American Society of Naturalists

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“A stochastic model for predicting age and mass at maturity of insects”

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Geoffrey Legault and Joel G. Kingsolver (Aug 2020)

A stochastic model of insect development predicts complex dependencies between age and mass at maturity

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Variation during development leads to complex trade-offs between insect age and mass

The tobacco hornworm (<i>Manduca sexta</i>), the focal organism for this study.<br />(From <i>American Insects</i>, 1904)
The tobacco hornworm (Manduca sexta), the focal organism for this study.
(From American Insects, 1904)

Two key questions in ecology and evolutionary biology are: (1) How long does it take individuals to mature (i.e., become adults)? and (2) How big are they when they do? Age at maturity is important because it determines when adults become active in the environment, which affects the timing of interactions such as herbivory and pollination. Mass at maturity is important because it affects demographic traits such as fecundity, hardiness, and dispersal ability. Finally, trade-offs between age and mass at maturity (e.g., fast maturation = small mass) are important because they determine which life history strategies are optimal.

Biologists Geoffrey Legault (University of British Columbia) and Joel Kingsolver (University of North Carolina at Chapel Hill) propose a new method for predicting the age and mass at maturity of insects. Their approach, which combines the theory of stochastic processes with the well known developmental biology of insects, reveals that variation during development can produce complex and previously unknown trade-offs between age and mass at maturity. Though their results focus on insect growth and maturation, they argue that similar trade-offs could occur in a wide variety of organisms with complex developmental processes.


Variation in age and mass at maturity is commonly observed in populations, even among individuals with the same genetic and environmental backgrounds. Accounting for such individual variation with a stochastic model is important for estimating optimal evolutionary strategies and for understanding potential trade-offs among life history traits. However, most studies employ stochastic models that are either phenomenological or account for variation in only one life history trait. We propose a model based on the developmental biology of the moth Manduca sexta that accounts for stochasticity in two key life history traits, age and mass at maturity. The model is mechanistic, describing feeding behavior and common insect developmental processes including the degradation of juvenile hormone prior to molting. We derive a joint probability density function for the model and explore how the distribution of age and mass at maturity is affected by different parameter values. We find that the joint distribution is generally non-normal and highly sensitive to parameter values. In addition, our model predicts previously observed effects of temperature change and nutritional quality on the expected values of insect age and mass. Our results highlight the importance of integrating multiple sources of stochasticity into life history models.