Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Number of Common Sites Visited by N Random Walkers

We compute analytically the mean number of common sites, W_N(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large t growth of W_N(t). These three regimes are separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane. For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the prefactor). For 2<d<d_c(N), W_N(t)\sim t^{\nu} where the exponent \nu= N-d(N-1)/2 varies with N and d. For d>d_c(N), W_N(t) approaches a constant as t\to \infty. Exactly at the critical dimensions there are logaritmic corrections: for d=2, we get W_N(t)\sim t/[\ln t]^N, while for d=d_c(N), W_N(t)\sim \ln t for large t. Our analytical predictions are verified in numerical simulations.Comment: 5 pages, 3 .eps figures include

The shape of ecological networks

We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. We treat them as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.Comment: 4 pages, 2 figure

Stochastic models in population biology and their deterministic analogs

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure

Unstable decay and state selection II

The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are occupied to be calculated by finding optimal paths, and fluctuations about them, in the weak noise limit. The method is illustrated on a system described by two coupled Langevin equations, which are found in the study of instabilities in fluid dynamics and superconductivity. The problem involves a subtle interplay between non-linearities and noise, and a naive approximation scheme which does not take this into account is shown to be unsatisfactory. The use of optimal paths is briefly reviewed and then applied to finding the conditional probability of ending up in one of the metastable states, having begun in the unstable state. There are several aspects of the calculation which distinguish it from most others involving optimal paths: (i) the paths do not begin and end on an attractor, and moreover, the final point is to a large extent arbitrary, (ii) the interplay between the fluctuations and the leading order contribution are at the heart of the method, and (iii) the final result involves quantities which are not exponentially small in the noise strength. This final result, which gives the probability of a particular state being selected in terms of the parameters of the dynamics, is remarkably simple and agrees well with the results of numerical simulations. The method should be applicable to similar problems in a number of other areas such as state selection in lasers, activationless chemical reactions and population dynamics in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.

The species diversity&nbsp;×&nbsp;fire severity relationship is hump-shaped in semiarid yellow pine and mixed conifer forests

The combination of direct human influences and the effects of climate change are resulting in altered ecological disturbance regimes, and this is especially the case for wildfires. Many regions that historically experienced low–moderate severity fire regimes are seeing increased area burned at high severity as a result of interactions between high fuel loads and climate warming with a number of negative ecological effects. While ecosystem impacts of altered fire regimes have been examined in the literature, little is known of the effects of changing fire regimes on forest understory plant diversity even though understory taxa comprise the vast majority of forest plant species and play vital roles in overall ecosystem function. We examined understory plant diversity across gradients of wildfire severity in eight large wildfires in yellow pine and mixed conifer temperate forests of the Sierra Nevada, California, USA. We found a generally unimodal hump-shaped relationship between local (alpha) plant diversity and fire severity. High-severity burning resulted in lower local diversity as well as some homogenization of the flora at the regional scale. Fire severity class, post-fire litter cover, and annual precipitation were the best predictors of understory species diversity. Our research suggests that increases in fire severity in systems historically characterized by low and moderate severity fire may lead to plant diversity losses. These findings indicate that global patterns of increasing fire size and severity may have important implications for biodiversity

Evaluation of the process of reabilitation of a stretch of Riparian forest in Itapemirim river watershed - ES

Este estudo foi realizado em uma área de floresta ciliar em processo de recuperação mediante reabilitação.A área de estudo está localizada na sub-bacia hidrográfica do rio Itapemirim, no Município de Alegre, ES, Brasil.A ocupação e uso do solo antes da revegetação eram de pastagem com Brachiaria sp. A revegetação da áreafoi feita em 1997, com espécies autóctones e alóctones arbóreas, em arranjo de distribuição aleatório, em umaárea de 1,2 ha. Para a realização dos estudos foram feitos inventários florestais nos períodos de 2004/2005e 2005/2006, sendo medidos os indivíduos de hábito arbustivo e arbóreo com circunferência à altura do peito(CAP) > 5 cm e suas alturas totais. As espécies encontradas na área foram identificadas e classificadas de acordocom seus grupos ecológicos, síndromes de dispersão e presença silvestre, sendo calculados os parâmetros florísticos,a estrutura vertical e a dinâmica estrutural desse povoamento. O objetivo do trabalho foi avaliar o desenvolvimentodo povoamento implantado para subsidiar práticas silviculturais quanto à seleção e implantação de espécies pararevegetação de áreas de floresta ciliar degradadas, em condições semelhantes. Os resultados demonstraram quefoi implantado um povoamento florestal com grande diversidade de espécies e a estratificação em classes dealtura foi à semelhança de povoamentos heterogêneos naturais. As espécies identificadas como edificadoras darevegetação da área estudada foram: Anadenanthera colubrina, Caesalpinia leyostachia, Acacia auriculiformis,Acacia mangium, Handroanthus serratifolius, Inga edulis, Joannesia princeps, Pterogyne nitens, Enterelobiumcontortisiliquum, Tabernaemontana hystrix e Anthocephalus indicus. A distribuição em classes de tamanho dacomunidade implantada ocorre em forma de "J" reverso, havendo a predominância de indivíduos pioneiros emtodas as classes de CAP. A dinâmica da estrutura horizontal apontou que, para o sucesso, continuidade e desenvolvimentoda recuperação da área, seja monitorada a regeneração natural em relação à sua presença e à eficiência dos fatoresbióticos e abióticos que nela interferem. A não observância de indivíduos arbustivos e arbóreos regenerados naturalmente,na classe de inclusão do estudo, indica a fragilidade inicial da área rumo à sustentabilidade do sistema.The study was realized in an area of riparian forest in process by means of rehabilitation. Thestudy area is located in Rio Itapemirim, in Alegre city, Brazil. The occupation and use of the soil beforethe recovery were of pasture with Brachiaria sp. The recovery of this area was in 1997, with autochthonousand allochthonous species, in casually distribution arrangement, in an area of 1,2 ha. For this studies wasrealized forest inventories in the periods of 2004/2005 and 2005/2006, being measured the arboreal individualswith circumference at breast height (CBH) and total heights. The species found in the area were identifiedand classified in this ecological groups, dispersion syndromes and wild presence, it forms calculated thefloristic parameters, the vertical structure and the structural dynamics of this plantation. The objective ofthis work went evaluate the development of the plantation implanted to subsidize practical silviculture withrelationship to the selection and plantation of species for the revegetation of degraded areas of riparianforest, in similar conditions. The results of the studies demonstrated that a forest plantation was implantedwith great diversity of species and the bedding in height classes it went to the likeness of natural heterogeneous.The species identified as builders of the plantation of the studied area were: Anadenanthera colubrina, Caesalpinia leyostachia, Acacia auriculiformis, Acacia mangium, Handroanthus serratifolius, Inga edulis, Joannesia princeps,Pterogyne nitens, Enterelobium contortisiliquum, Tabernaemontana hystrix, and Anthocephalus indicus . Theimplanted community's distribution diametric happens in reverse J shape having the pioneer individuals'predominance in all the classes of CBH. The dynamics of the horizontal structure points that for the success,continuity and development of the recovery of the area, the natural regeneration be monitored in relationto its presence and efficiency of the biotic factors and abiotic those interfere in the same. The not tree individualsobservance in natural regeneration, in the class of inclusion of the study, indicate the initial fragility of thearea heading for sustentabilidade of the system

Yeast biodiversity in vineyard environments is increased by human intervention

One hundred and five grape samples were collected during two consecutive years from 33 locations on seven oceanic islands of the Azores Archipelago. Grape samples were obtained from vineyards that were either abandoned or under regular cultivation involving common viticultural interventions, to evaluate the impact of regular human intervention on grape yeast biota diversity in vineyards. A total of 3150 yeast isolates were obtained and 23 yeast species were identified. The predominant species were Hanseniaspora uvarum, Pichia terricola, Starmerella bacillaris and Issatchenkia hanoiensis. The species Barnettozyma californica, Candida azymoides and Pichia cecembensis were reported in grapes or wine-associated environments for the first time. A higher biodiversity was found in active vineyards where regular human intervention takes place (Shannon index: 1.89 and 1.53 in the first and second years, respectively) when compared to the abandoned ones (Shannon index: 0.76 and 0.31). This finding goes against the assumptions that human intervention can destroy biodiversity and lead to homogeneity in the environment. Biodiversity indices were considerably lower in the year with the heaviest rainfall. This study is the first to report on the grape yeast communities from several abandoned vineyards that have undergone no human intervention.Joao Drumonde Neves is the recipient of a fellowship of the Azorean Government (M321/006/F/2008) and PROEMPREGO. This work was supported by the strategic programme UID/BIA/04050/2013 (POCI-01-0145-FEDER-007569) funded by national funds through the FCT I.P. and by the ERDF through the COMPETE2020 - Programa Operacional Competitividade e Internacionalizacao (POCI), and by national funds through FCT by the projects FCOMP-01-0124-008775, PTDC/AGR-ALI/103392/2008 and PTDC/AGR-ALI/121062/2010.info:eu-repo/semantics/publishedVersio