611 research outputs found

    Food Quality in Producer-Grazer Models: A Generalized Analysis

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    Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should not be neglected. However, it is not yet resolved how stoichiometry should be integrated in population dynamical models, as different modeling approaches are found to yield qualitatively different results. Here we investigate a unifying framework that reveals the differences and commonalities between previously proposed models for producer-grazer systems. Our analysis reveals that stoichiometric constraints affect the dynamics mainly by increasing the intraspecific competition between producers and by introducing a variable biomass conversion efficiency. The intraspecific competition has a strongly stabilizing effect on the system, whereas the variable conversion efficiency resulting from a variable food quality is the main determinant for the nature of the instability once destabilization occurs. Only if the food quality is high an oscillatory instability, as in the classical paradox of enrichment, can occur. While the generalized model reveals that the generic insights remain valid in a large class of models, we show that other details such as the specific sequence of bifurcations encountered in enrichment scenarios can depend sensitively on assumptions made in modeling stoichiometric constraints.Comment: Online appendixes include

    Spatiotemporal complexity of a ratio-dependent predator-prey system

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    In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.Comment: 6pages, revtex

    Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes

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    Spatial variation in population densities across a landscape is a feature of many ecological systems, from self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of populations. However the ways in which abiotic and biotic factors interact to determine the existence and nature of spatial patterns in population density remain poorly understood. Here we present a new approach to studying this question by analysing a predator–prey patch-model in a heterogenous landscape. We use analytical and numerical methods originally developed for studying nearest- neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a rich and highly complex array of coexisting stable patterns, located within an enormous number of unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable basins of attraction, making them significant in applications. We are able to identify mechanisms for these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby landscape heterogeneity can modulate the spatial scales at which these processes operate to structure the populations

    Generalized models as a universal approach to the analysis of nonlinear dynamical systems

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    We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socio-economic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web.Comment: 15 pages, 2 figures, (Fig. 2 in color
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