Evol Ecol Res 14: 757-768 (2012)     Full PDF if your library subscribes.

Numerical solutions and animations of group selection dynamics

Burton Simon1 and Aaron Nielsen2

1Department of Mathematical and Statistical Sciences, University of Colorado at Denver, Denver, Colorado, USA and  2Statistics Department, Colorado State University, Fort Collins, Colorado, USA

Correspondence: B. Simon, Department of Mathematical and Statistical Sciences, University of Colorado at Denver, 1250 Fourteenth Street, Denver, CO 80202, USA.
e-mail: burt.simon@ucdenver.edu


Question: What is the best way to illustrate the dynamical process of group selection, and study its long-term characteristics?

Approach: Numerically solve the dynamical equations for general two-level population processes, and then animate the results.

Mathematical methods: Numerical PDE, numerical ODE, stochastic simulation.

Key assumptions: Group selection is properly characterized in terms of the long-term behaviour of two-level population processes.

Main results: The dynamical process of group selection can be seen clearly in three different kinds of animations of the dynamical equations. The three kinds of animations, corresponding to different scalings of the basic model, highlight different aspects of the phenomenon. Group selection appears to be a potent evolutionary force under a variety of conditions.

Keywords: evolutionary birth–death process, group extinction, group fissioning, multi-level selection, population dynamics.

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