Spatial Scaling in Model Plant Communities

We present an analytically tractable variant of the voter model that provides a quantitatively accurate description of beta-diversity (two-point correlation function) in two tropical forests. The model exhibits novel scaling behavior that leads to links between ecological measures such as relative species abundance and the species area relationship.Comment: 10 pages, 3 figure

Integrating Species Traits into Species Pools

Despite decades of research on the species‐pool concept and the recent explosion of interest in trait‐based frameworks in ecology and biogeography, surprisingly little is known about how spatial and temporal changes in species‐pool functional diversity (SPFD) influence biodiversity and the processes underlying community assembly. Current trait‐based frameworks focus primarily on community assembly from a static regional species pool, without considering how spatial or temporal variation in SPFD alters the relative importance of deterministic and stochastic assembly processes. Likewise, species‐pool concepts primarily focus on how the number of species in the species pool influences local biodiversity. However, species pools with similar richness can vary substantially in functional‐trait diversity, which can strongly influence community assembly and biodiversity responses to environmental change. Here, we integrate recent advances in community ecology, trait‐based ecology, and biogeography to provide a more comprehensive framework that explicitly considers how variation in SPFD, among regions and within regions through time, influences the relative importance of community assembly processes and patterns of biodiversity. First, we provide a brief overview of the primary ecological and evolutionary processes that create differences in SPFD among regions and within regions through time. We then illustrate how SPFD may influence fundamental processes of local community assembly (dispersal, ecological drift, niche selection). Higher SPFD may increase the relative importance of deterministic community assembly when greater functional diversity in the species pool increases niche selection across environmental gradients. In contrast, lower SPFD may increase the relative importance of stochastic community assembly when high functional redundancy in the species pool increases the influence of dispersal history or ecological drift. Next, we outline experimental and observational approaches for testing the influence of SPFD on assembly processes and biodiversity. Finally, we highlight applications of this framework for restoration and conservation. This species‐pool functional diversity framework has the potential to advance our understanding of how local‐ and regional‐scale processes jointly influence patterns of biodiversity across biogeographic regions, changes in biodiversity within regions over time, and restoration outcomes and conservation efforts in ecosystems altered by environmental change

Random copying in space

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations" at UCL, September 2010. To appear in ACS - Advances in Complex System

Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection

The process of `Evolutionary Diffusion', i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of local peaks with a characteristic width that undergo drift, even in the infinite population limit. We analytically calculate the mean peak width and the effective random walk step size, and obtain the distribution of the peak width which has a power law tail. We find that independent local mutations act as a diffusion of interacting particles with increased stepsize.Comment: 4 pages, 2 figures. Paper now representative of published articl

Biology is simple

This paper explores the potential for simplicity to reveal new biological understanding. Borrowing selectively from physics thinking, and contrasting with Crick's reductionist philosophy, the author argues that greater emphasis on simplicity is necessary to advance biology and its applications.</p

Non-neutral theory of biodiversity

We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems in presence of migration. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two extreme limits either as the unified neutral theory of biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a condensation phase transition where one species becomes the dominant one, the diversity in the ecosystems is strongly reduced and the ecosystem is non-stationary. This phase transition extend the principle of competitive exclusion to open ecosystems and might be relevant for the study of the impact of invasive species in native ecologies.Comment: 4 pages, 3 figur

Fixation and consensus times on a network: a unified approach

We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure.Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted by Phys. Rev. Let

The edge of neutral evolution in social dilemmas

The functioning of animal as well as human societies fundamentally relies on cooperation. Yet, defection is often favorable for the selfish individual, and social dilemmas arise. Selection by individuals' fitness, usually the basic driving force of evolution, quickly eliminates cooperators. However, evolution is also governed by fluctuations that can be of greater importance than fitness differences, and can render evolution effectively neutral. Here, we investigate the effects of selection versus fluctuations in social dilemmas. By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging 'edge of neutral evolution' that delineates regimes of neutral and Darwinian evolution. Our results reveal that cooperation is significantly maintained in the neutral regimes. In contrast, the classical predictions of evolutionary game theory, where defectors beat cooperators, are recovered in the Darwinian regimes. Our studies demonstrate that fluctuations can provide a surprisingly simple way to partly resolve social dilemmas. Our methods are generally applicable to estimate the role of random drift in evolutionary dynamics.Comment: 17 pages, 4 figure

Radiative and Auger decay data for modelling nickel K lines

Radiative and Auger decay data have been calculated for modelling the K lines in ions of the nickel isonuclear sequence, from Ni$^+$ up to Ni$^{27+}$. Level energies, transition wavelengths, radiative transition probabilities, and radiative and Auger widths have been determined using Cowan's Hartree--Fock with Relativistic corrections (HFR) method. Auger widths for the third-row ions (Ni$^+$--Ni$^{10+}$) have been computed using single-configuration average (SCA) compact formulae. Results are compared with data sets computed with the AUTOSTRUCTURE and MCDF atomic structure codes and with available experimental and theoretical values, mainly in highly ionized ions and in the solid state.Comment: submitted to ApJS. 42 pages. 12 figure

Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units