Fig. 4.

The linear regression of phenotype on the moving optimum gives insights about the predictability of chaotic evolutionary dynamics. (A) The fraction of the total temporal variation in the evolving phenotype explained by movements of the optimum, as captured by the R² of the regression, is higher when the optimum oscillates with larger amplitudes and longer periods. (B) The ratio of amplitudes between the tracking component of oscillations in the evolving phenotype and oscillations in the optimum, as estimated by slope of the regression, is smaller under short-period optimum oscillations. (C) Temporal variation in evolutionary dynamics introduced by chaos, beyond the variation attributable to tracking of the moving optimum, is captured by the variance of residuals in the regression. Conditions that allow for close tracking of the optimum in (B) also lead to dampened chaotic oscillations. We show the average (lines and points) and standard error (shading) over 100 simulations for each combination of amplitude and period of optimum oscillation.