arXiv subjects

Sandro Azaele

Publications and source records attributed to Sandro Azaele.

At least 37 records · Page 2Linked to original sources

arXiv2023

Generalization of Fluctuation-Dissipation Theorem to Systems with Absorbing States

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes with absorbing states, the total probability decays with time, eventually reaching zero and rendering the predictions from the standard response theory invalid. In this article, we investigate how such processes respond to external perturbations and develop a new theory that extends the framework of the fluctuation-dissipation theorem. We apply our theory to two paradigmatic examples that span vastly different fields - a birth-death process in forest ecosystems and a targeted search on DNA by proteins. These systems can be affected by perturbations which increase their rate of extinction/absorption, even though the average or the variance of population sizes are left unmodified. These effects, which are not captured by the standard response theory, are exactly predicted by our framework. Our theoretical approach is general and applicable to any system with absorbing states. It can unveil important features of the path to extinction masked by standard approaches.

cond-mat.stat-mech↗

arXiv2023

Large system population dynamics with non-Gaussian interactions

We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.

q-bio.PE↗

arXiv2021

Effect of delay on the emergent stability patterns in Generalized Lotka-Volterra ecological dynamics

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on Generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modeled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, we introduce a measure of stability that holds for out of equilibrium dynamics and we show that in the oscillatory regime induced by the delay stability increases for increasing ecosystem diversity.

q-bio.PE↗

arXiv2021

Effective Resource-Competition Model for Species Coexistence

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider a consumer-resource model in which a coarse-graining procedure accounts for a variety of ecological mechanisms and leads to effective spatial effects which favour species coexistence. Herein, we provide conditions for several species to live in an environment with very few resources. In fact, the model displays two different phases depending on whether the number of surviving species is larger or smaller than the number of resources. We obtain conditions whereby a species can successfully colonize a pool of coexisting species. Finally, we analytically compute the distribution of the population sizes of coexisting species. Numerical simulations as well as empirical distributions of population sizes support our analytical findings.

q-bio.PE↗

arXiv2021

Neutral Theory for competing attention in social networks

We used an ecological approach based on a neutral model to study the competition for attention in an online social network. This novel approach allow us to analyze some ecological patterns that has also an insightful meaning in the context of information ecosystem. Specifically, we focus on the study of patterns related with the persistence of a meme within the network and the capacity of the system to sustain coexisting memes. Not only are we able of doing such analysis in an approximated continuum limit, but also we get exact results of the finite-size discrete system.

physics.soc-ph↗

arXiv2021

Ginzburg-Landau amplitude equation for nonlinear nonlocal models

Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The modulations of patterns, occurring on long spatial and temporal scales, can not be captured by linear approximation analysis. Here, we show that, starting from a general model with long range couplings displaying patterns, the spatio-temporal evolution of large scale modulations at the onset of instability is ruled by the well-known Ginzburg-Landau equation, independently of the details of the dynamics. Hence, we demonstrate the validity of such equation in the description of the behavior of a wide class of systems. We introduce a novel mathematical framework that is also able to retrieve the analytical expressions of the coefficients appearing in the Ginzburg-Landau equation as functions of the model parameters. Such framework can include higher order nonlocal interactions and has much larger applicability than the model considered here, possibly including pattern formation in models with very different physical features.

cond-mat.stat-mech↗

arXiv2020

Asymmetric Stochastic Resetting: Modeling Catastrophic Events

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then, the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. We present a general framework to obtain the exact non-equilibrium steady state of the system and the mean first passage time for the system to reach the origin. Employing this framework, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement.

cond-mat.stat-mech↗

arXiv2019

Spatial patterns emerging from a stochastic process near criticality

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulæ is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

physics.bio-ph↗

arXiv2018

Zipf's and Taylor's Laws

Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individuals dynamics without fine tuning. Here we show that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e. fluctuations of parameters, or correlations, i.e. dependence between individuals. Under these assumptions, we show numerically and with theoretical arguments that the conditional variance of the population increments scales as the square of the population and that the corresponding stationary distribution of the processes follows Zipf's law.

physics.soc-ph↗

arXiv2016

A phenomenological spatial model for macro-ecological patterns in species-rich ecosystems

Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The relative abundance of species, which informs us about the commonness and rarity of species, changes its shape from small to large spatial scales. The average number of species as a function of area has a steep initial increase, followed by decreasing slopes at large scales. Finally, if we find a species in a given location, it is more likely we find an individual of the same species close-by, rather than farther apart. Such spatial turnover depends on the geographical distribution of species, which often are spatially aggregated. This reverberates on the abundances as well as the richness of species within a region, but so far it has been difficult to quantify such relationships. Within a neutral framework, which considers all individuals competitively equivalent, we introduce a spatial stochastic model, which phenomenologically accounts for birth, death, immigration and local dispersal of individuals. We calculate the pair correlation function, which encapsulates spatial turnover, and the conditional probability to find a species with a certain population within a given circular area. Also, we calculate the macro-ecological patterns, which we have referred to above, and compare the analytical formulæ with the numerical integration of the model. Finally, we contrast the model predictions with the empirical data for two lowland tropical forest inventories, showing always a good agreement.

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

Statistical Mechanics of Ecological Systems: Neutral Theory and Beyond

The simplest theories often have much merit and many limitations, and in this vein, the value of Neutral Theory (NT) has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain pervasive patterns observed in the organization of ecosystems. Its originally tepid reception among ecologists contrasted starkly with the excitement it caused among physicists and mathematicians. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented towards ecologists, our goal here is to review the quantitative results of NT and its extensions for physicists who are interested in learning what NT is, what its successes are and what important problems remain unresolved. Furthermore, we hope that this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. We propose to make these more accessible by extracting them and presenting them in a logical fashion. We conclude the review by discussing how one might introduce realistic non-neutral elements into the current models.

q-bio.PE↗

arXiv2014

Spatial maximum entropy modeling from presence/absence tropical forest data

Understanding the assembly of ecosystems to estimate the number of species at different spatial scales is a challenging problem. Until now, maximum entropy approaches have lacked the important feature of considering space in an explicit manner. We propose a spatially explicit maximum entropy model suitable to describe spatial patterns such as the species area relationship and the endemic area relationship. Starting from the minimal information extracted from presence/absence data, we compare the behavior of two models considering the occurrence or lack thereof of each species and information on spatial correlations. Our approach uses the information at shorter spatial scales to infer the spatial organization at larger ones. We also hypothesize a possible ecological interpretation of the effective interaction we use to characterize spatial clustering.

q-bio.PE↗

arXiv2014

Phenomenological modeling of the motility of self-propelled microorganisms

The motility of microorganisms in liquid media is an important issue in active matter and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a Gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus Colpidium, which do not agree with the Gaussian white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion, such as velocity distribution and velocity autocorrelation.

physics.bio-ph↗

arXiv2012

Absence of Detailed Balance in Ecology

Living systems are typically characterized by irreversible processes. A condition equivalent to the reversibility is the detailed balance, whose absence is an obstacle for analytically solving ecological models. We revisit a promising model with an elegant field-theoretic analytic solution and show that the theoretical analysis is invalid because of an implicit assumption of detailed balance. A signature of the difficulties is evident in the inconsistencies appearing in the many-point correlation functions and in the analytical formula for the species area relationship.

cond-mat.stat-mech↗

arXiv2012

Spatial aggregation and the species-area relationship across scales

There has been a considerable effort to understand and quantify the spatial distribution of species across different ecosystems. Relative species abundance (RSA), beta diversity and species area relationship (SAR) are among the most used macroecological measures to characterize plants communities in forests. In this article we introduce a simple phenomenological model based on Poisson cluster processes which allows us to exactly link RSA and beta diversity to SAR. The framework is spatially explicit and accounts for the spatial aggregation of conspecific individuals. Under the simplifying assumption of neutral theory, we derive an analytical expression for the SAR which reproduces tri-phasic behavior as sample area increases from local to continental scales, explaining how the tri-phasic behavior can be understood in terms of simple geometric arguments. We also find an expression for the endemic area relationship (EAR) and for the scaling of the RSA.

q-bio.PE↗

arXiv2012

Spontaneously Broken Neutral Symmetry in an Ecological System

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest) --regardless of the species they belong to-- have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species while treating the dynamics in a species-symmetric manner. We demonstrate that the dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

q-bio.PE↗

arXiv2010

System size expansion for systems with an absorbing state

The well known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.

cond-mat.stat-mech↗