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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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Reconstruction of the function governing the growth of colonies of the neotropical social spider A. eximius given two methods to assign points to possible catastrophic events: visual assessment, using the A. domingo pattern (Figure 4) as a guide, and using a boosting regression tree method (see Methods for details).Dashed lines are a best fit line using eq. 1 and fitting all the data; solid lines are the fit excluding points suspected to have been affected by catastrophes. The graphs illustrate how lacking knowledge of catastrophes can lead to the nonsensical inference of a population that cannot exist, while after suspected catastrophes are removed the inference of intrinsic dynamical instability (i.e., a slope steeper than −1) is supported. In both cases, the presence of an Allee effect is detected. Inferred values after suspected catastrophes are removed: IUE: 10 (1.07, 97.58) (95% C.I.); slope: −1.33 (−0.51, −1.92); and in estimated catastrophes from random forests IUE: 21 (4.82, 117.21); slope: −1.29 (−0.46, −1.81). Note that the figures do not show two data points with extreme values on the x-axis (([7654, 0] and [16637,0]); these points, however, were included in the analyses. The five colonies shown with an asterix and excluded from the analyses underwent a proliferation event in the transition between generations, thus belonging to a different dynamical regime.
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pone-0110049-g003: Reconstruction of the function governing the growth of colonies of the neotropical social spider A. eximius given two methods to assign points to possible catastrophic events: visual assessment, using the A. domingo pattern (Figure 4) as a guide, and using a boosting regression tree method (see Methods for details).Dashed lines are a best fit line using eq. 1 and fitting all the data; solid lines are the fit excluding points suspected to have been affected by catastrophes. The graphs illustrate how lacking knowledge of catastrophes can lead to the nonsensical inference of a population that cannot exist, while after suspected catastrophes are removed the inference of intrinsic dynamical instability (i.e., a slope steeper than −1) is supported. In both cases, the presence of an Allee effect is detected. Inferred values after suspected catastrophes are removed: IUE: 10 (1.07, 97.58) (95% C.I.); slope: −1.33 (−0.51, −1.92); and in estimated catastrophes from random forests IUE: 21 (4.82, 117.21); slope: −1.29 (−0.46, −1.81). Note that the figures do not show two data points with extreme values on the x-axis (([7654, 0] and [16637,0]); these points, however, were included in the analyses. The five colonies shown with an asterix and excluded from the analyses underwent a proliferation event in the transition between generations, thus belonging to a different dynamical regime.

Mentions: In both our actual and simulated data it is clear that the slope estimate when catastrophes are included (slope at the intersection of the dashed and identity lines, Figures 3 and 4) is much flatter than when catastrophes are removed (slope corresponding to the solid line). When we fit all the data for A. eximius, the function does not intersect the identity line (Figures 3, dashed lines), indicating that our model fit predicts a population that cannot exist. Removing points suspected to reflect the effect of catastrophes (Figure 3, solid lines), however, reveals a significant Allee effect and a slope steeper than −1 (see legend Figure 3, for inferred IUE and slope values). Our fits of the A. domingo data including documented catastrophes estimate a larger IUE and a flatter slope than when we removed colonies subject to catastrophes (Figure 4, dashed and solid lines, respectively). Our analyses thus reveal that colonies of both species exhibit an Allee effect and may be subject to strong intrinsic dynamical instability. They are also consistent with our predictions of catastrophes causing an underestimation of the slope and an overestimation of the IUE, the latter especially so when the Allee effect is small. A similar pattern is obtained in our simulated data (Figure 4). Note that the boosted regression tree model, which we used to infer points likely affected by catastrophes in the A. eximius data set, had a misclassification rate of 32% when applied to the A. domingo data set and 12–20%, when applied to the simulation data sets. Any inferences derived from this model, therefore, should be considered tentative.


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

Hart EM, Avilés L - PLoS ONE (2014)

Reconstruction of the function governing the growth of colonies of the neotropical social spider A. eximius given two methods to assign points to possible catastrophic events: visual assessment, using the A. domingo pattern (Figure 4) as a guide, and using a boosting regression tree method (see Methods for details).Dashed lines are a best fit line using eq. 1 and fitting all the data; solid lines are the fit excluding points suspected to have been affected by catastrophes. The graphs illustrate how lacking knowledge of catastrophes can lead to the nonsensical inference of a population that cannot exist, while after suspected catastrophes are removed the inference of intrinsic dynamical instability (i.e., a slope steeper than −1) is supported. In both cases, the presence of an Allee effect is detected. Inferred values after suspected catastrophes are removed: IUE: 10 (1.07, 97.58) (95% C.I.); slope: −1.33 (−0.51, −1.92); and in estimated catastrophes from random forests IUE: 21 (4.82, 117.21); slope: −1.29 (−0.46, −1.81). Note that the figures do not show two data points with extreme values on the x-axis (([7654, 0] and [16637,0]); these points, however, were included in the analyses. The five colonies shown with an asterix and excluded from the analyses underwent a proliferation event in the transition between generations, thus belonging to a different dynamical regime.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0110049-g003: Reconstruction of the function governing the growth of colonies of the neotropical social spider A. eximius given two methods to assign points to possible catastrophic events: visual assessment, using the A. domingo pattern (Figure 4) as a guide, and using a boosting regression tree method (see Methods for details).Dashed lines are a best fit line using eq. 1 and fitting all the data; solid lines are the fit excluding points suspected to have been affected by catastrophes. The graphs illustrate how lacking knowledge of catastrophes can lead to the nonsensical inference of a population that cannot exist, while after suspected catastrophes are removed the inference of intrinsic dynamical instability (i.e., a slope steeper than −1) is supported. In both cases, the presence of an Allee effect is detected. Inferred values after suspected catastrophes are removed: IUE: 10 (1.07, 97.58) (95% C.I.); slope: −1.33 (−0.51, −1.92); and in estimated catastrophes from random forests IUE: 21 (4.82, 117.21); slope: −1.29 (−0.46, −1.81). Note that the figures do not show two data points with extreme values on the x-axis (([7654, 0] and [16637,0]); these points, however, were included in the analyses. The five colonies shown with an asterix and excluded from the analyses underwent a proliferation event in the transition between generations, thus belonging to a different dynamical regime.
Mentions: In both our actual and simulated data it is clear that the slope estimate when catastrophes are included (slope at the intersection of the dashed and identity lines, Figures 3 and 4) is much flatter than when catastrophes are removed (slope corresponding to the solid line). When we fit all the data for A. eximius, the function does not intersect the identity line (Figures 3, dashed lines), indicating that our model fit predicts a population that cannot exist. Removing points suspected to reflect the effect of catastrophes (Figure 3, solid lines), however, reveals a significant Allee effect and a slope steeper than −1 (see legend Figure 3, for inferred IUE and slope values). Our fits of the A. domingo data including documented catastrophes estimate a larger IUE and a flatter slope than when we removed colonies subject to catastrophes (Figure 4, dashed and solid lines, respectively). Our analyses thus reveal that colonies of both species exhibit an Allee effect and may be subject to strong intrinsic dynamical instability. They are also consistent with our predictions of catastrophes causing an underestimation of the slope and an overestimation of the IUE, the latter especially so when the Allee effect is small. A similar pattern is obtained in our simulated data (Figure 4). Note that the boosted regression tree model, which we used to infer points likely affected by catastrophes in the A. eximius data set, had a misclassification rate of 32% when applied to the A. domingo data set and 12–20%, when applied to the simulation data sets. Any inferences derived from this model, therefore, should be considered tentative.

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