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

Abstract

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.

Keywords: agricultural insect pests; approximate dynamic programming; dynamic programming; look-ahead policy; resistance management; stage structure; transgenic insect releases.

Figure 1

Insecticide resistance allele trajectories for four alternative policies attempting to manage a hypothetical insect pest over a 16‐week season using insecticidal sprays and releases of transgenic male insects carrying a late‐acting male‐selecting transgene. Black lines depict trajectories for a myopic policy with a planning horizon of H = 0 while red, blue, and orange lines portray look‐ahead policies with planning horizons of H = 1, H = 2, and H = 3, respectively. For all policies, H is measured in weeks. All panels within the same row share the same initial resistance allele frequency r ₀ (indicated by a horizontal black line, from $r_0=0.3(a,b,c)$, to $r_0=0.5(d,e,f)$ to $r_0=0.7\left(g,h,i\right)$.), and all panels within the same column share the same dominance of resistance h (completely recessive resistance, $h=0\left(a,d,g\right)$; additive resistance, $h=0.5\left(b,e,h\right)$; dominant resistance, $h=1\left(c,f,i\right)$).

Figure 2

Insecticide resistance allele trajectories for four alternative policies attempting to manage a hypothetical insect pest over a 16‐week season using insecticidal sprays and releases of transgenic male insects carrying an early‐acting male‐selecting transgene. Black lines depict trajectories for a myopic policy with a planning horizon of H = 0 while red, blue, and orange lines portray look‐ahead policies with planning horizons of H = 1, H = 2, and H = 3, respectively. For all policies, H is measured in weeks. All panels within the same row share the same initial resistance allele frequency r ₀ (indicated by a horizontal black line, from $r_0=0.3\left(a,b,c\right)$, to $r_0=0.5\left(d,e,f\right)$ to$r_0=0.7\left(g,h,i\right)$.), and all panels within the same column share the same dominance of resistance h (completely recessive resistance, $h=0\left(a,d,g\right)$; additive resistance, $h=0.5\left(b,e,h\right)$; dominant resistance, $h=1\left(c,f,i\right)$).

Figure 3

Frequencies of implemented actions over a 16‐week season for a look‐ahead policy with a planning horizon of H = 3 weeks. In a given week, the model may select to do nothing (null), apply foliar insecticide (spray), or choose from one of six transgenic male insect release ratios (here aggregated together as one category: release). Red bars, transgenic males carry an early‐acting female lethal construct; blue bars, construct is late acting. All panels within the same row share the same initial resistance allele frequency r ₀ (indicated by a horizontal black line), and all panels within the same column share the same dominance of resistance h. Moving from the top row to the bottom row the initial resistance allele frequency increases from $r_0=0.3\left(a,b,c\right)$, to $r_0=0.5\left(d,e,f\right)$ to $r_0=0.7\left(g,h,i\right)$. Panels in the left column illustrate results for completely recessive resistance $h=0\left(a,d,g\right)$, panels in the central column show results for additive resistance $h=0.5\left(b,e,h\right)$, while panels in the right column show results for dominant resistance $h=1\left(c,f,i\right)$.