RT Journal Article
SR 00
ID 10.1016/j.jtbi.2016.07.011
A1 Ito, H.
A1 Sasaki, A.
T1 Evolutionary branching under multi-dimensional evolutionary constraints
JF Journal of Theoretical Biology
YR 2016
FD 2016-10-21
VO 407
SP 409
OP 428
K1 Adaptive evolution; Ecological interaction; Frequency-dependent selection; Speciation; Evolutionary constraint; Lagrange multiplier method
AB 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.
PB Elsevier
SN 0022-5193
LK https://pure.iiasa.ac.at/id/eprint/13550/