Self-propelled adaptive evolution on malleable dynamic fitness landscapes

Evolving populations, from cells to organisms, adapt to the demands of their environment, yet in modifying their environment, they directly alter the selective pressures they experience, thereby reshaping their local fitness landscape. Here we present a minimal two-field model to capture this eco-evolutionary feedback loop. We consider two coupled, antisymmetric dynamical equations, one to govern the adapting population, and another to govern the shifting landscape that it traverses, with a scalar parameter to set the relative balance of evolutionary and ecological change. We analyze these joint dynamics to quantify the extent to which this feedback loop can dramatically accelerate the rate of evolution and enable a population to self-propel through trait space, not only to climb local selection gradients, but also to evolve in the absence of or against these gradients. We calculate the speciation (evolutionary branching) rate and the onset of chaos, derive approximate moment equations to extend Fisher's fundamental theorem, and highlight connections with adaptive dynamics and the generalized Lotka-Volterra formalism. We comment on the interpretation of our equations in the context of niche construction, ecological inheritance, and climate change.