Abstract
Heritable trait variation is a central and necessary ingredient of evolution. Trait variation also directly affects ecological processes, generating a clear link between evolutionary and ecological dynamics. Despite the changes in variation that occur through selection, drift, mutation, and recombination, current eco-evolutionary models usually fail to track how variation changes through time. Moreover, eco-evolutionary models assume fitness functions for each trait and each ecological context, which often do not have empirical validation. We introduce a new type of model, Gillespie eco-evolutionary models (GEMs), that resolves these concerns by tracking distributions of traits through time as eco-evolutionary dynamics progress. This is done by allowing change to be driven by the direct fitness consequences of model parameters within the context of the underlying ecological model, without having to assume a particular fitness function. GEMs work by adding a trait distribution component to the standard Gillespie algorithm - an approach that models stochastic systems in nature that are typically approximated through ordinary differential equations. We illustrate GEMs with the Rosenzweig-MacArthur consumer-resource model. We show not only how heritable trait variation fuels trait evolution and influences eco-evolutionary dynamics, but also how the erosion of variation through time may hinder eco-evolutionary dynamics in the long run. GEMs can be developed for any parameter in any ordinary differential equationmodel and, furthermore, can enable modeling of multiple interacting traits at the same time. We expect GEMs will open the door to a new direction in eco-evolutionary and evolutionary modeling by removing long-standing modeling barriers, simplifying the link between traits, fitness, and dynamics, and expanding eco-evolutionary treatment of a greater diversity of ecological interactions. These factors make GEMs much more than a modeling advance, but an important conceptual advance that bridges ecology and evolution through the central concept of heritable trait variation.
Highlights
The effect of ecological processes on evolutionary dynamics has long been acknowledged, but ecologists have historically dismissed the possibility of evolution affecting ecological dynamics in the short term based on the assumption that evolutionary processes occur on longer timescales than ecological ones (Thompson 1998, 2005; Hairston et al 2005)
We develop a new class of eco-evolutionary model that incorporates and tracks the amount of heritable variation in multiple traits controlling ecological interactions while eliminating the need for assumed fitness functions. This new type of model, called a Gillespie eco-evolutionary model (GEM), involves adding a side-loop to the standard Gillespie stochastic algorithm (Gillespie 1977) in which (1) both the mean and variance of a trait in the population may influence the dynamics; (2) fitness is determined by the effect that a particular parameter value has on birth and death rates of the evolving organism in the context of the model; and (3) offspring traits depend on the population variance and heritability of the trait (Fig. 1)
We argue that GEMs are a powerful and general way of evaluating the effect of contemporary trait evolution on ecological dynamics for any process that can be modeled using ordinary differential equations (ODEs)
Summary
The effect of ecological processes on evolutionary dynamics has long been acknowledged, but ecologists have historically dismissed the possibility of evolution affecting ecological dynamics in the short term based on the assumption that evolutionary processes occur on longer timescales than ecological ones (Thompson 1998, 2005; Hairston et al 2005). We develop a new class of eco-evolutionary model that incorporates and tracks the amount of heritable variation in multiple traits controlling ecological interactions while eliminating the need for assumed fitness functions.
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