DOI: 10.15482/usda.adc/1529797
title: Modeling long-term, stage-structured dynamics of Tribolium castaneum at food facilities with and without two types of long-lasting insecticide netting

description: Insecticide Netting
In this study, we focused on two types of long-lasting insecticide netting (LLIN) that have been found to be effective for managing various stored product insect pests. One is an LLIN consisting of a polyethylene netting (2 × 2 mm mesh, D-Terrence, Vestergaard, Inc., Lausanne, Switzerland) with 0.4% deltamethrin active ingredient (a.i.), while the second one is Carifend® net (40 deniers with mesh size 97 knots/cm2; BASF AG, Ludwigshafen, Germany) containing 0.34% α-cypermethrin (a.i.).
Foundational Model
We used a standard Lefkovitch matrix model to project population growth for Tribolium castaneum, with four life stages (e.g., egg, larva, pupa, and adult;(Lefkovitch,1965). In equation (1), the Leftkovitch matrix L matrix (4 × 4) represents the life-stage structure of T. castaneum which has an egg, larvae, pupae, and an adult, where only the adults contribute to the fecundity, F. By multiplying L with the population vector ni(t), where t is time step (e.g., generation) and i is a life stage, we obtain the resultant vector ni(t + 1), which reveals the distribution of individuals across different life stages in the subsequent time period.
In equation (1), P1 represents the probability of staying in the egg stage and G1 is the probability of moving from the egg to the larval stage, P2 is the probability of staying in the larval stage, G2 is probability of moving from the larval stage to pupal stage, P3 is the probability of staying in the pupal stage, G3 is probability of moving from the pupal stage to adult, while P4 is the probability of staying in the adult stage (Figure 1).
Model Parameterization and Scenarios
We simulated population outcomes for up to 15 generations by using the life table data for T. castaneum using the R package popbio. Survivorship, fecundity, and transition information for each stage were derived from the literature (summarized in Table 1). The developmental duration of eggs, larvae, and pupae were 3.82 ± 0.005, 22.81 ± 0.67, and 6.24 ± 0.071 days (Kollros,1944). The average life duration of the adult used in this study was 221.16 days (Park et al., 1961). We used 94 offspring for fertility from the study Park et al.,(1965) and 99% rate of eclosion from pupae to adult.
In order to explore the sensitivity of the base model to changes in mortality and fecundity, both of these parameters were systematically varied from near zero to their maximum value given in the base model (e.g., F = 94, P4 = 0.871). The parameters were varied alone or in combination and the resulting population growth was plotted. All plots were created using ggplot2 (Wickham, 2016) in R software (R Core Team, 2022).
Three empirical scenarios from the literature were modeled containing estimates of fecundity reduction only, survivorship reduction only, or both fecundity and survivorship reduction when using LLIN (R.V. Wilkins et al., 2021; Gerken et al., 2021;Scheff et al., 2021, Scheff et al., 2023; Table 2). An individual projection matrix was constructed for each of the three scenarios and combinations of the reductions in fecundity, survivorship, or both. Population growth and proportion in each life stage was projected for 15 generations for each case, including the base model. Overall variation and oscillation were calculated to compare trends among proportion of life stages in each case. In order to compare differences in population sizes between cases for all generations and for generation 15 only, population sizes for each generation were bootstrapped 1000 times to provide iterative replication. The bootstrapped data were then compared one case to another using proc ttest in SAS (Version 9.4) for all generations and for generation 15 only.  In addition, a sensitivity analysis was performed to determine which stage should be targeted to most greatly affect the population growth after exposure to the netting. Moreover, a mortality function based on empirical data with LLIN exposure collected in the laboratory on T. castaneum was implemented.
The three scenarios are derived from:
Gerken, A. R., J. F. Campbell, S. R. Abts, F. Arthur, W. R. Morrison, and D. S. Scheff. 2021. “Long-Lasting Insecticide-Treated Netting Affects Reproductive Output and Mating Behavior in Tribolium castaneum (Coleoptera: Tenebrionidae) and Trogoderma variabile (Coleoptera: Dermestidae).” Edited by Rizana Mahroof. Journal of Economic Entomology 114 (6): 2598–2609. https://doi.org/10.1093/jee/toab204.
Scheff, D. S., A. R. Gerken, W. R. Morrison, J. F. Campbell, F. H. Arthur, and K. Y. Zhu. 2021. “Assessing Repellency, Movement, and Mortality of Three Species of Stored Product Insects after Exposure to Deltamethrin-Incorporated Long-Lasting Polyethylene Netting.” Journal of Pest Science 94 (3): 885–98. https://doi.org/10.1007/s10340-020-01326-3.
Wilkins, R.V., J.F. Campbell, K.Y. Zhu, L.A. Starkus, T. McKay, and W.R. Morrison. 2021. “Long-Lasting Insecticide-Incorporated Netting and Interception Traps at Pilot-Scale Warehouses and Commercial Facilities Prevents Infestation by Stored Product Beetles.” Frontiers in Sustainable Food Systems 4:  https://doi.org/10.3389/fsufs.2020.561820.
Resources in this dataset:

Resource Title: Script for Modeling of LLIN effects on T. castaneum MS
File Name: ranabhat_etal_modeling_MS_r_script_final_agdata_commons.R