Growth-rate distributions of gut microbiota time series: neutral models and temporal dependence

Logarithmic growth-rates are fundamental observables for describing ecological systems and the characterization of their distributions with analytical techniques can greatly improve their comprehension. Here a neutral model based on a stochastic differential equation with demographic noise, which presents a closed form for these distributions, is used to describe the population dynamics of microbiota. Results show that this model can successfully reproduce the log-growth rate distribution of the considered abundance time-series. More significantly, it predicts its temporal dependence, by reproducing its kurtosis evolution when the time lag $\tau$ is increased. Furthermore, its typical shape for large $\tau$ is assessed, verifying that the distribution variance does not diverge with $\tau$. The simulated processes generated by the calibrated stochastic equation and the analysis of each time-series, taken one by one, provided additional support for our approach. Alternatively, we tried to describe our dataset by using a logistic model with an environmental stochastic term. Analytical and numerical results show that this model is not suited for describing the leptokurtic log-growth rates distribution found in our data. These results effectively support a neutral model with demographic stochasticity for describing the growth-rate dynamics and the stationary abundance distribution of the considered microbiota. This suggests that there are no significant parametric demographic differences among the species, which can be statistically characterized by the same vital rates.Comment: 14 pages, 6 figure

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 formulae 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

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

Redundancy-selection trade-off in phenotype-structured populations

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies

Downscaling species occupancy from coarse spatial scales

The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling

Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation

In this paper we investigate the finite-time and fixed-time consensus problems of multiagent networks with pinning control and noise perturbation. In order to reach the finite-time and fixed-time consensus, several pinning protocols are proposed. Compared with the consensus protocols without pinning control, the proposed finite-time and fixed-time protocols need to control only a small fraction of agents, which is practical and has advantages from the physical viewpoint of energy consumption. More specifically, the deterministic and stochastic protocols include the graph $(p+1)$-Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that, unlike the protocols with the standard (linear) graph Laplacian, those with the graph $(p+1)$-Laplacian solve the finite-time as well as the fixed-time consensus problems. By using the finite-time and fixed-time stability theory and the algebra graph theory, sufficient conditions are established to ensure the finite-time and fixed-time consensus. Finally, numerical simulations are presented to illustrate the correctness of the theoretical results

Towards a unified descriptive theory for spatial ecology: predicting biodiversity patterns across spatial scales

A key challenge for both ecological researchers and biodiversity managers is the measurement and prediction of species richness across spatial scales. Typically, biodiversity is assessed at fine scales (e.g. in quadrats or transects) for practical reasons, but often we are interested in coarser-scale (field, regional, global) diversity issues. Moreover, the pressures affecting biodiversity patterns are often scale specific, making multiscale assessment a crucial methodological priority. As species richness is not additive, it is difficult to translate from the scale of measurement to the scale(s) of interest. A number of methods have been proposed to tackle this problem, but most are too model specific or too rigid to allow general application. Here, we present a general framework (and a specific implementation of it) that allows such scale translations to be performed. Building on the intrinsic relationships among patterns of species richness, abundance and spatial turnover, we introduce a framework that links and predicts the profile of the species-area relationship and the species-abundance distributions across scales when a limited number of fine-scale scattered samples are available. Using the correlation in species' abundances between pairs of samples as a function of the distance between them, we are able to link the effects of aggregation, similarity decay, species richness and species abundances across scales. Our approach allows one to draw inferences about biodiversity scaling under very general assumptions pertaining to the nature of interactions, the geographical distributions of individuals and ecological processes. We demonstrate the accuracy of our predictions using data from two well-studied forest stands and also demonstrate the potential value of such methods by examining the effects of management on farmland insects across scales. The framework has important applications to biodiversity research and conservation practice

Polymorphism Data Can Reveal the Origin of Species Abundance Statistics

What is the underlying mechanism behind the fat-tailed statistics observed for species abundance distributions? The two main hypotheses in the field are the adaptive (niche) theories, where species abundance reflects its fitness, and the neutral theory that assumes demographic stochasticity as the main factor determining community structure. Both explanations suggest quite similar species-abundance distributions, but very different histories: niche scenarios assume that a species population in the past was similar to the observed one, while neutral scenarios are characterized by strongly fluctuating populations. Since the genetic variations within a population depend on its abundance in the past, we present here a way to discriminate between the theories using the genetic diversity of noncoding DNA. A statistical test, based on the Fu-Li method, has been developed and enables such a differentiation. We have analyzed the results gathered from individual-based simulation of both types of histories and obtained clear distinction between the Fu-Li statistics of the neutral scenario and that of the niche scenario. Our results suggest that data for 10–50 species, with approximately 30 sequenced individuals for each species, may allow one to distinguish between these two theories

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, treating the dynamics in a species-symmetric manner. We demonstrate that dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry

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) of biodiversity 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 several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. 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 toward ecologists, the goal here is to review the quantitative aspects 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, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed