Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice

ABSTRACT Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions.

[1]  Xiangzheng Deng,et al.  Effects of land use and insecticides on natural enemies of aphids in cotton: First evidence from smallholder agriculture in the North China Plain , 2014 .

[2]  Petr Pyšek,et al.  Elton, C.S. 1958: The ecology of invasions by animals and plants. London: Methuen , 2007 .

[3]  A. Zink,et al.  Estimating the Impact of Lygus hesperus on Cotton: The Insect, Plant, and Human Observer as Sources of Variability , 2006 .

[4]  S. Shaw,et al.  New, native species of Peristenus (Hymenoptera : Braconidae) parasitizing Lygus hesperus (Hemiptera : Miridae) in Idaho : Biology, importance, and description , 1999 .

[5]  M. Symonds,et al.  A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike’s information criterion , 2010, Behavioral Ecology and Sociobiology.

[6]  H. Banks,et al.  AN EXTENSION OF RSS-BASED MODEL COMPARISON TESTS FOR WEIGHTED LEAST SQUARES , 2012 .

[7]  B. Croft,et al.  Pesticide side-effects on arthropod natural enemies: A database summary , 1988 .

[8]  A. Honěk,et al.  Population Dynamics of Aphids on Cereals: Digging in the Time-Series Data to Reveal Population Regulation Caused by Temperature , 2014, PloS one.

[9]  H. O. Lancaster,et al.  The chi-squared distribution , 1971 .

[10]  P. White,et al.  Natural disturbance and patch dynamics: an introduction. , 1985 .

[11]  S. Fleischer,et al.  Spatial and Temporal Dynamics of Colorado Potato Beetle (Coleoptera: Chrysomelidae) in Fields with Perimeter and Spatially Targeted Insecticides , 2002 .

[12]  Roger Vargas,et al.  How risky is risk assessment: the role that life history strategies play in susceptibility of species to stress. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Harvey Thomas Banks,et al.  Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems , 2016 .

[14]  Peter Calow,et al.  The extrapolation problem and how population modeling can help , 2008, Environmental toxicology and chemistry.

[15]  David Ruppert,et al.  Transformation and Weighting , 2014 .

[16]  R. May,et al.  Biological populations obeying difference equations: stable points, stable cycles, and chaos. , 1975, Journal of theoretical biology.

[17]  P. White,et al.  The Ecology of Natural Disturbance and Patch Dynamics , 1986 .

[18]  H. T. Banks,et al.  Information content in data sets for a nucleated-polymerization model , 2015, Journal of biological dynamics.

[19]  Roger Vargas,et al.  Incorporating Ecologically Relevant Measures of Pesticide Effect for Estimating the Compatibility of Pesticides and Biocontrol Agents , 2007, Journal of economic entomology.

[20]  Harvey Thomas Banks,et al.  Modeling and Inverse Problems in the Presence of Uncertainty , 2014 .

[21]  V. Krischik,et al.  Effects of Systemic Imidacloprid on Coleomegilla maculata (Coleoptera: Coccinellidae) , 1999 .

[22]  R. Freckleton,et al.  The Ecological Detective: Confronting Models with Data , 1999 .

[23]  A. Christopoulos,et al.  Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting , 2004 .

[24]  H. Banks,et al.  Mathematical and Experimental Modeling of Physical and Biological Processes , 2001 .

[25]  Robert M. May,et al.  Patterns of Dynamical Behaviour in Single-Species Populations , 1976 .

[26]  J. Stark,et al.  Incorporating variability in point estimates in risk assessment: Bridging the gap between LC50 and population endpoints , 2015, Environmental toxicology and chemistry.

[27]  Ray Hilborn,et al.  The Ecological Detective , 2013 .

[28]  Volker Grimm,et al.  Integrating population modeling into ecological risk assessment , 2010, Integrated environmental assessment and management.

[29]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[30]  John E Banks,et al.  Population-level effects of pesticides and other toxicants on arthropods. , 2003, Annual review of entomology.

[31]  L. Skovgaard.  NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[32]  P. Calow,et al.  Is the per capita rate of increase a good measure of population‐level effects in ecotoxicology? , 1999 .

[33]  H. T. Banks,et al.  Model comparison tests to determine data information content , 2015, Appl. Math. Lett..

[34]  H. Banks,et al.  Optimal sampling frequency and timing of threatened tropical bird populations: A modeling approach , 2015 .

[35]  Andrej Pázman,et al.  Nonlinear Regression , 2019, Handbook of Regression Analysis With Applications in R.

[36]  Harvey Thomas Banks,et al.  Statistical methods for model comparison in parameter estimation problems for distributed systems , 1990 .

[37]  F. J. O'rourke.  Insects , 1951, Atlas of Yellowstone.

[38]  F. Thompson,et al.  The role of disturbance in the ecology and conservation of birds , 2001 .

[39]  J. Stark,et al.  Using semifield studies to examine the effects of pesticides on mobile terrestrial invertebrates. , 2014, Annual review of entomology.

[40]  G. C. Cutler,et al.  Insects, Insecticides and Hormesis: Evidence and Considerations for Study , 2013, Dose-response : a publication of International Hormesis Society.

[41]  A. Jensen,et al.  Transgenic Bt potato and conventional insecticides for Colorado potato beetle management: comparative efficacy and non‐target impacts , 2001 .

[42]  Axel Decourtye,et al.  The sublethal effects of pesticides on beneficial arthropods. , 2007, Annual review of entomology.