Impact of non-linearities in density dependence beyond the range of the data on predicting population extinction risk

Staples, David F.; Taper, Mark L.

doi:10.1016/j.jnc.2005.08.005

Cited by 3 publications

(1 citation statement)

References 22 publications

(26 reference statements)

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“…Note that predictions may still lead to unrealistically high population densities due to, for example, ignoring a regulation mechanism affecting the population at high levels. In such cases, our bound on the rate of increase can be combined with a bound on population density as in Staples and Taper (2006).…”

Section: Predictionmentioning

confidence: 99%

Bounding reproductive rates in state‐space models for animal population dynamics

Sköld

Knape

2018

Ecosphere

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Citation: Sk€ old, M., and J. Knape. 2018. Bounding reproductive rates in state-space models for animal population dynamics. Ecosphere 9(5):e02215. 10.1002/ecs2.2215Abstract. Time-series models applied in the study of animal population dynamics commonly assume linearity on the log-scale, leading to log-normally distributed rates of increase. While this is often computationally convenient, in particular when performing statistical inference in the presence of observation error, it may lead to unrealistic predictions for animals with a limited reproduction. We introduce a model that includes an explicit bound on the reproductive rate of an individual, and apply this to a population time series of ungulates in Kruger National Park, South Africa. Due to observational error, the year-to-year increases in animal counts occasionally exceeded the maximal reproductive rate of the animals. In such cases, the traditional unbounded model showed a tendency of overfitting data, leading to unrealistic predictions of the underlying population increase. An observed increase above the maximal reproductive rate also provides empirical confirmation that observation error exists. The model with an explicit bound was able to utilize this in order to separate observational error from population process noise, which the traditional unbounded model was unable to do. We conclude that enforcing a strict upper bound on the reproductive rate of an animal population model may lead to more realistic statistical inference than commonly applied log-linear models when an explicit bound on reproductive rate is known. We further conclude that introducing a bound on reproduction can greatly assist in separating observational error and population process noise for slow life histories, or more generally, when the rate of sampling is high compared to reproductive rates.

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Section: Predictionmentioning

confidence: 99%

Bounding reproductive rates in state‐space models for animal population dynamics

Sköld

Knape

2018

Ecosphere

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Recruitment, Mortality and Longevity

Jönsson

2011

Ecology of Atlantic Salmon and Brown Trout

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Likelihood ridges and multimodality in population growth rate models

Polansky

Valpine

Lloyd‐Smith

et al. 2009

Ecology

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Abstract. A central problem in population ecology is to use time series data to estimate the form of density dependence in the per capita growth rate (pgr). This is often accomplished with phenomenological models such as the theta-Ricker or generalized Beverton-Holt. Using the theta-Ricker model as a simple but flexible description of density dependence, we apply theory and simulations to show how multimodality and ridges in the likelihood surface can emerge even in the absence of model misspecification or observation error. The message for model fitting of real data is to consider the likelihood surface in detail, check whether the bestfit model is located on a likelihood ridge and, if so, evaluate predictive differences of biologically plausible models along the ridge. We present a detailed analysis of a focal data set showing how multimodality and ridges emerge in practice for fits of several parametric models, including a state-space model with explicit accommodation of observation error. Best-fit models for these data are biologically dubious beyond the range of the data, and likelihood ratio confidence regions include a wide range of more biologically plausible models. We demonstrate the broad relevance of these findings by presenting analyses of 25 additional data sets spanning a wide range of taxa. The results here are relevant to information-theoretic and Bayesian methods, which also rely on likelihoods. Beyond presentation of best-fit models and confidence regions around individual parameters, effort toward understanding features of the likelihood surface will help ensure the most robust translation from statistical analysis to biological interpretation.

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Impact of non-linearities in density dependence beyond the range of the data on predicting population extinction risk

Cited by 3 publications

References 22 publications

Bounding reproductive rates in state‐space models for animal population dynamics

Bounding reproductive rates in state‐space models for animal population dynamics

Recruitment, Mortality and Longevity

Likelihood ridges and multimodality in population growth rate models

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