A sampling theory for dispersal-limited, niche-structured communities

We introduce the first analytical model of a dispersal-limited, niche-structured community to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Dynamics of the multivariate species abundance distribution (SAD) for an asymmetric local community are modeled explicitly as a dispersal-limited sampling of the surrounding metacommunity. Coexistence may arise either from approximate functional equivalence or a competition-colonization tradeoff. At equilibrium, these symmetric and asymmetric mechanisms both generate unimodal SADs. Multiple modes only arise in asymmetric communities and provide a strong indication of non-neutral dynamics. Although these stationary distributions must be calculated numerically in the general theory, we derive the first analytical sampling distribution for a nearly neutral community where symmetry is broken by a single species distinct in ecological fitness and dispersal ability. Novel asymptotic expansions of hypergeometric functions are developed to make evaluations of this distribution tractable for large communities

Trophic interactions and range limits: the diverse roles of predation

Interactions between natural enemies and their victims are a pervasive feature of the natural world. In this paper, we discuss trophic interactions as determinants of geographic range limits. Predators can directly limit ranges, or do so in conjunction with competition. Dispersal can at times permit a specialist predator to constrain the distribution of its prey—and thus itself—along a gradient. Conversely, we suggest that predators can also at times permit prey to have larger ranges than would be seen without predation. We discuss several ecological and evolutionary mechanisms that can lead to this counter-intuitive outcome

Scale Invariance and Universality: Organizing Principles in Complex Systems

This paper is a brief summary of a talk that was designed to address the question of whether two of the pillars of the #eld of phase transitions and critical phenomena -- scale invariance and universality -- can be useful in guiding research on a broad class of complex phenomena. We shall see that while scale invariance has been tested for many years, universality is relatively more rarely discussed. In particular, we shall develop a heuristic argument that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena, and suggest that this argument could be developed into a possible coherent approach to understanding the ubiquity of scale invariance and universality in a wide range of complex systems. c 2000 Elsevier Science B.V. All rights reserved