Long-Distance Rescue and Slow Extinction Dynamics Govern Multiscale Metapopulations

The authors address the influence that within- and between-island colonization and island heterogeneity (size, in terms of number of patches) have on metapopulation dynamics.  A proposed model is presented which incorporates three different levels:

1. local populations that are either at demographic equilibrium that can become extinct with a specific population
2. islands which contain “submetapopulations” which rely on the balance of short distance colonization (c_in) and extinction
3. the regional set of islands described by a island size distribution where colonization between islands can occur (c_out)

It had been shown that local metapopulation extinction time strongly depend on the size of the island with smaller becoming extinct faster than larger islands.  The authors hypothesize that regions of islands with heterogenous sizes goes extinct slower than regions with homogenous ISD. They also expect that when long distance colonization is stronger (c_out is high), larger islands that survive can “rescue” smaller islands. Lastly, the authors describe the condition for which regions exhibit “quasistationary” persistence and slow extinction.

The model they used consisted of infinite islands with a finite set of population sites.  They were interested in the mean number of sites per island and the variance influence metapopulation dynamics.  The model describe the colonization and extinction dynamics of habitat sites.  The sites within an island create “submetapopulations” where within-island (short distance) colonization can occur.  These islands then form a region where between-island (long distance) colonization can occur.  For all simulation it was assumed that the short distance colonization rate was greater than the long distance (c_in >> c_out).

To begin, they assumed that long distance colonization cannot occur (c_out=0). That found that with homogenous ISD, larger island sizes result in slower extinction dynamics.  When the island size is larger than one habitat site, the occupancy to extinction is non-monotonic. When ISD is heterogenous, again, we see a decline to extinction however when compared to homogenous ISD these declines are much slower. The larger the variance of the ISD, the longer the extinction time.

When long distance colonization can occur, the metapopulation reaches a stable occupied frequency under most conditions.  When the ISD is homogenous, smaller long distance dispersals results in extinction equilibrium however larger results in stable, non-null equilibriums.  With heterogenous ISD, all metapopulations reach a non-null equilibrium occupancy.

Lastly, they show that increasing both short and long distance colonization can increase the proportion of sites occupied in the model.  However, for small values of short distance colonization, there exist critical values for long distance colonization for the metapopulation to have non-null equilibrium.

Huth, G., B. Haegeman, E. Pitard, and F. Munoz. 2015. Long-Distance Rescue and Slow Extinction Dynamics Govern Multiscale Metapopulations. American Naturalist 186:460–469.