Maury Poggiale JTB2013

Journal of Theoretical Biology, 2013

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Journal of Theoretical Biology, 2004

A new time-dependent continuous model of biomass size spectra is developed. In this model, predation is the single process governing the energy flow in the ecosystem, as it causes both growth and mortality. The ratio of predator to prey is assumed to be distributed: predators may feed on a range of prey sizes. Under these assumptions, it is shown that linear size spectra are stationary solutions of the model. Exploited fish communities are simulated by adding fishing mortality to the model: it is found that realistic fishing should affect the curvature and stability of the size spectrum rather than its slope.

Biophysics, 2013

We present a mathematical model of an aquatic community, where the size and age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between zooplank ton, peaceful fish, and predatory fish are described. We show that interactions between separate components of the aquatic community can give rise to long period oscillations in fish population size. The period of these oscillations is on the order of decades. With this model we also show that an increase in the zooplankton growth rate may entail a sequence of bifurcations in the fish population dynamics: steady states → regular oscillations → quasicycles → dynamic chaos.

Russian Journal of Numerical Analysis and Mathematical Modelling, 2015

We present a mathematical model of an aquatic community, which includes zooplankton and sh reproduction, and age-weight-structured trophic relationships. We show that interactions between separate components of the aquatic community can give rise to long-period oscillations in sh population size. The period of these oscillations is on the order of decades. We show that predatory sh can be an element, which gives rise to the long-period oscillations. With this model we also show that an increase in the zooplankton growth rate may entail a sequence of bifurcations in the sh population dynamics: steady states → regular oscillations → quasicycles → dynamic chaos. Since aquatic, and in particular, lake ecosystems are spatially heterogeneous, they are often considered as consisting of separate habitats, which are distinguished by their hydrophysical and ecological characteristics. We show that interhabitat sh migration can lead to dramatic changes in the sh population dynamics. In particular, the sh migration can destabilize both stationary states and chaotic regimes giving rise to regular and quasiregular oscillations in the sh population size.

Progress in Oceanography, 2010

The modeling of mid-trophic organisms of the pelagic ecosystem is a critical step in linking the coupled physical-biogeochemical models to population dynamics of large pelagic predators. Here, we provide an example of a modeling approach with definitions of several pelagic mid-trophic functional groups. This application includes six different groups characterized by their vertical behavior, i.e., occurrence of diel migration between epipelagic, mesopelagic and bathypelagic layers. Parameterization of the dynamics of these components is based on a temperature-linked time development relationship. Estimated parameters of this relationship are close to those predicted by a model based on a theoretical description of the allocation of metabolic energy at the cellular level, and that predicts a species metabolic rate in terms of its body mass and temperature. Then, a simple energy transfer from primary production is used, justified by the existence of constant slopes in log-log biomass size spectrum relationships. Recruitment, ageing, mortality and passive transport with horizontal currents, taking into account vertical behavior of organisms, are modeled by a system of advection-diffusion-reaction equations. Temperature and currents averaged in each vertical layer are provided independently by an Ocean General Circulation Model and used to drive the mid-trophic level (MTL) model. Simulation outputs are presented for the tropical Pacific Ocean to illustrate how different temperature and oceanic circulation conditions result in spatial and temporal lags between regions of high primary production and regions of aggregation of mid-trophic biomass. Predicted biomasses are compared against available data. Data requirements to evaluate outputs of these types of models are discussed, as well as the prospects that they offer both for ecosystem models of lower and upper trophic levels.

bio.vu.nl

This paper presents a DEB-based mathematical model of the size-structured dynamics of marine communities which integrates individual, population and community levels. The model represents the transfer of energy in both time and structural volume (size) of an infinite number of interacting fish species characterized by their maximum structural volume and covering the entire range of possible life histories from very small to very large species. The model is based on standard DEB assumptions as well as a set of important ecological processes such as opportunistic size-based predation, competition for food, density-dependent schooling probability, schooling-dependent availability of prey and schooling-dependent disease mortality. Resting on the inter-specific body-size scaling relationships of the DEB theory, the diversity of life-history traits (i.e. biodiversity) is explicitly integrated. The stationary solutions of the model as well as the transient solutions arising when environmental signals (e.g. variability of primary production and temperature) propagate through the ecosystem are studied using numerical simulations. It is shown that in the absence of densitydependent feedback processes, the model exhibits unstable oscillations. Schooling-dependent predatory and disease mortalities are proposed to be important stabilizing factors allowing stationary solutions to be reached. At the community level, the shape and slope of the obtained quasi-linear community spectrum matches well empirical studies. At the species level, the simulations show that small and large species dominate the community successively (small species being more abundant at small sizes and large species being more abundant at large sizes) and that the total biomass of a species decreases with its maximal size which again corroborates empirical studies. We define the function Φ as the relative contribution of each species to the total biomass of the ecosystem, for any given structural volume. We argue that this function is a measure of the functional role of biodiversity characterizing the impact of the structure of the community (its species composition) on its function (the relative proportions of losses, dissipation and biological work). When oscillations of primary production are simulated, the model predicts that the variability propagates along the spectrum in a given frequency-dependent size range before decreasing for larger sizes.

Chaos, Solitons & Fractals, 2002

A fairly realistic three-species food chain model based on the Leslie±Gower scheme is investigated by using tools borrowed from the nonlinear dynamical systems theory. It is observed that two co-existing attractors may be generated by this ecological model. A type-I intermittency is characterized and a homoclinic orbit is found. Ó : S 0 9 6 0 -0 7 7 9 ( 0 0 ) 0 0 2 3 9 -3

Theoretical Population Biology, 1987

We investigated the dynamics of models of aquatic food webs using stability analysis methods previously applied to other types of food web models. Our models expanded traditional Lotka-Volterra models of predator-prey interactions in several ways. We added life history structure to these models in order to investigate its effects. Life history omnivory is different life history stages of a species feeding in trophically different positions in a food web. Such a species might appear omnivorous, integrating across all stages, but the individual stage might not be. Other important additions to the basic models included stock-recruitment relationships between adults and young and food-dependent maturation rates for early life history stages. Complex models of multispecies interactions were built from basic ones by adding new features sequentially. Our analysis revealed five major features of our multispecies, multi-life-stage models. Omnivory reduces stability, as it does in food web models without life history structure. However, life history omnivory reduces stability much less than single life stage omnivory does. Stock recruitment relationships affect the likelihood of finding stable models. If the maturation rate of young varies with their food supply, the chance of finding stable models decreases. Finally, predation loops of the type A eats B, B eats A, or A eats B, B eats C, C eats A greatly reduce model stability. We present both biological and mathematical explanations for these findings. We also discuss their implications for management of marine resources. 0 1987 Academic Press, Inc.

Bulletin of mathematical biology, 2010

Progress in Oceanography, 2007

This paper presents an original size-structured mathematical model of the energy flow through marine ecosystems, based on established ecological and physiological processes and mass conservation principles. The model is based on a nonlocal partial differential equation which represents the transfer of energy in both time and body weight (size) in marine ecosystems. The processes taken into account include size-based opportunistic trophic interactions, competition for food, allocation of energy between growth and reproduction, somatic and maturity maintenance, predatory and starvation mortality. All the physiological rates are temperature-dependent. The physiological bases of the model are derived from the dynamic energy budget theory. The model outputs the dynamic size-spectrum of marine ecosystems in term of energy content per weight class as well as many other size-dependent diagnostic variables such as growth rate, egg production or predation mortality.