Population dynamics in variable environments I. Long-run growth rates and extinction

Tuljapurkar, Shripad; Orzack, Steven Hecht

doi:10.1016/0040-5809(80)90057-x

Cited by 317 publications

(282 citation statements)

References 32 publications

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“…In our model of overwinter survival, because stochasticity is demographic, the appropriate fitness currency is expected future reproductive success, where the expectation is across possible predator densities. If, instead, stochasticity is environmental, the appropriate currency is geometric mean future reproductive success [13,14]. As McNamara [15] shows, maximizing geometric mean future reproductive success is equivalent to maximizing arithmetic mean future reproductive success, but with a modified weighting of the probabilities of possible environmental conditions.…”

Section: Resultsmentioning

confidence: 99%

It is optimal to be optimistic about survival

McNamara

Trimmer

Houston³

2012

Biol. Lett.

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We investigate the optimal behaviour of an organism that is unable to obtain a reliable estimate of its mortality risk. In this case, natural selection will shape behaviour to be approximately optimal given the probability distribution of mortality risks in possible environments that the organism and its ancestors encountered. The mean of this distribution is the average mortality risk experienced by a randomly selected member of the species. We show that if an organism does not know the exact mortality risk, it should act as if the risk is less than the mean risk. This can be viewed as being optimistic. We argue that this effect is likely to be general.

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Section: Resultsmentioning

confidence: 99%

It is optimal to be optimistic about survival

McNamara

Trimmer

Houston³

2012

Biol. Lett.

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“…where V denotes variance and where σ 2 is independent of the initial probabilities of the chain and of the initial (non-zero) population vector z 0 ≥ 0 [63]. Therefore σ 2 is a measure of the rate nσ 2 at which the variance of log z(n) grows for large values of n. Moreover, if σ 2 > 0 the population size is asymptotically lognormal in the sense that…”

Section: Behavior Of the Original And The Reduced Modelsmentioning

confidence: 99%

“…case the stochastic model can have dynamics very different from the deterministic model built by taking expectations, can be explained using the properties of the lognormal distribution of population size. Indeed this distribution is very skewed and its long tale makes the expected value be very high although most of the probability is concentrated around zero [63].…”

Section: Non-structured Population Living In a Multipatch Environmentmentioning

confidence: 99%

Approximate Aggregation Methods in Discrete Time Stochastic Population Models

Sanz

Alonso

2010

Math. Model. Nat. Phenom.

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Abstract. Approximate aggregation techniques consist of introducing certain approximations that allow one to reduce a complex system involving many coupled variables obtaining a simpler "aggregated system" governed by a few variables. Moreover, they give results that allow one to extract information about the complex original system in terms of the behavior of the reduced one. Often, the feature that allows one to carry out such a reduction is the presence of different time scales in the system under consideration. In this work we deal with aggregation techniques in stochastic discrete time models and their application to the study of multiregional models, i.e., of models for an age structured population distributed amongst different spatial patches and in which migration between the patches is usually fast with respect to the demography (reproduction-survival) in each patch. Stochasticity in population models can be of two kinds: environmental and demographic. We review the formulation and the main properties of the dynamics of the different models for populations evolving in discrete time and subjected to the effects of environmental and demographic stochasticity. Then we present different stochastic multiregional models with two time scales in which migration is fast with respect to demography and we review the main relationships between the dynamics of the original complex system and the aggregated simpler one. Finally, and within the context of models with environmental stochasticity in which the environmental variation is Markovian, we make use these techniques to analyze qualitatively the behavior of two multiregional models in which the original complex system is intractable. In particular we study conditions under which the population goes extinct or grows exponentially.

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“…T-oo T is (except under bizarre circumstances) the long-term average growth rate of every realization of the model with probability 1 (Furstenberg and Kesten, 1960;Cohen, 1976;Tuljapurkar and Orzack, 1980;Caswell, 2001 (Caswell, 2005, pg. 80 Equation (6.18) gives the proportional change in log A, with net reproductive rate over many stochastic simulations.…”

Section: One Stage With Disturbancementioning

confidence: 99%

Metapopulation dynamics of the softshell clam, Mya arenaria

Strasser¹

2008

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Population dynamics in variable environments I. Long-run growth rates and extinction

Cited by 317 publications

References 32 publications

It is optimal to be optimistic about survival

It is optimal to be optimistic about survival

Approximate Aggregation Methods in Discrete Time Stochastic Population Models

Metapopulation dynamics of the softshell clam, Mya arenaria

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