Competition and Stragglers as Mediators of Developmental Synchrony in Periodical Cicadas.

Periodical cicadas are enigmatic organisms: broods spanning large spatial ranges consist of developmentally synchronized populations of 3-4 sympatric species that emerge as adults every 13 or 17 years. Only one brood typically occupies any single location, with well-defined boundaries separating distinct broods. The cause of such synchronous development remains uncertain, but it is known that synchronous emergence of large numbers of adults in a single year satiates predators, allowing a substantial fraction of emerging adults to survive long enough to reproduce. Competition among nymphs feeding on tree roots almost certainly plays a role in limiting populations. However, due to the difficulty of working with such long-lived subterranean life stages, the mechanisms governing competition in periodical cicadas have not been identified. A second process that may affect synchrony among periodical cicadas is their ability to delay or accelerate their emergence as adults by 1 year and accelerate it by 4 years (stragglers). We develop a nonlinear Leslie matrix-type model that describes cicada dynamics accounting for predation, competition, and stragglers. Using numerical simulations, we identify conditions that generate dynamics in which a single brood occupies a given geographical location. Our results show that while stragglers have the potential for introducing multiple sympatric broods, the interaction of interbrood competition with predation-driven Allee effects creates a system resistant to such invasions, and populations maintain developmental synchrony.

Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology.

Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees.

Emergent long-range synchronization of oscillating ecological populations without external forcing described by Ising universality.

Understanding the synchronization of oscillations across space is fundamentally important to many scientific disciplines. In ecology, long-range synchronization of oscillations in spatial populations may elevate extinction risk and signal an impending catastrophe. The prevailing assumption is that synchronization on distances longer than the dispersal scale can only be due to environmental correlation (the Moran effect). In contrast, we show how long-range synchronization can emerge over distances much longer than the length scales of either dispersal or environmental correlation. In particular, we demonstrate that the transition from incoherence to long-range synchronization of two-cycle oscillations in noisy spatial population models is described by the Ising universality class of statistical physics. This result shows, in contrast to all previous work, how the Ising critical transition can emerge directly from the dynamics of ecological populations.

Phylogenetic prediction of the maximum per capita rate of population growth.

The maximum per capita rate of population growth, r, is a central measure of population biology. However, researchers can only directly calculate r when adequate time series, life tables and similar datasets are available. We instead view r as an evolvable, synthetic life-history trait and use comparative phylogenetic approaches to predict r for poorly known species. Combining molecular phylogenies, life-history trait data and stochastic macroevolutionary models, we predicted r for mammals of the Caniformia and Cervidae. Cross-validation analyses demonstrated that, even with sparse life-history data, comparative methods estimated r well and outperformed models based on body mass. Values of r predicted via comparative methods were in strong rank agreement with observed values and reduced mean prediction errors by approximately 68 per cent compared with two null models. We demonstrate the utility of our method by estimating r for 102 extant species in these mammal groups with unknown life-history traits.

Multivariate Moran process with Lotka-Volterra phenomenology.

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology and, on the other, allows us to study Lotka-Volterra dynamics within the finite populations of a Moran process. Applications to community ecology, population genetics, and evolutionary game theory are discussed.

A sampling theory for asymmetric communities.

We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community dynamics, while an analogous extension of Hubbell's metacommunity dynamics is deferred to an appendix. We find that mass-effects may facilitate coexistence in asymmetric local communities and generate unimodal species abundance distributions indistinguishable from those of symmetric communities. Multiple modes, however, only arise from asymmetric processes and provide a strong indication of non-neutral dynamics. Although the exact stationary distributions of fully asymmetric communities must be calculated numerically, we derive approximate sampling distributions for the general case and for nearly neutral communities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability. In the latter case, our approximate distributions are fully normalized, and novel asymptotic expansions of the required hypergeometric functions are provided to make evaluations tractable for large communities. Employing these results in a bayesian analysis may provide a novel statistical test to assess the consistency of species abundance data with the neutral hypothesis.