Evolutionary branching under slowly evolving constraints

Biological populations have been evolving in multi-dimensional trait spaces. Ecological interactions can induce the evolutionary diversification of a biological population into distinct multiple populations, which is called evolutionary branching in adaptive dynamics theory. If possible mutations are restricted to certain directions due to developmental, physiological, or physical constraints, the resulting evolutionary dynamics may be restricted to subspaces with fewer dimensions than the original trait spaces. In general, such constraints are also evolving slowly, due to rare and slight mutational deviations from the constraint subspaces. In this sense, constraints are not strict. However, the method for describing non-strict constraints that is globally consistent has yet to be developed. This study proposes a general and flexible method for constructing a non-strict constraint subspace from the corresponding strict constraint subspace. This method enables efficient analysis of adaptive evolution including evolutionary branching under non-strict constraints in the framework of adaptive dynamics theory. Applying this method to a resource competition model shows that the shape of the carrying capacity distribution can be treated as a non-strict constraint curve, and that the likelihood of evolutionary branching is affected not only by the shape of the constraint curve but also by its slow evolution.