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Reconstructing local population dynamics in noisy metapopulations--the role of random catastrophes and Allee effects.

Hart EM, Avilés L - PLoS ONE (2014)

Bottom Line: Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large.Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects.Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of British Columbia, Vancouver, British Columbia, Canada.

ABSTRACT
Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity--demographic, environmental, and random catastrophes--affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity--positive and negative environmental fluctuations--caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.

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Related in: MedlinePlus

Plots of mean normal factor bias and error in estimates of the slope of the growth function at the identity line in small populations with a weak Allee effect, large populations with a weak Allee effect, small populations with a strong Allee effect, and large populations with a strong Allee effect.The magnitude of the bias (eq. 4) can be seen in the distance of the estimate from the 0.0 line, with a bias >0.0 indicating that the parameter was more negative than the true value and a bias <0.0, that it was more positive than the true value (i.e., in the latter case, the slope was flatter than its actual value), this is because the true value in this case is negative. Vertical bars represent error on the bias estimate (eq. 5). Environmental stochasticity increases along the x-axis. Bias was always greatest in populations with a strong Allee effect.
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pone-0110049-g001: Plots of mean normal factor bias and error in estimates of the slope of the growth function at the identity line in small populations with a weak Allee effect, large populations with a weak Allee effect, small populations with a strong Allee effect, and large populations with a strong Allee effect.The magnitude of the bias (eq. 4) can be seen in the distance of the estimate from the 0.0 line, with a bias >0.0 indicating that the parameter was more negative than the true value and a bias <0.0, that it was more positive than the true value (i.e., in the latter case, the slope was flatter than its actual value), this is because the true value in this case is negative. Vertical bars represent error on the bias estimate (eq. 5). Environmental stochasticity increases along the x-axis. Bias was always greatest in populations with a strong Allee effect.

Mentions: Demographic stochasticity alone introduced no error or bias to the estimates of the slope and led only to a slight overestimation of the IUE at the smaller population size with weak Allee effects (Figures 1 and 2, long-dashed line in each panel, corresponding to 0 catastrophes, and zero environmental stochasticity). Added environmental stochasticity, in the absence of catastrophes, resulted in increasingly less precise estimates as the level of noise increased (Figure 1 and 2, long-dashed line), but introduced no bias to the slope or IUE estimates (Figure 1 and 2, vertical bars on long-dashed lines) under most circumstances. The exception was at the highest levels of environmental stochasticity when there was an interaction with Allee effect size such that the slope parameter was estimated to be flatter when Allee effects were large, and the IUE was overestimated with small Allee effects (Figure 2). Catastrophes (short-dashed and solid lines), on the other hand, always led to the estimation of a less steep slope parameter (i.e. a slope value closer to 0 than the true value), thus predicting more stable dynamics than actually present (Figure 1). Catastrophes also led to over-estimation of the IUE, which in relative terms was more dramatic for populations with small Allee effects (Figure 2). Generally errors caused by catastrophes were large even for low levels of environmental stochasticity (Figures 1 and 2), indicating that catastrophes introduced both bias and error, while other forms of noise, with some exceptions, introduced mostly error.


Reconstructing local population dynamics in noisy metapopulations--the role of random catastrophes and Allee effects.

Hart EM, Avilés L - PLoS ONE (2014)

Plots of mean normal factor bias and error in estimates of the slope of the growth function at the identity line in small populations with a weak Allee effect, large populations with a weak Allee effect, small populations with a strong Allee effect, and large populations with a strong Allee effect.The magnitude of the bias (eq. 4) can be seen in the distance of the estimate from the 0.0 line, with a bias >0.0 indicating that the parameter was more negative than the true value and a bias <0.0, that it was more positive than the true value (i.e., in the latter case, the slope was flatter than its actual value), this is because the true value in this case is negative. Vertical bars represent error on the bias estimate (eq. 5). Environmental stochasticity increases along the x-axis. Bias was always greatest in populations with a strong Allee effect.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4216000&req=5

pone-0110049-g001: Plots of mean normal factor bias and error in estimates of the slope of the growth function at the identity line in small populations with a weak Allee effect, large populations with a weak Allee effect, small populations with a strong Allee effect, and large populations with a strong Allee effect.The magnitude of the bias (eq. 4) can be seen in the distance of the estimate from the 0.0 line, with a bias >0.0 indicating that the parameter was more negative than the true value and a bias <0.0, that it was more positive than the true value (i.e., in the latter case, the slope was flatter than its actual value), this is because the true value in this case is negative. Vertical bars represent error on the bias estimate (eq. 5). Environmental stochasticity increases along the x-axis. Bias was always greatest in populations with a strong Allee effect.
Mentions: Demographic stochasticity alone introduced no error or bias to the estimates of the slope and led only to a slight overestimation of the IUE at the smaller population size with weak Allee effects (Figures 1 and 2, long-dashed line in each panel, corresponding to 0 catastrophes, and zero environmental stochasticity). Added environmental stochasticity, in the absence of catastrophes, resulted in increasingly less precise estimates as the level of noise increased (Figure 1 and 2, long-dashed line), but introduced no bias to the slope or IUE estimates (Figure 1 and 2, vertical bars on long-dashed lines) under most circumstances. The exception was at the highest levels of environmental stochasticity when there was an interaction with Allee effect size such that the slope parameter was estimated to be flatter when Allee effects were large, and the IUE was overestimated with small Allee effects (Figure 2). Catastrophes (short-dashed and solid lines), on the other hand, always led to the estimation of a less steep slope parameter (i.e. a slope value closer to 0 than the true value), thus predicting more stable dynamics than actually present (Figure 1). Catastrophes also led to over-estimation of the IUE, which in relative terms was more dramatic for populations with small Allee effects (Figure 2). Generally errors caused by catastrophes were large even for low levels of environmental stochasticity (Figures 1 and 2), indicating that catastrophes introduced both bias and error, while other forms of noise, with some exceptions, introduced mostly error.

Bottom Line: Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large.Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects.Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.

View Article: PubMed Central - PubMed

Affiliation: Department of Zoology, University of British Columbia, Vancouver, British Columbia, Canada.

ABSTRACT
Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity--demographic, environmental, and random catastrophes--affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity--positive and negative environmental fluctuations--caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are applicable to metapopulation or time series data and are relevant for predicting extinction in conservation applications or the management of invasive species.

Show MeSH
Related in: MedlinePlus