Animal Modeling

C. R. Allen¹, K. Simpson², and A. R. Johnson² 

¹South Carolina Cooperative Fish and Wildlife Research Unit, Department of Aquaculture, Fisheries and Wildlife, Clemson University, Clemson, South Carolina

²Department of Environmental Toxicology, Clemson University, Clemson, South Carolina

Introduction

High resolution maps of broad extent, such as those generated for gap analyses (Scott et al. 1993), create new problems in species mapping, especially by potentially inflating errors of commission―the chance of erroneously including the presence of a species in a habitat where it is absent.  On high-resolution maps, commission errors are likely to be high when creating species models based simply on species-habitat associations.  A habitat patch as small as 30 m² (though in practice GAP maps have a much larger MMU) may be identified as a discrete unit.  However, a discrete 30 m² patch (or one much larger) in isolation will not support an individual of many vertebrate species, and even considerably larger patches will not support viable populations of most vertebrates (Allen et al. 2001).

Protecting biodiversity requires sustaining populations of species into the foreseeable future.  Protecting species requires sufficient habitat to support a minimum viable population (MVP) over time.  Incorporating information on the spatial use of habitat by species should increase the accuracy of species models by reducing the commission error rates.  Information on the home range and dispersal distances of mammals has been incorporated to estimate minimum critical areas (MCA) to support MVPs for each mammal species in Florida (Allen et al. 2001).  However, while those models were an improvement, better models are attainable.  Patches of suitable habitat too small to support a MVP may still be occupied if multiple patches within the species’ dispersal capabilities form a network that, in aggregate, is large enough to support a viable population.  These patches may be considered “functionally connected.”  Here we describe our ongoing efforts to refine GAP vertebrate models by incorporating MCA methods across multiple patches and functional connectivity. 

Methodological and Conceptual Framework

Although the habitat of a species may be fragmented, linkages between local populations may maintain a functional connection across the landscape if individuals are sufficiently able to disperse among patches.  Keitt et al. (1997) introduced a computational procedure to evaluate the functional connectivity of a network of patches relative to the dispersal capabilities of the organism.  They applied their methodology to evaluating functional connectivity of habitat patches for the Mexican Spotted Owl (Strix occidentalis lucida).  They used “correlation length,” a measure of connectivity inspired by percolation theory.  They demonstrated that connectivity jumps abruptly as the dispersal ability of the organism crosses a critical threshold, and that certain patches play a disproportionately large role in maintaining connectivity, and thus population viability.  This measure of connectivity can be applied if we have an estimate of dispersal ability for the species.  For mammals, such estimates are generally available (e.g., Allen et al. 2001).  For species for which estimates are not available, Sutherland et al. (2000) have derived a series of allometric relationships for predicting natal dispersal distances of birds and mammals based on body size.  It may not be able to assess functional connectivity for many reptile and amphibian species because of the limited number of studies of home range and dispersal for these species.

Although there has been discussion in the scientific literature devoted to the problem of determining minimum viable population numbers for species, the determination of a “viable” population size is still wrought with uncertainty.  Franklin (1980) stated that determining effective population size (N_e; the number of individuals in a population breeding and contributing to the gene pool) is paramount, not the census population size (i.e., all individuals in a population).  However, determination of effective versus census population size is difficult.  Allen et al. (2001) used an estimated minimum population size of 50, the estimated size necessary to avoid extinction due to demographic stochasticity.  However, to avoid the loss of genetic heterozygosity resulting from inbreeding and genetic drift, MVP size may be in the order of 500 individuals (Franklin 1980, Soulé 1980).  Our interest in incorporating measures of MCA and functional connectivity into GAP models is not to determine the true viable population size, but to decrease commission errors in our models and produce models that are more accurate and biologically defensible.  Our current modeling efforts in South Carolina will utilize MVP estimates of both 50 and 500. 

Determining Minimum Critical Area - Minimum critical area is determined based on species home range size estimates from peer-reviewed literature, using the following simple equation:

MCA = [(home range area)N_e]

2

where “2” accounts for intersexual overlap of socially interactive species (e.g., most mammals) and N_e is either 50 or 500 (Allen et al. 2001).

Determining Dispersal Distances - Dispersal distances for many species are available in peer-reviewed literature.  Where there is no value available, published allometric equations based on trophic level and body mass are available (Sutherland et al. 2000).

Building Models Incorporating MCA and Functional Connectivity - For each species, patches of suitable habitat too small to support viable populations are eliminated by selecting only those patches > MCA.  Those methods are described in Allen et al. (2001).  Dispersal is incorporated in two ways (Figure 1).  First, patches ³ MCA are buffered by species dispersal distance, and those patches < MCA but within a species dispersal range from a large patch are included as occupied habitat.  Second, a buffer equivalent to the dispersal distance for a species is applied to all patches.  Networks of patches that are individually < MCA but in aggregate ³ MCA and connected by dispersal are also included as occupied habitat.

Figure 1.  Illustration of minimum critical area and functional connectivity for the eastern harvest mouse in South Carolina.  Patches too small to support a MVP in isolation may in aggregate support a MVP, if functionally connected. 

Population Viability Analyses and Risk- For selected species at risk of extinction or local extirpation, where demographic parameters are available from previous studies, it is possible to incorporate population viability analyses (PVA) as part of the Gap Analysis process.  Population viability analyses are particularly relevant to populations in fragmented habitat, where loss of functional connectivity may have serious consequences for population viability.  Viability may be assessed by running metapopulation models utilizing current distributions of the target species.  Simulations may be conducted using RAMAS/GIS modeling software (Akçakaya 1998).  A stage-classified population growth model can be used to project population dynamics, with demographic parameters derived from the literature (if possible) or expert judgment.  Dispersal between patches can be modeled as an exponentially declining function of distance up to a maximal cutoff.  Risk is expressed as the probability of local extinction for each habitat patch based on Monte Carlo simulations (e.g., many iterations as run in RAMAS/GIS) of metapopulation dynamics.  The Monte Carlo approach allows uncertainties to be propagated through the model so as to produce a distribution of risk estimates.

Identification of Critical Patches - Some patches are disproportionately important in maintaining functional connectivity within networks of patches (Keitt et al. 1997) or between large blocks of habitat.  Identification of these patches is important for biological conservation, as they are necessary to maintain connectivity within a landscape.  Note that the identification of these critical patches depends upon the species of interest, its scale of environmental use, and in particular its dispersal capabilities.  Figure 2 illustrates the concept of functionally important patches in two contexts. 

Figure 2.  The identification of functionally critical patches.  Animal dispersal between preferred habitat patches is shown by double-ended arrows.  The smaller circles represent a number of “small” patches (i.e., area less than MCA value) which, on their own, cannot support a MVP but in aggregate form a functionally connected cluster that adds up to meet or exceed MCA requirements.  These clusters, along with the “large” patch (i.e., area greater than or equal to MCA value) may be functionally connected to each other by one or more small patches.  These small patches are of interest because they are important for maintaining connectivity and thus genetic flow and variation; loss of such patches may be detrimental to the (meta)population as a whole.  For rare species, identifying these patches may be crucial in order for conservation efforts to be effective.

Preliminary Results

We ran models incorporating minimal critical areas and functional connectivity for a taxonomic and geographic subset of South Carolina (ten mammals in Oconee, Pickens, and Greenville counties: star-nosed mole Condylura cristata, black bear Ursus americanus, eastern cottontail Sylvilagus floridanus, grey squirrel Sciurus carolinensis, bobcat Felis rufus, grey fox Urocyon cinereoargenteus, eastern harvest mouse Reithrodontomys humulis, mink Mustela vison, white-tailed deer Odocoileus virginianus, and Eastern wood rat Neotoma floridana). 

Our results indicate that minimum patch size models generally decrease the area modeled as occupied by a species (Table 1, MCA area).  Minimum patch size models coupled with functional connectivity considerations may increase the area modeled as occupied compared to models with minimum patch size criteria only.  For species with long-range dispersal capabilities, simple GAP habitat affinity models and models with minimum critical area and functional connectivity may be identical (Table 1, Total functional area).  However, for species with limited dispersal capabilities, GAP models overestimate occupied area, presumably leading to increased commission error rates (Table 1, Eastern harvest mouse, Star-nosed mole).  These methods may be most useful for medium-sized mammals; large mammals have long dispersal capabilities, and entire landscapes may be functionally connected for such species, and small mammals may have such limited dispersal capabilities that few patches are connected.  However, patchiness not only depends upon the organism in question, but also the resolution of the mapping effort (i.e., land cover) and the natural scale of patchiness upon the landscape.

Discussion

Characterizing minimum critical areas in patch networks, functional connectivity across habitat patches, and metapopulation dynamics for key species will allow the identification of landscape patches key to the viability of target species, and thus the patches most critical for the conservation of viable populations.  That, in turn, provides the basis for exploring the consequences of landscape changes in terms of risk to species and overall biodiversity.

The methods we are developing may have general and specific utility and will demonstrate the usefulness of approaches that incorporate the consideration of minimum areas for viable populations and critical patches of habitat.  Our methodology to account for viable populations based on minimum critical areas and improved to include areas in networks of patches can be incorporated simply into all gap analyses.  Determination of functional connectivity and the identification of patches critical for maintaining functional connectivity will have more specific application in guiding and weighing land use and conservation decisions applied to particular patches.  We expect to conduct an accuracy assessment of a subset of the vertebrate models to compare standard GAP methods versus our methods incorporating MCA and patch networks. 

Literature Cited

Akçakaya, H.R.  1998.  RAMAS GIS: Linking landscape data with Population Viability Analysis (version 3.0).  Applied Biomathematics, Setauket, New York.

Allen, C.R., L.G. Pearlstine, and W.M. Kitchens.  2001.  Modeling viable mammal populations in gap analyses.  Biological Conservation 99:135-144.

Franklin, I.A.  1980.  Evolutionary change in small populations.  Pages 135-149 in M.E. Soulé and B.A. Wilcox, editors.  Conservation biology:  An evolutionary-ecological perspective.  Sinauer Associates, Sunderland, Massachussetts.

Keitt, T.H., D.L. Urban, and B.T. Milne.  1997.  Detecting critical scales in fragmented landscapes.  Conservation Ecology 1(1):4 [on-line] URL: http://www.consecol.org/vol1/iss1/art4.

Scott, J.M., F. Davis, B. Csuti, R. Noss, B. Butterfield, C. Groves, H. Anderson, S. Caicco, F. D’Erchia, T.C. Edwards, Jr., J. Ulliman, and R.G. Wright.  1993.  Gap Analysis:  A geographical approach to protection of biological diversity.  Wildlife Monograph 123.

Soulé, M.E.  1980.  Thresholds for survival: Maintaining fitness and evolutionary potential.  Pages 151-169 in M.E. Soulé and B.A. Wilcox, editors.  Conservation Biology:  An evolutionary-ecological perspective.  Sinauer Associates, Sunderland, Massachussetts.

Sutherland, G.D., A.S. Harestad, K. Price, and K.P. Lertzman.  2000.  Scaling of natal dispersal distances in terrestrial birds and mammals.  Conservation Ecology 4(1):16 [on-line] URL: http://www.consecol.org/vol4/iss1/art16.