Resolving the paradox of stasis models with stabilizing

Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales Suzanne Estes & Stevan J. Arnold

Introduction The following slides illustrate the behavior of the quantitative genetic models for trait evolution used in Estes & Arnold 2007 Amer Nat 169: 227244. Additional details for the models are given in that article and in the indicated references.

Disclaimer The animations in the slides that follow are caricatures of model behavior, they are not actual simulations. In actual simulations of these stochastic models, behavior would vary from replicate run to replicate run. For this reason, the behavior of the trait mean at any generation, t, can be characterized by a statistical distribution, , with an expected mean and a variance.

Conventions • The upper panel in each slide shows the adaptive landscape (average populations fitness as a function of average trait value). • The lower panel in each slide shows the frequency distribution of a normally-distributed, phenotypic trait, z, as it evolves in response to the adaptive landscape. • In the case of landscapes with an intermediate optimum, the vertical dotted line marks the position of that optimum trait value, θ.

NEUTRAL MODEL W z p(z) z Lande 1976

W ADAPTIVE LANDSCAPE WITH INTERMEDIATE OPTIMUM θ z p(z) z weak stabilizing selection

W ADAPTIVE LANDSCAPE WITH INTERMEDIATE OPTIMUM θ z p(z) z strong stabilizing selection

DISPLACED OPTIMUM MODEL W θ z p(z) z Lande 1976

MOVING OPTIMUM MODEL W θ z p(z) z Lynch & Lande 1995

STATIONARY OPTIMUM WITH WHITE NOISE MOTION W θ z p(z) z Lynch & Lande 1995

PEAK SHIFT MODEL W b a z p(z) z Lande 1985

References • Lande, R. 1976. Evolution 30: 314 -334. • Lande, R. 1985. PNAS USA 82: 7641 -5. • Lynch, M. & R. Lande 1995. Pp. 2234 -250, IN: Kareiva et al. (eds. ), Biotic Interactions and Global Change, Sinauer, Sunderland, MA