1. Ecology
  2. Evolutionary Biology
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Point of View: Towards a mechanistic foundation of evolutionary theory

  1. Michael Doebeli  Is a corresponding author
  2. Yaroslav Ispolatov
  3. Burt Simon
  1. University of British Columbia, Canada
  2. Universidad de Santiago de Chile, Chile
  3. University of Colorado, United States
Feature Article
Cite this article as: eLife 2017;6:e23804 doi: 10.7554/eLife.23804
1 figure and 2 videos

Figures

Deterministic approximations of evolutionary birth-death processes.

Adaptive dynamics, given by Equation 3, derived for the two examples of evolutionary birth-death processes shown in Video 1 and Video 2. Adaptive dynamics yields a deterministic approximation of the evolutionary dynamics, which is shown in the left panels (cyclic dynamics in 2-dimensional phenotypes space in the top left panel, chaotic attractor in 3-dimensional phenotype space in the bottom left panel). The panels on the right show the corresponding trajectories of the centres of mass of the clouds of points representing the two evolutionary birth-death processes in Video 1 and Video 2. For details see (Ispolatov et al., 2016).

https://doi.org/10.7554/eLife.23804.004

Videos

Video 1
Evolving populations as clouds of points moving in phenotype space.

The points in the cloud represent the individual organisms, which can give birth (spawn a new point in the cloud) and die (the corresponding dot disappears from the cloud). The video shows a single species undergoing cyclic evolutionary dynamics in a 2-dimensional phenotype space. The x- and y-axis are the two phenotypes, and the cloud of points represents the evolving population. In this example, all individuals had the same constant birth rate, whereas individual death rates were determined by competition from other individuals in the population. Specifically, the death rate of an individual with phenotype (x,y) was equal to (α(x,y,u,v))/K(x,y), where α(x,y,u,v) is the competition kernel, which measures the competitive impact of (u,v) on (x,y), K(x,y) is the carrying capacity of phenotype (x,y), and the sum runs over all other individuals (u,v) in the current population. The video shows the same scenario as Figure 1 in Ispolatov et al. (2016), to which we refer for details of the simulations, as well as of the particular functions chosen for α and K.

https://doi.org/10.7554/eLife.23804.002
Video 2
A single species undergoing chaotic evolutionary dynamics in a 3-dimensional phenotype space.

The cloud of points represents the evolving population. In this example, all individuals had the same constant birth rate, whereas individual death rates were determined by competition from other individuals in the population in a way that is analogous to the example shown in Video 1, i.e., based on a particular competition kernel α and a carrying capacity function K (now having 3-dimensional vectors as arguments). The video shows the same scenario as Figure 2 in Ispolatov et al. (2016), to which we refer for details of the simulations, as well as of the particular functions chosen for α and K.

https://doi.org/10.7554/eLife.23804.003

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