Impact of small fitness costs on pest adaptation to crop varieties with multiple toxins: a heuristic model

A deterministic two-locus model was used to examine how small fitness costs to individuals carrying resistance alleles could impact the risk of panmictic insect pest populations adapting to crop varieties that produced two distinct toxins. Parameters examined were (1) level of toxicity of each toxin, (2) initial frequencies of alleles for adaptation to the toxins, (3) percentage of population feeding on nontoxic plants, and (4) level of fitness cost associated with adaptation to each of the two toxins. Resistance to each toxin was assumed to be biochemically independent, controlled by a resistance coding allele at a single locus, and inherited as a partially recessive trait in the field. When plants are extremely toxic to the pest, effective refuge size is 10%, and there is a fitness cost to resistance alleles only when in homozygous form (5%), the pest population is never predicted to adapt to either toxin as long as the initial frequencies of the resistance alleles are below 0.05. Even if the initial frequency of the allele for adapting to one toxin is 0.95 when a two-toxin cultivar completely replaces a one-toxin cultivar, the model predicts that a low equilibrium allelic frequency will develop for both resistance alleles, as long as the frequency of the allele for adapting to the second toxin is initially 0.001 or less. If cultivars with one and two toxins are planted, the model predicts that resistance will develop. Nonrandom mating and stochastic variation within subpopulations also could lead to evolution of resistance.