How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and Physics. In this context, modeling the stable coexistence of species competing for limited resources is a particularly challenging task. From a mathematical point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species' relative abundances neutrally cycling without converging to a stable equilibrium. Although in recent years several mechanisms have been proposed, models able to explain species coexistence in competitive communities are still limited. Here we identify locality in the interactions as one of the simplest mechanisms leading to stable species coexistence. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes within a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate, within the scope of our model, that species coexist reaching a stable equilibrium when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance. On the contrary, when one of these ingredients is missing, large oscillations and neutral cycles emerge.
Statistical averaging and asynchronous population dynamics as portfolio mechanisms are considered as the most important processes with which biodiversity contributes to ecosystem stability. However, portfolio theories usually regard biodiversity as a fixed property, but overlook the dynamics of biodiversity altered by other ecosystem components. Here, we proposed a new mechanistic food chain model with nutrient-diversity feedback to investigate how dynamics of phytoplankton species diversity determines ecosystem stability. Our model focuses on nutrient, community biomass of phytoplankton and z…
Explaining biodiversity in nature is a fundamental problem in ecology. An outstanding challenge is embodied in the so-called Competitive Exclusion Principle: two species competing for one limiting resource cannot coexist at constant population densities, or more generally, the number of consumer species in steady coexistence cannot exceed that of resources. The fact that competitive exclusion is rarely observed in natural ecosystems has not been fully understood. Here we show that by forming chasing triplets among the consumers and resources in the consumption process, the Competitive Exclusio…
We study a mathematical model inspired by a common scenario in northern Patagonia consisting of humans and their livestock living together with native wildlife. The main production system in this area is sheep farming, which due to wrong historical management has led to desertification of the habitat, with impact on both native wildlife and livestock. Particularly the largest native herbivore, the guanaco, has reflected in their numbers this alteration induced in the environment. We analyze a mathematical model that captures the main characteristics of the interaction between sheep and guanaco…
The savanna biome is characterised by a continuous vegetation cover, comprised of herbaceous and woody plants. The coexistence of species in arid savannas, where water availability is the main limiting resource for plant growth, provides an apparent contradiction to the classical principle of competitive exclusion. Previous theoretical work using nonspatial models has focussed on the development of an understanding of coexistence mechanisms through the consideration of resource niche separation and ecosystem disturbances. In this paper, we propose that a spatial self-organisation principle, ca…
Structure, composition and stability of ecological populations are shaped by the inter- and intra-species interactions within these communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, control the structure, diversity and the long term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multi-species ecological communities that incorporates competition, immigration and demographic noise. We find that the complete phase diagram exhibits r…
Vegetation patterns are abundant in arid and semiarid ecosystems, but how they form remains unclear. One of the most extended theories lies in the existence of scale-dependent feedbacks (SDF) in plant-to-plant and plant-water interactions. Short distances are dominated by facilitative interactions, whereas competitive interactions dominate at larger scales. These feedbacks shape spatially inhomogeneous distributions of water that ultimately drive the emergence of patterns of vegetation. Even though the presence of facilitative and competitive interactions is clear, they are often hard to disen…
The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics of organisms that must modify their habitats in order to survive, the so-called ecosystem engineers, requires the explicit incorporation of abiotic interactions in the models. Here we study a model of ecosystem engineers that is discrete both in space and time, and where the engineers and their habitats are arranged in patches fixed to the sites of regular la…
The complexity of an ecological community can be distilled into a network, where diverse interactions connect species in a web of dependencies. Species interact not only with each other but indirectly through environmental effects, however the role of these ecosystem engineers has not yet been considered in models of ecological networks. Here we explore the dynamics of ecosystem assembly, where the colonization and extinction of species within a community depends on the constraints imposed by trophic, service, and engineering dependencies. We show that our assembly model reproduces many key fe…
Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among individual organisms even within the same species, causing heterogeneity in their interaction strengths with other species. The consequences of such heterogeneous interactions for the ecosystem have not been studied systematically. As a theoretical exploration, we analyze a simple ecosystem with trophic interactions between two predators and a shared prey, wh…
Towards a less spherical cow: Species differences dilute the stabilizing effect of higher-order interactions
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB（跨学科物理与复杂系统研究所（CSIC-UIB））；Centro Studi e Ricerche “Enrico Fermi” (CREF)（“恩里科·费米”研究与学习中心）；Institute for Applied Mathematics Mauro Picone (IAC) CNR（马乌罗·皮科内应用数学研究所（CNR））；Estación Biológica de Doñana (CSIC)（多尼亚纳生物站（CSIC））；University of Oxford（牛津大学）
The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different resource dynamics affect this bound. Here, we analyze a generalized consumer resource model with externally supplied resources and show that -- in contrast to self-renewing resources -- species can occupy only half of all available environmental niches. This motivates us to construct a new schema for classifying ecosystems based on species packing propertie…
Disturbance accelerates the transition from low- to high- diversity state in a model ecosystem
干扰对固着和相互竞争物种的模型生态系统的影响[Mathiesen et al. Phys. Rev. Lett. 107，188101（2011）; Mitarai等人Phys.Rev.E86，011929（2012）]。随机干扰将个体从系统中移除，并且所创建的空站点被邻近物种重新殖民。我们表明，稳定的高多样性状态，保持偶尔循环物种的相互作用，创造孤立的补丁的元种群，是强大的小干扰。我们进一步证明，有限扰动可以通过扩散具有对峙关系的物种之间的边界来帮助创建小斑块，从而加速从低多样性状态到高多样性状态的转变。
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where some species out-compete or dominate over some others are key to describe natural ecosystems. Here we develop ecological theory using a stochastic, synthetic framework for plant community assembly that leads to predictions amenable to empirical testing. We propose two stochastic continuous-time Markov models that incorporate competitive dominance through a h…
Recent work draws attention to community-community encounters ("coalescence") as likely an important factor shaping natural ecosystems. This work builds on MacArthur's classic model of competitive coexistence to investigate such community-level competition in a minimal theoretical setting. It is shown that the ability of a species to survive a coalescence event is best predicted by a community-level "fitness" of its native community rather than the intrinsic performance of the species itself. The model presented here allows formalizing a macroscopic perspective whereby a community harboring or…
Relations among species in ecosystems can be represented by complex networks where both negative (competition) and positive (mutualism) interactions are concurrently present. Recently, it has been shown that many ecosystems can be cast into mutualistic networks, and that nestedness reduces effective inter-species competition, thus facilitating mutually beneficial interactions and increasing the number of coexisting species or the biodiversity. However, current approaches neglect the structure of inter-species competition by adopting a mean-field perspective that does not deal with competitive …
Center for Mechanisms of Evolution, Biodesign Institute, Arizona State University（亚利桑那州立大学生物设计研究所进化机制中心）；School of Mathematical and Statistical Sciences, Arizona State University（亚利桑那州立大学数学与统计科学学院）；Centro de Investigaciones en Matemáticas（数学研究中心）；Center for Genomic Sciences, Universidad Nacional Autónoma de México（墨西哥国立自治大学生命科学中心）
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 o…
Coexistence coalitions in propagule disperser quasi-communities
Centre d’Estudis Avançats de Blanes, Consejo Superior de Investigaciones Científicas (CEAB-CSIC)（布兰斯高级研究中心，西班牙国家研究委员会）；Universidad Politécnica de Madrid（马德里理工大学）
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stoch…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stoch…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which mechanisms confer an advantage to a given species against the other(s)? In general, it is expected that the species with the higher reproductive/death ratio will win the competition, but other mechanisms, such as asymmetry in interspecific competition or unequal diffusion rates, have been found to change this scenario dramatically. In this work, we examine compe…
Spatio temporal data are more ubiquitous and richer than even before and the availability of such data poses great challenges in data analytics. Ecological facilitation, the positive effect of density of individuals on the individual's survival across a stress gradient, is a complex phenomenon. A large number of tree individuals coupled with soil moisture, temperature, and water stress data across a long temporal period were followed. Data driven analysis in the absence of hypothesis was performed. Information theoretic analysis of multiple statistical models was employed in order to quantify …
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）
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction and coexistence criteria when there are one or two interacting species. We then use these tools in order to see when harvesting leads to extinction or persistence of species, as well as what the optimal harvesting strategies, which maximize the expected long term yield, look like. For single species systems, we show under certain conditions that the optimal ha…
