An inverse analysis of a matrix population model using a genetic algorithm

Demographic responses underlying eco-evolutionary dynamics as revealed with inverse modelling

Changes in population dynamics due to interacting evolutionary and ecological processes are the direct result of responses in vital rates, that is stage‐specific growth, survival and fecundity. Quantifying through which vital rates population fitness is affected, instead of focusing on population trends only, can give a more mechanistic understanding of eco‐evolutionary dynamics.

The aim of this study was to estimate the underlying demographic rates of aphid (Myzus persicae) populations. We analysed unpublished stage‐structure population dynamics data of a field experiment with caged and uncaged populations in which rapid evolutionary dynamics were observed, as well as unpublished results from an individual life table experiment performed in a glasshouse.

Using data on changes in population abundance and stage distributions over time, we estimated transition matrices with inverse modelling techniques, in a Bayesian framework. The model used to fit across all experimental treatments included density as well as clone‐specific caging effects. We additionally used individual life table data to inform the model on survival, growth and reproduction.

Results suggest that clones varied considerably in vital rates, and imply trade‐offs between reproduction and survival. Responses to densities also varied between clones. Negative density dependence was found in growth and reproduction, and the presence of predators and competitors further decreased these two vital rates, while survival estimates increased. Under uncaged conditions, population growth rates of the evolving populations were increased compared to the expectation based on the pure clones.

Our inverse modelling approach revealed how much vital rates contributed to the eco‐evolutionary dynamics. The decomposition analysis showed that variation in population growth rates in the evolving populations was to a large extent shaped by plant size. Yet, it also revealed an impact of evolutionary changes in clonal composition. Finally, we discuss that inverse modelling is a complex problem, as multiple combinations of individual rates can result in the same dynamics. We discuss assumptions and limitations, as well as opportunities, of this approach.