A knowledge-based approach to designing control strategies for agricultural pests

Chemical control of insect pests remains vital to agricultural productivity, but limited mechanistic understanding of the interactions between crop, pest and chemical control agent have restricted our capacity to respond to challenges such as the emergence of resistance and demands for tighter environmental regulation. Formulating efective control strategies that integrate chemical and non-chemical management for soil-dwelling pests is particularly problematic owing to the complexity of the soil-root-pest system and the variability that occurs between sites and between seasons. Here, we present a new concept, termed COMPASS, that integrates ecolo-gical knowledge on pest development and behaviour together with crop physiology and mechanistic under- standing of chemical distribution and toxic action within the rhizosphere. The concept is tested using a two-dimensional systems model (COMPASS-Rootworm) that simulates root damage in maize from the corn rootworm Diabrotica spp. We evaluate COMPASS-Rootworm using 119 ield trials that investigated the eicacy of insecticidal products and placement strategies at four sites in the USA over a period of ten years. Simulated root damage is consistent with measurements for 109 ield trials. Moreover, we disentangle factors inluencing root damage and pest control, including pest pressure, weather, insecticide distribution, and temporality between the emergence of crop roots and pests. The model can inform integrated pest management, optimize pest control strategies to reduce environmental burdens from pesticides, and improve the eiciency of insecticide develop- ment.


Introduction
Global crop production depends on eicient protection from insect damage. Wheat, rice, maize, barley, potato, soybean, sugar beet, and cotton yield losses attributed to animal pests (primarily insects) were estimated to be 10% in 2002, ranging from 7% in barley to 24% in rice and 37% in cotton; losses to animal pests constituted 58% of the theoretical loss in the absence of crop protection measures (Oerke, 2006). Modern crop protection from insect pests is delivered through a combination of breeding and varietal selection, rotation, soil and crop husbandry, biological and microbial control, and chemical insecticides.
In particular, chemical insecticides have been a cornerstone of agricultural intensiication since the introduction of organochlorine insecticides in the 1960s (Peshin et al., 2009). Gianessi (2009) estimated that US growers spent $1.2 billion on insecticides in 2008 to treat 17% of the 1.1 million km 2 of land cultivated with the 50 main crops, and that this resulted in a yield beneit of $22.9 billion. More than 650 insecticides have been registered for use on the global market. Compared with the earliest insecticides, modern active substances have improved mammalian toxicological proiles and greater selectivity; targeted placement into the crop, for example as a seed treatment or banded application, can achieve use rates lower than 50 g of active substance (a.s.)/ha (Lamberth et al., 2013).
Despite these advances, there are major challenges to the continued availability of insecticides, owing to the combined efects of pest resistance, changing pest distributions, regulatory pressure on existing products, and ineiciencies in the development of new products. Globally, nearly 600 species of insects have been reported to be resistant to one or more of 325 insecticides and/or ive genetically modiied insecticidal traits (Sparks and Nauen, 2015); this necessitates the development, maintenance, and use of pesticides with a variety of modes of action, and the adoption of integrated pest management to https://doi.org/10.1016/j.agsy.2020.102865   (Wilson et al., 2018). Trade and transport have been important factors in the spread of pest species, and climate change will modify the range of agricultural pests. Substantial positive latitudinal shifts in pest populations have been observed in the Northern Hemisphere from 1960 onwards, with Acari, Coleoptera, Hemiptera, Lepidoptera, and Fungi shifting polewards and Nematoda shifting toward the Equator (Bebber et al., 2013).
Environmental concerns about the use of insecticides have resulted in tighter regulatory control. Stehle and Schulz (2015) found that 52% of 11,300 reported concentrations of insecticides in surface waters exceeded regulatory threshold levels where efects on macroinvertebrates can be expected. Exposure to pollen and nectar contaminated with neonicotinoid insecticides has been identiied as one of several factors implicated in the global decline in the number of pollinators (Sanchez-Bayo and Goka, 2014). Furthermore, insecticide use on crops has been linked to declines in terrestrial biodiversity in general (Geiger et al., 2010) as well as to declines speciically in the number of farmland birds (Mineau and Whiteside, 2013). Regulatory schemes have responded to these indings with high-proile actions, such as the moratoriums imposed by many countries on neonicotinoid seed treatments, and through restrictions and deregistration of active substances already on the market (Balderacchi and Trevisan, 2010).
Agrochemical discovery is almost exclusively based on a "chemistry-irst" paradigm that has focused on the identiication of leads through high-throughput, in vivo testing of chemical libraries (Lamberth et al., 2013). Mean times to discovery have remained in the range of 3-4 years for the past half-century, with a 70-fold increase in the number of compounds screened per product discovered (currently ca. 160,000) counteracted by the adoption of virtual screening and the use of techniques from pharmaceutical discovery, such as structurebased design, fragment-based design, and genome sequencing (Lamberth et al., 2013). Post-discovery, the cost (up to $286 million) and time (8-12 years) required to take a new pesticide through the development and registration process have increased signiicantly (Sparks and Lorsbach, 2016). These increases have led to a reluctance to invest in pest control for minor use crops (Sparks and Nauen, 2015).
Product development accounts for ca. 50% of the total cost to introduce a new agrochemical (Sparks and Lorsbach, 2016), and comprises a linear sequence of steps, from high-throughput identiication of an eicacious lead using standard bioassays, to laboratory studies on target pests, glasshouse experiments, and inally ield studies using a range of crops and environmental conditions (Kalamarakis and Markellou, 2007). The development sequence is largely empirical, with little feedback of mechanistic information into upstream development processes.
This study argues for a new approach to developing pest control strategies that is termed COMPASS (Comprehensive Model for Pesticide Activity in Soils). The concept integrates mechanistic understanding of pest ecology, insecticide fate, and insecticide efects on the pest into a systems-based, spatially-explicit model of root damage by pests. The models that result from taking such an approach deliver an in silico testbed of the soil-root-pest-chemical interfaces acting within the soil proile that aims to capture variability in inluencing factors across diferent sites and agricultural seasons.
We illustrate the COMPASS concept with the COMPASS-Rootworm model using a test system comprising corn (Zea mays L.) root damage and yield losses caused by the corn rootworm (Diabrotica spp.). Corn rootworm is a commercially signiicant pest that is widespread in North America, Central America, and Europe, with annual yield and control losses in the USA alone that were estimated to be greater than $1 billion between 2005 and 2007 (Dun et al., 2010). We demonstrate the validity of the COMPASS approach using a decade of ield data (119 ield trials) for the chemical control of corn root damage by rootworm larvae (University of Illinois Extension, 2005-2014. We quantify the beneits in terms of agricultural yields, environmental protection, and integrated pest management, and discuss step changes to our understanding of crop protection that can be delivered through the application of this knowledge-based approach to the design of pest control strategies.
Each trial comprised four replicate plots for a given treatment and the control. Damage assessment was undertaken 62 to 111 days after planting by extracting and washing ive root systems per replicate plot and then using the Node Injury Scale (NIS; Oleson et al., 2005) to quantify damage, with values ranging from 0.00 (no damage) to 3.00 (three full nodes or the equivalent across all nodes are lost; the maximum possible value).

COMPASS-Rootworm model
COMPASS-Rootworm is a two-dimensional systems model that describes the development and spatial distribution of corn roots and corn rootworm pest, as well as the fate, distribution, and toxic action of chemical insecticide; in combination, this allows simulation of root damage (and hence yield loss) by the pest under diferent environmental conditions, as well as the efectiveness of diferent chemical and non-chemical control strategies. The primary processes, inputs and outputs for the model are illustrated in Fig. 1.
COMPASS-Rootworm is coded in the freely available NetLogo 5.3 (Wilensky, 1999). The spatial discretization describes a vertical soil proile of 76 × 100 cm (x-and y-axes) and 1 cm depth (z-axis) that was selected to simulate a cross-section through the root system of a single corn plant in a ield with row spacing of 76 cm. Each patch/grid represents 1 cm 3 . Most processes are updated once per hour, and all the processes are updated at least once a day. The model runs from the beginning of the calendar year to the day of the NIS assessment using Julian days as the temporal measure. The model runs start at the beginning of a year, as both the pest model and the pesticide fate model require site-speciic weather data preceding the actual corn and corn rootworm season to simulate the temporal and two-dimensional occurrence and distribution of the root, pest, and pesticide owing to their dependency on temperature and water content in the soil proile.

Pest ecology
Pest ecology is described with an individual-based population model for the western corn rootworm Diabrotica virgifera virgifera (discretized at a 1-cm resolution) . A spatially-explicit root growth submodel describes the stochastic appearance and development of new roots within a deined nodal structure. The pest model simulates the development of eggs, the three larval instars, and the pupa of the corn rootworm, with the transition between life stages controlled by temperature-dependent developmental-rate functions. Speed of larval movement toward food (and, thus, larval foraging success and the survival of both larvae and roots) is dependent on soil type (Strnad and Dunn, 1990). The larval instars feed at diferent rates and consume roots of diferent ages (Clark et al., 2006;. Root consumption is linked to root damage (NIS) and yield loss through the direct loss of biomass and pruning of roots. Site-speciic weather data (air temperature and precipitation) are used to generate two-dimensional proiles of soil temperature and water content, which in turn drive the dynamics between pest and root systems. A previous evaluation using long-term data for Central Illinois showed that the corn rootworm model predicted the date of the irst appearance of both larvae and adults to within one week of the irst recorded sightings and accurately simulated the site-and season-speciic root damage recorded in the ield in the absence of pest control .
Initial pest pressure (i.e., the density of eggs in the soil from the preceding season) is an important input to the model, but is not normally measured in ield studies of corn rootworm. The previous evaluation of the pest model demonstrated that measured damage is simulated accurately for control plots when pest pressure is measured and used directly as a model input , so we conclude that pest pressure can be parameterized. Thus, we used measured damage in the control plots of the ield trials to parameterize pest pressure (a single value for all trials undertaken at each unique site-year combination; SD Table S2) and then held this value constant in model runs to simulate the impact of the various pesticide treatments on root damage. As all sites were ploughed, egg positioning was set to the tillage option  with homogeneous distribution in the horizontal plane, and vertical distribution as given by Vidal et al. (2005) (21% of eggs within the upper 10 cm, 45% of eggs at 10-20 cm, and 34% of eggs at 20-30 cm).

Pesticide fate
The model of pesticide fate in soil simulates temporally and spatially explicit water and pesticide transport in the soil proile by running simulations from Julian day 1 (January 1st) until harvest under the inluence of the explicit and stochastic development of root segments on a daily basis . This procedure allows the model to describe the microscale movement of pesticides in relation to root segments, which represents an important addition relative to existing models of pesticide fate in soil. In addition to the root growth model described above, the crop processes within the model include shoot development, spatially explicit uptake of water in response to transpiration demand, interception of rainfall and irrigation by the canopy, and evaporation from the canopy. The model captures spatial variation in inputs of precipitation (due to canopy interception and stem low) and irrigation to the soil surface. Movement of water within the soil proile is modeled using the soil capacity approach and occurs sequentially in the horizontal and vertical planes; the rate of water movement is deined using a maximum hydraulic gradient that is userdeined in each plane. Currently the model is set up for lat sites, but it could be modiied to incorporate the efect of a sloping site on water transport. Uptake of water by roots occurs locally in soil according to the spatial distribution of root segments. Upward movement of water can occur in response to evaporation from the soil surface and root uptake, but water that lows from the base of the soil proile is considered lost from the system.
Pesticides can be applied to the soil as a seed treatment or as an infurrow, banded, or broadcast application, and they are subsequently subject to irst-order degradation and linear, instantaneous sorption, with both processes modiied according to the water content and temperature of the respective 1-cm 3 grid. Dissolved pesticides are available for transport through soil with moving water and uptake by roots adjusted for the relative ease of uptake of diferent pesticides .

Toxicity to rootworms
Toxic action of insecticide on rootworms is described using the toxicokinetic-toxicodynamic approach of the General Uniied Threshold Model of Survival (GUTS; Jager et al., 2011). Rootworm larvae  Agatz et al. (2018). Larvae of the rootworm were exposed to diferent concentrations of one of the three chemicals homogeneously mixed into silt loam soil, and the number of surviving larvae was recorded after 24, 72, and 120 h (SD Table S3). Calibrated parameter values are shown in Table 1.
Previous rhizotron experiments carried out with ield-relevant application rates and placement strategies demonstrated that clothianidin, chlorpyrifos, and teluthrin can induce reduced feeding in rootworms, either by direct feeding inhibition or by impairing their ability to sense or move toward food (Agatz et al., 2018). In those experiments, clothianidin had a repellent efect on larvae, whereas chlorpyrifos provoked premature pupation and reduced the growth of larvae in comparison to nonexposed organisms. Teluthrin caused a loss of control over movement. At present, we lack the toxicokinetic-toxicodynamic models for the sublethal efects of chemical toxicants in soil pest species that would have allowed the simulation of the impacts on larval feeding . Instead, we incorporated a compoundspeciic parameter (prun-red) into our modeling framework that accounts for the sublethal impacts of a compound in terms of a reduction of root-pruning damage relative to that in the absence of the compound. For each compound, this parameter was itted to NIS data from one ield trial carried out in Urbana in 2007 (i.e. the training set comprised three of the 122 ield trials; Table 1). The calibrated value of prun-red for each compound was then held constant in all simulations of the remaining 119 independent ield trials used for model evaluation.

Model evaluation
Field trials in the evaluation set were modeled according to the information obtained for the ield trial site (application time, application rate, application type, duration for the trial, i.e. sowing time to day of harvest; SD Table S2) using weather data (obtained from the Illinois Climate Network 2016) recorded by weather stations in Bondville, DeKalb, Monmouth, and Perry that are located close to the University of Illinois ield stations where the trials were undertaken. The USDA (2017) Web Soil Survey tool was used to generate site-speciic soil information for the simulations (SD Table S4). The physicochemical properties of the active substances used were derived from the literature (University of Hertfordshire, 2013) and are summarized in SD Table S5. We considered that a predicted NIS damage value was in agreement with the observed NIS damage value if the 95% conidence interval of the predicted NIS damage value fell within ± 0.83 NIS damage units of the observed NIS damage value, as explained in the results section.

Limiting factors for pesticide efficacy
To analyze the interplay between the NIS and the application rate, we used the weather proile recorded for Urbana (IL, USA) in 2014 and ran the model framework by applying increasing application rates of clothianidin at planting on Julian day 131 (May 10th) as a furrow application on Drummer soil (SD Table S4), with eicacy assessment 72 days after planting. The initial pest pressure was 108 eggs/L soil.
To analyze the interplay between placement strategy and application rate, we simulated the eicacy of clothianidin in one region and one season by altering the compound application type and rate using the weather proile recorded for Urbana (IL, USA) SD Table S2 for details).
A cost-beneit analysis was undertaken for several simulations. Details are provided in the SD.

Integrated pest management
Globally, there is demand to adopt agronomic practices with reduced pesticide inputs. For example, the EU Sustainable Use Directive deines integrated pest management as a system that integrates measures to discourage the development of populations of harmful organisms, considers all available plant protection methods, and only uses control methods to levels that are economically and ecologically justiied (Lefebvre et al., 2015). Hatching of pest larvae is determined by soil temperature (degree days above a threshold; Davis et al., 1996) and extent of root damage in the absence of control measures is strongly inluenced by the relative timing of emergence of roots and pest larvae. The model framework captures this efect of inter-year variability in weather conditions, so it could be used to deliver reduced pesticide usage by identifying those conditions where insecticide use is not economically and ecologically justiied, and/or by optimizing sowing date in a given year to reduce the need for pest control. This was investigated for all data summarized in SD Table S2 by normalizing the observed NIS damage values in the control plots and the simulated NIS damage values from all treatment plots to a single, common pest pressure of 45 eggs/L soil and normalizing the temporal variation in the data by correlating the normalized NIS damage values to the number of days between the simulated root emergence and the day the irst egg developed into a larvae.

Table 1
Compound-speciic parameter values for the COMPASS-Rootworm model. Three parameters of the GUTS-RED-SD special case model (Jager et al., 2011;Jager and Ashauer, 2018) are used to characterize lethal efects, and the parameter Prun-red is used to account for sublethal efects.

COMPASS-Rootworm performance
The eicacy to control root damage by corn rootworm (indicated by a reduction in NIS) of products tested in the 119 ield trials used for model evaluation ranged from 0 to 99% (median 76%); the value for each trial was calculated from averages given in reports, and assuming 0% eicacy for trials where the damage to plants in treated plots was equal to or greater than that in the untreated controls. The amount of rootworm damage in the control plots varied among trial sites and years, with the greatest overall damage sustained in Urbana and the least overall damage sustained in Perry. SD Fig. S1 illustrates the variability in the eicacy of products tested in each ield trial by plotting the NIS damage values recorded in the treatment plots against those observed in the control plots. In 6.6% of the trials used for evaluation, the average NIS damage value in the control plot was lower than in the treatment plot, with a maximum discrepancy of 0.83 NIS damage units. Owing to the absence of a direct measure of uncertainty associated with the NIS assessments (because raw data for the ield trials were not accessible), we used this diference of ± 0.83 NIS damage units as an indication of the overall uncertainty of the results from the ield trials. SD Fig. S1 shows that in 38 of the 119 trials, the difference in the NIS damage value between the treatment and control was less than 0.83, indicating that in 32% of all trials, the eicacy of the pesticide to reduce pest pressure was not conirmed. Oleson et al. (2005) note that precision in node injury assessment is a function of both extent of root damage and sample size.
COMPASS-Rootworm was able to simulate the outcome of the 119 ield trials with all three active substances investigated and across the large range of observed eicacy. Overall, the average of simulated root damage (N = 40) was within ± 0.83 NIS of the average value observed in the ield for 91% of trials (95% conidence interval 80-98%; Fig. 2, SD Table S2). Thus, the model framework accounts for the combined efects of environmental, chemical, and biological factors that determine the eicacy of a plant protection product for a given site/ season combination within our dataset. This variation in environmental conditions between sites and years has been identiied previously as an important source of unexplained variability across large databases of ield eicacy trials (Tinsley et al., 2016). Future work should expand the evaluation to a wider set of conditions, particularly for locations impacted by corn rootworm in Central America and Europe. Rasche and Taylor (2019) also demonstrated successful simulation of ield eicacy trials by coupling a crop model with an above-ground insect population dynamics model. There, the authors found that they had to calibrate insecticide dose-mortality relationships to account for laboratory to ield extrapolation. In contrast, the current study simulates toxicity mechanistically based on toxicokinetics/toxicodynamics allowing a successful simulation of ield efects using parameters derived from laboratory toxicity tests.
The simulation performance tended to decrease with increased strength of pesticide sorption to soil (Fig. 2); 100% of the simulations were within the uncertainty of the ield trials for the most weakly sorbed compound, clothianidin, and this decreased to 89 and 85% of the simulations for the more strongly sorbed compounds chlorpyrifos and teluthrin, respectively. The soil-water partition coeicient which deines sorption is a sensitive parameter in all pesticide fate models (Dubus et al., 2003) and stronger sorption will act to decrease the volume of the root zone where the pesticide is present at any given point in time. When separating the ield trials into those that demonstrated the eicacy of a product (i.e., the diference between control and treatment NIS damage values was greater than the uncertainty of the ield trials) and those that did not meet this criterion, then the model was able to predict 86% of the 81 ield observations proving eicacy and 95% of the 38 ield observations that did not show eicacy. Variability in product performance across a limited number of ield trials (Toth et al., 2020) can be a major constraint on product development. A ield study may fail to demonstrate eicacy for an otherwise eicacious product because of low pest pressure (Furlan et al., 2006), a redistribution of the pesticide within the soil proile that occurs too quickly or too slowly depending on rainfall (Sutter et al., 1989;Sutter et al., 1991), the use of an application strategy that limits eicacy (Tinsley et al., 2016), or because too much time elapses between pesticide application and the appearance of the pest (Sutter et al., 1989). A mechanistic model that can be used as a virtual ield study to explain apparent anomalies in product performance will thus strengthen product development.

Limiting factors for pesticide efficacy
Field eicacy trials serve to optimize the application parameters for the product (Kalamarakis and Markellou, 2007). We used COMPASS-Rootworm to evaluate root damage for one environmental scenario as a function of the application rate of clothianidin applied as a furrow treatment at the time of sowing (Fig. 3). The model demonstrates that the insecticide cannot deliver full control of root damage in this scenario; thus NIS decreased as the amount of insecticide applied to the system increased, but only up to a limit value of 0.95 NIS (dotted red line in Fig. 3). The model simulations indicate that compound distribution within the soil proile was the limiting factor preventing further control because the compound did not reach all parts of the soil proile where the pest causes damage to the root system. COMPASS-Rootworm allows calculation of the application rate that provides an optimal economic return (68 g a.s./ha) based on the costs of pesticide application versus yield lost to the pest (Fig. 3), and thus supports the aim of sustainable intensive agriculture by delivering a secure supply of food while minimizing the use of agrochemicals (Popp et al., 2013). The model shows that for this scenario, the farmer could reduce the application rate by 49% from the economic optimum to 35 g a.s./ha and still deliver 92% of the maximum pest control and 98% of the maximum inancial return.
One response to the residual root damage that is demonstrated in Circled points indicate the trials in which the 95% conidence interval of the simulations and the maximum error from ield trials do not overlap (2 out of 119 ield trials). Fig. 3 could be to use a modiied formulation or product placement strategy for clothianidin (Buntin and All, 2013). Fig. 4 presents a virtual ield trial where COMPASS-Rootworm was used to assess four diferent product placement strategies for one season/soil combination: seed treatment, and furrow, band, and broadcast application. Seed treatment was the most efective strategy at low application rates, delivering 70% of the maximum achievable eicacy at 10 g a.s./ha. At higher application rates, the 40-cm band application was most eicacious, surpassing seed treatment at a rate of 35 g a.s./ha. This is in line with Tinsley et al. (2016) who constructed eicacy functions using corn rootworm control trials from Illinois and Nebraska, concluding that seed treatments were unlikely to be as efective as soil insecticide treatments (at full dose, seed treatments resulted in an average 86% greater damage), Here, narrower band applications and furrow application were not optimal strategies for the scenario evaluated. In practice, broadcast application would have provided the highest level of control of all, but this would have required application rates two-or tenfold greater than those for banded and seed treatment applications, respectively (data not shown). A detailed regional analysis of placement strategies, application rates, and treatment costs with COMPASS could produce farm decision trees to balance the competing demands of high inancial return and low risk to the environment. Rossi et al. (2019) identify calibration and validation of decision tools as a critical factor for successful uptake by end users. The development of a class of insecticides generally begins with discovery of a new structural class, followed by modiications of functional groups around the central scafold (Lamberth, 2018). COMPASS can be used to inform this development by simulating changes to the physicochemical properties of a pesticide that will modify its fate in soil and, thus, modify interactions with the target pest. We deined a hypothetical insecticide and used COMPASS-Rootworm to investigate how pest control would change in response to changes in the mobility and persistence of the compound, expressed as the organic carbon partition coeicient (Koc) and degradation half-life (DT50), respectively. The analysis considered three seasons with contrasting weather conditions and pest pressures. We found that mobility had a much stronger inluence on eicacy than persistence with a decrease in Koc of ca. 40 mL/g consistently doubling the eicacy of the hypothetical compound, even though there was a large variation in the absolute eicacy values across the three seasons (Fig. 5). The model results indicate that the spatial co-occurrence of pest larvae and pesticides was a more important limitation to eicacy than the period over which the pesticide was biologically active in soil. If mechanistic information relating to the optimal physicochemical properties were to be fed back into the selection of agrochemical leads (Rao et al., 2015) and product development pipeline, this would reduce the cost and time currently required to take a new pesticide through to registration.

Integrated pest management
Hatching of pest larvae is determined by soil temperature (degree days above a threshold; Davis et al., 1996), and the relative timing of emergence of roots and pest larvae determines the extent of root damage in a particular year and in turn will strongly inluence the eicacy of insecticide use (Clark et al., 2006). However, this efect is masked in the ield dataset because pest pressure also varies between sites and seasons (5-164 eggs/L soil in our dataset), and this has a strong inluence on root damage and insecticide eicacy. To overcome this problem, we used COMPASS-Rootworm to reanalyze the complete ield dataset for insecticide eicacy with the efect of pest pressure on root damage eliminated by normalizing the ield trials to a consistent pest pressure of 45 eggs/L soil. Fig. 6a (black dots/line) shows that when larvae emerged very soon (< 10 days) after irst root emergence, pest damage was minimal because the spatial extent of roots was limited, meaning that few larvae intercepted roots before they died from starvation. Normalized root damage increased exponentially up to a peak in NIS of 2.27 at an interval of 26 days between root emergence and egg hatch. At longer intervals, root damage decreased, because the roots were older at onset of pest pressure, and older roots are known to be unpalatable to irst instar larvae 24 . Although all pesticide treatments with clothianidin, chlorpyrifos, and teluthrin reduced root damage relative to the control ( Fig. 6a; colored dots/blue line) the reduction in the normalized NIS compared to the control was only above the uncertainty for NIS of 0.83 when egg hatch occurred 19-29 days after root emergence. Fig. 6b shows that the relative eicacy of all three compounds increased as the time interval between root emergence and egg hatch increased, and was maximal when egg hatch occurred 20-30 days after root emergence. At short intervals between root emergence and Fig. 3. Damage and revenue curve for clothianidin used as furrow treatment in one region and one season as a function of the application rate. Circles: Simulated damage (given according to the node injury scale (NIS)) as a function of the application rate as average of 40 COMPASS-Rootworm simulations for each diferent application rate (blue line: it through data; R 2 = 0.976). The red line indicates the limit to product eicacy for this scenario. The green curve (with the associated standard deviation (dashed curves)) illustrates the scenario-speciic pesticide-related revenue as a function of the application rate. The vertical green line indicates the application rate where revenue in relation to pesticide cost is at its maximum. (For interpretation of the references to colour in this igure legend, the reader is referred to the web version of this article.) Fig. 4. COMPASS-Rootworm simulated scenario-speciic eicacy of clothianidin in one region and one season relative to the maximum eicacy that can be delivered at an assumed maximum application rate of 65 g a.s./ha (i.e. band application with 40 cm band width). Data are shown for seed, furrow, broadcast and three band applications of diferent band width (10, 20, and 40 cm) as a function of the application rate. Lines: global it to the average of all the model predictions (N = 40 per application rate) with a 3 parameter exponential rise to maximum (R 2 = 0.983).
A. Agatz, et al. A g r ic u lt u r a l S y s t e m s 1 8 3 ( 2 0 2 0 ) 1 0 2 8 6 5 egg hatch, our model indicates that the spatial redistribution of a pesticide within the soil proile limited the zone providing efective protection to the growing roots. After approximately 30 days, there was a very sharp decrease in the relative pesticide eicacy and our model suggests that this is because the root system outgrew the soil zone with eicacious concentrations of pesticide (typically for corn root nodes 4 and above). Malard et al. (2020) also identiied a strong inluence of timing on the success of pest control action when modeling the lepidopteran Opisina arenosella as a pest of coconut farming in Sri Lanka; use of their modeling approach to determine optimal timing of biological control was found to outperform timing that was either on a ixed date or determined by pest population thresholds. Given that egg hatch is determined by soil temperature, and thus independent of root emergence, our analysis identiies a strategy for integrated pest management because sowing at or just before the time of egg hatch carries a low risk of root damage. Speciically, when the interval between root emergence and egg hatch is less than 10 days, the NIS is generally less than 0.5 NIS; this value was calculated as the threshold below which pesticide application is not economic assuming treatment costs of $36/ha (Alford and Krupke, 2017). Medium-range weather forecasting is increasingly reliable out to 10 days; this allows prediction of site-speciic timing of egg hatch , and supports decisions regarding the optimal time for sowing and either a reduced pesticide application intensity such as in-furrow treatment, or potentially the omission of pesticide treatment altogether. By reducing both the frequency and intensity of insecticide use, this approach could contribute to controlling the development of pest resistance to chemical insecticides (Sparks and Nauen, 2015). Where plowing is planned, sitespeciic prediction of egg hatch also ofers the potential to bring forward egg hatch by plowing; this would expose eggs (which are most abundant at 11-20 cm depth; Vidal et al., 2005) to the warmer upper soil layers thus encouraging earlier egg hatch, and the efect can be simulated in the model as it accounts for redistribution of eggs due to plowing. The alternative strategy of aiming to maximize the time between root emergence and egg hatch is not plausible because this would require accurate long-range forecasting of at least 30 days.   6. COMPASS-Rootworm simulated average damage and pesticide eicacy plotted against the interval between root emergence and the irst egg hatch. a) Rootworm damage shown as the node injury scale (NIS). b) Pesticide eicacy relative to the damage in the corresponding control. Data have been normalized to a consistent pest pressure of 45 eggs/L soil: trials with NIS in the control plot < 0.20 and > 2.80 are excluded owing to uncertainty in assigning the level of root damage at very small or large values for NIS. Lines: global it to all model predictions (N = 40) with a 3 parameter exponential rise to maximum (R 2 = 0.803).

Conclusion
Insect pests are a global threat to agricultural productivity and this threat is increasing due to changing pest distributions and spread of resistance to chemical insecticides, at the same time as the public is demanding more sustainable agricultural systems. Despite the high level of threat, development of pest control strategies ultimately depends on ield studies that are largely empirical. The COMPASS-rootworm model delivers a knowledge-based approach to the design of control strategies for a globally-signiicant pest that integrates knowledge across the disciplines of pest ecology, root physiology, soil hydrology, and insecticide fate and toxicity. Evaluation of the model against an extensive dataset of ield trials for root damage in maize caused by the corn rootworm shows that the model is able to capture much of the variability in damage to maize crops from corn rootworm and efectiveness of pest control strategies that is seen across diferent locations and agricultural seasons. The approach that is presented delivers virtual ield trials, allowing the development of mechanistic understanding of the system. This allows, for example, the optimization of insecticide selection and use to achieve maximum eicacy with minimal risk to the environment or normalization of yield loss to different pest pressures, weather, or treatment timing to develop guidance on integrated pest management strategies and resistance management. Whilst the research presented here is framed by agricultural losses due to corn rootworm, the new approach will have applications across a much wider range of agricultural pests.