Stability of ecological communities with antagonistic interactions (original) (raw)
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Stability Analysis of an Ecological Model
For a new family of ecological systems, we prove the global asymptotic stability of a positive equilibrium point. That way, we show how the consideration of an intra-specific dependency in the population growth functions can explain not only the persistence of several species in competition for a single resource but also attractivity of a positive equilibrium point.
Theoretical Ecology, 2015
The relationship between structure and stability in ecological networks, and the effect of spatial dynamics on natural communities have both been major foci of ecological research for decades. Network research has traditionally focused on a single interaction type at a time (e.g., food webs, mutualistic networks). Networks comprising different types of interactions have recently started to be empirically characterized. Patterns observed in these networks and their implications for stability demand for further theoretical investigations. Here we employed a spatially explicit model to disentangle the effects of mutualism:antagonism ratios in food web dynamics and stability. We found that increasing levels of plant-animal mutualistic interactions generally resulted in more stable communities. More importantly, increasing the proportion of mutualistic vs. antagonistic interactions at the base of the food web affects different aspects of ecological stability in different directions, although never negatively. Stability is either not influenced by increasing mutualism-for the cases of population stability and species' spatial distributions-or is positively influenced by it-for spatial aggregation of species. Additionally, we observe that the relative increase of mutualistic relationships decreases the strength of biotic interactions in general within the ecological network. Our work highlights the importance of considering several dimensions of stability simultaneously to understand the dynamics of communities comprising multiple interaction types.
Alternative steady states in ecological networks
Physical Review E, 2017
In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When the competition matrix is random, the number of SUs depends on the average value of its entries and the variance. Here we consider the problem in the limit of weak competition and large variance. Using a yes/no interaction model, we show that the number of SUs corresponds to the number of maximum cliques in a network close to its fully connected limit. The number of SUs grows exponentially with the number of species in this limit, unless the network is completely asymmetric. In the asymmetric limit the number of SUs is O(1). Numerical simulations suggest that these results are valid for models with continuous distribution of competition terms.
Stability and species richness in complex communities
Ecology Letters, 2000
Using both numerical simulations and analytical methods, we investigate how the stability of ecological communities depends on the number of species they contain. To investigate complex communities, we construct communities from modular`s ubcommunities'' that can have arbitrary community structure; e.g. subcommunities could consist of pairs of predator and prey species, trios of prey, specialist predator and generalist predator, or any collection of interacting species. By building entire communities from subcommunities, we can change the number of species in the community without changing community structure. We further suppose that species sharing the same ecological role in different subcommunities act additively on the per capita population growth rates of other species. Under these assumptions, the interactions between species from different subcommunities have no effect on communitylevel stability, measured by the variability in the combined densities of species sharing the same ecological role in different subcommunities. Furthermore, increasing species richness (i.e. the number of subcommunities comprising the community) increases community-level stability only when it introduces species that respond differently to environmental fluctuations. Therefore, our results support the``insurance hypothesis'' that species richness increases community-level stability by insuring that some species in a community are tolerant of different environmental fluctuations.
Journal of mathematical biology, 2003
The nature of the association between two species may vary depending on population abundances, age or size of individuals, or environmental conditions. Interactions may switch between beneficial and detrimental depending on the net balance of costs and benefits involved for each species. We study the repercussion of the ecological setting on the outcomes of conditional or variable interactions by means of a model that incorporates density-dependent interaction coefficients; that is, interaction α-functions. These characterize the responsiveness and sensitivity of the association to changes in partner's abundance, and can take positive and negative values. Variable outcomes -and transitions between them -are categorized as homeo-or allo-environmental, that is, occurring under the same ecological setting, or not, respectively. Bifurcation analyses show that these dynamics are moulded by ecological factors that are: intrinsic to the nature of the association (concerning the sensitivity of the interaction), and extrinsic to the association itself (the quality of the environment referred to each species alone). The influence of these factors may be conflicting; consequently, the dynamics involve catastrophic events. In a facultative variable association, stable coexistence is expected when environmental conditions are adverse; otherwise, the exclusion of one species is the likely outcome. Remarkable situations as the switching of victim-exploiter roles illustrate the theoretical perspective.
Stability of Degree Heterogeneous Ecological Networks
arXiv (Cornell University), 2014
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies, few if any of these advances address one of the most fundamental properties of network structure: heterogeneity among nodes with different numbers of links. Here we systematically explore this property of "degree heterogeneity" and find that its effects on stability systematically vary with different types of interspecific interactions. Degree heterogeneity is always destabilizing in ecological networks with both competitive and mutualistic interactions while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e., the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity stabilizes food webs except those with the most contiguity. These findings help explain previously unexplained observations that food webs are highly but not completely contiguous and, more broadly, deepens our understanding of the stability of complex ecological networks with important implications for other types of dynamical systems. Understanding the intricate relationship between the structure and dynamics of complex ecological systems has been one of the key issues in ecology [1-4]. Equilibrium stability of ecological systems, a measure that considers an ecological system stable if it returns to its equilibrium after a small perturbation, has been a central research topic for over four decades [1, 5-15]. Empirical observations suggest that communities with more species are more stable, i.e., a positive diversity-stability relationship [16]. Yet, these intuitive ideas were challenged by
Short-term instabilities and long-term community dynamics
Trends in Ecology & Evolution, 1989
Competition in a temporally variable environment leads to sequences of short-term instabilities that in some cases are the mechanism of long-term coexistence; in other cuses they promote long-term instability. Recent work associates long-term stability with a positive relationship between environmental and competitive effects and with population growth rates that are buffered against iointly unfavorable environmental and competitive events. Buffered growth rates arise from population subdivision over life-history stages, microenvironments or phenotypes. A distinct but related mechanism of longterm stability relies on population growth rates that are nonlinear functions of competition. New ways of understanding and investigating species diversity follow from these results. Shorkterm Instabilities and Longterm Community Dynamics Although it is recognized that the stability of an ecological community depends on the temporal scale on which it is viewed, it is not well-appreciated that in some systems long-term stability may be a consequence of short-term instabilities. As viewed here, long-term stability is the tendency of a community to recover from extreme perturbations of the densities of any of its component species'. Short-term instabilities are trends on a short timescale that would lead to extinctions if extrapolated into the future (Box 11. We review models that demonstrate the potential for short-term instabilities to contribute to long-term coexistence of species, and we discuss data that are consistent with these models.
Spatial and Ecological Scaling of Stability in Spatial Community Networks
Frontiers in Ecology and Evolution, 2022
There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regionalscale analyses consider the whole network. Similarly, species-and community-level analyses either account for single species or for the whole community. Furthermore, stability itself can be defined in multiple ways, including resistance (the inverse of the relative displacement caused by a perturbation), initial resilience (the rate of return after a perturbation), and invariability (the inverse of the relative amplitude of the population fluctuations). Here, we analyze the scale-dependence of these stability properties. More specifically, we ask how spatial scale (local vs. regional) and ecological scale (species vs. community) influence these stability properties. We find that regional initial resilience is the weighted arithmetic mean of the local initial resiliences. The regional resistance is the harmonic mean of local resistances, which makes regional resistance particularly vulnerable to nodes with low stability, unlike regional initial resilience. Analogous results hold for the relationship between community-and species-level initial resilience and resistance. Both resistance and initial resilience are "scale-free" properties: regional and community values are simply the biomass-weighted means of the local and species values, respectively. Thus, one can easily estimate both stability metrics of whole networks from partial sampling. In contrast, invariability generally is greater at the regional and community-level than at the local and species-level, respectively. Hence, estimating the invariability of spatial or ecological networks from measurements at the local or species level is more complicated, requiring an unbiased estimate of the network (i.e., region or community) size. In conclusion, we find that scaling of stability depends on the metric considered, and we present a reliable framework to estimate these metrics.
Feasibility and coexistence of large ecological communities
Nature Communications, 2017
The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity–feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically pre...