Bifurcation theory, adaptive dynamics and dynamic energy budget-structured populations of iteroparous species

Kooi, Bob W.; Meer, Jaap van der

doi:10.1098/rstb.2010.0173

Cited by 14 publications

(14 citation statements)

References 40 publications

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“…Jager & Klok (2010) use DEB-structured individuals in matrix and continuous Euler-Lotka population models to extrapolate toxic effects from individuals to populations. Kooi & van der Meer (2010) use a physiological-structured population to model the dynamics of a population in a semi-chemostat environment where reproduction is a discrete event process. In the case of organisms that reproduce by division, the transition from the individual to the population is simpler, because organisms can be considered as V1-morphs, i.e.…”

Section: (C) the Population Levelmentioning

confidence: 99%

Dynamic energy budget theory restores coherence in biology

Sousa¹,

Domingos²,

Poggiale

et al. 2010

Phil. Trans. R. Soc. B

226

185

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We present the state of the art of the development of dynamic energy budget theory, and its expected developments in the near future within the molecular, physiological and ecological domains. The degree of formalization in the set-up of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occam's razor, is discussed. We place the various contributions in the theme issue within this theoretical setting, and sketch the scope of actual and potential applications.Keywords: dynamic energy budget theory; biology; metabolism; ecology; evolution; energetics REACHING OUT FOR GENERALITYIn physics, there is a quest for a unified theory. Physical theories have a broad spectrum of application, a strong mathematical background and are subject to numerous empirical tests. By contrast, in biology, mathematical theory has played a secondary role because biology is frequently seen as a science of exceptions and particular cases, with little interest in abstraction and generalization. Exceptions are the research being done in the fields of theoretical biology and mathematical biology. However, theoretical and mathematical biology have frequently been carried out without a concern for empirical testing. When this concern appears, models are of narrow application, reducing their theoretical breadth. The dynamic energy budget (DEB) theory starts from the Dutch tradition of theoretical and mathematical biology, but couples it with a fundamental concern in producing general theory that is subjected to careful empirical testing.DEB theory aims to capture the quantitative aspects of metabolism at the individual level for organisms of all species. It builds on the premise that the mechanisms that are responsible for the organization of metabolism are not species-specific (Kooijman 2001(Kooijman , 2010. This hope for generality is supported by (i) the universality of physics and evolution and (ii) the existence of widespread biological empirical patterns among organisms . Table 1 synthesizes the essential criteria for any general model for the metabolism of individuals. We explore the links between DEB theory and each of the proposed criteria in the following paragraphs. DEB theory is explicitly based on the conservation of mass, isotopes, energy and time, including the inherent degradation of energy associated with all processes. So it complies to criteria 1, table 1.The DEB theory is biologically implicit, so it applies to all species. Species-specific restrictions of DEB models are explained and predicted by the theory (criterion 5, table 1). For example, consider the most important difference between DEB models, the number of reserves (biomass components that fuel metabolism) and structures (biomass components that have maintenance needs) that are delineated. This depends on the degree of coupling of the various substrates an organism needs. Animals feed on other organisms, which couples uptake of the various substrates (proteins, carbohydrates, lipids, nutrients) tightly and ex...

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Section: (C) the Population Levelmentioning

confidence: 99%

Dynamic energy budget theory restores coherence in biology

Sousa¹,

Domingos²,

Poggiale

et al. 2010

Phil. Trans. R. Soc. B

226

185

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“…Mathematical analyses suggest that successful invasion of a community in a cyclic regime requires positive growth over the entire limit cycle (Kooi & van der Meer ). This result may be generally valid for dynamical systems that do not have an extinction threshold (Bob Kooi, personal communication).…”

Section: Discussionmentioning

confidence: 99%

Mild cycles open closed communities to ecological restoration

Tielke

Karreman

Vos

2020

Restoration Ecology

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Species loss is a global issue. With up to a million species at risk and insufficient protected area to maintain the world's biodiversity, humanity will increasingly need to rely on species re‐introductions to locally restore diversity and function. However, such restoration attempts are bound to fail when ecological communities get locked in a closed state that is resistant to recovery. It is presently unknown how to repair these closed systems. We use mathematical models to identify ways out of this problem. We first show how ecological communities may enter a closed state, to then explain how to open them up again for restoration of their original diversity. We find that restoration is often still possible shortly after initial species loss, as (1) the secondary extinctions that produce closure have not happened yet and (2) mild population fluctuations still allow successful repair during a transient postdisturbance phase. However, after this typically short window of opportunity for restoration, the system enters a new equilibrium, which may be a closed state. Our analysis shows how to take ecological communities out of the closed state: Appropriate management of carrying capacities produces a regime of mild population fluctuations that opens a window for successful species re‐introductions. These windows can be perpetually recurring or permanently open. Such opportunities for repair can be absent under regimes of wild cycles or perfect stability. We conclude that mild cycles may open windows of opportunity for the repair of communities that have become resistant to recovery.

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“…We have in the past (Metz & Diekmann 1986) promulgated representing structured population models by partial (integro-)differential equations (PDEs) for the density of the population over its i-state space, like in Kooi & van der Meer (2010) for example. In hindsight, in a strict mathematical sense a lot turned out to be wrong with this formulation, as it can be interpreted rigorously only for a very special subset of the biological systems for which it was envisioned as representational.…”

Section: Discussionmentioning

confidence: 99%

How to lift a model for individual behaviour to the population level?

Diekmann

Metz

2010

Phil. Trans. R. Soc. B

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The quick answer to the title question is: by bookkeeping; introduce as p(opulation)-state a measure telling how the individuals are distributed over their common i(ndividual)-state space, and track how the various i-processes change this measure. Unfortunately, this answer leads to a mathematical theory that is technically complicated as well as immature. Alternatively, one may describe a population in terms of the history of the population birth rate together with the history of any environmental variables affecting i-state changes, reproduction and survival. Thus, a population model leads to delay equations. This delay formulation corresponds to a restriction of the p-dynamics to a forward invariant attracting set, so that no information is lost that is relevant for long-term dynamics. For such equations there exists a well-developed theory. In particular, numerical bifurcation tools work essentially the same as for ordinary differential equations. However, the available tools still need considerable adaptation before they can be practically applied to the dynamic energy budget (DEB) model. For the time being we recommend simplifying the i-dynamics before embarking on a systematic mathematical exploration of the associated p-behaviour. The long-term aim is to extend the tools, with the DEB model as a relevant goal post.

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Bifurcation theory, adaptive dynamics and dynamic energy budget-structured populations of iteroparous species

Cited by 14 publications

References 40 publications

Dynamic energy budget theory restores coherence in biology

Dynamic energy budget theory restores coherence in biology

Mild cycles open closed communities to ecological restoration

How to lift a model for individual behaviour to the population level?

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