Evolutionary distributions: A theoretical framework

5 Adaptive traits are inherited with small mutations. They are sub6 ject to natural selection. An adaptive space is made of a set of adaptive 7 traits. Within this adaptive space live distributions of the density of 8 phenotypes. The dynamics of this density reflect evolution by natural 9 selection. We call these distributions Evolutionary Distributions (ED). 10 The adaptive space with its ED form the evolutionary space. ED are 11 derived from first principles of population dynamics: birth, death, mu12 tations and selection. This approach leads to a rich behavior of ED 13 with and without stability. With ED, it is easy to understand how 14 we may find phenotypes with different fitness values at evolutionary 15 stability. The theory of ED considers the dynamics of densities of all 16 possible phenotypes on a set of adaptive traits. Thus, invasions by 17 mutants represent perturbations to the ED. Stable ED therefore do 18 not allow invasion of mutants and as such, are akin to the concept 19 of evolutionary stable strategies (ESS). We apply the theory to three 20 common coevolutionary interactions: competition, predation and host 21 pathogen. We also apply the theory to (open) ecosystems and illus22 trate application in the context of primary producers and primary 23 consumers ecosystems. We also illustrate applications of coevolution 24 in the context of global change. The theory is restricted to (not nec25 essarily continuous) adaptive traits that can be characterized by real 26 numbers. 27