 220 (8.9) Ali et al. (1977) Germany 85–90 (10.5) Guppy and Harcourt (1978) Ottawa 105 (7) 166 (7) Guppy and Harcourt (1978) Ottawa 87 (9) 137 (9) Kidd et al. (2002) North Carolina 165 (8.9) 349 (8.9) Blodgett et al. (2004) Montana 253 (7.17) Evans et al. (2006) Utah 90 (8.9) 150 (8.9) 105 (8.9) 240 (8.9) Hoffman and Rao (2010) Canada 88 (9) Philips et al. (2012) Virginia 182 (8) Egg peak + 17.5 Evans et al. (2014) Utah Variable Combined (http://uspest.org/wea) 80 (9) 180 (9) 360 (9) View Large All the approaches mentioned in Table 1 studied the relationship between GDD and a certain life cycle stage. However, for practical insight into the phenology of the pest insect, predicting pest incidence on field level is important as well. Therefore, Ihrig et al. (2001) studied the relationship between CLB egg counts and the number of insects in the fourth-instar stage and the impact of fourth-instar population on winter wheat. A significant linear relationship was found between the 50th percentile of the number of eggs (x) and the density of the fourth-instar population (y) (y = 0.36x − 0.01; R2 = 0.79). Potentially detrimental larval infestations were forecast from egg populations present during the stem elongation to flag leaf emergence developmental stages. A significant positive linear relationship between total fourth-instar larvae stem population estimates (x) and percent flag leaf defoliation (y) was detected (y = 20.29x + 1.34; R2 = 0.60). Furthermore, a weaker, but still significant linear relationship between the total fourth-instar population estimates (x) and percent yield loss (y) was found (y = 11.74x + 6.51; R2 = 0.26), indicating that factors in addition to flag leaf injury, primarily by fourth instars, also contributed to reduced yields. Materials and Methods During the wheat growing seasons 2014–2015, 2015–2016, and 2016–2017, respectively, 29, 33, and 32 winter wheat fields throughout Flanders (Belgium) were monitored for the presence of CLBs and natural enemies. Starting from the end of April, when the plants reached growth stage BBCH 32 (stem elongation), until the beginning of July, when plants reached plant growth stage BBCH 87 (hard dough stage), the number of insects was counted weekly. These fields were selected in areas with significant wheat cultivation (Polders, Schelde Polders, Zuid-Vlaanderen, Vlaams-Brabant, and Haspengouw). All monitored fields were managed according to common crop husbandry practices. Densities of CLBs were registered on 30 stems, selected randomly, per plot. Plots lay in four replicates along the border of the field and in the middle of the fields and occupied 16 m2 per plot. In total, 240 plants per field were monitored (8 plots × 30 plants) on a weekly basis. At each monitoring time, eggs, larvae, and pupae of CLB were counted. Dates of first and peak occurrence of CLB larvae and eggs were determined based on the field monitoring of the 94 locations. Daily weather data (maximum, minimum, and mean temperatures were used for the construction of the GDD models, and precipitation and/or relative humidity for the regression models) were monitored using the automated weather stations across Flanders (distance < 5 km from the fields), directed from the Agricultural Centre for Potato Research (Kruishoutem). To predict the different growth stages of CLBs, the various GDD models, mentioned above, have been developed each having its own base temperature and GDD threshold. To determine the applicability of these thresholds for predicting CLB phenology in Belgian wheat fields, these models were validated using the field data collected in Belgium. Belgium is a Western European country with a temperate sea-climate with mild winters and cool summers. In the summer it can be rainy, humid, and cloudy. The annual average temperature is 10°C, with July being the hottest month (18°C) and February the coldest (3°C). The wettest month is June with an average total rainfall of 90 mm. To determine the length and starting time of the periods in which environmental variables were associated with annual fluctuations of CLB eggs and larvae, the window-pane methodology was adopted. The concept underlying window-pane analysis is the specification of a time window of predefined length or duration and the construction of summary environmental variables (e.g., means) for the specified window. This time window is moved along the total time frame of interest (e.g., a year or a growing season) in daily increments, so that the environmental data from the entire time frame are ultimately considered in the data analysis (Kriss et al. 2010). For this study, a window length of 25 d was chosen. The first window began on 1 January (time 0) and ended on 25 January, the second window began on 2 January and ended on 26 January, etc. until the end of June. So, two successive windows share all but 1 d of data. For each 25-d window, summary variables of temperature (sum), rainfall (sum), and relative humidity (mean) were calculated and the correlation with the date of the first CLB egg or larvae and the peak dates were calculated. Based on this window-pane methodology, the variables with the highest correlation with a certain life stage and with a low mutual correlation (i.e., a low correlation between the predictor variables) were chosen. So, the variable selection was based on the correlation analysis. To construct prediction models for the occurrence of CLB eggs and larvae, we used an ordinary multiple linear regression approach and a ridge regression approach. Ordinary multiple linear regression is the simplest and best-known metric regression model. This modeling approach involves a minimization of the residual sum of squares. Yet, it is known that least-squares minimization in multiple linear regression may not always provide accurate predictions for a number of reasons, such as a lack of robustness to outliers and missing mechanisms for handling multicollinearity and controlling the complexity in the presence of many predictor variables. Ridge regression offers a solution to the last two problems by shrinking the regression coefficients toward 0. As such, a penalized residual sum of squares is minimized (Hastie et al. 2008). Regression trees were used as a third type of prediction model, which allows for the construction of nonlinear functions, unlike the two former regression techniques. Trees are built using a process known as binary recursive partitioning. The algorithm recursively splits the data into two groups based on a splitting rule. The split that maximizes the reduction in impurity is chosen, the data set split and the process repeated. Splitting continues until the terminal nodes are too small or too few to be split. The partitioning intends to increase the homogeneity of the two resulting subsets or nodes, based on the response variable. The partitioning stops when no splitting rule can improve the homogeneity of the nodes significantly (Hastie et al. 2008). To validate the models, two versions of cross-validation (CV) were considered. The first version involved a standard random 10-fold CV for which the data were randomly subdivided into 10 parts. Subsequently, 10 iterations of model calibration and validation were performed, also known as training and testing, leaving out one particular fold for testing in each iteration, while using the remaining nine folds for training. The second evaluation strategy was a more specific cross-year cross-location (CYCL) validation strategy proposed in Landschoot et al. (2012). This strategy allows to obtain an unbiased estimate of the model performance for future years and new locations. Results Evaluation of the GDD Models In Fig. 1, the variability of predicted dates for the first CLB egg, the first CLB larvae, the egg, and larvae peak are shown together with the dates on which the first eggs, first larvae, or larvae peak were observed. These boxplots give a first indication of the model performance. It is clear that some models from literature do not succeed in predicting the various life stages within an acceptable margin of error (clearly different boxes), necessary for being suitable as a tool for growers. However, even if two boxes are similar this does not guarantee that the observations are correctly predicted. To gain insight in the predictive performance, the mean absolute errors (MAEs) were calculated. Furthermore, based on these observations and temperature data, similar to literature, the base temperatures and GDD thresholds resulting in the best fit for our data were determined. So, for a set of base temperatures, ranging from 0°C until 10°C, the average GDD threshold was determined. In a next step, the predictive performance of the thresholds associated with each base temperature was calculated. The GDD thresholds and base temperatures listed in Tables 2–5 are the values resulting in the lowest MAE. On average, the first eggs in Belgium occurred at 624 GDD (with a base temperature of 1°C) and the egg peak occurred at 924 GDD (with a base temperature of 0°C). However, the MAEs were still 8 and 6 d, respectively (Tables 2 and 3). The best prediction for the first and peak larvae were obtained for a 85 GGD threshold and a base temperature of 10°C and a 245 GDD threshold and a base temperature of 8.7°C, respectively. The MAEs were 6 and 5 d, respectively (Tables 4 and 5). The predicted dates versus the observed dates of the first egg, peak egg, first larvae, and peak larvae are represented in Supp Fig. S1 [online only]. The dots are scattered randomly around the line x = y and do not follow an increasing trend illustrating the poor predictive power of the models. Supp Table S1 [online only] lists the correlations between the predicted and observed values. None of these correlations appears to be significant. Furthermore, note that the SDs of the date of the first egg, egg peak, first larvae, and peak larvae are 9.21, 6.18, 5.74, and 5.58 d, respectively. These values are in line with the MAEs, and for a good model we expected MAEs to be considerably lower than the SD. So, it turned out that a GDD approach alone is not sufficient to predict CLB populations in Flanders. A more detailed study is necessary to map the driving factors determining the CLB populations. Fig. 1. View largeDownload slide View largeDownload slide Variation in predicted (gray) and observed (white) dates of the first CLB eggs (A–C), first larvae (D–F), egg peak (G–I), and peak larvae (J–L) in the monitored fields. The dark gray box represents the variation of the predicted dates using a GDD threshold of 624 and a Tbase of 1°C for the first egg, a GDD threshold of 85 and a Tbase of 10°C for the first larvae, a GDD threshold of 924 and a Tbase of 0°C for the egg peak, and a GDD threshold of 245 and a Tbase of 8.7°C for the peak larvae. Fig. 1. View largeDownload slide View largeDownload slide Variation in predicted (gray) and observed (white) dates of the first CLB eggs (A–C), first larvae (D–F), egg peak (G–I), and peak larvae (J–L) in the monitored fields. The dark gray box represents the variation of the predicted dates using a GDD threshold of 624 and a Tbase of 1°C for the first egg, a GDD threshold of 85 and a Tbase of 10°C for the first larvae, a GDD threshold of 924 and a Tbase of 0°C for the egg peak, and a GDD threshold of 245 and a Tbase of 8.7°C for the peak larvae. Table 2. MAE of the different GDD models predicting the date of the first eggs Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 View Large Table 2. MAE of the different GDD models predicting the date of the first eggs Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 Ali_et_al. (85(10.5)) Ali_et_al. (90(10.5)) Guppy_et_al. (105(7)) Guppy_et_al. (87(9)) Hoffman_et_al. (88(9)) Evans_et_al. (90(9)) Combined (80(9)) Optimal (624(1)) 2015 19.58 21.08 8.29 3.96 4.13 3.92 3.46 3.25 2016 24.14 26.00 12.41 17.66 17.59 9.03 16.86 12.03 2017 22.32 23.32 23.21 14.26 14.21 14.05 13.37 9.37 C 22.14 23.65 10.24 12.19 12.21 12.13 11.47 8.40 View Large Table 3. MAE of the different GDD models predicting the date of the first larvae Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 View Large Table 3. MAE of the different GDD models predicting the date of the first larvae Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 Gage_et_al. (220(9)) Kid_et_al. (165(9)) Evans_et_al. (105(9)) Combined (180(9)) Optimal (85(10)) 2015 28.26 18.48 7.00 22.91 10.83 2016 18.19 8.96 4.81 12.52 4.59 2017 8.23 3.70 5.60 5.43 3.03 C 17.35 9.73 5.74 12.85 5.80 View Large Table 4. MAE of the different GDD models predicting the date of the egg peak Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 View Large Table 4. MAE of the different GDD models predicting the date of the egg peak Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 Philips_et_al. (182(8)) Evans_et_al. (Var) Guppy_et_al. (166(7)) Guppy_et_al. (137(9)) Evans_et_al. (150(9) Optimal (924(0)) 2015 7.95 16.82 9.27 8.55 10.18 5.64 2016 6.46 25.38 6.77 6.27 6.92 4.81 2017 5.88 46.52 15.28 5.96 6.32 6.80 C 6.71 30.04 10.44 6.85 7.70 5.74 View Large Table 5. MAE of the different GDD models predicting the date of the larvae peak Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 View Large Table 5. MAE of the different GDD models predicting the date of the larvae peak Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 Kid_et_al. (349(9)) Evans_et_al. (240(9)) Philips_et_al. (+17)) Combined (360(9)) Optimal (245(8.7)) 2015 22.27 8.00 7.45 24.23 7.45 2016 13.85 4.41 4.65 16.26 4.62 2017 9.57 3.11 4.11 11.54 3.42 C 14.70 4.96 5.25 16.82 4.92 View Large Development of a Prediction Model As mentioned above, a window-pane analysis was carried out to find the periods during which the weather conditions have the highest influence on the development of CLBs. For each independent variable (day number of the first egg, egg peak, first larvae, and larvae peak), six variables were selected as predictor variables (Table 6). As temperature is the main factor influencing the growth and development, most predictor variables are temperature based. Furthermore, it can be seen that for the first egg and egg peak, the correlations with the temperature for the selected periods were negative indicating that in case temperatures are lower, the first egg and egg peak come earlier. Furthermore, the correlation with rainfall during spring was positive indicating that the first egg and egg peak occur later in case of a lot of rainfall during that period. For the larvae the correlations with temperature are sometimes positive and sometimes negative, meaning that during some periods higher temperatures fasten development, while during other ones they delay development. Table 6. Periods during which weather variables were significantly correlated with the first egg, egg peak, first larvae, and peak larvae of monitored CLBs (based on the data from 2014 until 2017) No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 View Large Table 6. Periods during which weather variables were significantly correlated with the first egg, egg peak, first larvae, and peak larvae of monitored CLBs (based on the data from 2014 until 2017) No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 No. First egg Egg peak First larvae Peak larvae Variable + period Cor. Variable + period Cor. Variable + period Cor. Variable + period Cor. 1 Avg temp 16-I–9-II −0.50 Avg temp 3-II–27-I −0.11 Avg temp 3-I–27-I −0.36 Avg temp 3-I–27-I 0.54 2 Avg temp 10-III–3-IV −0.23 Avg temp 15-II–11-III −0.11 Avg temp 28-I–21-II 0.41 Avg temp 11-I–4-II 0.48 3 Avg temp 29-III–22-IV −0.13 Avg temp 3-III–27-III −0.10 Avg temp 22-II–18-III 0.19 Avg temp 22-II–18-III −0.48 4 Avg temp 1-V–25-V −0.39 Rel. Humidity 2-V–26-V −0.29 Avg temp 23-III–16-IV 0.46 Avg temp 23-III–16-IV −0.28 5 Rainfall 22-II–18-III −0.56 Rainfall 14-III–7-IV 0.15 Avg temp 17-IV–11-V −0.46 Avg temp 17-IV–11-V 0.36 6 Rainfall 25-IV–19-V 0.49 Rainfall 31-III–24-IV 0.14 Rainfall 19-II–15-III 0.47 Rainfall 10-V–3-VI 0.20 View Large These variables were used as predictors to construct multiple linear regression models, ridge regression models, and regression trees. The coefficients of the resulting models are listed in Table 7; it can be seen that the absolute values of the coefficients of the ridge regression model are smaller compared to the coefficients of the linear regression model since ridge regression puts constraints on the coefficients to avoid overfitting. The MAE of each model, validated without CV, with random CV, and with CYCL validation are represented in Table 8. Without validation, the regression tree model performed best (lowest MAE), followed by the ridge regression model and the linear regression model. In case random CV was applied, the ridge regression model performed better than the linear regression model. The CYCL validation led to the highest MAE for each modeling approach. Furthermore, the regression trees outperformed the other models. Table 7. Coefficients associated with the different variables included in the multiple linear regression model and the ridge regression model No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 View Large Table 7. Coefficients associated with the different variables included in the multiple linear regression model and the ridge regression model No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 No. First egg Egg peak First larvae Peak larvae Linear Ridge Linear Ridge Linear Ridge Linear Ridge Intercept 76.11 92.17 167.72 166.96 117.89 128.76 162.15 157.00 1 −0.083 −0.063 −0.050 −0.035 −0.181 −0.067 0.048 0.030 2 −0.051 −0.032 −0.067 −0.021 0.147 0.033 0.033 0.050 3 0.049 0.053 0.100 0.047 −0.076 −0.033 −0.086 −0.041 4 0.169 0.096 −0.478 −0.447 −0.064 0.033 0.026 −0.008 5 −0.216 −0.188 0.031 0.019 0.135 −0.002 −0.013 0.001 6 0.036 0.059 −0.037 −0.004 0.044 0.044 −0.110 −0.057 View Large Table 8. Performance (MAE) of the multiple linear regression models, ridge regression models, and regression trees predicting the day number of the first egg, egg peak, first larvae, and larvae peak, without CV, with random 10-fpm CVa, and with CYCL validation Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 a10-fold cross-validation. bCYCL validation. View Large Table 8. Performance (MAE) of the multiple linear regression models, ridge regression models, and regression trees predicting the day number of the first egg, egg peak, first larvae, and larvae peak, without CV, with random 10-fpm CVa, and with CYCL validation Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 Without CV Random 10-fold CV CYCL Vb Linear Rigde Tree Linear Rigde Tree Linear Rigde Tree First egg 5.38 6.96 3.51 6.11 6.01 3.51 14.12 10.30 3.51 Egg peak 4.57 4.80 3.81 5.02 5.03 3.81 8.33 5.24 3.81 First larvae 3.75 4.70 2.81 5.24 4.35 2.14 5.95 5.57 4.88 Larvae peak 3.58 4.08 3.00 4.02 4.01 3.00 19.23 19.03 3.00 a10-fold cross-validation. bCYCL validation. View Large In the previous section, the optimal GDD thresholds and optimal base temperatures for our data were based on the entire data set, so the data were not split into a test and training set. In a next step, the applicability of these thresholds and base temperatures to predict the first egg, first larvae, larvae peak, and peak was determined. Since no test-train splitting was done to determine the optimal thresholds and base temperatures, the MAE of the GDD models should be compared with the MAE of the regression models without CV. It can be seen in Table 8 that the MAE of the GDD models is always higher compared to the MAE of the models without CV. So, our proposed models perform better compared to the GDD approach. However, it can be argued that an MAE of 3–4.88 d is still too high for an accurate prediction model to be used in practice. Discussion During seasons with a high insect pressure, CLBs can cause significant yield losses in winter wheat. To avoid potential economic damages, unwarranted calendar-based insecticide sprays are applied. Since the population size of these organisms fluctuates greatly from year to year and from location to location, the need and optimal timing of an insecticide application varies from year to year and from location to location. To avoid unnecessary insecticide treatments in view of IPM, models predicting the timing and magnitude of CLBs infestation are critically important. The different aspects of the CLB life cycle are mainly estimated using simple GDD models. The main differences between the various models are the accumulated GDD threshold and base temperature. The available GDD models from literature were subjected to an evaluation on our data; however, it turned out that none of the previously established thresholds was appropriate for our data. Literature shows that with decreasing latitude, the base temperature will be higher and the sum of effective temperatures will be lower (Honek 1996). This suggests that development will be slower at lower altitudes, which is in agreement that the American models predict specific life stages too late for our CLB population. Even in case we reparametrized the models with the optimal GDD threshold and base temperature for our data, the mean absolute errors were too high, in general as high as the SD of our data. So, these GDD models have little predictive value. It can be concluded that models based on accumulated temperature (from 1 January) are not appropriate to predict CLB populations under the prevailing Belgian weather conditions. The low predictive power can be explained by several factors. Firstly, in contrast to regions for which the GDD models were developed, the CLB incidence in the monitored fields was very low. Secondly, the CLB population in Belgium is a composite of several species, all with a similar, though slightly different temperature-based phenology (Ali et al. 1977, 1979; Morlacchi et al. 2007), which makes it more difficult to set a general temperature-based threshold. In addition, Guppy (1979) proved that there exist slight differences in optimum temperatures between European species and CLBs found in North America. For GDD models, it is assumed that a temperature increase influences the insect in exactly the same way whether it comes 1 d before the start of the season or a couple of months before the season starts. However, that might not be a correct assumption. Keeping this in mind, we performed a window-pane correlation analysis to reveal the periods during which weather conditions are most influential. Based on this information, various modeling approaches were explored to predict the date of the first egg, first larvae, egg peak, and larvae peak. These models performed considerably better compared to the common GDD models. Based on our correlation analysis, it was seen that for the larvae the correlations with temperature are sometimes positive and sometimes negative, meaning that during some periods higher temperatures fasten development, while during others they delay development. Based on the results gathered during 3 yr, we found that CLB larvae occurred earlier in the years with, e.g., a ‘colder’ winter. This seems at first sight biologically irrelevant; however, it has to be added that Flanders has a mild climate, e.g., the average temperatures in February 2015, 2016, and 2017 were, respectively, 6.3, 4.5, and 6.1°C. It seems that temperatures during winter were not really a limiting factor in delaying development. In addition, temperature fluctuations, cold periods during winter followed by warmer periods can accelerate the termination of the diapause resulting in an earlier CLB development. Furthermore, negative correlations between winter temperatures and CLBs have also been found in literature. Daamen and Stol (1993) found that in the Netherlands, the phenology and crop injury due to CLB to be negatively correlated with mean temperatures of winter months December, January, and February. Correspondingly, Ali et al. (1979) proved that mortality of overwintering beetles severely increases above 10°C. Concerning the different modeling approaches, multiple linear regression, ridge regression, and regression trees, it was concluded that regression trees outperformed linear regression and ridge regression. In case CV was applied, the multiple linear regression performed worst, since linear regression is prone to overfitting, whereas ridge regression and regression trees are more robust toward overfitting. Ridge regression puts constraints on the model coefficients by adding a penalty term to the loss function. Minimizing loss with this penalty term means we tend to avoid very large coefficient values, which ensures that the coefficients are not skewed due to outliers. Furthermore, the performance based on CYCL validation is the worst, but also the most realistic, as this is the performance that can be expected for new years and new locations. In conclusion, this analysis shows that GDD models, even with optimized thresholds for our data, have little predictive value to predict CLBs. Linear regression, ridge regression, and regression trees performed considerably better. However, in case CV was applied, to gain insight in the future predictive value, the MAEs were too high. As crop husbandry practices also influence CLB occurrence, these can be included as additional variables. It is indeed the intention to refine these models by incorporating additional data on crop husbandry practices (e.g., sowing density and date, crop rotation, fertilization application), natural enemies, etc., which should improve the efficacy of the models. In a last phase we intend to implement these models in a decision support system. Supplementary Data Supplementary data are available at Environmental Entomology online. Acknowledgments This work was financially supported by the agency Flanders Innovation & Entrepreneurship, VLAIO (Brussels, Belgium). Furthermore, we are grateful to the staff of the Bottelare Research Farm, Ghent University, University College Ghent, Inagro, and the Soil Service of Belgium for the participation in the field monitoring. References Cited Akyuz , F. A. , H. Kandel , and D. Morlock . 2017 . Developing a growing degree day model for North Dakota and Northern Minnesota soybean . Agr. Forest Meteorol . 239 : 134 – 140 . 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Environmental EntomologyOxford University Press

Published: Jun 5, 2018

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