Figure 5.

Conditions for trait loss to take longer than 10⁸ generations in a metapopulation. A. The minimum number of demes needed as a function of $\overline{\tau }$ and θ. Eqs. C1 and C2 are used for exponentially-distributed sojourn times, Eqs. D1, D2 and D3 for fixed sojourn times, and simulations are performed as described in Online Appendix D. We see that there is little difference between the large N (fixed τ) and small N (exponentially-distributed τ) curves, unless the minimum number of demes is very small. B. By fitting a straight line of gradient −1 to the curves shown, we calculate that the trait can be maintained with 100 demes so long as $\overline{\tau }$ > 1.3/θ for exponentially distributed τ or $\overline{\tau }$ > 1/θ for fixed τ. The simulation results in part A suggest that the true cutoff for exponentially distributed τ may also be closer to $\overline{\tau }$ > 1.3/θ, so this conservative criterion is used throughout. This criterion is fairly insensitive to the precise number of demes: for example, for 50 demes, the criterion for exponentially-distributed τ is $\overline{\tau }$ > 1.5/θ.