Robustness analysis of communities of structured populations

Background/Question/Methods

We present a methodological framework for assessing the robustness of coexistence in communities of interacting structured populations. Community robustness in this context means the volume of parameter space allowing for stable coexistence. The framework receives a set of model equations, and in return yields specific measures of how sensitive each of the species’ abundances are to various perturbations of external parameters. This kind of framework has already been established in the context of equilibrium populations (Meszena et al 2006), and stationarily fluctuating ones (Barabas et al 2011). Both of these approaches consider unstructured populations only. Although Szilagyi and Meszena (2009) tried to extend these results to equilibrium structured populations, they only considered very special kinds of perturbations and so their approach is limited. Here we extend these results to arbitrary regions of parameter space. The emerging framework can be used to identify key types of species differences in a given model leading to robust coexistence, and reveals a certain mathematical unity between the three basic coexistence-enhancing mechanisms: functional, habitat, and temporal species segregation. Finally, we apply our approach to a specific model of seed size diversity, gaining insights into coexistence along a tradeoff between species’ fecundity and stress tolerance.

Results/Conclusions

In the unstructured framework, the two important quantities determining the robustness of coexistence both concerned the species’ relationship to the factors regulating their populations. The first is the sensitivity of the growth rate to a change in regulation (e.g. resource supply), the other is the impact of the population on the regulating factor. In the structured framework these two quantities are retained, albeit with certain modifications. The sensitivity is now weighted by both the stable stage structure and the reproductive value of the focal population, while the impact becomes the scalar product of the impacts of the individual stage classes and the stable stage structure vector. Applying these results to the tolerance-fecundity tradeoff model, valuable information can be gained on the coexistence of species without actually having to solve the model equations at all. In particular, a knowledge of the species’ tolerance functions, i.e. the dependence of their tolerance on stress level, is enough to assess the robustness of coexistence in this model.