Research Article Received: 23 December 2013
Revised: 00 0000
Accepted article published: 19 March 2014
Published online in Wiley Online Library: 28 April 2014
(wileyonlinelibrary.com) DOI 10.1002/ps.3778
Validating spatiotemporal predictions of an important pest of small grains Scott C Merrill,a* Thomas O Holtzer,b Frank B Peairsb and Philip J Lesterc Abstract BACKGROUND: Arthropod pests are typically managed using tactics applied uniformly to the whole field. Precision pest management applies tactics under the assumption that within-field pest pressure differences exist. This approach allows for more precise and judicious use of scouting resources and management tactics. For example, a portion of a field delineated as attractive to pests may be selected to receive extra monitoring attention. Likely because of the high variability in pest dynamics, little attention has been given to developing precision pest prediction models. Here, multimodel synthesis was used to develop a spatiotemporal model predicting the density of a key pest of wheat, the Russian wheat aphid, Diuraphis noxia (Kurdjumov). RESULTS: Spatially implicit and spatially explicit models were synthesized to generate spatiotemporal pest pressure predictions. Cross-validation and field validation were used to confirm model efficacy. A strong within-field signal depicting aphid density was confirmed with low prediction errors. CONCLUSION: Results show that the within-field model predictions will provide higher-quality information than would be provided by traditional field scouting. With improvements to the broad-scale model component, the model synthesis approach and resulting tool could improve pest management strategy and provide a template for the development of spatially explicit pest pressure models. © 2014 Society of Chemical Industry Keywords: Diuraphis noxia; model synthesis; predictive model; spatial model; cross-validation; invasive species
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INTRODUCTION
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and then subjecting these at-risk areas to intense study to determine environmental factors that may be altered to decrease the impact of pest outbreaks or to improve resistance management strategy.3,4 One difficulty with developing and using precision pest management is the high variability associated with pest pressure.5 Highly variable pest pressure exacerbates the economic balancing act of weighing the costs associated with delineating variation against costs associated with assuming homogeneity. However, if predictable variation can be correlated with remotely sensed data (such as weather or topographic variables), prediction costs can be exceptionally low. The environmental factors governing the Russian wheat aphid, Diuraphis noxia (Kurdjumov) (Homoptera: Aphididae), a significant pest of small grains, presents an opportunity to create such a precision forecasting tool. D. noxia has been a major pest of small grains since its introduction into North America in the mid-1980s, with losses in the hundreds of millions of dollars.6,7 D. noxia reproduces
∗
Correspondence to: Scott C Merrill, Department of Plant and Soil Science, University of Vermont, Burlington, VT 05405, USA. E-mail: [email protected]
a Department of Plant and Soil Science, University of Vermont, Burlington, VT, USA b Department of Bioagricultural Sciences and Pest Management, Colorado State University, Fort Collins, CO, USA c School of Biological Sciences, Victoria University of Wellington, Wellington, New Zealand
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Precision pest management, a subcategory of precision agriculture, employs such techniques as directed scouting and precision targeting of pest control tactics (e.g. precision pesticide applications).1 Traditional field scouting assumes that fields are homogeneously infested or that pest densities in sampled areas can be extrapolated directly to the unsampled portion of the field. Field scouts use pest estimation tools to make decisions about the use of control tactics such as pesticide applications. Because of profitability constraints, fields are unlikely to be scouted at sufficient intensity to allow decisions on the use of control tactics at a fine scale within a field. For example, because intensive scouting of wheat fields is cost prohibitive, scouts are unlikely to be contracted to provide the nuanced information needed accurately to depict within-field differences in aphid density.2 Instead, scouts typically provide categorical (e.g. treat or don’t treat) advice regarding an entire field. Directed scouting assumes heterogeneity and uses knowledge of pest ecology (e.g. likely pest distribution and abundance) spatially to focus scouting efforts, minimize scouting time and maximize the information gained per unit of scouting time. Additionally, precision application of control tactics can be used effectively to reduce pest pressure. For example, within potato fields in Pennsylvania, adequate control of Colorado potato beetle was achieved by treating only the portion of the fields infested by the beetle, which reduced the amount of pesticide needed by 30–40%.1 Alternatively, a pest management strategy may include damage mitigation. Mitigation may be accomplished by delineating at-risk areas (e.g. by employing a population density model)
www.soci.org parthenogenetically, with an exceptionally high intrinsic rate of increase under optimal conditions.8,9 Substantial research efforts have provided insights into relationships between field conditions and the population dynamics of D. noxia.10 Unfortunately, no spatially explicit models have been created that generate predictions for within-field population densities. However, multiple D. noxia models do exist that provide elements of a spatially explicit prediction model. For example, Merrill et al.11 developed a spatially explicit model for D. noxia in winter wheat in Colorado. Their model depicted the density of D. noxia across sampled agroecosystems. However, their model does not provide the boundary conditions necessary to fit predictions for unsampled years or unsampled locations. Therefore, without the addition of information quantifying boundary conditions, their model cannot be used explicitly to predict D. noxia density. Merrill and Holtzer12 developed a prediction model quantifying spatially implicit D. noxia density based on weather variables. This model provides good regional estimates of D. noxia densities. However, on a within-field basis (as required for precision pest management), obtaining spatially accurate temperature and precipitation data is logistically difficult and cost prohibitive. Therefore, this model cannot provide spatially explicit D. noxia density predictions. Other population density models13,14 provide insights into D. noxia density, but these models have data constraints causing either limited accuracy or poor precision. Two estimation tools have been used in field scouting protocols to predict yield loss caused by aphid feeding damage: (1) the percentage of aphid-infested tillers and (2) the number of aphids per tiller.15 These two tools are found to be highly correlated with each other and both provide good predictions of yield loss.16 Thus, using either the field calculated percentage of infested tillers or the density of aphids per tiller, scouts may provide categorical advice such as ‘Your field needs to be sprayed’, ‘You do not need to worry about spraying’ or ‘We should look again in a week or two’. However, some scouts may provide the percentage of infested tillers or number of aphids per tiller to the producers and let them make a management decision. The present authors have sought to produce a predictive model for spatial and temporal delineation of D. noxia population densities that could be used as a pest management tool. The resulting model uses topography, satellite imagery and weather variables to generate predictions of D. noxia density in dryland winter wheat agroecosystems. The model synthesizes existing models and data from multiple sources. Model predictions could be used directly to guide pesticide application decisions (both at field and within-field scales). Alternatively, information from the model could be used to direct scouting efforts. Either use of the model’s predictions would reduce direct input costs associated with scouting and pesticide application and indirect costs such as development of pesticide resistance, and reduce environmental damage.
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EXPERIMENTAL METHODS
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A spatially explicit D. noxia density model generated within-field estimates of D. noxia density per tiller at a 30 m grid size, using topography variables, Landsat 7 ETM+ satellite imagery and soil variables.11 Topography variables are easily obtainable. However, digitized soil characteristics are difficult to obtain and parameterize. Moreover, the Landsat 7 satellite has developed sensor errors. Therefore, the model developed by Merrill et al.11 was modified to use Landsat 5 imagery and to remove soil variables. They obtained D. noxia density data from two sites for three overwintering
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seasons. Sites were established near Last Chance, Colorado (39∘ 44′ N, 103∘ 48′ W), and near Lamar, Colorado (37∘ 58′ N, 102∘ 30′ W). Each year, ca 80 georeferenced plots were established at each field site. Plots consisted of three consecutive 1 m rows of dryland winter wheat. Plots were infested in the fall with approximately 450 D. noxia (biotype 1, obtained from a colony reared at Colorado State University) using a Davis inoculator.17 Density data were collected over two late-winter and early-spring sampling periods per site per year for 3 years. Data for one of the two sampling periods were not obtained in the second season at the Lamar field site because of equipment failure. To calculate aphid density, wheat tillers were clipped, placed into zipper storage bags and transported to Colorado State University’s Agricultural Research Development and Education Center (ARDEC), Fort Collins. Tillers were then removed from the zipper storage bags and placed into Berlese funnels for approximately 24 h to extract the aphids for counting under a dissecting microscope.18 D. noxia densities were calculated per tiller. Plot densities were normalized using the log + 0.1 method. Over 3 years at the two sites, D. noxia densities were obtained at 641 plots. Following model selection methodology similar to that used by Merrill et al.,11 candidate models (gr ) were developed using the format ln (D.noxia + 0.1) = intercept + 𝛽x ∗ predictor variables Candidate models were selected for prediction of D. noxia density using 21 predictor variables: landshape (e.g. delineating whether the plot was on a ridge top or in a valley within a 90 m radius), slope, relative elevation (i.e. a measure of within-site elevational differences), aspect, north–south aspect, imagery from spring and winter Landsat 5 imagery [Landsat 5 bands and indices: band 1 (450–515 nm), band 2 (525–605 nm), band 3 (630–690 nm), band 4 (750–900 nm), band 5 (1500–1750 nm), thermal band 6 (10 400–12 500 nm), band 7 (2090–2950 nm) and the vegetation indices NDVI (spring) and NDVI (winter)]. A set of a priori candidate models was developed using all subsets of the predictor variables using the GLmulti package in R.19,20 To reduce model selection bias, use was made of the corrected Akaike’s information criterion (AICc) for model selection and multimodel inference.21,22 AICc values provide an estimate of the likelihood that the selected model will be the best candidate model given the data. AICc values are relative to other models within the candidate model set. A ΔAICc value is calculated for each candidate model and measures the difference between it and the model with the lowest (best) AICc value. Therefore, the lowest-AICc-value model has a ΔAICc of 0, with candidate model specific ΔAICc values increasing as the likelihood of the candidate model being a good model decreases. AICc weights are derived for each model on the basis of the ΔAICc value, with decreased AICc weights associated with increasing ΔAICc values. Model AICc weights can then be used for model averaging, with quality models receiving more weight when calculating a model-averaged result. Candidate models were selected for model averaging if their model likelihood was greater than 0.05 or had a ΔAICc less than 7. Selected candidate models were averaged on the basis of their model AICc weight.21,22 The result is a model-averaged prediction for D. noxia densities using predictor variables from each of the selected candidate models. The model-averaged result will henceforth be referred to as the spatially explicit D. noxia model (SED model), and will be the model component used to inform the within-field variability in D. noxia densities. The other component needed to generate spatially explicit D. noxia density predictions is a quantification of the regional density
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of D. noxia. Specifically, the SED model describes within-field variability but requires initial conditions (i.e. regional D. noxia density) to generate D. noxia predictions. The weather-mediated D. noxia density model developed by Merrill and Holtzer,12 and henceforth referred to as the WM model, generates regional D. noxia density per tiller estimates. Regional D. noxia density estimates are based on accumulated degree days above 0 ∘ C (DD +0 ∘ C), accumulated degree days below 0 ∘ C (DD −0∘ ), precipitation (PPT) and an index (the PD index) that averages DD +0∘ and normalized precipitation values. Degree days are a measure of heat or cold units above or below a temperature threshold per day, and were calculated by Degree days = average daily temperature − temperature threshold Accumulated degree days are calculated by summing degree days over the time period of interest. For example, assuming a developmental threshold of 0 ∘ C, if the average daily temperatures on days 1 to 3 were 10, 12 and 9 ∘ C, then 31 degree days above 0 ∘ C would accumulate during this 3-day period. The WM model was parameterized as follows: ln (D.noxia density per tiller + 0.1) = −1.491 + 0.393∗ (PD index) ( ) +3.707∗ DD + 0∘ + 0.596∗ (DD − 0∘ ) + 0.025∗ PPT − (4.456) ∗ (DD + 0∘ ) ∗ (DD − 0∘ )
(1)
where DD (both above and below zero) and precipitation began to accrue on 1 December. Final DD accumulations were divided by 1000 to avoid small parameterization values (i.e. to avoid small betas). The SED model and the WM model were synthesized to develop a spatially explicit D. noxia density prediction model that would provide predictions for unsampled locations or unsampled dates. In essence, the WM model provides a measure of aphid density on a regional basis, and the SED model provides estimates of within-field differences from the WM model density estimates. That is, the WM model provides an estimate of the mean aphid density in the field, and the SED model provides the within-field locations that are above or below the mean. The synthesized model can be used to inform management decisions such as directing scouting efforts.
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WM model density estimate − 𝛽 = estimated SED model density initial condition
(3)
2.2 Checking the synthesized model fit: model cross-validation 2.2.1 Cross-validation Cross-validation is a model validation tool that tests the predictive abilities of a model.23 Cross-validation removes data from a model dataset and refits the model on the basis of the remaining data, after which the refitted model is used to generate predictions for the removed data. Prediction errors are calculated by using the difference between predicted values from the refitted model and the removed data values. An important characteristic of this cross-validation method is that ‘removed’ is synonymous with ‘unsampled’, because the removed data were not used to generate parameter estimates. Model validation using simple cross-validation typically removes one datum from the complete model dataset, refits the model on the basis of the remaining data and then tests the refitted model predictions against the removed datum. However, data that are spatially or temporally close (e.g. data sampled on a single day from a single wheat field) are unlikely to be independent. In such a case, simple cross-validation can lead to excessive confidence in cross-validation results. To address this issue, and to reduce the likelihood of dependence in the validation data, the minimum data removed during the present cross-validation procedure were all of the data from a site for all sampling dates within an entire year (approximately 1/6 of the data). That is, to avoid potential pitfalls associated with simple cross-validation, binned cross-validation was used. Data were separated (into bins) using covariates that were likely to include either spatial or temporal dependence: site, year and the site* year interaction (i.e. site* year bins would include all plot-level density data from one site for an entire growing season). Cross-validation procedures obtained prediction errors for three types of dataset (bin): cross-validation by site (e.g. developing cross-validation prediction errors for bins of data from the Last Chance field site against bins of data from the Lamar field site), cross-validation by year and cross-validation of the site by year combinations. For example, during the site* year cross-validation procedure, one bin would include all of the data that were obtained from the Last Chance field site during the spring of 2003. Cross-validation by site entailed removal of all bins of data from one of the field sites, then refitting the synthesized model and generating prediction errors from the refitted synthesized model predictions to the removed data. The following specific steps illustrate the process: (1) remove all data collected at the Last Chance field site; (2) refit the SED model using only the data collected at the Lamar field site; (3) recalculate the correction term 𝛽; (4) generate prediction errors between the refitted synthesized model and the Last Chance field site data; (5) repeat the above procedure with removal of the Lamar field site data; (6) average prediction errors from both portions of this procedure. Cross-validation by year followed a similar design as the cross-validation by site procedure. Cross-validation by year
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2.1 Generating whole-field density estimates for unsampled wheat fields The WM model also generates initial D. noxia density estimates for unsampled sites. Similarly, once initial aphid densities are estimated by the WM model, the SED model can determine within-field variation at unsampled sites. Data from Merrill et al.11 were used for parameterization of the SED model. These data were separated into 11 sets by sampling date. By running the SED model using the entire dataset, initial aphid densities were estimated for each of the 11 datasets (for each of the sampling dates). (The SED model can estimate initial densities for sampled sites, but cannot for unsampled sites.) Additionally, the WM model was used to estimate a mean D. noxia density for each of these 11 sets. Model estimates were related as follows: ∑ ∑ (WM model density estimates)∕11 = (SED_IC)∕11 + 𝛽 (2)
where 𝛽 is the correction term, and SED_IC refers to the parameterized SED model initial D. noxia density. The 𝛽 correction term quantifies the differences between model estimates and can be used to estimate SED model initial conditions if only WM model estimates are available (i.e. if climate variables are available but no field sampling has occurred):
www.soci.org removed bins of data from an entire year and refitted the SED model based on the remaining 2 years of data. Afterwards, predictions and prediction errors were generated for each year’s data. This process was repeated for all 3 years. Prediction errors from all 3 years were then averaged to generate cross-validation by year statistics. Cross-validation of the site by year combinations entailed removing bins of data from one of the six site* year combinations (e.g. removing all data from the Last Chance field site for 2003) and refitting the synthesized model using the remaining five site* year bins of data, after which cross-validation statistics (prediction errors) were generated. This process was repeated for all six site* year bins of data. Cross-validation was performed to answer the following questions: (1) How well does the synthesized model predict unsampled sites (simulated by cross-validation by site)? (2) How well does the synthesized model predict unsampled years (simulated by cross-validation by year)? (3) How well does the synthesized model predict an unsampled site by year combination (simulated by cross-validation of the site* year combination)? 2.2.2 Prediction errors There are a number of ways to view the structure of the error distribution between model predictions and field measured data. The mean absolute error (MAE) was chosen as a predictor variable of interest for two primary reasons: (1) MAE quantifies the mean difference between field measurements of density and predictions (in units of D. noxia per tiller); and (2) MAE does not assume a normal distribution of errors in the error structure. Also, and very importantly, from a practical decision-making point of view, the error of most interest to pest managers is the difference between modeled density estimates and field observations. The MAE was calculated between field measurements and back-transformed model predictions (i.e. model predictions were back-transformed into units of D. noxia per tiller as compared with log-transformed density units): (∑ ) MAE = |observed (x) − predicted (x)| ∕n (4) where x denotes plot-level density measurements. 2.2.3 Field variability The measure of field variability analogous to and comparable with the MAE is the average difference between the observed field mean per sampling date and the within-field plot measurement per sampling date (MDD – the mean density difference per sampling date). MDD is calculated as follows: [ ( )| ] | MDD = average |xi − mean xi | ∕ni , | | averaged across sampling dates i
2.3 Checking the synthesized model fit: field validation 2.3.1 Sampling design Data were collected explicitly to validate the spatiotemporal D. noxia density model. Data were collected at two sites in 2008 and 2009. Sites were located (1) near Briggsdale, Colorado (40∘ 29′ N, 104∘ 7′ W), and (2) near Lamar, Colorado (37∘ 59′ N, 102∘ 31′ W). Using winter wheat planted by the authors’ collaborators, 72 treatment plots were developed at each of the study sites. Each plot measured five 30 cm rows of winter wheat. Treatment plots had one of two infestation levels (i.e. natural infestation or augmented infestation). Specifically, half of the 72 treatment plots (i.e. plots) were infested (augmented) with approximately 100 Biotype 2 RWA in November using a Davis inoculator.17 The remaining 36 treatment plots were not artificially infested (i.e. infestation was from naturally occurring aphid populations). D. noxia were sampled approximately monthly, starting in March and continuing through harvest. Nine wheat tillers were removed from each plot, placed into a zipper bag and taken back to ARDEC, where aphids were processed. Tiller samples were placed in Berlese funnels18 for 24 h to extract D. noxia, after which aphids were counted using a dissecting microscope. Data were collected to inform the SED model from the same sources as were used to generate the original dataset. Specifically, weather data were obtained from nearby CoAgMet daily weather stations.24 Two sets of Landsat 5 reflective imagery were collected for each site for each year (one set of images from the winter time period and one from the spring). Topography data were obtained using a USGS 30 m digital elevation map. These data were used to generate SED model predictions for each treatment plot for each sample period. Prediction errors were generated between model predictions and measured aphid densities.
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RESULTS
3.1 SED model development and parameterization Effective separation and parameterization of the SED candidate model was achieved, making it possible to develop a model that distinguished differences in aphid density at a within-field scale. The SED model was parameterized using a model-averaged result from three models (Table 1). Because three candidate models (gr ) had model likelihoods [L(gr |data)] greater than 0.05, and each had a ΔAICc less than 7, each received good support for being the best approximating model to the data.21,22 Weighted model averaging, using each of the candidate model’s AICc weights,21,22 was conducted on these three models and resulted in the SED model: ln (D.noxia + 0.1) = −0.931 + xn ∗ IC + 1.577∗ NDVI (S) +0.804∗ band 3 (S) +0.221∗ band 2 (W) − 0.757∗ band 5 (W) + 0.733
(5)
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where x denotes plot-level density measurements and i denotes sampling date. If MDD is greater than MAE, then the model more accurately predicts variability than would be described by the measured field mean. That is, a field scout, when estimating aphid density, may make a decision based upon the mean aphid density from the scouted portion of the field. Thus, if the model predicts values closer to the observed plot-level values than the observed field mean, then the model will have value as an estimation tool.
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∗ band 3 (W) +1.048∗ slope − 0.704∗ R_Elevation
where xn is the parameter associated with the initial D. noxia density estimate calculated from the nth data bin, (S) and (W) indicate Landsat 5 image capture periods of spring (S) or winter (W), NDVI is the normalized difference vegetation index and R_Elevation is the relative elevation of the plot within the site. As noted earlier, if the above model is used for predictive purposes, all of the initial
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Pest Manag Sci 2015; 71: 131–138
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Table 1. Models averaged by AICc weight to generate the SED model Model 1 2 3
Variables
AICc
NDVI (S), band 3 (S), slope, R_Elevation, band 3 (W), band 5 (W) NDVI (S), band 3 (S), slope, R_Elevation, band 2 (W), band 5 (W) NDVI (S), band 3 (S), slope, R_Elevation
L(gr |data)
AICc w+(i) normalized
347.341
0.000
1.000
0.695
349.319
1.978
0.372
0.258
352.741
5.400
0.067
0.047
D. noxia density condition variables drop out. Interpretation of the above model-averaged SED model is identical to interpretation of any linear regression equation. The 𝛽 term was calculated as 1.938 [equation (2)]. Therefore, the synthesized model is as follows: ln (D.noxia + 0.1) = −0.931 + (WM model estimate − 1.938) +1.577 ∗ NDVI (S) +0.804 ∗ band 3 (S) + 0.221 ∗ band 2 (W) − 0.757 ∗ band 5 (W) + 0.733 ∗ band 3 (W) +1.048 ∗ slope − 0.704 ∗ R_Elevation
That is, given remotely sensed data inputs for the SED and WM models, spatially explicit estimates for D. noxia density per tiller can be calculated. For example, Fig. 1 depicts modeled D. noxia density per tiller given conditions from the 2008–2009 growing season for 3 March 2009. 3.2 Prediction errors To determine the quality of the above synthesized model, cross-validation prediction errors were calculated using the described methods. The measured field variability (MDD) was calculated to be 2.08 D. noxia per tiller [equation (5)]. Therefore, if MAE is less than 2.08 D. noxia per tiller, the model accurately predicts the spatiotemporal variation in D. noxia densities. 3.3 Cross-validation results Cross-validation demonstrated that the synthesized model detected a real signal in the aphid data. Specifically, across all cross-validation procedures, the synthesized model prediction errors (MAE) were less than the field variability (MDD). The lowest MAE was generated from cross-validation by year (MAE = 1.73). That is, predictions were on average 0.35 aphids per tiller less than MDD. MAE for surfaces calculated using cross-validation by site (MAE = 2.02) and cross-validation of the site by year combinations (MAE = 1.80) were both lower than the MDD.
years was 0.008 D. noxia per tiller. Moreover, natural infestation levels were low at both sites during both years, with an average of 0.010 D. noxia per tiller observed during the early-March sampling periods. On average, the SED model predicted aphid density better than the field mean at the Lamar site (MAE < MDD), and predicted very poorly compared with the field mean at the Briggsdale site (MAE > MDD). However, the strong results at the Lamar site may be deceptive because the field mean in the naturally infested plots was lower than that in the augmented infestation plots. To avoid artificially inflated confidence in the present results (from correlation of data within the infestation regime), plots were separated into bins of naturally infested and augmented plots. Even with this highly conservative measure, the SED model predicts well in four out of six of the augmented infestation plot sampling dates, but in zero out of six of the naturally infested plot sampling dates (Table 2). Closer examination of the errors reveals that most of the predictive error is due to a very poor fit in the WM model component of the SED model. Further examination found that, when using a best fit for the WM model component instead of the modeled value, the SED model accurately predicts aphid density whenever the aphid field mean is greater than ca 0.020 D. noxia per tiller (Fig. 2; Table 2). That is, the within-field spatial component of the SED model accurately predicts aphid density when aphids are present at a minimum level.
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DISCUSSION AND CONCLUSIONS
Remotely sensed data can be used accurately to predict pest density. Cross-validation statistics suggest that model predictions more accurately forecast aphid density than results obtained using the estimated field mean (a comparison selected to mimic information provided by a traditional field scout). Field validation of the SED model found accurate prediction of within-field aphid densities, excluding cases where overwintering conditions resulted in localized extinction. Specifically, the WM model component is incapable of predicting localized aphid extinction, and because no modeling mechanism exists that allows for localized extinctions, predictions in such cases are imprecise. Previous research suggests that small-grain aphid populations are influenced by a variety of factors, including fall precipitation, spring precipitation and the weather conditions occurring during the previous oversummering period.14,25,26 Thus, predicting year-to-year aphid population density is a highly complex problem that likely includes numerous threshold effects, such as quantifying aforementioned localized extinction scenarios. However, complexity would be greatly reduced with limited spring sampling. Regional sampling combined with remotely sensed data should provide robust boundary conditions to use as inputs into the within-field SED model component. However, the supposition that the WM component has good precision potential with the addition of regional aphid density sampling will require further study. Additional effort to
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3.4 Field validation results The present 2 year field validation of the synthesized model demonstrated that well-modeled, remotely sensed data could be used to predict pest density. In total, 923 validation field samples were collected during 2008 and 2009 from the two field sites (Table 2). The average number of aphids observed per tiller during the first sampling of the year was much lower than expected, with the Briggsdale site showing near complete overwintering mortality (localized extinction) during both years. Specifically, the average density during the early-March sampling period of both Pest Manag Sci 2015; 71: 131–138
DAICc
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3 March 2009 D. noxia per tiller High : 0.27
Low : 0.00
Figure 1. A modeled D. noxia density (aphids per tiller) surface for a field site near Briggsdale, Colorado. Densities are modeled on the basis of conditions during the 2008–2009 growing season for 3 March 2009. Roads are depicted on the right and top of the field. The field boundary is delineated by the solid black line. Table 2. Field validation meta-data Site
Infestation level
Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale
Uninfested Uninfested Uninfested Infested Infested Infested Uninfested Uninfested Uninfested Infested Infested Infested Uninfested Uninfested Uninfested Uninfested Infested Infested Infested Infested Uninfested Uninfested Uninfested Infested Infested Infested
Sampling date 11 Mar 2008 1 Apr 2008 16 Apr 2008 11 Mar 2008 1 Apr 2008 16 Apr 2008 5 Mar 2009 7 Apr 2009 19 May 2009 5 Mar 2009 7 Apr 2009 19 May 2009 4 Mar 2008 23 Apr 2008 7 May 2008 4 Jun 2008 4 Mar 2008 23 Apr 2008 7 May 2008 4 Jun 2008 3 Mar 2009 8 Apr 2009 18 May 2009 3 Mar 2009 8 Apr 2009 18 May 2009
Modeled WM component −0.738 −0.208 0.301 −0.738 −0.208 0.301 −0.093 0.692 2.981 −0.094 0.692 2.981 −1.194 1.091 2.063 5.279 −1.194 1.091 2.063 5.279 −0.330 0.571 1.484 −0.330 0.571 1.484
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improve the precision of the WM model is warranted because using a fitted estimate of the WM model component resulted in model predictions that accurately described within-field aphid densities. With a robust WM model component, the synthesized model could predict aphid densities, direct scouting efforts and thus increase management and scouting efficiency. Moreover, if managers decided to apply pesticides, applications could be limited to areas of the field where D. noxia densities warranted control, which would reduce pesticide application and
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Field mean 0.000 0.015 0.015 0.546 0.692 3.149 0.015 0.009 1.454 0.034 0.022 3.593 0.009 0.003 0.025 0.519 0.000 0.006 0.031 1.574 0.015 0.000 0.022 0.007 0.003 0.024
MAE (modeled WM) 0.095 0.215 0.435 0.515 0.613 2.810 0.040 0.119 2.127 0.049 0.112 3.028 0.291 3.833 10.277 258.723 0.269 3.519 9.448 237.151 0.183 0.627 2.987 0.190 0.626 2.979
MDD 0.000 0.027 0.027 0.548 0.615 2.217 0.029 0.017 1.636 0.057 0.038 3.471 0.017 0.006 0.045 0.562 0.000 0.012 0.048 1.856 0.028 0.000 0.039 0.012 0.006 0.041
MAE (fitted WM) 0.026 0.038 0.040 0.499 0.602 2.061 0.040 0.034 1.238 0.048 0.041 3.025 0.025 0.019 0.040 0.479 0.020 0.025 0.041 1.458 0.026 0.023 0.043 0.033 0.018 0.040
environmental costs, reduce potential risks to non-target organisms and have resistance management implications. Figure 1 highlights the potential advantages gained by using the synthesized model. For example, under depicted field conditions, densities are relatively low near the roads. Thus, scouting for aphids by simply sampling locations that are easily accessible (along roadways) might result in an estimate of aphid density that is lower than the actual aphid density throughout the field.
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REFERENCES
Figure 2. Modeled D. noxia density error compared with observed field error using the modeled weather-mediated component [i.e. equation (1)] or using a best-fit weather-mediated component. Points appearing under the 1:1 line indicate an accurate prediction of D. noxia density.
Merrill et al.11 suggest, by not spraying areas modeled to have low aphid density, crop managers could realize a 30% reduction in pesticide inputs with adequate control of D. noxia populations within examined fields. While the use of the synthesized model likely could reduce within-field pesticide application, directing precision pesticide applications without an improved WM component or regional sampling is premature. The authors suggest a conservative approach to its use because of the large costs associated with applying pesticides when they are not justified or failing to apply them when application is justified. However, using the present model as a tool to direct scouting efforts is encouraged and should result in increased monitoring efficiency and thus indirectly reduce pesticide application costs. These efforts demonstrate that effective pest prediction models, derived solely from remotely sensed data, have the potential to revolutionize integrated pest management. The present multimodel synthesis approach for predicting pest pressure is highly economical and environmentally friendly, and may provide better predictions than are available through traditional scouting efforts. Many pest population dynamic models exist but are unable functionally to predict pest densities. Synthesizing multiple models and validating model predictions will generate applicable management tools, such as maps to direct scouting efforts or focus precision control tools. Ideally, this type of management tool will help resistance management efforts (e.g. resistant cultivar placement), reduce pesticide application errors (e.g. through directed scouting and precision pesticide applications) and enable novel tactics (e.g. altering planting dates on the basis of the effects of climate change on pest dynamics).
ACKNOWLEDGEMENTS
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The authors would like to thank John Stulp, Joe Kalcevic and Cary and Todd Wickstrom for allowing access to their wheat cropping systems. This study was funded by the USDA National Research Initiative (grant number 2000–02992) and by the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (grant numbers COLO-2007-02967 and COLO-2009-02178).
1 Weisz R, Fleischer S and Smilowitz Z, Site-specific integrated pest management for high-value crops: impact on potato pest management. J Econ Entomol 89(2):501–509 (1996). 2 Peairs FB (ed.), Wheat Production and Pest Management. Colorado State University, Fort Collins, CO (2010). 3 Jepsen JU, Hagen SB, Hogda KA, Ims RA, Karlsen SR, Tommervik H et al., Monitoring the spatio-temporal dynamics of geometrid moth outbreaks in birch forest using MODIS-NDVI data. Remote Sens Environ 113(9):1939–1947 (2009). 4 Merrill SC, Walter SM, Peairs FB and Hoeting JA, Spatial variability of western bean cutworm populations in irrigated corn. Environ Entomol 40(3):654–660 (2011). 5 Pierce FJ and Nowak P, Aspects of precision agriculture. Adv Agron 67:1–85 (1999). 6 Morrison WP and Peairs FB, Response model concept and economic impact, in Response Model for an Introduced Pest – the Russian Wheat Aphid, ed. by Quisenberry SS and Peairs FB. Thomas Say Publications in Entomology, Entomological Society of America, Lanham, MD, pp. 1–11 (1998). 7 Webster JA, Amosson S, Brooks L, Hein GL, Johnson GD, Legg DE et al., Economic impact of the Russian wheat aphid in the western United States: 1992–1993. Report No. 152, Russian Wheat Aphid Task Force to the Great Plains Agricultural Council, Stillwater, OK (1994). 8 Merrill SC, Peairs FB, Miller HR, Randolph TL, Rudolph JB and Talmich EE, Reproduction and development of Russian wheat aphid biotype 2 on crested wheatgrass, intermediate wheatgrass, and susceptible and resistant wheat. J Econ Entomol 101(2):541–545 (2008). 9 Burd JD, Butts RA, Elliott NC and Shufran KA, Seasonal development, overwintering biology, and host plant interactions of Russian wheat aphid (Homoptera: Aphididae) in North America, in Response Model for an Introduced Pest – the Russian Wheat Aphid, ed. by Quisenberry SS and Peairs FB. Thomas Say Publications in Entomology, Entomological Society of America, Lanham, MD, pp. 65–99 (1998). 10 Quisenberry SS and Peairs FB (eds), Response Model for an Introduced Pest – the Russian Wheat Aphid. Thomas Say Publications in Entomology, Entomological Society of America, Lanham, MD (1998). 11 Merrill SC, Holtzer TO, Peairs FB and Lester PJ, Modeling spatial variation of Russian wheat aphid overwintering population densities in Colorado winter wheat. J Econ Entomol 102(2):533–541 (2009). 12 Merrill SC and Holtzer TO, Using weather data to generate estimates of Russian wheat aphid overwintering success. Technical report TR10-14, Colorado State University Agricultural Experiment Station (2010). 13 Armstrong JS and Peairs FB. Environmental parameters related to winter mortality of the Russian wheat aphid (Homoptera: Aphididae): basis for predicting mortality. J Econ Entomol 89(5):1281–1287 (1996). 14 Legg DE and Brewer MJ, Relating within-season Russian wheat aphid (Homoptera, Aphididae) population-growth in dryland winter-wheat to heat units and rainfall. J Kans Entomol Soc 68(2):149–158 (1995). 15 Archer TL and Bynum ED, Economic injury level for the Russian wheat aphid (Homoptera, Aphididae) on dryland winter-wheat. J Econ Entomol 85(3):987–992 (1992). 16 Girma M, Wilde GE and Harvey TL, Russian wheat aphid (Homoptera, Aphididae) affects yield and quality of wheat. J Econ Entomol 86(2):594–601 (1993). 17 Davis FM and Oswalt TG, Hand inoculator for dispensing lepidopterous larvae. Admin. Southern Ser. 9, Agricultural (Southern Region), US Department of Agricultural Science and Education, New Orleans, LA (1979). 18 Trägårdh I, Methods of automatic collecting for studying the fauna of the soil. Bull Entomol Res 24:203–214 (1933). 19 Calcagno V, glmulti: Model Selection and Multimodel Inference Made Easy. R Package Version 1.0.4. [Online]. (2012). Available: http://CRAN.R-project.org/package=glmulti [accessed 12 April 2014]. 20 R: A Language and Environment for Statistical Computing. [Online]. R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria (2008). Available: http://www.R-project.org [accessed 12 April 2014]. 21 Burnham KP and Anderson DR, Model Selection and Multimodel Inference: the Practical Information Theoretic Approach, 2nd edition. Springer, New York, NY (2002).
www.soci.org 22 Burnham KP and Anderson DR. Multimodel inference – understanding AIC and BIC in model selection. Sociol Meth Res 33(2):261–304 (2004). 23 Hevesi JA, Istok JD and Flint AL, Precipitation estimation in mountainous terrain using multivariate geostatistics. 1. Structural analysis. J Appl Meteorol 31(7):661–676 (1992). 24 Andales AA, Bauder TA and Doesken NJ, The Colorado Agricultural Meteorological Network (CoAgMet) and Crop ET Reports. [Online]. Colorado Counties Contract No. 4.723, Colorado State University,
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US Department of Agriculture, Fort Collins, CO (2009). Available: www.coagmet.com [accessed 12 April 2014]. 25 Ma ZS and Bechinski EJ. Developmental and phenological modeling of Russian wheat aphid (Hemiptera: Aphididae). Ann Entomol Soc Am 101(2):351–361 (2008). 26 Merrill SC and Peairs FB, Quantifying Russian wheat aphid pest intensity across the Great Plains. Environ Entomol 41(6):1505–1515 (2012).
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Revised: 00 0000
Accepted article published: 19 March 2014
Published online in Wiley Online Library: 28 April 2014
(wileyonlinelibrary.com) DOI 10.1002/ps.3778
Validating spatiotemporal predictions of an important pest of small grains Scott C Merrill,a* Thomas O Holtzer,b Frank B Peairsb and Philip J Lesterc Abstract BACKGROUND: Arthropod pests are typically managed using tactics applied uniformly to the whole field. Precision pest management applies tactics under the assumption that within-field pest pressure differences exist. This approach allows for more precise and judicious use of scouting resources and management tactics. For example, a portion of a field delineated as attractive to pests may be selected to receive extra monitoring attention. Likely because of the high variability in pest dynamics, little attention has been given to developing precision pest prediction models. Here, multimodel synthesis was used to develop a spatiotemporal model predicting the density of a key pest of wheat, the Russian wheat aphid, Diuraphis noxia (Kurdjumov). RESULTS: Spatially implicit and spatially explicit models were synthesized to generate spatiotemporal pest pressure predictions. Cross-validation and field validation were used to confirm model efficacy. A strong within-field signal depicting aphid density was confirmed with low prediction errors. CONCLUSION: Results show that the within-field model predictions will provide higher-quality information than would be provided by traditional field scouting. With improvements to the broad-scale model component, the model synthesis approach and resulting tool could improve pest management strategy and provide a template for the development of spatially explicit pest pressure models. © 2014 Society of Chemical Industry Keywords: Diuraphis noxia; model synthesis; predictive model; spatial model; cross-validation; invasive species
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INTRODUCTION
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and then subjecting these at-risk areas to intense study to determine environmental factors that may be altered to decrease the impact of pest outbreaks or to improve resistance management strategy.3,4 One difficulty with developing and using precision pest management is the high variability associated with pest pressure.5 Highly variable pest pressure exacerbates the economic balancing act of weighing the costs associated with delineating variation against costs associated with assuming homogeneity. However, if predictable variation can be correlated with remotely sensed data (such as weather or topographic variables), prediction costs can be exceptionally low. The environmental factors governing the Russian wheat aphid, Diuraphis noxia (Kurdjumov) (Homoptera: Aphididae), a significant pest of small grains, presents an opportunity to create such a precision forecasting tool. D. noxia has been a major pest of small grains since its introduction into North America in the mid-1980s, with losses in the hundreds of millions of dollars.6,7 D. noxia reproduces
∗
Correspondence to: Scott C Merrill, Department of Plant and Soil Science, University of Vermont, Burlington, VT 05405, USA. E-mail: [email protected]
a Department of Plant and Soil Science, University of Vermont, Burlington, VT, USA b Department of Bioagricultural Sciences and Pest Management, Colorado State University, Fort Collins, CO, USA c School of Biological Sciences, Victoria University of Wellington, Wellington, New Zealand
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Precision pest management, a subcategory of precision agriculture, employs such techniques as directed scouting and precision targeting of pest control tactics (e.g. precision pesticide applications).1 Traditional field scouting assumes that fields are homogeneously infested or that pest densities in sampled areas can be extrapolated directly to the unsampled portion of the field. Field scouts use pest estimation tools to make decisions about the use of control tactics such as pesticide applications. Because of profitability constraints, fields are unlikely to be scouted at sufficient intensity to allow decisions on the use of control tactics at a fine scale within a field. For example, because intensive scouting of wheat fields is cost prohibitive, scouts are unlikely to be contracted to provide the nuanced information needed accurately to depict within-field differences in aphid density.2 Instead, scouts typically provide categorical (e.g. treat or don’t treat) advice regarding an entire field. Directed scouting assumes heterogeneity and uses knowledge of pest ecology (e.g. likely pest distribution and abundance) spatially to focus scouting efforts, minimize scouting time and maximize the information gained per unit of scouting time. Additionally, precision application of control tactics can be used effectively to reduce pest pressure. For example, within potato fields in Pennsylvania, adequate control of Colorado potato beetle was achieved by treating only the portion of the fields infested by the beetle, which reduced the amount of pesticide needed by 30–40%.1 Alternatively, a pest management strategy may include damage mitigation. Mitigation may be accomplished by delineating at-risk areas (e.g. by employing a population density model)
www.soci.org parthenogenetically, with an exceptionally high intrinsic rate of increase under optimal conditions.8,9 Substantial research efforts have provided insights into relationships between field conditions and the population dynamics of D. noxia.10 Unfortunately, no spatially explicit models have been created that generate predictions for within-field population densities. However, multiple D. noxia models do exist that provide elements of a spatially explicit prediction model. For example, Merrill et al.11 developed a spatially explicit model for D. noxia in winter wheat in Colorado. Their model depicted the density of D. noxia across sampled agroecosystems. However, their model does not provide the boundary conditions necessary to fit predictions for unsampled years or unsampled locations. Therefore, without the addition of information quantifying boundary conditions, their model cannot be used explicitly to predict D. noxia density. Merrill and Holtzer12 developed a prediction model quantifying spatially implicit D. noxia density based on weather variables. This model provides good regional estimates of D. noxia densities. However, on a within-field basis (as required for precision pest management), obtaining spatially accurate temperature and precipitation data is logistically difficult and cost prohibitive. Therefore, this model cannot provide spatially explicit D. noxia density predictions. Other population density models13,14 provide insights into D. noxia density, but these models have data constraints causing either limited accuracy or poor precision. Two estimation tools have been used in field scouting protocols to predict yield loss caused by aphid feeding damage: (1) the percentage of aphid-infested tillers and (2) the number of aphids per tiller.15 These two tools are found to be highly correlated with each other and both provide good predictions of yield loss.16 Thus, using either the field calculated percentage of infested tillers or the density of aphids per tiller, scouts may provide categorical advice such as ‘Your field needs to be sprayed’, ‘You do not need to worry about spraying’ or ‘We should look again in a week or two’. However, some scouts may provide the percentage of infested tillers or number of aphids per tiller to the producers and let them make a management decision. The present authors have sought to produce a predictive model for spatial and temporal delineation of D. noxia population densities that could be used as a pest management tool. The resulting model uses topography, satellite imagery and weather variables to generate predictions of D. noxia density in dryland winter wheat agroecosystems. The model synthesizes existing models and data from multiple sources. Model predictions could be used directly to guide pesticide application decisions (both at field and within-field scales). Alternatively, information from the model could be used to direct scouting efforts. Either use of the model’s predictions would reduce direct input costs associated with scouting and pesticide application and indirect costs such as development of pesticide resistance, and reduce environmental damage.
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A spatially explicit D. noxia density model generated within-field estimates of D. noxia density per tiller at a 30 m grid size, using topography variables, Landsat 7 ETM+ satellite imagery and soil variables.11 Topography variables are easily obtainable. However, digitized soil characteristics are difficult to obtain and parameterize. Moreover, the Landsat 7 satellite has developed sensor errors. Therefore, the model developed by Merrill et al.11 was modified to use Landsat 5 imagery and to remove soil variables. They obtained D. noxia density data from two sites for three overwintering
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seasons. Sites were established near Last Chance, Colorado (39∘ 44′ N, 103∘ 48′ W), and near Lamar, Colorado (37∘ 58′ N, 102∘ 30′ W). Each year, ca 80 georeferenced plots were established at each field site. Plots consisted of three consecutive 1 m rows of dryland winter wheat. Plots were infested in the fall with approximately 450 D. noxia (biotype 1, obtained from a colony reared at Colorado State University) using a Davis inoculator.17 Density data were collected over two late-winter and early-spring sampling periods per site per year for 3 years. Data for one of the two sampling periods were not obtained in the second season at the Lamar field site because of equipment failure. To calculate aphid density, wheat tillers were clipped, placed into zipper storage bags and transported to Colorado State University’s Agricultural Research Development and Education Center (ARDEC), Fort Collins. Tillers were then removed from the zipper storage bags and placed into Berlese funnels for approximately 24 h to extract the aphids for counting under a dissecting microscope.18 D. noxia densities were calculated per tiller. Plot densities were normalized using the log + 0.1 method. Over 3 years at the two sites, D. noxia densities were obtained at 641 plots. Following model selection methodology similar to that used by Merrill et al.,11 candidate models (gr ) were developed using the format ln (D.noxia + 0.1) = intercept + 𝛽x ∗ predictor variables Candidate models were selected for prediction of D. noxia density using 21 predictor variables: landshape (e.g. delineating whether the plot was on a ridge top or in a valley within a 90 m radius), slope, relative elevation (i.e. a measure of within-site elevational differences), aspect, north–south aspect, imagery from spring and winter Landsat 5 imagery [Landsat 5 bands and indices: band 1 (450–515 nm), band 2 (525–605 nm), band 3 (630–690 nm), band 4 (750–900 nm), band 5 (1500–1750 nm), thermal band 6 (10 400–12 500 nm), band 7 (2090–2950 nm) and the vegetation indices NDVI (spring) and NDVI (winter)]. A set of a priori candidate models was developed using all subsets of the predictor variables using the GLmulti package in R.19,20 To reduce model selection bias, use was made of the corrected Akaike’s information criterion (AICc) for model selection and multimodel inference.21,22 AICc values provide an estimate of the likelihood that the selected model will be the best candidate model given the data. AICc values are relative to other models within the candidate model set. A ΔAICc value is calculated for each candidate model and measures the difference between it and the model with the lowest (best) AICc value. Therefore, the lowest-AICc-value model has a ΔAICc of 0, with candidate model specific ΔAICc values increasing as the likelihood of the candidate model being a good model decreases. AICc weights are derived for each model on the basis of the ΔAICc value, with decreased AICc weights associated with increasing ΔAICc values. Model AICc weights can then be used for model averaging, with quality models receiving more weight when calculating a model-averaged result. Candidate models were selected for model averaging if their model likelihood was greater than 0.05 or had a ΔAICc less than 7. Selected candidate models were averaged on the basis of their model AICc weight.21,22 The result is a model-averaged prediction for D. noxia densities using predictor variables from each of the selected candidate models. The model-averaged result will henceforth be referred to as the spatially explicit D. noxia model (SED model), and will be the model component used to inform the within-field variability in D. noxia densities. The other component needed to generate spatially explicit D. noxia density predictions is a quantification of the regional density
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of D. noxia. Specifically, the SED model describes within-field variability but requires initial conditions (i.e. regional D. noxia density) to generate D. noxia predictions. The weather-mediated D. noxia density model developed by Merrill and Holtzer,12 and henceforth referred to as the WM model, generates regional D. noxia density per tiller estimates. Regional D. noxia density estimates are based on accumulated degree days above 0 ∘ C (DD +0 ∘ C), accumulated degree days below 0 ∘ C (DD −0∘ ), precipitation (PPT) and an index (the PD index) that averages DD +0∘ and normalized precipitation values. Degree days are a measure of heat or cold units above or below a temperature threshold per day, and were calculated by Degree days = average daily temperature − temperature threshold Accumulated degree days are calculated by summing degree days over the time period of interest. For example, assuming a developmental threshold of 0 ∘ C, if the average daily temperatures on days 1 to 3 were 10, 12 and 9 ∘ C, then 31 degree days above 0 ∘ C would accumulate during this 3-day period. The WM model was parameterized as follows: ln (D.noxia density per tiller + 0.1) = −1.491 + 0.393∗ (PD index) ( ) +3.707∗ DD + 0∘ + 0.596∗ (DD − 0∘ ) + 0.025∗ PPT − (4.456) ∗ (DD + 0∘ ) ∗ (DD − 0∘ )
(1)
where DD (both above and below zero) and precipitation began to accrue on 1 December. Final DD accumulations were divided by 1000 to avoid small parameterization values (i.e. to avoid small betas). The SED model and the WM model were synthesized to develop a spatially explicit D. noxia density prediction model that would provide predictions for unsampled locations or unsampled dates. In essence, the WM model provides a measure of aphid density on a regional basis, and the SED model provides estimates of within-field differences from the WM model density estimates. That is, the WM model provides an estimate of the mean aphid density in the field, and the SED model provides the within-field locations that are above or below the mean. The synthesized model can be used to inform management decisions such as directing scouting efforts.
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WM model density estimate − 𝛽 = estimated SED model density initial condition
(3)
2.2 Checking the synthesized model fit: model cross-validation 2.2.1 Cross-validation Cross-validation is a model validation tool that tests the predictive abilities of a model.23 Cross-validation removes data from a model dataset and refits the model on the basis of the remaining data, after which the refitted model is used to generate predictions for the removed data. Prediction errors are calculated by using the difference between predicted values from the refitted model and the removed data values. An important characteristic of this cross-validation method is that ‘removed’ is synonymous with ‘unsampled’, because the removed data were not used to generate parameter estimates. Model validation using simple cross-validation typically removes one datum from the complete model dataset, refits the model on the basis of the remaining data and then tests the refitted model predictions against the removed datum. However, data that are spatially or temporally close (e.g. data sampled on a single day from a single wheat field) are unlikely to be independent. In such a case, simple cross-validation can lead to excessive confidence in cross-validation results. To address this issue, and to reduce the likelihood of dependence in the validation data, the minimum data removed during the present cross-validation procedure were all of the data from a site for all sampling dates within an entire year (approximately 1/6 of the data). That is, to avoid potential pitfalls associated with simple cross-validation, binned cross-validation was used. Data were separated (into bins) using covariates that were likely to include either spatial or temporal dependence: site, year and the site* year interaction (i.e. site* year bins would include all plot-level density data from one site for an entire growing season). Cross-validation procedures obtained prediction errors for three types of dataset (bin): cross-validation by site (e.g. developing cross-validation prediction errors for bins of data from the Last Chance field site against bins of data from the Lamar field site), cross-validation by year and cross-validation of the site by year combinations. For example, during the site* year cross-validation procedure, one bin would include all of the data that were obtained from the Last Chance field site during the spring of 2003. Cross-validation by site entailed removal of all bins of data from one of the field sites, then refitting the synthesized model and generating prediction errors from the refitted synthesized model predictions to the removed data. The following specific steps illustrate the process: (1) remove all data collected at the Last Chance field site; (2) refit the SED model using only the data collected at the Lamar field site; (3) recalculate the correction term 𝛽; (4) generate prediction errors between the refitted synthesized model and the Last Chance field site data; (5) repeat the above procedure with removal of the Lamar field site data; (6) average prediction errors from both portions of this procedure. Cross-validation by year followed a similar design as the cross-validation by site procedure. Cross-validation by year
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2.1 Generating whole-field density estimates for unsampled wheat fields The WM model also generates initial D. noxia density estimates for unsampled sites. Similarly, once initial aphid densities are estimated by the WM model, the SED model can determine within-field variation at unsampled sites. Data from Merrill et al.11 were used for parameterization of the SED model. These data were separated into 11 sets by sampling date. By running the SED model using the entire dataset, initial aphid densities were estimated for each of the 11 datasets (for each of the sampling dates). (The SED model can estimate initial densities for sampled sites, but cannot for unsampled sites.) Additionally, the WM model was used to estimate a mean D. noxia density for each of these 11 sets. Model estimates were related as follows: ∑ ∑ (WM model density estimates)∕11 = (SED_IC)∕11 + 𝛽 (2)
where 𝛽 is the correction term, and SED_IC refers to the parameterized SED model initial D. noxia density. The 𝛽 correction term quantifies the differences between model estimates and can be used to estimate SED model initial conditions if only WM model estimates are available (i.e. if climate variables are available but no field sampling has occurred):
www.soci.org removed bins of data from an entire year and refitted the SED model based on the remaining 2 years of data. Afterwards, predictions and prediction errors were generated for each year’s data. This process was repeated for all 3 years. Prediction errors from all 3 years were then averaged to generate cross-validation by year statistics. Cross-validation of the site by year combinations entailed removing bins of data from one of the six site* year combinations (e.g. removing all data from the Last Chance field site for 2003) and refitting the synthesized model using the remaining five site* year bins of data, after which cross-validation statistics (prediction errors) were generated. This process was repeated for all six site* year bins of data. Cross-validation was performed to answer the following questions: (1) How well does the synthesized model predict unsampled sites (simulated by cross-validation by site)? (2) How well does the synthesized model predict unsampled years (simulated by cross-validation by year)? (3) How well does the synthesized model predict an unsampled site by year combination (simulated by cross-validation of the site* year combination)? 2.2.2 Prediction errors There are a number of ways to view the structure of the error distribution between model predictions and field measured data. The mean absolute error (MAE) was chosen as a predictor variable of interest for two primary reasons: (1) MAE quantifies the mean difference between field measurements of density and predictions (in units of D. noxia per tiller); and (2) MAE does not assume a normal distribution of errors in the error structure. Also, and very importantly, from a practical decision-making point of view, the error of most interest to pest managers is the difference between modeled density estimates and field observations. The MAE was calculated between field measurements and back-transformed model predictions (i.e. model predictions were back-transformed into units of D. noxia per tiller as compared with log-transformed density units): (∑ ) MAE = |observed (x) − predicted (x)| ∕n (4) where x denotes plot-level density measurements. 2.2.3 Field variability The measure of field variability analogous to and comparable with the MAE is the average difference between the observed field mean per sampling date and the within-field plot measurement per sampling date (MDD – the mean density difference per sampling date). MDD is calculated as follows: [ ( )| ] | MDD = average |xi − mean xi | ∕ni , | | averaged across sampling dates i
2.3 Checking the synthesized model fit: field validation 2.3.1 Sampling design Data were collected explicitly to validate the spatiotemporal D. noxia density model. Data were collected at two sites in 2008 and 2009. Sites were located (1) near Briggsdale, Colorado (40∘ 29′ N, 104∘ 7′ W), and (2) near Lamar, Colorado (37∘ 59′ N, 102∘ 31′ W). Using winter wheat planted by the authors’ collaborators, 72 treatment plots were developed at each of the study sites. Each plot measured five 30 cm rows of winter wheat. Treatment plots had one of two infestation levels (i.e. natural infestation or augmented infestation). Specifically, half of the 72 treatment plots (i.e. plots) were infested (augmented) with approximately 100 Biotype 2 RWA in November using a Davis inoculator.17 The remaining 36 treatment plots were not artificially infested (i.e. infestation was from naturally occurring aphid populations). D. noxia were sampled approximately monthly, starting in March and continuing through harvest. Nine wheat tillers were removed from each plot, placed into a zipper bag and taken back to ARDEC, where aphids were processed. Tiller samples were placed in Berlese funnels18 for 24 h to extract D. noxia, after which aphids were counted using a dissecting microscope. Data were collected to inform the SED model from the same sources as were used to generate the original dataset. Specifically, weather data were obtained from nearby CoAgMet daily weather stations.24 Two sets of Landsat 5 reflective imagery were collected for each site for each year (one set of images from the winter time period and one from the spring). Topography data were obtained using a USGS 30 m digital elevation map. These data were used to generate SED model predictions for each treatment plot for each sample period. Prediction errors were generated between model predictions and measured aphid densities.
3
RESULTS
3.1 SED model development and parameterization Effective separation and parameterization of the SED candidate model was achieved, making it possible to develop a model that distinguished differences in aphid density at a within-field scale. The SED model was parameterized using a model-averaged result from three models (Table 1). Because three candidate models (gr ) had model likelihoods [L(gr |data)] greater than 0.05, and each had a ΔAICc less than 7, each received good support for being the best approximating model to the data.21,22 Weighted model averaging, using each of the candidate model’s AICc weights,21,22 was conducted on these three models and resulted in the SED model: ln (D.noxia + 0.1) = −0.931 + xn ∗ IC + 1.577∗ NDVI (S) +0.804∗ band 3 (S) +0.221∗ band 2 (W) − 0.757∗ band 5 (W) + 0.733
(5)
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where x denotes plot-level density measurements and i denotes sampling date. If MDD is greater than MAE, then the model more accurately predicts variability than would be described by the measured field mean. That is, a field scout, when estimating aphid density, may make a decision based upon the mean aphid density from the scouted portion of the field. Thus, if the model predicts values closer to the observed plot-level values than the observed field mean, then the model will have value as an estimation tool.
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∗ band 3 (W) +1.048∗ slope − 0.704∗ R_Elevation
where xn is the parameter associated with the initial D. noxia density estimate calculated from the nth data bin, (S) and (W) indicate Landsat 5 image capture periods of spring (S) or winter (W), NDVI is the normalized difference vegetation index and R_Elevation is the relative elevation of the plot within the site. As noted earlier, if the above model is used for predictive purposes, all of the initial
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Table 1. Models averaged by AICc weight to generate the SED model Model 1 2 3
Variables
AICc
NDVI (S), band 3 (S), slope, R_Elevation, band 3 (W), band 5 (W) NDVI (S), band 3 (S), slope, R_Elevation, band 2 (W), band 5 (W) NDVI (S), band 3 (S), slope, R_Elevation
L(gr |data)
AICc w+(i) normalized
347.341
0.000
1.000
0.695
349.319
1.978
0.372
0.258
352.741
5.400
0.067
0.047
D. noxia density condition variables drop out. Interpretation of the above model-averaged SED model is identical to interpretation of any linear regression equation. The 𝛽 term was calculated as 1.938 [equation (2)]. Therefore, the synthesized model is as follows: ln (D.noxia + 0.1) = −0.931 + (WM model estimate − 1.938) +1.577 ∗ NDVI (S) +0.804 ∗ band 3 (S) + 0.221 ∗ band 2 (W) − 0.757 ∗ band 5 (W) + 0.733 ∗ band 3 (W) +1.048 ∗ slope − 0.704 ∗ R_Elevation
That is, given remotely sensed data inputs for the SED and WM models, spatially explicit estimates for D. noxia density per tiller can be calculated. For example, Fig. 1 depicts modeled D. noxia density per tiller given conditions from the 2008–2009 growing season for 3 March 2009. 3.2 Prediction errors To determine the quality of the above synthesized model, cross-validation prediction errors were calculated using the described methods. The measured field variability (MDD) was calculated to be 2.08 D. noxia per tiller [equation (5)]. Therefore, if MAE is less than 2.08 D. noxia per tiller, the model accurately predicts the spatiotemporal variation in D. noxia densities. 3.3 Cross-validation results Cross-validation demonstrated that the synthesized model detected a real signal in the aphid data. Specifically, across all cross-validation procedures, the synthesized model prediction errors (MAE) were less than the field variability (MDD). The lowest MAE was generated from cross-validation by year (MAE = 1.73). That is, predictions were on average 0.35 aphids per tiller less than MDD. MAE for surfaces calculated using cross-validation by site (MAE = 2.02) and cross-validation of the site by year combinations (MAE = 1.80) were both lower than the MDD.
years was 0.008 D. noxia per tiller. Moreover, natural infestation levels were low at both sites during both years, with an average of 0.010 D. noxia per tiller observed during the early-March sampling periods. On average, the SED model predicted aphid density better than the field mean at the Lamar site (MAE < MDD), and predicted very poorly compared with the field mean at the Briggsdale site (MAE > MDD). However, the strong results at the Lamar site may be deceptive because the field mean in the naturally infested plots was lower than that in the augmented infestation plots. To avoid artificially inflated confidence in the present results (from correlation of data within the infestation regime), plots were separated into bins of naturally infested and augmented plots. Even with this highly conservative measure, the SED model predicts well in four out of six of the augmented infestation plot sampling dates, but in zero out of six of the naturally infested plot sampling dates (Table 2). Closer examination of the errors reveals that most of the predictive error is due to a very poor fit in the WM model component of the SED model. Further examination found that, when using a best fit for the WM model component instead of the modeled value, the SED model accurately predicts aphid density whenever the aphid field mean is greater than ca 0.020 D. noxia per tiller (Fig. 2; Table 2). That is, the within-field spatial component of the SED model accurately predicts aphid density when aphids are present at a minimum level.
4
DISCUSSION AND CONCLUSIONS
Remotely sensed data can be used accurately to predict pest density. Cross-validation statistics suggest that model predictions more accurately forecast aphid density than results obtained using the estimated field mean (a comparison selected to mimic information provided by a traditional field scout). Field validation of the SED model found accurate prediction of within-field aphid densities, excluding cases where overwintering conditions resulted in localized extinction. Specifically, the WM model component is incapable of predicting localized aphid extinction, and because no modeling mechanism exists that allows for localized extinctions, predictions in such cases are imprecise. Previous research suggests that small-grain aphid populations are influenced by a variety of factors, including fall precipitation, spring precipitation and the weather conditions occurring during the previous oversummering period.14,25,26 Thus, predicting year-to-year aphid population density is a highly complex problem that likely includes numerous threshold effects, such as quantifying aforementioned localized extinction scenarios. However, complexity would be greatly reduced with limited spring sampling. Regional sampling combined with remotely sensed data should provide robust boundary conditions to use as inputs into the within-field SED model component. However, the supposition that the WM component has good precision potential with the addition of regional aphid density sampling will require further study. Additional effort to
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3.4 Field validation results The present 2 year field validation of the synthesized model demonstrated that well-modeled, remotely sensed data could be used to predict pest density. In total, 923 validation field samples were collected during 2008 and 2009 from the two field sites (Table 2). The average number of aphids observed per tiller during the first sampling of the year was much lower than expected, with the Briggsdale site showing near complete overwintering mortality (localized extinction) during both years. Specifically, the average density during the early-March sampling period of both Pest Manag Sci 2015; 71: 131–138
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3 March 2009 D. noxia per tiller High : 0.27
Low : 0.00
Figure 1. A modeled D. noxia density (aphids per tiller) surface for a field site near Briggsdale, Colorado. Densities are modeled on the basis of conditions during the 2008–2009 growing season for 3 March 2009. Roads are depicted on the right and top of the field. The field boundary is delineated by the solid black line. Table 2. Field validation meta-data Site
Infestation level
Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Lamar Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale Briggsdale
Uninfested Uninfested Uninfested Infested Infested Infested Uninfested Uninfested Uninfested Infested Infested Infested Uninfested Uninfested Uninfested Uninfested Infested Infested Infested Infested Uninfested Uninfested Uninfested Infested Infested Infested
Sampling date 11 Mar 2008 1 Apr 2008 16 Apr 2008 11 Mar 2008 1 Apr 2008 16 Apr 2008 5 Mar 2009 7 Apr 2009 19 May 2009 5 Mar 2009 7 Apr 2009 19 May 2009 4 Mar 2008 23 Apr 2008 7 May 2008 4 Jun 2008 4 Mar 2008 23 Apr 2008 7 May 2008 4 Jun 2008 3 Mar 2009 8 Apr 2009 18 May 2009 3 Mar 2009 8 Apr 2009 18 May 2009
Modeled WM component −0.738 −0.208 0.301 −0.738 −0.208 0.301 −0.093 0.692 2.981 −0.094 0.692 2.981 −1.194 1.091 2.063 5.279 −1.194 1.091 2.063 5.279 −0.330 0.571 1.484 −0.330 0.571 1.484
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improve the precision of the WM model is warranted because using a fitted estimate of the WM model component resulted in model predictions that accurately described within-field aphid densities. With a robust WM model component, the synthesized model could predict aphid densities, direct scouting efforts and thus increase management and scouting efficiency. Moreover, if managers decided to apply pesticides, applications could be limited to areas of the field where D. noxia densities warranted control, which would reduce pesticide application and
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Field mean 0.000 0.015 0.015 0.546 0.692 3.149 0.015 0.009 1.454 0.034 0.022 3.593 0.009 0.003 0.025 0.519 0.000 0.006 0.031 1.574 0.015 0.000 0.022 0.007 0.003 0.024
MAE (modeled WM) 0.095 0.215 0.435 0.515 0.613 2.810 0.040 0.119 2.127 0.049 0.112 3.028 0.291 3.833 10.277 258.723 0.269 3.519 9.448 237.151 0.183 0.627 2.987 0.190 0.626 2.979
MDD 0.000 0.027 0.027 0.548 0.615 2.217 0.029 0.017 1.636 0.057 0.038 3.471 0.017 0.006 0.045 0.562 0.000 0.012 0.048 1.856 0.028 0.000 0.039 0.012 0.006 0.041
MAE (fitted WM) 0.026 0.038 0.040 0.499 0.602 2.061 0.040 0.034 1.238 0.048 0.041 3.025 0.025 0.019 0.040 0.479 0.020 0.025 0.041 1.458 0.026 0.023 0.043 0.033 0.018 0.040
environmental costs, reduce potential risks to non-target organisms and have resistance management implications. Figure 1 highlights the potential advantages gained by using the synthesized model. For example, under depicted field conditions, densities are relatively low near the roads. Thus, scouting for aphids by simply sampling locations that are easily accessible (along roadways) might result in an estimate of aphid density that is lower than the actual aphid density throughout the field.
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Validating spatiotemporal predictions of a pest of small grains
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REFERENCES
Figure 2. Modeled D. noxia density error compared with observed field error using the modeled weather-mediated component [i.e. equation (1)] or using a best-fit weather-mediated component. Points appearing under the 1:1 line indicate an accurate prediction of D. noxia density.
Merrill et al.11 suggest, by not spraying areas modeled to have low aphid density, crop managers could realize a 30% reduction in pesticide inputs with adequate control of D. noxia populations within examined fields. While the use of the synthesized model likely could reduce within-field pesticide application, directing precision pesticide applications without an improved WM component or regional sampling is premature. The authors suggest a conservative approach to its use because of the large costs associated with applying pesticides when they are not justified or failing to apply them when application is justified. However, using the present model as a tool to direct scouting efforts is encouraged and should result in increased monitoring efficiency and thus indirectly reduce pesticide application costs. These efforts demonstrate that effective pest prediction models, derived solely from remotely sensed data, have the potential to revolutionize integrated pest management. The present multimodel synthesis approach for predicting pest pressure is highly economical and environmentally friendly, and may provide better predictions than are available through traditional scouting efforts. Many pest population dynamic models exist but are unable functionally to predict pest densities. Synthesizing multiple models and validating model predictions will generate applicable management tools, such as maps to direct scouting efforts or focus precision control tools. Ideally, this type of management tool will help resistance management efforts (e.g. resistant cultivar placement), reduce pesticide application errors (e.g. through directed scouting and precision pesticide applications) and enable novel tactics (e.g. altering planting dates on the basis of the effects of climate change on pest dynamics).
ACKNOWLEDGEMENTS
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The authors would like to thank John Stulp, Joe Kalcevic and Cary and Todd Wickstrom for allowing access to their wheat cropping systems. This study was funded by the USDA National Research Initiative (grant number 2000–02992) and by the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (grant numbers COLO-2007-02967 and COLO-2009-02178).
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