Biodiversity and robustness of large ecosystems (original) (raw)
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Biodiversity, extinctions, and evolution of ecosystems with shared resources
Physical review. E, 2017
We investigate the formation of stable ecological networks where many species share the same resource. We show that such a stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of coexisting species, and we find a relation describing how many species that may become 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 the system to converge, by extinctions. When that stress parameter is large, we obtain that the species traits are concentrated at certain values. This stress parameter is thereby a parameter that determines the level of final biodiversity of the system. Moreover, we show that the dynamics of this limit system can be described by simple differential equations.
Biodiversity in model ecosystems, I: coexistence conditions for competing species
Journal of Theoretical Biology, 2005
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is . Here we review and generalize this analysis, beyond the "mean-field"-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host.
A general theory of coexistence and extinction for stochastic ecological communities
Journal of Mathematical Biology, 2021
We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous time (stochastic differential equations), compact and non-compact state spaces and degenerate or non-degenerate noise. In addition, we can also include in the dynamics auxiliary variables that model environmental fluctuations, population structure, eco-environmental feedbacks or other internal or external factors. We are able to significantly generalize the recent discrete time results by Benaim and Schreiber (Journal of Mathematical Biology '19) to non-compact state spaces, and we provide stronger persistence and extinction results. The continuous time results by Hening and Nguyen (Annals of Applied Probability '18) are strengthened to include degenerate noise and auxiliary variables. Using the general theory, we work out several examples. In discrete time, we classify the dynamics when there are one or two species, and look at the Ricker model, Log-normally distributed offspring models, lottery models, discrete Lotka-Volterra models as well as models of perennial and annual organisms. For the continuous time setting we explore models with a resource variable, stochastic replicator models, and three dimensional Lotka-Volterra models.
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.
Extinction in population dynamics
Physical Review E, 2004
The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. arXiv:cond-mat/0309568v1 [cond-mat.stat-mech] We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead to certain extinction. Standard continuum mean field models in one dimension yield a critical refuge length Lc such that a population in a refuge larger than this is assured survival. Herein we extend the model to take into account the discreteness and finiteness of the population, which leads us to a stochastic description. We present a particular critical criterion for likely extinction, namely, that the standard deviation of the population be equal to the mean. According to this criterion, we find that while survival can no longer be guaranteed for any refuge size, for sufficiently weak competition one can make the refuge large enough (certainly larger than Lc) to cause extinction to be unlikely. However, beyond a certain value of the competition rate parameter it is no longer possible to escape a likelihood of extinction even in an infinite refuge. These unavoidable fluctuations therefore have a severe impact on refuge design issues.
Biodiversity dynamics under intransitive competition and habitat destruction
Species are faced with a multitude of risk factors for extinction including small carrying capacity, large environmental variation, habitat loss, climate change, and invasive species (Drake 2006; Kuussaari et al. 2009). These factors naturally occur at certain baseline levels, but modern humans have contributed to an astonishing increase in the degree to which they exacerbate risks of biodiversity loss.
Extinction rate fragility in population dynamics
Physical Review Letters, 2009
Population extinction is of central interest for population dynamics. It may occur from a large rare fluctuation. We find that, in contrast to related large-fluctuation effects like noise-induced interstate switching, quite generally extinction rates in multipopulation systems display fragility, where the height of the effective barrier to be overcome in the fluctuation depends on the system parameters nonanalytically. We show that one of the best-known models of epidemiology, the susceptible-infectious-susceptible model, is fragile to total population fluctuations.
Phenotypic Diversity and Stability of Ecosystem Processes
Theoretical Population Biology, 1999
The resistance of an ecosystem to perturbations and the speed at which it recovers after the perturbations, which is called resilience, are two important components of ecosystem stability. It has been suggested that biodiversity increases the resilience and resistance of aggregated ecosystem processes. We test this hypothesis using a theoretical model of a nutrient-limited ecosystem in a heterogeneous environment. We investigate the stability properties of the model for its simplest possible configuration, i.e., a system consisting of two plant species and their associated detritus and local resource depletion zones. Phenotypic diversity within the plant community is described by differences in the nutrient uptake and mortality rates of the two species. The usual measure of resilience characterizes the system as a whole and thus also applies to aggregated ecosystem processes. As a rule this decreases with increased diversity, though under certain conditions it is maximum for an intermediate value of diversity. Resistance is a property that characterizes each system component and process separately. The resistance of the inorganic nutrient pools, hence of nutrient retention in the ecosystem, decreases with increased diversity. The resistance of both total plant biomass and productivity either monotonically decreases or increases over part of the parameter range with increased diversity. Furthermore, it is very sensitive to parameter values. These results support the view that there is no simple relationship between diversity and stability in equilibrium deterministic systems, whether at the level of populations or aggregated ecosystem processes. We discuss these results in relation to recent experiments.
Unusual dynamics of extinction in a simple ecological model
Proceedings of the National Academy of Sciences, 1996
Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a
This paper investigates how optimal economic growth can affect the natural evolution of the ecological system. Policy makers may perform defensive actions to protect biodiversity. These actions, however, may deeply modify the natural ecological dynamics so that the resulting equilibrium has different dynamic features with respect to the equilibrium that would have naturally emerged without human intervention. To investigate this issue more deeply, we analyze the impact that economic activity and environmental defensive choices can have on the natural ecological dynamics depending on whether agents care or do not care for biodiversity. Using an optimal growth model with pollution, in which biodiversity loss may be caused by the negative side-effects of aggregate production, we show that human action can modify the stability of the ecological fixed points. In particular, from the simple analytical formulations adopted in the paper, it emerges that – when the levels of the species is sufficiently low at the fixed point and agents care for biodiversity – human intervention may cause a stabilization of the fixed point and thus avoid the extinction of a species, even in the absence of defensive expenditures specifically finalized at the protection of that species. It follows that the protection of biodiversity (through the stabilization of the ecological system) may come at the cost of a change in the original features of the natural dynamics. Moreover, it is shown that a limit cycle may arise through a Hopf bifurcation from the interaction of the economic and ecological systems even though none of the two systems taken separately admits a limit cycle.