Reading Group: Species-fragmented area relationship

leal1Species-area relationships (SARs) are perhaps the closest thing we have to a law of community ecology. Accordingly, they’ve received copious study over the last two decades, from theoretical development and formalisation, to parameterisation for natural systems and use in conservation planning.

Species-area relationships are often modelled with a power law function relating species richness to habitat area. One underlying theoretical idea is that SARs represent a relationship between habitat area and extinction risk for individual species: more habitat = lower extinction risk per species = more species. But what if habitat is fragmented? In human-dominated landscapes, for example, loss of habitat almost always entails habitat fragmentation, which should have important consequences for species-area relationships. Metapopulation and metacommunity theory says that it must, because habitat fragmentation increases extinction risk for species over-and-above the loss of habitat extent. As such, traditional species-area relationships might significantly overestimate species richness in fragmented landscapes.

In our most recent reading group, we looked at a potential solution to the overestimation problem published by Ilkka Hanski and colleagues in 2013. In one of his last major projects, Hanski produced a simple but elegant adjustment to the power law relationship between habitat area and species richness to account for the degree of habitat fragmentation. The adjustment is a multiplication of the traditional species-area relationship by the fraction of species that would persist for a given amount of habitat fragmentation, denoted P(λ), where λ is the ‘metapopulation capacity’ of the fragmented landscape (itself a function of patch areas, inter-patch distances and species’ dispersal capacities). Assuming a generic λ, Hanski et al. used the following form for estimating P(λ):

P(λ) = exp(-b/λ),

where b is a parameter to be estimated from species richness data among fragmented landscapes. This fraction can simply be multiplied by a standard SAR formulation to adjust it for fragmentation. In the example in the paper, the commonly used power law formulation: cAz (where A is the area, and c and z are parameters) is adjusted to yield an expected number of species: S = cAz exp(-b/λ). The fragmentation component could in theory be bolted on to other SAR formulations too.

Hanski et al. demonstrated that their simple formulation worked quite well for both simulated and real data, and we felt that its derivation from first principles is a major strength. Nevertheless, we wondered if some slight extensions could make the approach more flexible and powerful, and improve its application to real-world datasets.

Of course we hear you cry, λ requires knowledge of extinction and migration rates, how are you going to derive those extra parameters? Well, in the PNAS paper Hanski et al. argue and demonstrate that the assumption of similarity among species, meaning a single value for each of b and λ, has little effect on the overall model fit when the focus is taxonomically or ecologically related species (e.g., forest birds). We felt that further work in other empirical cases would be beneficial to validate this. And indeed, as another way of dealing with the parameterisation, we talked about how one might use a hierarchical model to estimate b from likely sparse observations across species in real-world datasets.

One of the drawbacks of the simple power law SAR is that the parameters don’t have a direct biological interpretation and must be estimated from species-area data for each context. This model can be used by ecologists to fit curves to their data, but not to predict the number of species in other ecosystems (though there are other SAR functional forms that are more interpretable). Whilst λ in the SFAR is deeply rooted in ecological theory, the paper doesn’t provide an ecological interpretation for the parameter b or for the functional form of P(λ). If we could interpret (or reformulate) P(λ), it could be bolted on to a more interpretable SAR model, and enable us to make and test real predictions about species counts in fragmented habitats.

Overall, we felt this study provides a solid first step for adjusting SARs for the near-universal issue of habitat fragmentation. Further empirical testing of the approach is fertile ground for future research, as is refinement of the approach to relax assumptions required in the estimation of b and P(λ), inject clarity as to their ecological interpretation and allow greater flexibility to tackle messy real world datasets.

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