Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

Stochastic differential equations and diffusion processes

River rehabilitation for the delivery of multiple ecosystem services at the river network scale.

The development of catchment-scale stream rehabilitation programmes in many parts of the world marks a shift from the application of reach-based engineering principles towards an adoption of ecosystem-centred, adaptive and participatory approaches to river management. From a biophysical viewpoint, this represents recognition of the importance of the inherent geodiversity of aquatic ecosystems and the benefits that are gained through enhancing natural recovery mechanisms. As this approach to river management matures, it is important that its key elements and assumptions are subjected to critical appraisal. In this paper, the main features of contemporary catchment-wide programmes are examined through a review of pertinent literature and through examination of various case studies from North America, Europe, Asia and Australia. Emerging challenges and tensions include those of generating an authentic and functional biophysical vision at the catchment scale, of developing a proactive adaptive management approach, of achieving genuine community participation and of integrating biophysical and social factors in a transdisciplinary framework. Issues of scale, natural variability and complexity must be addressed in meeting these challenges.

A critical review of catchment-scale stream rehabilitation programmes

Understanding the mechanisms that maintain diversity is important for managing ecosystems for species persistence. Here we used a long-term data set to understand mechanisms of coexistence at the local and regional scales in the Cape Floristic Region, a global hotspot of plant diversity. We used a dataset comprising 81 monitoring sites, sampled in 1966 and again in 1996, and containing 422 species for which growth form, regeneration mode, dispersal distance and abundances at both the local (site) and meta-community scales are known. We found that species presence and abundance were stable at the meta-community scale over the 30 year period but highly unstable at the local scale, and were not influenced by species' biological attributes. Moreover, rare species were no more likely to go extinct at the local scale than common species, and that alpha diversity in local communities was strongly influenced by habitat. We conclude that stochastic environmental fluctuations associated with recurrent fire buffer populations from extinction, thereby ensuring stable coexistence at the meta-community scale by creating a “neutral-like” pattern maintained by niche-differentiation.

/pdf/stochastic-species-turnover-and-stable-coexistence-in-a-2n5saayyti.pdf

Stochastic species turnover and stable coexistence in a species-rich, fire-prone plant community.

Humans have altered the environment so severely that extinction events are now occurring at rates unprecedented in modern history. In order to slow this trend, conservation actions must be taken to protect biodiversity, beyond just saving flagship species. Some governmental and conservation organizations have responded by committing to ecosystem conservation but, as yet, there is no coherent strategy for how this can be carried out. This report introduces many of the theoretical aspects that will need to be considered for the development of a coherent ecosystem conservation policy. The approach includes analyzing a hierarchy of interaction-based local coexistence mechanisms within a regional and historical context. This approach points toward the need for prioritizing sensitive habitats using local interaction models; considering the effects of historical exploitation mechanisms, which are now often missing; and evaluating regional diversity influences further to identify circumstances where system-wide habitat improvements deserve more emphasis.

Towards a theoretical basis for ecosystem conservation

We introduce an interacting particle system of vegetation dynamics and show its convergence towards a generalized, spatially extended Staver-Levin model in an appropriate scaling limit. The proof of convergence relies on coupling techniques for stochastic jump processes, and allows the derivation of limiting dynamics for macro-scale (finite patch locations) and mesoscale (continuous vegetation cover) models. The limiting equations are McKean-Vlasov jump processes - processes solving stochastic differential equations with self-consistent jump rates depending on the law of the solution. The generalized Kolmogorov equations of these processes in a macroscopic setting with one patch are precisely the classical Staver-Levin model, and, in spatial settings, the Kolmogorov equations constitute a nonlocal integro-differential extension of the classical model. These results have a number of theoretical and ecological consequences. In particular, our models provide an elementary example of jump processes that do not converge to a stationary distribution but rather oscillate in law. The mesoscale particle system can incorporate environmental heterogeneity, allowing us to exhibit solutions presenting waves of invasion and front pinning. Remarkably, the dynamical behavior of the particle systems finely recovers the bifurcation structure of the mean-field limit. To understand this consistency, despite almost-sure absorption in finite-size particle systems, we computed the quasi-stationary distribution (QSD) and derived the absorption probability as a function of parameters. The QSD matches the bifurcation diagram of the corresponding ODE closely and is especially relevant for the system dynamics since the absorption probability drops sharply to zero as nontrivial equilibria emerge in the corresponding ODE.

Probabilistic Foundations of the Staver-Levin Model

/pdf/supporting-online-material-for-uninformed-individuals-374cnc3bhj.pdf

Supporting Online Material for Uninformed Individuals Promote Democratic Consensus in Animal Groups

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Towards a theoretical basis for ecosystem conservation

Probabilistic Foundations of the Staver-Levin Model

Supporting Online Material for Uninformed Individuals Promote Democratic Consensus in Animal Groups