Correlated extinction in a Leadbeater's possum metapopulation
Michael A. McCarthy & David B. Lindenmayer
Centre for Resource and Environmental Studies, The Australian National University, Canberra ACT 0200, Australia
A poster presented at the 82nd Annual Meeting of the Ecological Society of America, Albuquerque, New Mexico, 10-14 August 1997. An error in the original poster (Fig. 6b) has been corrected in this version.
1. Introduction
Previous models of metapopulation viability have either ignored correlated extinction of patches, or have included uniform correlations, with the correlation between nearby patches being the same as the correlation between distant patches (Lindenmayer et al. 1995). The importance of considering spatially-correlated extinction in metapopulation viability analyses was assessed using a model of the population dynamics of Leadbeater's possum (Gymnobelideus leadbeateri), an endangered species inhabiting montane forests in south-eastern Australia.
2. The model
The model of Leadbeater's possum metapopulation dynamics was based on that of Lindenmayer & Possingham (1995). Potential possum habitat was represented in the model by 27 patches of old growth forest distributed within the Ada Forest Block, a 5500 ha area of forest dominated by mountain ash stands (Figs 1 & 2). Younger forest within the Ada Forest Block was not included in the model because areas outside the reserved old growth patches are logged on a rotation (50-80 years) that precludes the development of suitable habitat for Leadbeater's possum. Leadbeater's possum requires a combination of many hollow-bearing trees for reproduction and shelter, and a dense understorey of Acacia species for foraging (Lindenmayer et al. 1991).
Fig. 1. The location of the Ada Forest Block in the Central Highlands of Victoria, south-eastern Australia.
Fig. 2. Schematic representation of old growth forest patches in the Ada Forest Block.
The model simulated Leadbeater's possum population dynamics by randomly determining survival and reproduction of individuals. The dynamics of the metapopulation was driven by the incidence of fire in habitat patches. Fire caused the local extinction of Leadbeater's possum and modified habitat suitability, which influenced the level of reproduction in each patch (Lindenmayer & Possingham 1995).
2.1. Homogenous patches
Both spatially-correlated fires, in which the correlation between the incidence of fire declined with distance, and uniformly-correlated fires were simulated. Initially, it was assumed that a patch was affected homogeneously when a fire occurred. Spatially-correlated fires were modeled by specifiying the correlation between the incidence of fire at any two points and the distance between them. This component of the model was parameterised on the basis of a fire that occurred in the Ada Forest Block in 1983 (Fig. 3). Spatially- correlated fires were simulated by generating correlated Bernoulli random numbers (Emrich & Piedmonte 1991, McCarthy & Lindenmayer in press).
Fig. 3. Correlation between the incidence of the 1983 fire in mountain ash forest of the Ada Forest Block as a function of distance between two points. The fitted line was used in the simulations, and the dotted lines were extremes used in sensitivity analysis.
The method of Lindenmayer & Possingham (1995) was used to simulate uniformly-correlated fires. Risky fire years occurred with a specified probability (y), and in these years the risk of a patch burning was equal to a. Fires did not occur in other years. The correlation between the incidence of fire for all pairs of patches was equal to a(1-y)/(1-ay), which varied between zero (y=1) and one (a=1).
2.2. Heterogeneous patches
The above methods account for correlation in the incidence of fire betweenpairs of patches, but it assumes that patches are entirely burnt when there is a fire (i.e. the incidence of fire within patches is perfectly correlated). Such homogeneity may be reasonable for small patches, but the chance that a patch will be only partly burnt is likely to increase with patch size. Heterogeneity within patches was accounted for by representing each patch as an aggregation of 1-ha cells. Cells were exposed to spatially-correlated fires, with cells close together being more likely to burn in the same year than cells far apart (Fig. 3).
2.3. Simulation
The risk of extinction of Leadbeater's possum within the old growth patches of the Ada Forest Block was predicted by 1000 random iterations of the model. The risk of extinction was equal to the proportion of times that the metapopulation went extinct within 100 years.
The strength of spatial correlation was submitted to sensitivity analysis by halving and doubling the linear extent of the correlation function (Fig. 3). The faster the correlation function approaches zero, the weaker the strength of the spatial correlation.
For simulating uniformly-correlated patches, three different values for the annual probability of fire (y) were used: 0.02, 0.1, and 1.0. These values correspond to fires being able to occur on average every 50 years, every 10 years, or annually. The probability of a patch burning given that fires could occur in that year (a) was set to give an average fire interval of 75, 100 or 200 years within each patch.
Correlation between the incidence of fire in patches did not influence the average number of fires each year, but the variance in the number of fires each year increased with the strength of correlation. This variance was recorded during the simulations to summarise the influence of correlation on the incidence of fires.
The average between patch migration distance of Leadbeater's possum is uncertain. We assumed a value of 2 km as used by Lindemayer & Possingham (1995), and conducted a sensitivity analysis by varying the mean migration distance between 0.5 km and 8 km.
3. Results
The predicted risk of extinction increased as the variance in the number of fires each year increased (Fig. 4), as the mean fire interval decreased (Fig. 5), and as the mean migration distance decreased (Fig. 4, 5 & 6). Spatial correlation in the incidence of fires between patches had no discernible effect on the results, provided that the variance in the number of fires each year was the same (Fig. 4). However, incorporating spatial correlation in the incidence of fire within patches, which allowed partial burning of patches, reduced the predicted risk of extinction, but only slightly (Fig. 6).
Fig. 4. The risk of extinction of Leadbeater's possum versus the variance in the number of fires per year for three different mean migration distances: 0.5 km green; 2.0 km pink; and 8.0 km orange. Circles represent uniformly-correlated fires, and triangles represent spatially-correlated fires. The mean fire interval was 100 years.
Fig. 5. The risk of extinction of Leadbeater's possum versus the mean fire interval for three different mean migration distances: 0.5 km, green diamonds; 2.0 km, pink circles; and 8.0 km, orange triangles. Fires were spatially-correlated and patches burnt completely.
Fig. 6. The risk of extinction of Leadbeater's possum versus the mean migration distance under the influence of spatially-correlated fires with a 100-year mean interval. Cases where patches were a) entirely burnt, and b) potentially partially burnt are compared for different strengths of spatial correlation (Fig. 3).
References
Emrich & Piedmonte (1991) A method for generating high-dimensional multivariate binary variables. Am. Stat. 45: 302-304.
Lindenmayer, Cunningham, Tanton, Nix & Smith (1991) The conservation of arboreal marsupials in the montane forests of the Central Highlands of Victoria, south-east Australia. III. The habitat requirements of Leadbeater's possum, Gymnobelideus leadbeateri and models of the diversity and abundance of arboreal marsupials. Biol. Cons. 56: 295-315.
Lindenmayer & Possingham (1995) The risk of extinction: ranking management options for Leadbeater's possum using populatioun viability analysis, ANU, Australia.
Lindenmayer, Burgman, Akcakaya, Lacy & Possingham (1995) A review of the generic computer programs ALEX, RAMAS/space and VORTEX for modelling the viability of wildlife metapopulations. Ecol. Mod. 82: 161-174.
McCarthy & Lindenmayer (in press) Multi-aged mountain ash forest, wildlife conservation and timber harvesting. For. Ecol. Manage.
Return to my home page...
Last updated 28 October 1997