caa a22 4500 445330015 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00285-010-0380-6 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0380-6 Oligomorphic dynamics for analyzing the quantitative genetics of adaptive speciation [Elektronische Daten] [Akira Sasaki, Ulf Dieckmann] Ecological interaction, including competition for resources, often causes frequency-dependent disruptive selection, which, when accompanied by reproductive isolation, may act as driving forces of adaptive speciation. While adaptive dynamics models have added new perspectives to our understanding of the ecological dimensions of speciation processes, it remains an open question how best to incorporate and analyze genetic detail in such models. Conventional approaches, based on quantitative genetics theory, typically assume a unimodal character distribution and examine how its moments change over time. Such approximations inevitably fail when a character distribution becomes multimodal. Here, we propose a new approximation, oligomorphic dynamics, to the quantitative genetics of populations that include several morphs and that therefore exhibit multiple peaks in their character distribution. To this end, we first decompose the character distribution into a sum of unimodal distributions corresponding to individual morphs. Characterizing these morphs by their frequency (fraction of individuals belonging to each morph), position (mean character of each morph), and width (standard deviation of each morph), we then derive the coupled eco-evolutionary dynamics of morphs through a double Taylor expansion. We show that the demographic, convergence, and evolutionary stability of a population's character distribution correspond, respectively, to the asymptotic stability of frequencies, positions, and widths under the oligomorphic dynamics introduced here. As first applications of oligomorphic dynamics theory, we analytically derive the effects (a) of the strength of disruptive selection on waiting times until speciation, (b) of mutation on conditions for speciation, and (c) of the fourth moments of competition kernels on patterns of speciation. Springer-Verlag, 2010 Adaptive dynamics nationallicence Quantitative genetics theory nationallicence Moment dynamics nationallicence Adaptive speciation nationallicence Evolutionarily stable strategy nationallicence Convergence stability nationallicence Sasaki Akira Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, 240-0193, Kanagawa, Japan aut Dieckmann Ulf Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361, Laxenburg, Austria aut Journal of Mathematical Biology Springer-Verlag 63/4(2011-10-01), 601-635 0303-6812 63:4<601 2011 63 285 https://doi.org/10.1007/s00285-010-0380-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0380-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sasaki Akira Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, 240-0193, Kanagawa, Japan aut NATIONALLICENCE 700 1- Dieckmann Ulf Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361, Laxenburg, Austria aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/4(2011-10-01), 601-635 0303-6812 63:4<601 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer