arXiv subjects

Nadav M. Shnerb

Publications and source records attributed to Nadav M. Shnerb.

At least 37 records · Page 2Linked to original sources

arXiv2018

Environmental stochasticity and the speed of evolution

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

q-bio.PE↗

arXiv2018

Theory of time-averaged neutral dynamics with environmental stochasticity

Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is governed by demographic (shot) noise, with a steady state species abundance distribution (SAD) that reflects a mutation-extinction equilibrium. Recently, many empirical and theoretical studies emphasized the importance of environmental variations that affect coherently the relative fitness of entire populations. Here we consider two generic time-averaged neutral models, in both the relative fitness of each species fluctuates independently in time but its mean is zero. The first (model A) describes a system with local competition and linear fitness-dependence of the birth-death rates, while in the second (model B) the competition is global and the fitness dependence is nonlinear. Due to this nonlinearity, model B admits a noise-induced stabilization mechanism that facilitates the invasion of new mutants. A self-consistent mean-field approach is used to reduce the multi-species problem to two-species dynamics, and the large-$N$ asymptotics of the emerging set of Fokker-Planck equations is presented and solved. Our analytic expressions are shown to fit the SADs obtained from extensive Monte-Carlo simulations and from numerical solutions of the corresponding master equations.

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arXiv2017

Fixation and absorption in a fluctuating environment

A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with Markovian, zero-sum dynamics driven by stochastic birth-death events, the mutant population eventually reaches either fixation or extinction. The classical analysis, provided by Kimura and his coworkers, is focused on the neutral case, [where the dynamics is only due to demographic stochasticity (drift)], and on \emph{time-independent} selective forces (deleterious/beneficial mutation). However, both theoretical arguments and empirical analyses suggest that in many cases the selective forces fluctuate in time (temporal environmental stochasticity). Here we consider a generic model for a system with demographic noise and fluctuating selection. Our system is characterized by the time-averaged (log)-fitness $s_0$ and zero-mean fitness fluctuations. These fluctuations, in turn, are parameterized by their amplitude $γ$ and their correlation time $δ$. We provide asymptotic (large $N$) formulas for the chance of fixation, the mean time to fixation and the mean time to absorption. Our expressions interpolate correctly between the constant selection limit $γ\to 0$ and the time-averaged neutral case $s_0=0$.

q-bio.PE↗

arXiv2017

Simulation of Spatial Systems with Demographic Noise

Demographic (shot) noise in population dynamics scales with the square root of the population size. This process is very important, as it yields an absorbing state at zero field, but simulating it, especially on spatial domains, is a non-trivial task. Here we compare the results of two operator-splitting techniques suggested for simulating the corresponding Langevin equation, one by Pechenik and Levine (PL) and the other by Dornic, Chaté and Muñoz (DCM). We identify an anomalously strong bias toward the active phase in the numerical scheme of DCM, a bias which is not present in the alternative scheme of PL. This bias strongly distorts the phase diagram determined via the DCM procedure for the range of time-steps used in such simulations. We pinpoint the underlying cause in the inclusion of the diffusion, treated as an on-site decay with a constant external source, in the stochastic part of the algorithm. Treating the diffusion deterministically is shown to remove this unwanted bias while keeping the simulation algorithm stable, thus a hybrid numerical technique, in which the DCM approach to diffusion is applied but the diffusion is simulated deterministically, appears to be optimal.

cond-mat.stat-mech↗

arXiv2017

Front propagation and effect of memory in stochastic desertification models with an absorbing state

Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.

q-bio.PE↗

arXiv2017

Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition

The process of desertification in the semi-arid climatic zone is considered by many as a catastrophic regime shift, since the positive feedback of vegetation density on growth rates yields a system that admits alternative steady states. Some support to this idea comes from the analysis of static patterns, where peaks of the vegetation density histogram were associated with these alternative states. Here we present a large-scale empirical study of vegetation dynamics, aimed at identifying and quantifying directly the effects of positive feedback. To do that, we have analyzed vegetation density across $~2.5 \times 10^6 \ \rm{km}^2$ of the African Sahel region, with spatial resolution of $30 \times 30$ meters, using three consecutive snapshots. The results are mixed. The local vegetation density (measured at a single pixel) moves towards the average of the corresponding rainfall line, indicating a purely negative feedback. On the other hand, the chance of spatial clusters (of many "green" pixels) to expand in the next census is growing with their size, suggesting some positive feedback. We show that these apparently contradicting results emerge naturally in a model with positive feedback and strong demographic stochasticity, a model that allows for a catastrophic shift only in a certain range of parameters. Static patterns, like the double peak in the histogram of vegetation density, are shown to vary between censuses, with no apparent correlation with the actual dynamical features.

q-bio.PE↗

arXiv2017

Alternative steady states in random ecological networks

In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When the competition matrix is random, the number of SUs depends on the average value of its entries and the variance. Here we consider the problem in the limit of weak competition and large variance. Using a yes/no interaction model, we show that the number of SUs corresponds to the number of maximum cliques in a network close to its fully connected limit. The number of SUs grows exponentially with the number of species in this limit, unless the network is completely asymmetric. In the asymmetric limit the number of SUs is ${\cal O} (1)$. Numerical simulations suggest that these results are valid for models with continuous distribution of competition terms.

q-bio.PE↗

arXiv2016

Stability of two-species communities: drift, environmental stochasticity, storage effect and selection

The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the relevant timescale depends on the underlying dynamics. The persistence time of the community has been calculated for neutral models, where the only drive of the system is drift (demographic stochasticity) and for models with strong selection. Following recent analyses that stress the importance of environmental stochasticity in empirical systems, we present here a general theory of persistence time of two-species community where drift, environmental variations and time independent selective advantage are all taken into account.

q-bio.PE↗

arXiv2016

Spatial neutral dynamics

Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we present a new technique, based on interface dynamics analysis, and apply it to the neutral dynamics in one, two and three spatial dimensions. New results are derived for the correlation length and for the main characteristics of the community, like total biodiversity and the species abundance distribution above the correlation length. Our results are supported by extensive numerical simulations, and provide qualitative and quantitative insights that allow for a rigorous comparison between model predictions and empirical data.

q-bio.PE↗

arXiv2016

Communities as cliques

High-diversity assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure. The competitive exclusion principle and May's complexity-diversity puzzle both suggest that a community can support only a small number of species, turning the spotlight at the dynamics of local patches or islands, where stable and uninvadable (SU) subsets of species play a crucial role. Here we map the community SUs question to the geometric problem of finding maximal cliques of the corresponding graph. We solve for the number of SUs as a function of the species richness in the regional pool, $N$, showing that this growth is subexponential, contrary to long-standing wisdom. We show that symmetric systems relax rapidly to an SU, where the system stays until a regime shift takes place. In asymmetric systems the relaxation time grows much faster with $N$, suggesting an excitable dynamics under noise.

q-bio.PE↗

arXiv2016

The effect of environmental stochasticity on species richness in neutral communities

Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We show that the incorporation of demographic noise into the model is essential to its applicability, yielding realistic behavior of the system when fitness variations are relatively weak. The dependence of species richness on the strength of environmental stochasticity changes sign when the correlation time of the environmental variations increases. This transition marks the point at which the storage effect no longer succeeds in stabilizing the community.

q-bio.PE↗

arXiv2015

Fronts and fluctuations at a critical surface

The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system admits a bistable solution and the external field governs the rate in which one phase invades the other. The second mechanism corresponds to a second order transition that, in the case of reactive systems, takes the form of a transcritical bifurcation at the crossing point. We solve for the front shape and its response to external white noise, showing that static properties and also some of the dynamics features cannot distinguish between the two scenarios. The only reliable indicator turns out to be the fluctuation statistics. These take a Gaussian form in the bifurcation case and a double-peak shape in a bistable system. The results of a recent analysis of the morphogenesis process in Drosophila embryos are reanalyzed and we show, in contrast with the interpretation suggested by Krotov et. al., that the plausible underlying dynamics is bistable and not bifurcational.

nlin.PS↗

arXiv2015

Predicting catastrophic shifts

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes, such as desertification and coral reef collapses, which are considered as a prominent threat to sustainability and to the well-being of millions. Still, the methods proposed so far for the prediction of an imminent transition are quite ineffective, and some empirical and theoretical studies suggest that actual transitions may occur smoothly, without an abrupt shift. Here we present a new diagnostic tool, based on monitoring the dynamics of clusters through time. Our technique discriminates between systems with local positive feedback, where the transition is abrupt, and systems with negative density dependence, where the transition is smooth. Analyzing the spatial dynamics of these two generic scenarios, we show that changes in the critical cluster size provide a reliable early warning indicator for both transitions. Our method may allow for the prediction, and thus hopefully the prevention of such transitions, avoiding their destructive outcomes.

q-bio.PE↗

arXiv2015

Age-abundance relationships for neutral communities

Neutral models for the dynamics of a system of competing species are used, nowadays, to describe a wide variety of empirical communities. These models are used in many situations, ranging from population genetics and ecological biodiversity to macroevolution and cancer tumors. One of the main issues discussed within this framework is the relationships between the abundance of a species and its age. Here we provide a comprehensive analysis of the age-abundance relationships for fixed-size and growing communities. Explicit formulas for the average and the most likely age of a species with abundance $n$ are given, together with the full probability distribution function. We further discuss the universality of these results and their applicability to the tropical forest community.

q-bio.PE↗

arXiv2015

Neutral dynamics with environmental noise: age-size statistics and species lifetimes

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [${\cal{O}} ({\sqrt N})$] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems - age size relationships and species extinction time - in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics and discuss their relevance to realistic models of community dynamics.

q-bio.PE↗

arXiv2014

Spatial patterns in the tropical forest reveal connections between negative feedback, aggregation and abundance

The spatial arrangement of trees in a tropical forest reflects the interplay between aggregating processes, like dispersal limitation, and negative feedback that induces effective repulsion among individuals. Monitoring the variance-mean ratio for conspecific individuals along length-scales, we show that the effect of negative feedback is dominant at short scales, while aggregation characterizes the large-scale patterns. A comparison of different species indicates, surprisingly, that both aggregation and negative feedback scales are related to the overall abundance of the species. This suggests a bottom-up control mechanism, in which the negative feedback dictates the dispersal kernel and the overall abundance.

q-bio.PE↗

arXiv2014

A generalized model of island biodiversity

The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics structure with four qualitatively distinct phases is unfolded. When the overall interspecies competition is weak, the island species are a sample of the mainland species. For higher values of the competition parameter the system still admit an equilibrium community, but now some of the mainland species are absent on the island. Further increase in competition leads to an intermittent "chaotic" phase, where the dynamics is controlled by invadable combinations of species and the turnover rate is governed by the migration. Finally, the strong competition phase is glassy, dominated by uninvadable state and noise-induced transitions. Our model contains, as a spatial case, the celebrated neutral island theories of Wilson-MacArthur and Hubbell. Moreover, we show that slight deviations from perfect neutrality may lead to each of the phases, as the Hubbell point appears to be quadracritical.

q-bio.PE↗

arXiv2014

The glocal forest

Ecological spatial patterns reflect the underlying processes that shape the structure of species and communities. Mechanisms like inter and intra species competition, dispersal and host-pathogen interactions are believed to act over a wide range of scales, and the inference of the process from the pattern is, despite its popularity, a challenging task. Here we call attention to a quite unexpected phenomenon in the extensively studied tropical forest at the Barro-Colorado Island (BCI): the spatial deployment of (almost) all tree species is statistically equivalent, once distances are normalized by , the typical distance between neighboring conspecific trees. Correlation function, cluster statistics and nearest-neighbor distance distribution become species-independent after this rescaling. Global observables (species frequencies) and local spatial structure appear to be interrelated. This "glocality" suggests a radical interpretation of recent experiments that show a correlation between species' abundance and the negative feedback among conspecifics. For the forest to be glocal, the negative feedback must govern spatial patterns over all scales.

q-bio.PE↗