Symmetry and similarity in eco-evo: advective environments, dispersal, and climate change

I investigate effects of directional advective dispersal on eco-evolutionary invasion speeds, in either constant environmental gradients or under directional environmental change. I build upon a spatially-explicit phenotypic model that I have previously presented. The model incorporates both phenotypic sorting and gene swamping, and is used to study constant advective dispersal and trait-based habitat choice. Through analytical arguments on characteristic lengths and speeds, as well as by direct numerical solutions, I find that, in eco-evo scenarios, advective dispersal has two opposing effects on pulled invasion fronts. In shallow environmental gradients, the demographic effect of simply adding to the steady-state invasion speed dominates. As gradients get steeper, asymmetric gene flow, due to advective dispersal, becomes increasingly stronger, pulling the invasion front in an opposite direction. Steep gradients cause front reversals, where species ranges, counter-intuitively, slide upstream. Symmetry between velocity of advective dispersal and velocity of climate change leads to adaptation lags, abundance profiles, and invasion speeds that depend only on the velocity difference. Through characteristic lengths and speeds, I also identify similarity between demographic and evolutionary averaging or tracking of environmental heterogeneity. I connect climate change research to demographic models of persistence in advective environments — the so-called drift paradox. I additionally derive dimensionless ratios that have potential in facilitating comparisons among different species, populations, traits and locales, and in guiding micro- and mesocosm experiments and space-for-time substitutions. As an aside, I demonstrate how numerical solution and simulation of complex eco-evo models can be accelerated with GPU programming.