Evolutionary branching under slow directional evolution

Abstract

Highlights 13+ We derive conditions for evolutionary branching in directionally evolving populations. 14 + The derived conditions extend those for univariate trait spaces to bivariate trait spaces. univariate traits is the existence of a convergence stable trait value at which selection is 6 locally disruptive. Real populations, however, undergo simultaneous evolution in multiple 7 traits. Here we extend conditions for evolutionary branching to bivariate trait spaces in which 8 the response to disruptive selection on one trait can be suppressed by directional selection on 9 another trait. To obtain analytical results, we study trait-substitution sequences formed by 10 invasions that possess maximum likelihood. By deriving a sufficient condition for 11 evolutionary branching of bivariate traits along such maximum-likelihood-invasion paths 12 (MLIPs), we demonstrate the existence of a threshold ratio specifying how much disruptive 13 selection in one trait direction is needed to overcome the obstruction of evolutionary 14 branching caused by directional selection in the other trait direction. Generalizing this finding, 15we show that evolutionary branching of bivariate traits can occur along evolutionary-16 branching lines on which residual directional selection is sufficiently weak. We then present 17 numerical analyses showing that our generalized condition for evolutionary branching is a 18 good indicator of branching likelihood even when trait-substitution sequences do not follow 19MLIPs and when mutations are not rare. Finally, we extend the derived conditions for 20 evolutionary branching to multivariate trait spaces. 21Keywords 22 frequency-dependent selection, speciation, adaptive dynamics, two-dimensional traits, multi-23 dimensional traits 24 25

Evolutionary branching in distorted trait spaces

“…As for evolutionary branching in two-dimensional trait spaces, branching point conditions (Geritz et al, 2016) and branching line conditions (Ito and Dieckmann, 2012, 2014) are applicable only for non-distorted trait spaces (i.e., the mutation distribution does not depend on the resident phenotype). To apply those branching conditions for distorted trait spaces, we assume there exists a nonlinear transformation of the coordinate system s = ( x , y ) T into a new coordinate system in which the mutation distribution can be approximated with a bivariate Gaussian distribution that is constant at least locally around a focal point s 0 .…”

“…If a space composed of evolutionary traits has an evolutionary branching point, the point attracts a monomorphic population through directional selection, and then favors its diversification through disruptive selection (Geritz et al, 1997). Moreover, a trait space may have not only evolutionary branching points but also evolutionary branching lines (Ito and Dieckmann, 2012, 2014), if the trait space has a significant mutatability difference among directions so that mutation in some direction is significantly difficult compared to the other directions. Analogously to evolutionary branching points, an evolutionary branching line attracts a monomorphic population and then favors their evolutionary branching through disruptive selection (Ito and Dieckmann, 2014).…”

The Branching Bifurcation of Adaptive Dynamics

“…14 More effort is definitely needed to extend the methodology to the cases of structured populations and/or to multi-dimensional strategies [Vukics et al, 2003, Ito & Dieckmann, 2014.…”

Identifying conversion efficiency as a key mechanism underlying food webs evolution: A step forward, or backward?

“…It takes place along the line ∂ y f = 0 at points away from the curve ∂ η f = 0. This is explained by evolutionary branching along slow directional evolution, as described and analyzed by Ito and Dieckmann (2014). They claim that such evolutionary branching can occur along one direction of the trait space when the evolution in the orthogonal directions of the trait space is slow.…”