We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under two models of species extinction. One of these models is the generalized version of an earlier model in which extinction is influenced by some trait that can be classified into two states and which evolves on a tree according to a Markov process. Since more than one trait can affect the rates of species extinction, it is reasonable to allow, in the generalized model, k binary states that influence extinction rates. We compare this model to one that has matching marginal extinction probabilities for each species but for which the species extinction events are stochastically independent.
Why, contrary to theoretical predictions, do marine microbe communities harbor tremendous phenotypic heterogeneity? How can so many marine microbe species competing in the same niche coexist? We discovered a unifying explanation for both phenomena by investigating a non-cooperative game that interpolates between individual-level competitions and species-level outcomes. We identified all equilibrium strategies of the game. These strategies are characterized by maximal phenotypic heterogeneity. They are also neutral towards each other in the sense that an unlimited number of species can co-exist…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species and find a relation describing how many species that may go extinct as a result of a sharp environmental change. We introduce a special parameter that is a combination of species traits and resource characteristics used in the model formulation. This parameter describes the pressure on system to converge, by extinctions. When that stress paramet…
Properties of biodiversity indices that incorporate future extinction risk
University of Canterbury（坎特伯雷大学）；New Jersey Institute of Technology（新泽理工学院）；Northwestern University（西北大学）；The University of Chicago（芝加哥大学）；Simon Fraser University（西蒙菲莎大学）
Despite numerous mass extinctions in the Phanerozoic eon, the overall trend in biodiversity evolution was not blocked and the life has never been wiped out. Almost all possible catastrophic events (large igneous province, asteroid impact, climate change, regression and transgression, anoxia, acidification, sudden release of methane clathrate, multi-cause etc.) have been proposed to explain the mass extinctions. However, we should, above all, clarify at what timescale and at what possible levels should we explain the mass extinction? Even though the mass extinctions occurred at short-timescale …
We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are described by sequences of strings, which allows us to describe multiple traits. We define the mathematical framework for analyzing pattern forming instabilities in these models, showing surprisingly that the analytic linear theory predicts the asymptotically long time population distributions of niches in the model. We propose a test for identifying ecological …
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 wh…
Fluctuations in biodiversity, large and small, are pervasive in the fossil record, yet we do not understand the processes generating them. Here we extend theory from non-equilibrium statistical physics to describe the previously unaccounted for fat-tailed form of fluctuations in marine invertebrate richness through the Phanerozoic. Using this theory, known as superstatistics, we show that the simple fact of heterogeneous origination and extinction rates between clades and conserved rates within clades is sufficient to account for this fat-tailed form. We identify orders and the families they s…
The twin crises of climate change and biodiversity loss define a strong need for functional diversity monitoring. While the availability of high-quality ecological monitoring data is increasing, the quantification of functional diversity so far requires the identification of species traits, for which data is harder to obtain. However, the traits that are relevant for the ecological function of a species also shape its performance in the environment and hence should be reflected indirectly in its spatio-temporal distribution. Thus it may be possible to reconstruct these traits from a sufficient…
The magnitude and variability of Earth's biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework a…
Understanding how an extinction event affects ecosystem is fundamental to biodiversity conservation. For this reason, food web response to species loss has been investigated in several ways in the last years. Several studies focused on secondary extinction due to biodiversity loss in a bottom-up perspective using in-silico extinction experiments in which a single species is removed at each step and the number of secondary extinctions is recorded. In these binary simulations a species goes secondarily extinct if it loses all its resource species, that is, when the energy intake is zero. This pu…
Ecosystems are governed by dynamic processes such as competition for resources, reproduction and dispersal. These shape their biodiversity and how the system responds to change. Current approaches to modelling ecosystems, especially plants, focus on either describing fine-scale processes for individual species or broad-scale patterns for limited groups of plant functional types. Digitisation of herbarium and other plant records has unlocked a wealth of information that can be used to drive models of plant communities and make predictions for their future under different scenarios of climate ch…
Humans are increasingly stressing ecosystems via habitat destruction, climate change and global population movements leading to the widespread loss of biodiversity and the disruption of key ecological services. Ecosystems characterized primarily by mutualistic relationships between species such as plant-pollinator interactions may be particularly vulnerable to such perturbations because the loss of biodiversity can cause extinction cascades that can compromise the entire network. Here, we develop a general restoration strategy based on network-science for degraded ecosystems. Specifically, we …
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic replicator equations in the evolutionary game theory. However, intrinsic fluctuations arisen from the discreteness of populations lead to stochastic derivations from the smooth evolution trajectories. The role of these fluctuations is shown to be critical at causing extinction and deteriorating the biodiversity of ecosystem. We use children's rock-paper-scissors gam…
The rapid expansion of human activities threatens ocean-wide biodiversity loss. Numerous marine animal populations have declined, yet it remains unclear whether these trends are symptomatic of a chronic accumulation of global marine extinction risk. We present the first systematic analysis of threat for a globally-distributed lineage of 1,041 chondrichthyan fishes - sharks, rays, and chimaeras. We estimate that one-quarter are threatened according to IUCN Red List criteria due to overfishing (targeted and incidental). Large-bodied, shallow-water species are at greatest risk and five out of the…
Effects of changes in functional composition of soil communities on nutrient cycling are still not well understood. Models simulating community dynamics overcome the technical challenges of conducting species removal experiments in the field. However, to date, available soil food web models do not adequately represent the organic matter processing chain which is key for soil dynamics. Here, we present a new model of soil food web dynamics accounting for allometric scaling of metabolic rate, ontogeny of organic matter, and explicit representation of nitrogen and carbon flows. We use this model …
The terrestrial fossil record shows a significant variation in the extinction and origination rates of species during the past half billion years. Numerous studies have claimed an association between this variation and the motion of the Sun around the Galaxy, invoking the modulation of cosmic rays, gamma rays and comet impact frequency as a cause of this biodiversity variation. However, some of these studies exhibit methodological problems, or were based on coarse assumptions (such as a strict periodicity of the solar orbit). Here we investigate this link in more detail, using a model of the G…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of off-lattice Lotka-Volterra stochastic simulations, showing that the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals. We also investigate the dynamics in our simulations, finding an empirical relation characterizing the dependence of the characteristic peak frequency and amplitude on the total de…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. In this paper, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact o…
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dyna…
For many taxa, the current high rates of extinction are likely to result in a significant loss of biodiversity. The evolutionary heritage of biodiversity is frequently quantified by a measure called phylogenetic diversity (PD). We predict the loss of PD under a wide class of phylogenetic tree models, where speciation rates and extinction rates may be time-dependent, and assuming independent random species extinctions at the present. We study the loss of PD when $K$ contemporary species are selected uniformly at random from the $N$ extant species as the surviving taxa, while the remaining $N-K$…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such models to provide quantitative formalization of changes to Earth's biosphere. In this paper we propose and study a conceptual resource model that describes a simple and easily understandable mechanism for resource competition, generalizes the well-known Huisman and Weissing model, and takes into account species self-regulation, extinctions, and time depende…
Global, population-wide oscillations in models of cyclic dominance may result in the collapse of biodiversity due to the accidental extinction of one species in the loop. Previous research has shown that such oscillations can emerge if the interaction network has small-world properties, and more generally, because of long-range interactions among individuals or because of mobility. But although these features are all common in nature, global oscillations are rarely observed in actual biological systems. This begets the question what is the missing ingredient that would prevent local oscillatio…
The vulnerability to trawling on a species level is determined by a species' individual combination of biological traits that is related to the ecosystem functions. Trait-based indices of physical resistance RI and reproductive potential RPI were developed and combined into an overall vulnerability index on a species level, the RRI or Resistance and Reproductive Potential Index. The indices are used to explore how resistance and reproductive potentia change over a trawling gradient. The RRI allows for dividing the benthic community into groups expressing different levels of vulnerability that …
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable, either caused by external environment or intrinsic random competitions in finite populations, and the evolutionary dynamics is stochastic in nature. Here we show that, after appropriate coarse-graining, random fluctuations generate dissipation towards extinction because the evolution trajectories in the phase space of all competing species possess positive curvat…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these models revolve around speciation, dispersal, and extinction, but they usually neglect trophic structure. Here, we propose and study a spatially extended evolutionary food web model that allows us to study large spatial systems with several trophic layers. Our computer simulations show that the model gives rise simultaneously to several biodiversity patterns …
Non-transitive dominance and the resulting cyclic loop of three or more competing species provide a fundamental mechanism to explain biodiversity in biological and ecological systems. Both Lotka-Volterra and May-Leonard type model approaches agree that heterogeneity of invasion rates within this loop does not hazard the coexistence of competing species. While the resulting abundances of species become heterogeneous, the species who has the smallest invasion power benefits the most from unequal invasions. Nevertheless, the effective invasion rate in a predator and prey interaction can also be m…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the fragmentation of the habitat on biodiversity. A simple neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within ea…
Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
物种的循环优势已被确定为维持生物多样性的一种潜在机制，见例如B。Kerr，M. a.莱利，M。W. Feldman和B. J. M. Bohannan [Nature {\bf 418}，171（2002）]和B. Kirkup和M. a. Riley [Nature {\bf 428}，412（2004）].通过数值模拟支持的分析方法，我们解决了这个问题，通过研究一个典型的非空间三种群随机系统，即"石头剪刀布"或循环洛特卡-沃尔泰拉模型的属性。虽然确定性的方法（速率方程）预测的物种的共存导致定期（但中性稳定）振荡的人口密度，我们表明，在系统中产生的波动与\emph{finite number of agents}大大改变了这一局面，并负责灭绝：经过足够长的时间后，三个物种中的两个灭绝。作为主要发现，我们提供了在给定时间的灭绝概率的解析估计和数值计算。我们还讨论了我们的研究结果的影响，一类广泛的竞争人口系统。
Forward-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow "vertically" as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees (i.e., phylogenies of extant species). Alternatively, reconstructed trees can be modelled by coalescent point processes (CPP), where trees grow "horizontally" by the sequential addition of vertical edges. Each new edge starts at some random speciation time and ends at the present time; speciation times are drawn from the same distribution independently. CPP lead …
Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the relationships among character states, speciation rates, and extinction rates on phylogenetic trees- BiSSE, QuaSSE, GeoSSE, and related models - have been widely used to test hypotheses about character state-dependent diversification rates. Here, we document the disconcerting ease with which neutral traits are inferred to have statistically significant associations with …
In his highly influential view of evolution, G. G. Simpson hypothesized that clades of species evolve in adaptive zones, defined as collections of niches occupied by species with similar traits and patterns of habitat use. Simpson hypothesized that species enter new adaptive zones in one of three ways: extinction of competitor species, dispersal to a new geographic region, or the evolution of a key trait that allows species to exploit resources in a new way. However, direct tests of Simpson's hypotheses for the entry into new adaptive zones remain elusive. Here we evaluate the fit of a Simpson…
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 …
Decoding species coexistence: A reinforcement learning perspective
School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理与信息技术学院）；School of Physics and Electronic Science, East China Normal University（华东师范大学物理与电子科学学院）；School of Computer Science, Soochow University（苏州大学计算机科学与技术学院）；School of Physics, Ningxia University（宁夏大学物理学院）
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonizations and extinctions in a given geographic region. Empir…
The hypothesis of a companion object (Nemesis) orbiting the Sun was motivated by the claim of a terrestrial extinction periodicity, thought to be mediated by comet showers. The orbit of a distant companion to the Sun is expected to be perturbed by the Galactic tidal field and encounters with passing stars, which will induce variation in the period. We examine the evidence for the previously proposed periodicity, using two modern, greatly improved paleontological datasets of fossil biodiversity. We find that there is a narrow peak at 27 My in the cross-spectrum of extinction intensity time seri…
Understanding the emergence of biodiversity patterns in nature is a central problem in biology. Theoretical models of speciation have addressed this question in the macroecological scale, but little has been investigated in the macroevolutionary context. Knowledge of the evolutionary history allows the study of patterns underlying the processes considered in these models, revealing their signatures and the role of speciation and extinction in shaping macroevolutionary patterns. In this paper we introduce two algorithms to record the evolutionary history of populations in individual-based model…
Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types, of the species within the tree, upon which speciation and extinction rates depend. Although identifiability of parameters is necessary to justify parameter estimation with a model, it has not been formally established for these models, despite their adoption for inference. This work establishes generic identifiability up to label swapping for the parameters…
Failure of the fittest: limits on asexual adaptation to changing environments
Univ. Brest, CNRS UMR 6205, Laboratoire de Mathematiques de Bretagne Atlantique（布雷斯特大学）；BioSP, INRAE（法国国家农业食品与环境研究院）；Department of Ecology & Evolutionary Biology, University of Toronto（多伦多大学）
Dispersal diversity buffers species vulnerability to local extinction
University of Padova（帕多瓦大学）；National Biodiversity Future Center（国家生物多样性未来中心）；The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；University of Lausanne（洛桑大学）；Princeton University（普林斯顿大学）；CMCC Foundation, Euro Mediterranean Center on Climate Change（欧洲地中海气候变化中心基金会）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Quantifying Avian Morphological Evolution through Deep Representation Learning
Division of Ecology and Evolutionary Biology, School of Biological Science, University of Reading（阅读大学生物学科学学院生态与进化生物学系）；CAS Key Laboratory of Plant Germplasm Enhancement and Specialty Agriculture, Wuhan Botanical Garden, Chinese Academy of Sciences（中国科学院植物基因组改良与特色农业重点实验室、武汉植物园）
When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in which conditions vary somewhat between spatial locations, can exhibit chaotic dynamics which persist for extremely long times. We develop a theoretical framework, based on dynamical mean-field theory, to quantify the conditions under which these fluctuating states exist, and predict their properties. We uncover parallels with the persistence of externally-pert…
