Spatial spread models routinely assume that parameters governing the outcome and dynamics of biological invasions are invariant in space and time. However, this assumption may be unrealistic if natural selection ensues from invasion. Traits relevant to species interactions between invaders and natives often determine establishment success and may be especially prone to selection due to substantial fitness consequences of trophic or competitive interactions. We present the formulation of a discrete-time, continuous-space model that can be applied generally to any invader whose fitness depends on the value of a quantitative trait subject to evolution over the course of invasion. We allow the fitness conferred by this trait to be affected by interactions with natives and also account for changes in heritability and additive genetic variance due to selection and gene flow. To demonstrate the usefulness of this modeling framework, we present results from such a model in which an invasive predator’s spread dynamics are affected by its interactions with a native prey species, while similar results hold for competitive interactions. We consider two primary cases: 1) native prey are initially naïve but may subsequently evolve antipredator defenses, and 2) invasive predators are initially ill-equipped but may subsequently evolve increased capacity for prey capture. How the spread dynamics of these scenarios differ from the standard case in which no evolution occurs is considered by deriving asymptotic wave speed approximations where possible and by performing numerical simulations in light of key parameters, including dispersal rate, degree of initial maladaptation, genetic variance, heritability, and interaction strength.

Results/Conclusions

For realistic levels of heritability, results indicate that evolution of an invasive species may account for initial lags in spread, accelerate the spread of an initially maladapted invader, or enable the spread of invasive populations that might otherwise fail. When native populations are capable of evolution, gene flow from invaded regions to uninvaded populations – whether by natural or assisted means – can lead to substantial deceleration of invader spread, particularly as the invasion approaches the boundary of the native species' range. Finally, we discuss the conditions necessary for these evolutionary outcomes to manifest and their expected extent of occurrence in natural systems.