Understanding the effects of evolution on emergent population properties such as intrinsic growth rate, species abundance, or dynamical resilience is not only a key theoretical question, but has major empirical implications for conservation, agroecology, invasion ecology among others. Evolution can also lead to the maintenance of polymorphism based on niche differentiation among different phenotypes. Specifically, we aim to answer the following three questions. Can we clarify the evolutionary scenarios allowing the optimization of population growth rate and of total abundance ? Can we relate the eco-evolutionary emergence of polymorphism to the niche and fitness difference concepts sensu coexistence theory ? Can the population properties be optimized after a branching point due to niche-displacement. We revisit previous theoretical results, which state that eco-evolutionary dynamics optimize when the invasion fitness of a rare mutant morph is affected by the environment, set by the resident morph, in a uni-dimensional feedback loop and monotonically, using a classical Lotka-Volterra model describing ecological dynamics.
Depending on how the traits under selection affect species intrinsic growth rates or ecological interactions, we determine three scenarios, ranging from the optimization of all three population properties to no optimization. Furthermore, we provide a link between evolutionary dynamics and coexistence theory. We find, in general, that optimization is incompatible with niche differentiation sensu coexistence theory and, therefore, with the emergence of polymorphism. Niche displacement between resident and mutant phenotypes, and potentially polymorphism, only arise when we do not expect optimality to hold. Finally, we show how this approach can be generalized to coevolution and that optimization is unlikely to happen in such conditions. Along the three scenarios, we also propose biological scenarios and traits that may fall into them. Although it is possible to find traits for which optimality is expected, for the majority of the cases optimization arguments do not hold. Finally, we provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology.