Individual heterogeneity in life histories and eco-evolutionary dynamics

Abstract

Individual heterogeneity in life history shapes eco-evolutionary processes, and unobserved heterogeneity can affect demographic outputs characterising life history and population dynamical properties. Demographic frameworks like matrix models or integral projection models represent powerful approaches to disentangle mechanisms linking individual life histories and population-level processes. Recent developments have provided important steps towards their application to study eco-evolutionary dynamics, but so far individual heterogeneity has largely been ignored. Here, we present a general demographic framework that incorporates individual heterogeneity in a flexible way, by separating static and dynamic traits (discrete or continuous). First, we apply the framework to derive the consequences of ignoring heterogeneity for a range of widely used demographic outputs. A general conclusion is that besides the long-term growth rate lambda, all parameters can be affected. Second, we discuss how the framework can help advance current demographic models of eco-evolutionary dynamics, by incorporating individual heterogeneity. For both applications numerical examples are provided, including an empirical example for pike. For instance, we demonstrate that predicted demographic responses to climate warming can be reversed by increased heritability. We discuss how applications of this demographic framework incorporating individual heterogeneity can help answer key biological questions that require a detailed understanding of eco-evolutionary dynamics.

Keywords: Demographic heterogeneity; eco-evolutionary response; evolutionary demography; individual differences; structured population.

Figure 1

A schematic overview of the main model components and the demographic outputs considered in the analyses. Together with environmental variable(s) θ, the dynamic trait x and static trait y define individual vital rate functions. Here, these are illustrated for a constant environment (only means are shown for the offspring trait distribution and the distribution of dynamic transitions). The offspring inheritance is a joint distribution for and , in this illustration they are independent. Once vital rates are defined, demographic outputs are obtained by analysis of the projection kernel, for instance the stable structure and reproductive value in a given environment, as shown here. The final four outputs require an extension of the model to include demographic and/or environmental stochasticity (Appendix S1).

Figure 2

An example of a size-structured population of red and green individuals. Depending on whether colour and size is recognised, the vital rates will look different to the observer, as illustrated for survival and fecundity in panels (a–c) (for transition rates, see the provided R code). As a result, with the exception of λ estimates of demographic outputs will be biased in models b and c. Consequences of underlying heterogeneity on estimates of extinction risk (through demographic and environmental variance) are provided in the supplementary R code.

Figure 3

A length- and temperature-based model for pike, including length at age 1 as a static trait y in addition to length x and temperature T. Vital rates (A–D) are shown here for the mean temperature (in this example for offspring), for values in other temperatures see Appendix S3. The parameter α measures the effect of y on survival, negative values correspond to a negative effect and thus a trade-off with growth. Positive values correspond to positive effects representing ‘quality’ differences among individuals. Panels (E and F) show the resulting bias in various demographic outputs in a model that ignores y, as a function of α.

Figure 4

An example of eco-evolutionary dynamics in the pike model including length at age 1 as a static trait y, in addition to length x and temperature T (details in Appendix S3). A model with zero heritability of y (model 1) is compared to a model with a heritability of 0.6 (model 2), as shown in the upper left panels. The resulting reproductive value functions for the two models are shown for the mean temperature. The lower left panel shows effects of temperature on various demographic outputs in the two models, while the lower right panel shows the marginal stable trait distributions of y and x for two temperatures, in the two models.