Incorporating metapopulation dynamics of greater gliders into reserve design in disturbed landscapes

Sensitivity analysis

A sensitivity analysis was conducted to examine the effects of changes in the metapopulation model on the predicted risks of extinction. To reflect uncertainty about the average fire interval in mountain ash forests, the mean interval was varied between 75 yr and 200 yr. Similarly, the effect of spatial correlation was examined by doubling and halving the lineal extent of the correlation function (the dotted lines in [ILLUSTRATION FOR FIGURE 1 OMITTED]). This had the effect of changing the strength of the spatial correlation. Effects of uncertainty about the fecundity and survivorship of greater gliders on predicted risks of extinction were investigated by reducing these parameters to the point at which the deterministic growth rate under ideal conditions was equal to unity (Eq. 1). Risks also were determined for cases in which these life parameters were increased by the same amount. The predicted risk of extinction also was determined over a range of carrying capacities from 1.5 females/ha to 3.0 females/ha. Possingham et al. (1994) considered that 8 km would be the absolute upper bound for the dispersal capability of greater gliders. Given this, combined with the considerable uncertainty associated with appropriate data for migration, we completed sensitivity analyses using values for the mean migration distance ranging from 500 m to 8 km. The sensitivity analysis was conducted on the predicted risk of extinction in the Ada Forest Block and the predicted risk of extinction in a single patch. The results of these analyses were used to determine whether the optimum reserve configuration (the number of patches to minimize the risk of extinction within 300 and 1000 yr, and the number of patches to maximize the mean time to extinction) was sensitive to variation in the parameter values.

RESULTS

Extinction in a single patch

The probability of extinction of greater gliders within a single patch declined with patch size [ILLUSTRATION FOR FIGURE 2 OMITTED]. For smaller patches, the predicted risk of extinction was only marginally affected by whether patches were modeled as a single (homogeneous) entity or whether they were modeled as an aggregation of (heterogeneous) cells. However, the risk of extinction in large heterogeneous patches was less than the risk of extinction in homogeneous patches of the same size. As patch size increased, fluctuations in the age structure of heterogeneous patches decreased, lowering the risk of extinction. Fluctuations in age structure of the forest were maximized when patches were modeled as homogeneous areas, contributing to greater fluctuations in habitat quality [ILLUSTRATION FOR FIGURE 3 OMITTED]. Increasing the strength of spatial correlation (implying larger and/or more contiguous fires) would increase the risk of extinction, but this would not increase above the value predicted for the homogeneous case.

Lande's model

Log-linear regression relating patch size to the time to extinction illustrated a close correspondence with Lande's (1993) extinction model [ILLUSTRATION FOR FIGURE 4 OMITTED]. The mean number of years to extinction was approximated by