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Confounding environmental colour and distribution shape leads to underestimation of population extinction risk.

Fowler MS, Ruokolainen L - PLoS ONE (2013)

Bottom Line: We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models.This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations.We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

View Article: PubMed Central - PubMed

Affiliation: Population Ecology Group, Institut Mediterrani d'Estudis Avançats (UIB-CSIC), Esporles, Illes Balears, Spain. m.s.fowler@swansea.ac.uk

ABSTRACT
The colour of environmental variability influences the size of population fluctuations when filtered through density dependent dynamics, driving extinction risk through dynamical resonance. Slow fluctuations (low frequencies) dominate in red environments, rapid fluctuations (high frequencies) in blue environments and white environments are purely random (no frequencies dominate). Two methods are commonly employed to generate the coloured spatial and/or temporal stochastic (environmental) series used in combination with population (dynamical feedback) models: autoregressive [AR(1)] and sinusoidal (1/f) models. We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models. Increasing variability of sample Skewness and Kurtosis and decreasing mean Kurtosis of these series alter the frequency distribution shape of the realised values of the coloured stochastic processes. These changes in distribution shape alter patterns in the probability of single and series of extreme conditions. We show that the reduced extinction risk for undercompensating (slow growing) populations in red environments previously predicted with traditional 1/f methods is an artefact of changes in the distribution shapes of the environmental series. This is demonstrated by comparison with coloured series controlled to be normally distributed using spectral mimicry. Changes in the distribution shape that arise using traditional methods lead to underestimation of extinction risk in normally distributed, red 1/f environments. AR(1) methods also underestimate extinction risks in traditionally generated red environments. This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations. We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

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Statistical components of extinction risk for undercompensating populations forced by coloured environmental stochasticity.(A, B) show the standard deviation of population fluctuations, (C, D) show mean population densities. Left panels (A, C) show results based on 1/f stochastic processes, right panels (B, D) show AR(1) processes. Dashed lines show results based on environmental series generated with traditional methods, solid lines show results based on normally distributed series generated using spectral mimicry. Other details as in Figure 2.
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pone-0055855-g003: Statistical components of extinction risk for undercompensating populations forced by coloured environmental stochasticity.(A, B) show the standard deviation of population fluctuations, (C, D) show mean population densities. Left panels (A, C) show results based on 1/f stochastic processes, right panels (B, D) show AR(1) processes. Dashed lines show results based on environmental series generated with traditional methods, solid lines show results based on normally distributed series generated using spectral mimicry. Other details as in Figure 2.

Mentions: Differences in CVN with changing environmental colour can be understood by examining the component population level statistics, σN and µN (Fig. 3): σN increases at a faster rate than µN, resulting in the increase in extinction risk (CVN) from white to pink environments in all cases. The decrease in CVN under intermediate and strong (σε2≥0.1) traditional pink to red environments occurs as σN declines, despite the simultaneous decrease of mean population density in red 1/f environments and asymptote of µN in red AR(1) environments. No such declines in σN are present in pink to red environments controlled to have a normal distribution (Fig. 3).


Confounding environmental colour and distribution shape leads to underestimation of population extinction risk.

Fowler MS, Ruokolainen L - PLoS ONE (2013)

Statistical components of extinction risk for undercompensating populations forced by coloured environmental stochasticity.(A, B) show the standard deviation of population fluctuations, (C, D) show mean population densities. Left panels (A, C) show results based on 1/f stochastic processes, right panels (B, D) show AR(1) processes. Dashed lines show results based on environmental series generated with traditional methods, solid lines show results based on normally distributed series generated using spectral mimicry. Other details as in Figure 2.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3569452&req=5

pone-0055855-g003: Statistical components of extinction risk for undercompensating populations forced by coloured environmental stochasticity.(A, B) show the standard deviation of population fluctuations, (C, D) show mean population densities. Left panels (A, C) show results based on 1/f stochastic processes, right panels (B, D) show AR(1) processes. Dashed lines show results based on environmental series generated with traditional methods, solid lines show results based on normally distributed series generated using spectral mimicry. Other details as in Figure 2.
Mentions: Differences in CVN with changing environmental colour can be understood by examining the component population level statistics, σN and µN (Fig. 3): σN increases at a faster rate than µN, resulting in the increase in extinction risk (CVN) from white to pink environments in all cases. The decrease in CVN under intermediate and strong (σε2≥0.1) traditional pink to red environments occurs as σN declines, despite the simultaneous decrease of mean population density in red 1/f environments and asymptote of µN in red AR(1) environments. No such declines in σN are present in pink to red environments controlled to have a normal distribution (Fig. 3).

Bottom Line: We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models.This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations.We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

View Article: PubMed Central - PubMed

Affiliation: Population Ecology Group, Institut Mediterrani d'Estudis Avançats (UIB-CSIC), Esporles, Illes Balears, Spain. m.s.fowler@swansea.ac.uk

ABSTRACT
The colour of environmental variability influences the size of population fluctuations when filtered through density dependent dynamics, driving extinction risk through dynamical resonance. Slow fluctuations (low frequencies) dominate in red environments, rapid fluctuations (high frequencies) in blue environments and white environments are purely random (no frequencies dominate). Two methods are commonly employed to generate the coloured spatial and/or temporal stochastic (environmental) series used in combination with population (dynamical feedback) models: autoregressive [AR(1)] and sinusoidal (1/f) models. We show that changing environmental colour from white to red with 1/f models, and from white to red or blue with AR(1) models, generates coloured environmental series that are not normally distributed at finite time-scales, potentially confounding comparison with normally distributed white noise models. Increasing variability of sample Skewness and Kurtosis and decreasing mean Kurtosis of these series alter the frequency distribution shape of the realised values of the coloured stochastic processes. These changes in distribution shape alter patterns in the probability of single and series of extreme conditions. We show that the reduced extinction risk for undercompensating (slow growing) populations in red environments previously predicted with traditional 1/f methods is an artefact of changes in the distribution shapes of the environmental series. This is demonstrated by comparison with coloured series controlled to be normally distributed using spectral mimicry. Changes in the distribution shape that arise using traditional methods lead to underestimation of extinction risk in normally distributed, red 1/f environments. AR(1) methods also underestimate extinction risks in traditionally generated red environments. This work synthesises previous results and provides further insight into the processes driving extinction risk in model populations. We must let the characteristics of known natural environmental covariates (e.g., colour and distribution shape) guide us in our choice of how to best model the impact of coloured environmental variation on population dynamics.

Show MeSH
Related in: MedlinePlus