Abstract: Herbivorous insects can have strong negative effects on the growth and development of plants. To limit these negative effects, plants can produce chemical defenses that slow insects’ rates of feeding, growth, or reproduction. Many models have looked at this induced resistance as a possible feedback that affects herbivore population dynamics. These models, however, have largely ignored the potential effects of stage structure on these interactions.
Insects have several discrete life stages with different growth rates, feeding rates, and sensitivities to environmental change. Previous theory on the effects of induced resistance has ignored these insect life stages, despite mathematical models from other areas suggesting that stage structure is often important. We answered three questions: (1) does plant induced resistance change insect stable-state distributions and the time it takes to reach them, (2) does plant induced resistance alter population sensitivities to perturbations in stage transition probabilities, and (3) does the shape of the induction vs. herbivore density curve further affect stable state distributions and population sensitivities?
To address how insect stage structure and induced resistance affect insect populations, we employed a general discrete-time difference equation model. This model has six distinct stages to capture diversity in size, consumption, and growth throughout an insect’s life. Insects from each stage affect the quality of the plant based on their densities and overall consumption, and plant quality subsequently affects the growth and survival of each insect stage. We first compared models with induced resistance to those where plant defenses are constant and found that induced resistance reduces insect equilibrium population sizes. Beyond this, incorporating time lags between initial herbivore feeding and induced resistance amplifies cycles in the herbivore population sizes.
Manipulating the relationship between herbivore density/consumption and the level of induced resistance further changes the magnitude of these cycles. When some larval stages are more affected by induced resistance than others, those highly sensitive stages had a greater effect on the overall population sizes and stage distributions than the more tolerant stages. This suggests that stage-specific effects do change the results of induced resistance models and are important to consider. Further, it provides new insight into how best to manage or understand herbivorous insect populations by focusing on instars that we know are most sensitive to induced resistance.
