Individuals who invest more in the development of their dispersal-related traits often reduce their investment in reproduction. Thus, there are two possible eco-evolutionary strategies: grow faster or disperse faster (R-D arbitrage). Here we explore, through a reaction-diffusion model, how spatial heterogeneity can shape the $R-D$ trade-off by studying the spreading dynamics of a consumer species exploiting a resource in a spatially fragmented environment. Based on numerical simulations and analytical solutions derived from simpler models, we show that the classical mathematical symmetry between the effects of growth and dispersal on the spatial spreading speed is broken in the presence of competition between phenotypes. At the back of the forefront, the dynamics is almost always driven by the R specialists. On the forefront, R-strategies are favored in spatially homogeneous environments, but the introduction of heterogeneity leads to a shift towards D-strategies. This effect is even stronger when spatial heterogeneity affects the diffusion term and when spatial fragmentation is lower. Introducing mutations between phenotypes produces an advantage towards the R-strategy and homogenizes the distribution of phenotypes, also leading to more polymorphism on the forefront.
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