Stochastic analogues of deterministic single-species population models

Brännström, Åke; Sumpter, David J. T.

doi:10.1016/j.tpb.2006.01.006

Cited by 27 publications

(17 citation statements)

References 22 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A more recent derivation using discrete-time models has shown similar variance scaling to earlier work in continuous-time models (8). The recurrence properties of discrete-time models with both additive and multiplicative environmental variation have been studied (9)(10)(11).…”

mentioning

confidence: 73%

“…2, 8,26). These models are analytically tractable, and provide the building blocks for more complex model structures.…”

Section: Models and Methodsmentioning

confidence: 99%

“…Factors such as the amount or quality of available habitat may drive fluctuations in the strength of competition among individuals. This variability is multiplicative with abundance in the per-capita growth rate, instead of additive, and can cause fluctuations with a higher-order scaling in the population variance (7,8).Early theoretical work on stochastic population dynamics considered both additive and multiplicative models of environmental variability, although most recent efforts have ignored multiplicative models. Levins (1) showed that when the strength of density dependence in the logistic model fluctuates through time, the median population abundance is a weighted harmonic mean of the carrying capacities.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Evidence and implications of higher-order scaling in the environmental variation of animal population growth

Ferguson

Ponciano

2015

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Environmental stochasticity is an important concept in population dynamics, providing a quantitative model of the extrinsic fluctuations driving population abundances. It is typically formulated as a stochastic perturbation to the maximum reproductive rate, leading to a population variance that scales quadratically with abundance. However, environmental fluctuations may also drive changes in the strength of density dependence. Very few studies have examined the consequences of this alternative model formulation while even fewer have tested which model better describes fluctuations in animal populations. Here we use data from the Global Population Dynamics Database to determine the statistical support for this alternative environmental variance model in 165 animal populations and test whether these models can capture known population-environment interactions in two well-studied ungulates. Our results suggest that variation in the density dependence is common and leads to a higher-order scaling of the population variance. This scaling will often stabilize populations although dynamics may also be destabilized under certain conditions. We conclude that higher-order environmental variation is a potentially ubiquitous and consequential property of animal populations. Our results suggest that extinction risk estimates may often be overestimated when not properly taking into account how environmental fluctuations affect population parameters.time series | environmental variance | variance scaling | population viability analysis | stochastic model A key question for ecologists is determining how environmental fluctuations drive population variability. Stochastic models of population dynamics consider environmental fluctuations as temporal perturbations to the mean of the birth and death rates of individuals in a population (1, 2). Because specific information on environmental covariates is not required in these models, the approach allows ecologists to make significant progress understanding how environmental perturbations drive population variability. These models have also proven to be useful in empirical settings where a stochastic process model is combined with an observation model to construct a likelihood of the observed abundances that can then be used to make inferences about the processes underlying the population (3, 4). A potentially important aspect of these models is the specification of how environmental forces drive variation in model parameters.Current practice assumes that environmental variation occurs as an additive term in the log of the per-capita growth rate, defined as R t = ln ðN t =N t−1 Þ. This variation can be derived by assuming that the density-independent reproduction rate is a random variable, which leads to a population variance with the well-known quadratic scaling of the population variance on abundances (e.g., refs. 1, 5). This model will capture the effects of environmental factors, like temperature, that can affect the maximum reproductive rate of individuals (6). However, the additi...

show abstract

mentioning

confidence: 73%

“…2, 8,26). These models are analytically tractable, and provide the building blocks for more complex model structures.…”

Section: Models and Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Evidence and implications of higher-order scaling in the environmental variation of animal population growth

Ferguson

Ponciano

2015

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…In addition to the proposed scenarios, a potential area of application for the proposed parameterization of the negative binomial distribution is population dynamics, where process error in population size (or density) is likely to take a quadratic mean-variance relationship. Typically, demographic stochasticity will induce linear mean-variance relationships, while that of environmental stochasticity will be quadratic (Engen et al 1998, Bra¨nnstro¨m andSumpter 2006). The combination of potentially correlated demographic and environmental stochasticity will still correspond to the quadratic meanvariance relationship in Eq.…”

Section: Conclusion and Recommendationsmentioning

confidence: 99%

Using the negative binomial distribution to model overdispersion in ecological count data

Lindén

Mäntyniemi

2011

Ecology

406

282

View full text Add to dashboard Cite

Abstract. A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.

show abstract

“…(McDonald et al, 2002) To make the model more realistic one has to take into account different types of uncertainties introduced by diverse events as fires, pests, climate changes, government policies, stock prices etc. (Brannstrom & Sumpter, 2006). Very often these events might have long-range or short-range consequences on biological system.…”

Section: T X mentioning

confidence: 99%

Fractional Bioeconomic Systems: Optimal Control Problems, Theory and Applications

Filatova¹,

Grzywaczewski²,

Osmolovskii³

2010

Stochastic Control

View full text Add to dashboard Cite

Stochastic analogues of deterministic single-species population models

Cited by 27 publications

References 22 publications

Evidence and implications of higher-order scaling in the environmental variation of animal population growth

Evidence and implications of higher-order scaling in the environmental variation of animal population growth

Using the negative binomial distribution to model overdispersion in ecological count data

Fractional Bioeconomic Systems: Optimal Control Problems, Theory and Applications

Contact Info

Product

Resources

About