Management of a stage-structured insect pest: an application of approximate optimization

Insect pest control, approximate dynamic programming, and the management of the evolution of resistance

Ecological decision problems, such as those encountered in agriculture, often require managing conflicts between short-term costs and long-term benefits. Dynamic programming is an ideal method for optimally solving such problems but agricultural problems are often subject to additional complexities that produce state spaces intractable to exact solutions. In contrast, look-ahead policies, a class of approximate dynamic programming (ADP) algorithm, may attempt to solve problems of arbitrary magnitude. However, these algorithms focus on a temporally truncated caricature of the full decision problem over a defined planning horizon and as such are not guaranteed to suggest optimal actions. Thus, look-ahead policies may offer promising means of addressing detail-rich ecological decision problems but may not be capable of fully utilizing the information available to them, especially in scenarios where the best short- and long-term solutions may differ. We constructed and applied look-ahead policies to the management of a hypothetical, stage-structured, continually reproducing, agricultural insect pest. The management objective was to minimize the combined costs of management actions and crop damage over a 16-week growing season. The manager could elect to utilize insecticidal sprays or one of six release ratios of male-selecting transgenic insects where the release ratio determines the number of transgenic insects to be released for each wild-type male insect in the population. Complicating matters was the expression of insecticide resistance at non-trivial frequencies in the pest population. We assessed the extent to which look-ahead policies were able to recognize the potential threat of insecticide resistance and successfully integrate insecticides and transgenic releases to capitalize upon their respective benefits. Look-ahead policies were competent at anticipating and responding to ecological and economic information. Policies with longer planning horizons made fewer, better-timed insecticidal sprays and made more frequent transgenic releases, which consequently facilitated lower resistance allele frequencies. However, look-ahead policies were ultimately inefficient resistance managers, and directly responded to resistance only when it was dominant and prevalent. Effective long-term agricultural management requires the capacity to anticipate and respond to the evolution of resistance. Look-ahead policies can accommodate all the information pertinent to making the best long-term decision but may lack the perspective to actually do so.

Optimal control for disease vector management in SIT models: an integrodifference equation approach

Vector-borne diseases are a major public health concern inflicting high levels of disease morbidity and mortality. Vector control is one of the principal methods available to manage infectious disease burden. One approach, releasing modified vectors (such as sterile or GM mosquitoes) Into the wild population has been suggested as an effective method of vector control. However, the effects of dispersal and the spatial distribution of disease vectors (such as mosquitoes) remain poorly studied. Here, we develop a novel mathematical framework using an integrodifference equation (discrete in time and continuous in space) approach to understand the impact of releasing sterile insects into the wild population in a spatially explicit environment. We prove that an optimal release strategy exists and show how it may be characterized by defining a sensitivity variable and an adjoint system. Using simulations, we show that the optimal strategy depends on the spatially varying carrying capacity of the environment.