arXiv subjects

Nadav M. Shnerb

Publications and source records attributed to Nadav M. Shnerb.

At least 19 recordsLinked to original sources

arXiv2026

Correlations at criticality in ecological communities

Ecological communities are continually reshaped by invasion, exclusion, and diversification, processes that naturally drive them toward the boundary of dynamical stability. Near such a boundary, a soft mode relaxes increasingly slowly and, under stochastic forcing, is expected to dominate the fluctuations, effectively reducing the dynamics to one dimension and generating strong positive and negative abundance correlations. Such correlations have therefore been proposed as signatures of an imminent transition. Here we show that this expectation can fail even arbitrarily close to criticality. The reason is that spectral softness does not guarantee stochastic visibility: the soft mode must receive enough environmental forcing to dominate the fluctuation background generated by the remaining modes. We demonstrate this mechanism in three ecological scenarios: a synthetic feasible community, a local community assembled by immigration from a regional pool, and a community generated by repeated diversification. In all three, communities approach marginal stability without developing the near-perfect pairwise correlations predicted by the single-mode picture. Thus, proximity to ecological criticality need not be visible in equal-time pairwise correlations.

q-bio.PE↗

arXiv2026

When do correlations reflect biological similarity in ecological dynamics?

The structure of competitive ecological communities is shaped by the strength of interactions between species, which in turn reflects their biological similarity. At the same time, the stochastic forcing that drives abundance fluctuations is itself biologically grounded: species that are more similar may be expected to respond more similarly to environmental variation. This motivates the increasingly common use of correlations in abundance time series, particularly in microbial communities, as proxies for biological similarity or niche overlap. Here we analyze the relation between biological similarity and abundance correlations in stochastic community models. We require that the stochastic forcing acting on different species be correlated in proportion to their biological similarity, and ask how such forcing is reflected in abundance correlations. We show that this requirement cannot, in general, be satisfied within the widely used stochastic Lotka-Volterra framework, and that even when it is, abundance correlations carry no information about niche overlap. In contrast, consumer-resource models provide a natural framework for biologically grounded stochasticity. In this setting, however, the interpretation of abundance correlations depends strongly on the pathway through which noise enters the system: direct forcing of consumers and resource-mediated fluctuations encode different biological quantities. These results have implications both for the modeling of stochastic ecological communities and for understanding what can, and cannot, be inferred from correlations in community time series.

q-bio.PE↗

arXiv2025

Dynamics of critical cascades in interdependent networks

The collapse of interdependent networks, as well as similar avalanche phenomena, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on average, the failure of one other node. As nodes continue to fail, the network becomes increasingly fragile and the branching factor grows. If the failure process does not reach extinction during its critical phase, the network undergoes an abrupt collapse. Here, we implement the analogy between this dynamic and birth-death processes to derive new analytical results and significantly optimize numerical calculations. Using this approach, we analyze three key aspects of the dynamics: the probability of collapse, the duration of avalanches, and the length of the cascading plateau phase preceding a collapse. This analysis quantifies how system size and the intensity of the initial triggering event influence these characteristics.

physics.soc-ph↗

arXiv2025

Asymmetric Variability: The Impact of Uneven Stochasticity on Competitive Dynamics

Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for the random nature of birth and death processes (demographic stochasticity) as well as the variability of external conditions (environmental stochasticity). Recent studies have highlighted the importance of species life history, showing that differences in life history lead competing species to experience different levels of demographic stochasticity. Here, we propose a simple model of two-species competition with different life histories and derive analytical expressions for various properties (fixation probability, fixation time, absorption time, probability density) under a wide range of conditions, including migration, selection, and environmental stochasticity. These properties provide insights into the long-term outcomes of competition, such as species persistence, extinction risks, and the influence of environmental variability on the evenness of the community.

q-bio.PE↗

arXiv2024

Dominance to egalitarian transition in diverse communities

Diverse communities of competing species are generally characterized by substantial niche overlap and strongly stochastic dynamics. Abundance fluctuations are proportional to population size, so the dynamics of rare populations is slower. Hence, once a population becomes rare, its abundance gets stuck at low values. Here, we analyze the effect of this phenomenon on community structure. We identify two different phases: a dominance phase, in which a tiny number of species constitute most of the community, and an egalitarian phase, where it takes a finite fraction of all species to constitute most of the community. We demonstrate the validity of the theory using empirical findings for a variety of hyperdiverse communities, and clarify the role of demographic stochasticity in shaping patterns of commonness and rarity.

q-bio.PE↗

arXiv2024

Numerical Study of Interaction Network Structures in Competitive Ecosystems

We present a numerical analysis of local community assembly through weak migration from a regional species pool. At equilibrium, the local community consists of a subset ("clique") of species from the regional community. Our analysis reveals that the interaction networks of these cliques exhibit nontrivial architectures. Specifically, we demonstrate the pronounced nested structure of the clique interaction matrix in the case of symmetric interactions and the hyperuniform structure seen in asymmetric communities.

q-bio.PE↗

arXiv2023

Emergence of a Novel Phase in Population and Community Dynamics Due to Fat-Tailed Environmental Correlations

Temporal environmental noise (EN) is a prevalent natural phenomenon that controls population and community dynamics, shaping the destiny of biological species and genetic types. Conventional theoretical models often depict EN as a Markovian process with an exponential distribution of correlation times, resulting in two distinct qualitative dynamical categories: quenched (pertaining to short demographic timescales) and annealed (pertaining to long timescales). However, numerous empirical studies demonstrate a fat-tailed decay of correlation times. Here, we study the consequences of power-law correlated EN on the dynamics of isolated and competing populations. We reveal the emergence of a novel intermediate phase that lies between the quenched and annealed regimes. Within this phase, dynamics are primarily driven by rare, yet not exceedingly rare, long periods of almost-steady environmental conditions. For an isolated population, the time to extinction in this phase exhibits a novel scaling with the abundance, and also a non-monotonic dependence on the spectral exponent.

q-bio.PE↗

arXiv2023

Extinction time distributions of populations and genotypes

In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [PRL 128, 218301 (2022)] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study, we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. By employing these criteria, we can improve our understanding of the underlying mechanisms driving extinction processes.

q-bio.PE↗

arXiv2023

A metric for tradable biodiversity credits linked to the Living Planet Index and global species conservation

Difficulties identifying appropriate biodiversity impact metrics remain a major barrier to inclusion of biodiversity considerations in environmentally responsible investment. We propose and analyse a simple science-based local metric: the sum of proportional changes in local species abundances relative to their global species abundances, with a correction for species close to extinction. As we show, this metric quantifies changes in the mean long-term global survival probability of species. It links mathematically to a widely cited global biodiversity indicator, the Living Planet Index, for which we propose an improved formula that directly addresses the known problem of singularities caused by extinctions. We show that, in an ideal market, trade in our metric would lead to near-optimal allocation of resources to species conservation. We further show that the metric is closely related to several other metrics and indices already in use. Barriers to adoption are therefore low. Used in conjunction with metrics addressing ecosystem functioning and services, potential areas of application include biodiversity related financial disclosures and voluntary or legislated no net biodiversity loss policies.

q-bio.PE↗

arXiv2022

The time-identity tradeoff

Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations and the number of microscopic states, which determines entropy, is counted up to permutations. When the particles are distinguishable, wavefunctions have no symmetry and each permutation is a different microstate. This binary and discontinuous classification raises a few questions: one may wonder what happens if particles are almost identical, or when the property that distinguishes between them is irrelevant to the physical interactions in a given system. Here I sketch a general answer to these questions. For any pair of non-identical particles there is a timescale, $τ_d$, required for a measurement to resolve the differences between them. Below $τ_d$, particles seem identical, above it - different, and the uncertainty principle provides a lower bound for $τ_d$. Thermal systems admit a conjugate temperature scale, $T_d$. Above this temperature the system appears to equilibrate before it resolves the differences between particles, below this temperature the system identifies these differences before equilibration. As the physical differences between particles decline towards zero, $τ_d \to \infty$ and $T_d \to 0$.

cond-mat.stat-mech↗

arXiv2020

Taming the diffusion approximation through a controlling-factor WKB method

The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (large-deviations) method, which requires only the logarithm of a given quantity to be smooth over its state space. Combining the WKB scheme with asymptotic matching techniques, we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations, applicable for much wider regimes of parameters. We also introduce a scalable (independent of population size) WKB-based numerical technique. The method is applied to a central problem in population genetics and evolution, finding the chance of ultimate fixation in a zero-sum, two-types competition.

q-bio.PE↗

arXiv2020

Population dynamics in stochastic environments

Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference (master) equation, but closed-form solutions of these equations are rare. Analytical insights in fields like population genetics, ecology and evolution rely, almost exclusively, on an uncontrolled application of the diffusion approximation (DA) which assumes the smoothness of the relevant quantities over the set of integers. Here we combine asymptotic matching techniques with a first-order (controlling-factor) WKB method to obtain a theory whose range of applicability is much wider. This allows us to rederive DA from a more general theory, to identify its limitations, and to suggest alternative analytical solutions and scalable numerical techniques when it fails. We carry out our analysis for the calculation of the fixation probability in a fluctuating environment, highlighting the difference between (on average) deleterious and beneficial mutant invasion and the intricate distinction between weak and strong selection.

q-bio.PE↗

arXiv2020

Stochasticity-induced stabilization in ecology and evolution: a new synthesis

The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with mean logarithmic growth rates when rare, $\mathbb{E}[r]$, used as metrics for persistence. However, invasion probabilities and the times to extinction are not single-valued functions of $\mathbb{E}[r]$ and, in some cases, decrease as $\mathbb{E}[r]$ increases. Here, we present a synthesis of stochasticity-induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth $μ$ and its variance $g$. When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single valued, monotonic functions of $μ/g$. The storage effect in the lottery model, together with other well-known examples drawn from population genetics, microbiology and ecology (including discrete and continuous dynamics, with overlapping and non-overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life-history strategies and SIS, and study the dynamics of extinction when SIS fails.

q-bio.PE↗

arXiv2019

Evolutionary dynamics in populations with fluctuating size

Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. We consider a two-state Moran model, where selection intensity at equilibrium may differ (in amplitude and in sign) from selection during periods of sharp growth and sharp decline. Using Kimura's diffusion approximation we present simple formulae for effective population size and effective selection, and use it to calculate the chance of ultimate fixation, the time to fixation and the time to absorption (either fixation or loss). Our analysis shows perfect agreement with numerical solutions for neutral, beneficial and deleterious mutant. The contributions of different processes to the mean and the variance of abundance variations are additive and commutative. As a result, when selection intensity $s$ is weak such that ${\cal O}(s^2)$ terms are negligible, periodic or stochastic environmental variations yield identical results.

q-bio.PE↗

arXiv2019

A comprehensive phase diagram for logistic populations in fluctuating environment

Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular deterministic models (like logistic growth) support a transcritical bifurcation point between an extinction phase and an active phase. Here we provide a comprehensive analysis of the phases of that system, taking into account both the endogenous demographic noise (random birth and death events) and the effect of environmental stochasticity that causes variations in birth and death rates. Three phases are identified: in the inactive phase the mean time to extinction $T$ is independent of the carrying capacity $N$, and scales logarithmically with the initial population size. In the power-law phase $T \sim N^q$ and the exponential phase $T \sim exp(αN)$. All three phases and the transitions between them are studied in detail. The breakdown of the continuum approximation is identified inside the power-law phase, and the accompanied changes in decline modes are analyzed. The applicability of the emerging picture to the analysis of ecological timeseries and to the management of conservation efforts is briefly discussed.

q-bio.PE↗

arXiv2019

Phase diagram for a logistic system under bounded stochasticity

Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined effect of demographic and bounded environmental stochasticity. Three phases are identified: an inactive phase where the mean time to extinction $T$ increases logarithmically with the initial population size, an active phase where $T$ grows exponentially with the carrying capacity $N$, and temporal Griffiths phase, with power-law relationship between $T$ and $N$. The system supports an exponential phase only when the noise is bounded, in which case the continuum (diffusion) approximation breaks down within the Griffiths phase. This breakdown is associated with a crossover between qualitatively different survival statistics and decline modes. To study the power-law phase we present a new WKB scheme which is applicable both in the diffusive and in the non-diffusive regime.

q-bio.PE↗

arXiv2018

Noise-induced stabilization and fixation in fluctuating environment

The dynamics of a two-species community of $N$ competing individuals is considered, with an emphasis on the role of environmental variations that affect coherently the fitness of entire populations. The chance of fixation of a mutant population (and, in particular, of a single mutant) is calculated as a function of the mean relative fitness of the mutant, the amplitude of fitness variations and their typical duration. We emphasize the distinction between the case of local competition and the case of global competition; in the latter a noise-induced stabilization mechanism yields a higher chance of fixation for a single mutant. The distinction becomes dramatic in the weak selection phase, where the chance of fixation for a single deleterious mutant is an $N$-independent constant for global competition and decays like $(\ln N)^{-1}$ in the local competition case. The possibility of long-term persistence of ${\cal O} (N)$ suboptimal (and extinction-prone) populations is discussed, as well as its relevance to stochastic tunneling between fitness peaks.

q-bio.PE↗

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↗