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

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DOI: 10.7554/eLife.23804.002

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 $\left(\sum \alpha (x,y,u,v)\right)/K(x,y)$, where $\alpha (x,y,u,v)$ 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 $\alpha$ and $K$.

DOI: http://dx.doi.org/10.7554/eLife.23804.002