1,721,149 research outputs found
An exactly solvable coarse-grained model for species diversity
No full textWe present novel analytical results concerning ecosystem species diversity that stem from a proposed coarse-grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results from ecological neutral theory and empirical evidence on species diversity preservation. The neutral model of biodiversity deals with ecosystems at the same trophic level, where per capita vital rates are assumed to be species independent. Closed-form analytical solutions for the neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain to: the probability distribution function of the number of species in the ecosystem, both in transient and in stationary states; the n-point connected time correlation function; and the survival probability, defined as the distribution of time spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from an estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications for biodiversity and conservation biology
Disentangling the effect of hybrid interactions and of the constant effort hypothesis on ecological community stability
No full textIn the last years, a remarkable theoretical effort has been made in order to understand the relation between stability and complexity in ecological communities. Yet, what maintains species diversity in real ecological communities is still an open question. The non-random structures of ecological interaction networks have been recognized as one key ingredient impacting the maximum number of coexisting species within the ecological community. However most of the earlier theoretical studies have considered communities with only one interaction type (either antagonistic, competitive or mutualistic). Recently, it has been proposed that multiple interaction types might stabilize ecosystems and that, in this hybrid case, increasing complexity increases stability. Here we show that these results depend on ad hoc hypothesis that the authors used in their model and we highlight the need to disentangle the role of multiple interaction types and constant interaction effort allocation on community stability. Indeed, we find that mixing of mutualistic and predator-prey interaction types does not stabilize the community dynamics and we demonstrate that a positive correlation between complexity and stability is observed only if a constant effort allocation is imposed in the ecological interactions. Synthesis In recent years a sparkling research has been devoted to the search of new theoretical mechanisms to explain way ecosystems may persist despite their complexity. Here we show that, contrary to what recently suggested (Mougi et al. 2012), the mismatch between theoretical results and empirical evidences on the stability of ecological community is still there also for communities with both mutualistic and antagonistic interactions, and the 'complexity-stability' paradox is still alive. Indeed, we demonstrate that their results arise as an artifact of the peculiar rescaling of the interaction strengths they imposed. Our study suggests that further theoretical studies and experimental evidences are still needed to better understand the role of interaction strengths in real ecological communities
Early warning signs in social-ecological networks.
Full text linkA number of social-ecological systems exhibit complex behaviour associated with nonlinearities, bifurcations, and interaction with stochastic drivers. These systems are often prone to abrupt and unexpected instabilities and state shifts that emerge as a discontinuous response to gradual changes in environmental drivers. Predicting such behaviours is crucial to the prevention of or preparation for unwanted regime shifts. Recent research in ecology has investigated early warning signs that anticipate the divergence of univariate ecosystem dynamics from a stable attractor. To date, leading indicators of instability in systems with multiple interacting components have remained poorly investigated. This is a major limitation in the understanding of the dynamics of complex social-ecological networks. Here, we develop a theoretical framework to demonstrate that rising variance--measured, for example, by the maximum element of the covariance matrix of the network--is an effective leading indicator of network instability. We show that its reliability and robustness depend more on the sign of the interactions within the network than the network structure or noise intensity. Mutualistic, scale free and small world networks are less stable than their antagonistic or random counterparts but their instability is more reliably predicted by this leading indicator. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social-ecological networks
Species survival and scaling laws in hostile and disordered environments
No full textIn this work we study the likelihood of survival of single-species in
the context of hostile and disordered environments. Population dynamics
in this environment, as modeled by the Fisher equation, is characterized
by negative average growth rate, except in some random spatially
distributed patches that may support life. In particular, we are
interested in the phase diagram of the survival probability and in the
critical size problem, i.e., the minimum patch size required for
surviving in the long-time dynamics. We propose a measure for the
critical patch size as being proportional to the participation ratio of
the eigenvector corresponding to the largest eigenvalue of the
linearized Fisher dynamics. We obtain the (extinction-survival) phase
diagram and the probability distribution function (PDF) of the critical
patch sizes for two topologies, namely, the one-dimensional system and
the fractal Peano basin. We show that both topologies share the same
qualitative features, but the fractal topology requires higher spatial
fluctuations to guarantee species survival. We perform a finite-size
scaling and we obtain the associated scaling exponents. In addition, we
show that the PDF of the critical patch sizes has an universal shape for
the 1D case in terms of the model parameters (diffusion, growth rate,
etc.). In contrast, the diffusion coefficient has a drastic effect on
the PDF of the critical patch sizes of the fractal Peano basin, and it
does not obey the same scaling law of the 1D case
Effect of delay on the emergent stability patterns in generalized Lotka-Volterra ecological dynamics
Full text linkUnderstanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity.This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'
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