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. 2011 Nov 3;7(11):e1002260. doi: 10.1371/journal.pcbi.1002260

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Altrock et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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We show a phase portrait of the gradient of selection with . The arrows (length rescaled) indicate the most likely direction of selection given by Eqs. 6–9. The shading indicates the average speed of selection: The darker she shading, the faster the system is expected to leave the given state. Stable fixed points of the replicator dynamics are given by filled disks. Unstable fixed points and saddles are denoted by empty disks. Left panel: The migration rate is below the critical value , such that the replicator dynamics has internal stable fixed points. The number of alleles changes equally fast in both populations . Central panel: For the same migration rate, but with one population changing three times as fast compared to the other (), the selection pattern changes. However, the fixed points of the replicator dynamics Eq. 2 remain the same. Right panel: The stability of the fixed points of the replicator dynamics changes critically with the migration rate . For sufficiently high migration rate, , the system proceeds fast to fixation or loss of the mutant allele.

Inline graphic — We show a phase portrait of the gradient of selection with . The arrows (length rescaled) indicate the most likely direction of selection given by Eqs. 6–9. The shading indicates the average speed of selection: The darker she shading, the faster the system is expected to leave the given state. Stable fixed points of the replicator dynamics are given by filled disks. Unstable fixed points and saddles are denoted by empty disks. Left panel: The migration rate is below the critical value , such that the replicator dynamics has internal stable fixed points. The number of alleles changes equally fast in both populations . Central panel: For the same migration rate, but with one population changing three times as fast compared to the other (), the selection pattern changes. However, the fixed points of the replicator dynamics Eq. 2 remain the same. Right panel: The stability of the fixed points of the replicator dynamics changes critically with the migration rate . For sufficiently high migration rate, , the system proceeds fast to fixation or loss of the mutant allele.