title: Evolutionary branching under multi-dimensional evolutionary constraints.
abstract: The fitness of an existing phenotype and of a potential mutant should generally depend on the frequencies of other existing phenotypes. Adaptive evolution driven by such frequency-dependent fitness functions can be analyzed effectively using adaptive dynamics theory, assuming rare mutation and asexual reproduction. When possible mutations are restricted to certain directions due to developmental, physiological, or physical constraints, the resulting adaptive evolution may be restricted to subspaces (constraint surfaces) with fewer dimensionalities than the original trait spaces. To analyze such dynamics along constraint surfaces efficiently, we develop a Lagrange multiplier method in the framework of adaptive dynamics theory. On constraint surfaces of arbitrary dimensionalities described with equality constraints, our method efficiently finds local evolutionarily stable strategies, convergence stable points, and evolutionary branching points. We also derive the conditions for the existence of evolutionary branching points on constraint surfaces when the shapes of the surfaces can be chosen freely.
authors.affiliation: Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced Studies), Hayama, Kanagawa 240-0193, Japan. Electronic address: hiroshibeetle@gmail.com.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Ito
authors.affiliation: Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced Studies), Hayama, Kanagawa 240-0193, Japan; Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
authors.forename: Akira
authors.initials: A
authors.lastname: Sasaki
mesh_terms: D005075:Biological Evolution; D056084:Genetic Fitness; D008954:Models, Biological; D019655:Quantitative Trait, Heritable
keywords: Adaptive evolution; Ecological interaction; Evolutionary constraint; Frequency-dependent selection; Lagrange multiplier method; Speciation