Metapopulation viability analysis for amphibians


David Marsh, Department of Biology, Washington and Lee University, Lexington, VA 24450, USA.

A landscape-scale approach is critical for the conservation of pond-breeding amphibians. Individual demes at one or a few closely linked breeding sites are highly susceptible to local extinction. Recruitment in pond-breeding amphibians is often sensitive to hydroperiod and predation, and these factors can fluctuate greatly from year-to-year (Semlitsch et al., 1996). As a result, pond-breeding amphibians are subject to a high degree of stochasticity in population size, which can endanger these populations even in the absence of environmental stressors. Over somewhat longer time scales, many amphibian populations will decline due to succession within pond communities or in surrounding terrestrial habitats (Semlitsch, 2002; Skelly et al., 2005). And over even longer periods, ponds may gradually fill and be replaced by new ponds elsewhere in the landscape (Sjögren-Gulve, 1994). Together, all these factors virtually ensure that a single breeding site, or a group of closely linked sites, will not be sufficient for the long-term persistence of amphibians.

Approaches to amphibian conservation and management therefore need to focus on population viability at the landscape scale. Indeed, many of the most common strategies for protecting amphibian species are aimed at the metapopulation level. One example is the creation of new breeding ponds, either to mitigate the loss of wetlands to development or to expand the amount of available habitat. Amphibians may readily colonize these new sites from existing ponds, as long as the new sites are not too isolated (Lehtinen & Galatowitsch, 2001; Pechmann et al., 2001). A related strategy is to restore existing ponds by improving habitat quality or by removing introduced predators. In some cases, habitat improvement has resulted in surprisingly rapid recolonization of amphibians from surrounding ponds (Vredenburg, 2004). Lastly, reintroduction of amphibians to breeding sites can be viewed as a metapopulation-based approach, because it acts primarily to increase colonize rates and occupancy across the landscape (e.g. Muths, Johnson & Corn, 2001; Kinne, 2006).

The challenge, of course, is to know which of these approaches will be most effective for amphibian conservation. Creating new wetlands can be very costly and is still more of an art than a science. Removing introduced predators is also extremely difficult, as a few escapees can quickly reproduce to saturate a pond. Reintroduction is usually a less expensive way to enhance occupancy, but it carries a risk of spreading pathogens around the landscape (Seigel & Dodd, 2002). Thus, conservation planners need to be able to make predictions about the most productive strategies – they cannot simply try lots of different approaches and see what works.

The principal approach to making these predictions is metapopulation viability analysis (MPVA). The basic idea of MPVA is to use data on patterns of occurrence or turnover to parameterize a model for metapopulation dynamics. The model can then be projected forward under a variety of scenarios to determine which conservation strategies will lead to the most desirable outcome. One version of MPVA uses a statistical model, usually logistic regression, to examine the local and landscape predictors of extinction and colonization. Sjögren-Gulve & Ray (1996) used this approach with pool frogs in Sweden and determined that whereas the existing intensity of forestry would not threaten pool frogs, high-intensity forestry could disrupt migration among breeding sites and lead to metapopulation extinction. Another version of MPVA creates a demographic model for each breeding site, and then links these models by dispersal. Hels & Nachman (2002) used this approach to examine the viability of a spadefoot toad metapopulation and found that source–sink dynamics were fundamental to persistence. The third common version of MPVA uses an incidence function model (IFM) instead of logistic regression (Hanski, 1994). The IFM approach has been used on a variety of taxa, including butterflies, birds and mammals, but only rarely with amphibians (Vos, ter Braak & Nieuwenhuizen, 2000; Ter Braak & Etienne, 2003). It is this approach that is taken by Gilioli et al. (2008).

The principal advantages of the IFM approach are (1) that it requires only a single snapshot of occupancy data across the landscape and (2) that it parameterizes a biological model, rather than purely statistical one. On the other hand, the IFM approach also has some downsides. For one, it assumes quasi-stationarity in order to estimate parameters, so one can question its use for conservation planning when species might be declining (Etienne, ter Braak & Vos, 2004). Second, some parameters in the model are generally difficult to fit, most notably migration rate, a parameter for which Gilioli et al. have to rely on expert opinion rather than data from their study area. Third, as a biological model, the functional form of the IFM is less flexible than is logistic regression. For amphibians, the main problem with this lack of flexibility concerns the way that IFMs treat habitat area. In IFMs, habitat area is directly related to the extinction rate because area is assumed to scale with population size (Hanski, 1994). Additionally, the model establishes a minimum area requirement, below which the extinction rate is equal to one.

These assumptions are probably reasonable for habitat specialists like some butterflies and forest birds, but they make somewhat less sense for pond-breeding amphibians. In my experience, the importance of a breeding site for amphibians is rarely related to area in any obvious way. If anything, amphibians may prefer medium-sized ponds that reflect a trade-off between competition, predation risk and optimal hydrology. Very large ponds are often occupied but have reduced breeding populations, whereas some species (many Bufonids for example) seem to prefer smaller breeding sites. Gilioli et al. (2008) appear to have run into this problem, with area-related parameters in their IFM yielding flat likelihood surfaces. Although it is commendable that they conduct a sensitivity analysis for these parameters, one might have some concern about predictions from a model that is a poor match for the species of interest. Others using IFMs with amphibians have made an attempt to incorporate terrestrial habitat features (Vos et al., 2000) or aquatic habitat quality (Ter Braak & Etienne, 2003) into their models.

In any case, Gilioli et al. (2008) suggest that their major advance is not the use of the IFM per se, but their calculation of a Kullback–Leibler (K–L) divergence to evaluate how far away each conservation option is from the complete extinction of the metapopulation. This does appear to be a novel contribution and is certainly an interesting one. My understanding of the advantages of this approach is that it is computationally easier than calculating a probability of extinction by stochastic simulation and that it may require fewer assumptions.

I did have a few concerns, though. One is whether distance to complete extinction in probability space is really the appropriate metric. If I understand their method correctly [(i.e. equation (2)], ponds that have high incidence probabilities because they are situated close to source ponds would contribute to high K–L values even if they matter little for metapopulation persistence. This is in contrast to Hanski's ‘metapopulation capacity’ concept (Hanski & Ovaskainen, 2000) which can similarly be used to rank landscapes for conservation but which evaluates persistence in the context of a metapopulation model. Stochastic simulation approaches can take even more varied dynamics into account, including extinction and colonization rates that vary in space or time (Etienne et al., 2004). The point here is that a variety of processes might contribute to metapopulation extinction, but a K–L divergence measure does not appear to reflect these. Perhaps I have missed something; I would certainly be interested to hear the authors comment on when one should choose their method over these other approaches.

My second concern is how useful the K–L divergence would be for real-world conservation. While using simulation to arrive at a probability of extinction does require a number of assumptions, the resulting probabilities are quite simple to explain to conservation planners and government officials. One can intuitively assess whether a difference of 5 or 40% in extinction probability is meaningful over a given time horizon, and posterior probabilities of extinction (Ter Braak & Etienne, 2003) can even be incorporated into a framework that considers parameter uncertainty and management costs. However, I don't think I would want to have to explain to a policy-maker that an expensive approach to conservation should be undertaken because the resulting K–L divergence is 3 or 4 or 17 points higher than some more inexpensive option. This is not to criticize the underlying logic, just to point out that intuitive metrics do have some intrinsic advantages for real-world conservation.