Effects of evolution on niche displacement and emergent population properties, a discussion on optimality

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. In particular, could we classify evolutionary scenarios leading to optimisation of those properties, from the ones who do not. First, we uncover two classes of invasion fitness functions, only the first one allowing optimization of some (but typically not all) population properties. Second, we showed that our two classes are also strongly linked to niche displacement and emergence of polymorphism. Our results indicate that optimization is, in general, incompatible with niche differentiation and, therefore, with emergence of polymorphism through evolutionary branching. Actually, niche displacement between resident and mutant morphs, and potentially polymorphism, only arise when we do not expect optimality to hold. We extensively discuss which biological traits can fall into which class of invasion fitness. Although, it is possible to find traits for which optimality is expected, we argue that for the majority of the cases it does not hold. Finally, we provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology.