Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations which lead to coexistence in a uniform environment may favor alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes.
Contemporary Niche Theory is a useful framework for understanding how organisms interact with each other and with their shared environment. Its graphical representation, popularized by Tilman's Resource Ratio Hypothesis, facilitates the analysis of the equilibrium structure of complex dynamical models including species coexistence. This theory has been applied primarily to resource competition since its early beginnings. Here, we integrate mutualism into niche theory by expanding Tilman's graphical representation to the analysis of consumer-resource dynamics of plant-pollinator networks. We gr…
Reconciling metabolic scaling theory with observed variation in self-thinning trajectories: the relative roles of individual ontogeny, mode of competition, and resource limitation
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We include resource competition based on shared capture area separately. By varying relative rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the contex…
Resource competition theory predicts coexistence and exclusion patterns based on species R*s, the minimum resource values required for a species to persist. A central assumption of the theory is that all species have equal access to resources. However, many systems are characterized by preemption exploitation, where some species deplete resources before their competitors can access them (e.g., asymmetric light competition, contest competition among animals). We hypothesize that coexistence under preemption requires an R*-preemption tradeoff, i.e., the species with the priority access should ha…
Organisms shape their own environment, which in turn affects their survival. This feedback becomes especially important for communities containing a large number of species; however, few existing approaches allow studying this regime, except in simulations. Here, we use methods of statistical physics to analytically solve a classic ecological model of resource competition introduced by MacArthur in 1969. We show that the non-intuitive phenomenology of highly diverse ecosystems includes a phase where the environment constructed by the community becomes fully decoupled from the outside world.
The large variation in seed mass among species inspired a vast array of theoretical and empirical research attempting to explain this variation. So far, seed mass variation was investigated by two classes of studies: one class focuses on species varying in seed mass within communities, while the second focuses on variation between communities, most often with respect to resource gradients. Here, we develop a model capable of simultaneously explaining variation in seed mass within and between communities. The model describes resource competition (for both soil and light resources) in annual com…
We solve MacArthur's resource-competition model with random species-resource couplings in the `thermodynamic' limit of infinitely many species and resources using dynamical path-integrals a la De Domincis. We analyze how the steady state picture changes upon modifying several parameters, including the degree of heterogeneity of metabolic strategies (encoding the preferences of species) and of maximal resource levels (carrying capacities), and discuss its stability. Ultimately, the scenario obtained by other approaches is recovered by analyzing an effective one-species-one-resource ecosystem th…
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 n…
The Hassell model has been widely used as a general discrete-time population dynamics model that describes both contest and scramble intraspecific competition through a tunable exponent. Since the two types of competition generally lead to different degrees of inequality in the resource distribution among individuals, the exponent is expected to be related to this inequality. However, among various first-principles derivations of this model, none is consistent with this expectation. This paper explores whether a Hassell model with an exponent related to inequality in resource allocation can be…
Recent work suggests that cross-feeding -- the secretion and consumption of metabolic biproducts by microbes -- is essential for understanding microbial ecology. Yet how cross-feeding and competition combine to give rise to ecosystem-level properties remains poorly understood. To address this question, we analytically analyze the Microbial Consumer Resource Model (MiCRM), a prominent ecological model commonly used to study microbial communities. Our mean-field solution exploits the fact that unlike replicas, the cavity method does not require the existence of a Lyapunov function. We use our so…
The role of skill (fitness) and luck (randomness) as driving forces on the dynamics of resource accumulation in a myriad of systems have long puzzled scientists. Fueled by undisputed inequalities that emerge from actual competitions, there is a pressing need for better understanding the effects of skill and luck in resource accumulation. When such competitions are driven by externalities such as cumulative advantage (CA), the rich-get-richer effect, little is known with respect to fundamental properties such as their duration and intensity. In this work we provide a mathematical understanding …
In mutualisms where there is exchange of resources for resources, or resources for services, the resources are typically short lived compared with the lives of the organisms that produce and make use of them. This fact allows a separation of time scales, by which the numerical response of one species with respect to the abundance of another can be derived mechanistically. These responses can account for intra-specific competition, due to the partition of the resources provided by mutualists, in this way connecting competition theory and mutualism at a microscopic level. It is also possible to …
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in terms of reproduction rate. In the second case, resources are not uniformly distributed in space. In the third case, the two species are transported by a fluid flow. In all these cases, at varying the parameters, we observe a transition from a regime in which diffusing faster confers an effective selective advantage to one in which it constitutes a disadvantag…
Energy, space and competition: A model of territorial organization in camelids
Centro Atómico Bariloche (CNEA), CONICET（巴里洛切原子中心 (CNEA)，阿根廷国家科学研究委员会）；Universidad Nacional del Comahue（内乌肯国立大学）；Instituto Balseiro (Universidad Nacional de Cuyo)（巴尔塞罗研究所 (图库曼国立大学)）；Universidad Nacional de Cuyo（图库曼国立大学）；Universidad Nacional de Río Negro（里奥内格罗国立大学）
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio of realized species diversity to the number of resources. This ratio is set by competition, through the balance between species being pushed out and invading. When this ratio is smaller than one, dynamics will reach stable equilibria. When this ratio is larger than one, fixed-points are either unstable or marginally stable, as expected by the competitive ex…
