Consumer-Resource Dynamics (MPB-36)

Murdoch, William W.; Briggs, Cheryl J.; Nisbet, Roger M.

doi:10.1515/9781400847259

Cited by 247 publications

(265 citation statements)

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“…In this paper our goal is to show that long-living transients mimicking complex dynamics are likely to be a common property of a conceptual, baseline single species population dynamics model. Time delays are widely recognized as an inherent feature of population dynamics (Beretta and Kuang, 1998;Hansen et al, 1998;May, 2001;Murdoch et al, 2003;Ruan, 2006). Triggered by Hutchinson seminal work (Hutchinson, 1948), there have been a large number of theoretical studies concerned with the implications of time delays for populations and communities (Hastings, 1984;Aiello and Freedman, 1990;Murdoch et al, 2003;Ruan, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…Time delays are widely recognized as an inherent feature of population dynamics (Beretta and Kuang, 1998;Hansen et al, 1998;May, 2001;Murdoch et al, 2003;Ruan, 2006). Triggered by Hutchinson seminal work (Hutchinson, 1948), there have been a large number of theoretical studies concerned with the implications of time delays for populations and communities (Hastings, 1984;Aiello and Freedman, 1990;Murdoch et al, 2003;Ruan, 2009). Time delays are thought to have a destabilizing effect as a sufficiently long delay often turns an otherwise stable positive steady state unstable (Kuang, 1993;May, 2001, Ruan, 2006, and hence converts steady population densities into population cycles, although the generality of this scenario remains controversial, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Морозов

Banerjee

Petrovskii

2016

Journal of Theoretical Biology

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Traditionally, mathematical modelling in population ecology is mainly focused on asymptotical behaviour of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct.In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple 'conceptual' model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.3

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Морозов

Banerjee

Petrovskii

2016

Journal of Theoretical Biology

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“…Although much theoretical development in ecology has treated the stability and dynamics of predation and interspecific competition separately (e.g., May 1973, Tilman 1982, 1988, Kot 2001, Murdoch et al 2003, it is clear that in nature both processes occur simultaneously, often with strong interaction strengths (e.g., Wooton 1994, Schmitz et al 2000, Hampton et al 2006. Theory that explores the implications of food web complexity for community dynamics has generally been confined to analyses of stability and species persistence (e.g., May 1973, Martinez et al 2006, Allesina and Pascual 2008, and only rarely has the nature of the underlying temporal dynamics been considered (Fussmann and Heber 2002).…”

Section: Introductionmentioning

confidence: 99%

“…1 in Methods: Intraguild predation model, below, we present a more general version of their model and confirm that these predictions remain valid for the more general model). These predictions assume that the dynamics are not greatly affected by population structure (in particular, the cycles in the system must be consumer-resource cycles rather than delayed-feedback or other cycles driven by population age structure or stage structure [Murdoch et al 2003]). In addition, the parameters governing the interspecific interactions must be constant; if heritable variation allows those parameters to evolve on the time scale of the population dynamics, the resulting eco-evolutionary dynamics can exhibit a wide variety of patterns (Ellner and Becks 2011).…”

Section: Introductionmentioning

confidence: 99%

Temporal dynamics of a simple community with intraguild predation: an experimental test

Hiltunen

Jones²,

Ellner³

et al. 2013

Ecology

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Abstract. We explore how adding complexity to a typical predator-prey interaction affects temporal dynamics. Intraguild predation webs contain competition, predation, and omnivory in a system of three species where theory and empirical results can be compared. We studied a planktonic microcosm community in which an alga is consumed by a flagellate and by a rotifer that also consumes the flagellate. Previously published theory predicts that phase lags between the species are the outcome of a ''tug of war'' among the intraguild-predation links: rotifers$algae, flagellates$algae, and rotifers$flagellates. We observed sustained oscilltions with abundance peaks that corresponded exactly to theoretical predictions in all replicates: peaks of the rotifers and flagellates fell on either side of a quarter-period lag behind the prey (algae) peaks, with the peak of the intermediate predator (flagellates) preceding that of the top predator (rotifers). The phase lags in these experiments suggest that temporal variation in flagellate growth rate is primarily driven by variation in the intensity of its consumption by rotifers, rather than by variation in the density of its algal prey. This system illustrates how interaction strength affects the pattern of intraguild predation cycles and provides an opportunity to explore how evolution of interaction strength may affect those dynamics.

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“…It is therefore essential to clarify the links between such movements, the spatial patterns that they create, and the intensity of the associated trophic interactions in order to properly understand food web dynamics Murdoch et al 2003). A range of modeling approaches have been used to study the relationship between small scale movements and predator-prey dynamics, reflecting the wide variety of movements that different organisms perform.…”

Section: Introductionmentioning

confidence: 99%

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

Sjödin

Brännström

Söderquist

et al. 2014

Journal of Theoretical Biology

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In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighboring patches and when all patches are reached with equal probability.

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Consumer-Resource Dynamics (MPB-36)

Cited by 247 publications

References 0 publications

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Temporal dynamics of a simple community with intraguild predation: an experimental test

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

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