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Does litter size variation affect models of terrestrial carnivore extinction risk and management?

Devenish-Nelson ES, Stephens PA, Harris S, Soulsbury C, Richards SA - PLoS ONE (2013)

Bottom Line: Here, we focus on an important form of demographic stochasticity: variation in litter sizes.However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small.Importantly, however, the outcomes of demographic models were generally robust to the distribution used.

View Article: PubMed Central - PubMed

Affiliation: School of Biological and Biomedical Sciences, Durham University, Durham, United Kingdom. e.s.nelson@durham.ac.uk

ABSTRACT

Background: Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores.

Methodology/principal findings: We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species - the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used.

Conclusion/significance: These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes.

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Model outcomes for 12 probability distributions against the variance (left panel) and skew (right panel) of distributions, showing quasi-extinction probabilities and probability of successful disease control, with 95% confidence intervals.(A, B) Island fox Urocyon littoralis PVA: west and east subpopulations; (C, D) red fox Vulpes vulpes; (E, F) African wild dog Lycaon pictus PVA without an Allee effect; (G, H) African wild dog PVA with an Allee effect included as a decrease in litter size as a function of group size. Solid error bars indicate distributions with ΔAIC ≤6. ▾ indicates the estimate from the previously published model, with the empirical litter size variance in the left panels and empirical litter size skew in the right panels (except G and H, for which there is no previous model estimate).
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pone-0058060-g002: Model outcomes for 12 probability distributions against the variance (left panel) and skew (right panel) of distributions, showing quasi-extinction probabilities and probability of successful disease control, with 95% confidence intervals.(A, B) Island fox Urocyon littoralis PVA: west and east subpopulations; (C, D) red fox Vulpes vulpes; (E, F) African wild dog Lycaon pictus PVA without an Allee effect; (G, H) African wild dog PVA with an Allee effect included as a decrease in litter size as a function of group size. Solid error bars indicate distributions with ΔAIC ≤6. ▾ indicates the estimate from the previously published model, with the empirical litter size variance in the left panels and empirical litter size skew in the right panels (except G and H, for which there is no previous model estimate).

Mentions: The demographic modelling showed that the distribution chosen to represent litter size uncertainty in the three canid models has limited impacts, regardless of the fit of the distributions. PVA models for island foxes showed that estimating extinction probability was largely unaffected by the choice of distribution, with less than 1% difference in quasi-extinction probabilities between models that used the best and worst fitting litter size distributions (Fig. 2A, B). Similarly, regardless of whether the litter size distributions used in the model provided a good fit to empirical litter size data, there was only a 2% difference in the probability of successful disease control in the rabies model for red foxes (Fig. 2C, D). Likewise, quasi-extinction probabilities for African wild dogs showed only a 1% difference among models that employed different litter size distributions (Fig. 2E, F). When litter size was reduced as a function of group size, to simulate an Allee effect, the influence of the distributions was slightly greater (Fig. 2G, H), with an increase of approximately 4% between quasi-extinction probabilities for the best and worst-fitting distributions. Even in this case, only models employing the worst-fitting distributions differed substantially in their predictions from those of models employing other distributions. The variation in the skew and variance of the fitted distributions (Fig. 2) may be attributed to process and sampling error in the data, as well as properties of the distributions such as the tendency to favour overdispersion, e.g. the negative binomial. However, for all parsimonious distributions, these measures were generally consistent with the empirical distributions for all models except island foxes (Fig. 2). In this latter case, the variation in agreement between distributions with ΔAIC ≤6 and the empirical properties (Fig. 2A, B) is probably due to the small sample size increasing the uncertainty of the observed parameter estimates, translating into the selection of multiple distributions. Despite the widely varying variance, the resultant model outcomes were in general unaltered by the choice of distribution. Coefficients of variation (CV) were small for all model outcomes (Table S4), with the greatest variation in the African wild dog model with an Allee effect; the best-fitting distribution (CV  = 0.712) was 1.07 times more variable than for the worst fitting model (CV  = 0.668).


Does litter size variation affect models of terrestrial carnivore extinction risk and management?

Devenish-Nelson ES, Stephens PA, Harris S, Soulsbury C, Richards SA - PLoS ONE (2013)

Model outcomes for 12 probability distributions against the variance (left panel) and skew (right panel) of distributions, showing quasi-extinction probabilities and probability of successful disease control, with 95% confidence intervals.(A, B) Island fox Urocyon littoralis PVA: west and east subpopulations; (C, D) red fox Vulpes vulpes; (E, F) African wild dog Lycaon pictus PVA without an Allee effect; (G, H) African wild dog PVA with an Allee effect included as a decrease in litter size as a function of group size. Solid error bars indicate distributions with ΔAIC ≤6. ▾ indicates the estimate from the previously published model, with the empirical litter size variance in the left panels and empirical litter size skew in the right panels (except G and H, for which there is no previous model estimate).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3585178&req=5

pone-0058060-g002: Model outcomes for 12 probability distributions against the variance (left panel) and skew (right panel) of distributions, showing quasi-extinction probabilities and probability of successful disease control, with 95% confidence intervals.(A, B) Island fox Urocyon littoralis PVA: west and east subpopulations; (C, D) red fox Vulpes vulpes; (E, F) African wild dog Lycaon pictus PVA without an Allee effect; (G, H) African wild dog PVA with an Allee effect included as a decrease in litter size as a function of group size. Solid error bars indicate distributions with ΔAIC ≤6. ▾ indicates the estimate from the previously published model, with the empirical litter size variance in the left panels and empirical litter size skew in the right panels (except G and H, for which there is no previous model estimate).
Mentions: The demographic modelling showed that the distribution chosen to represent litter size uncertainty in the three canid models has limited impacts, regardless of the fit of the distributions. PVA models for island foxes showed that estimating extinction probability was largely unaffected by the choice of distribution, with less than 1% difference in quasi-extinction probabilities between models that used the best and worst fitting litter size distributions (Fig. 2A, B). Similarly, regardless of whether the litter size distributions used in the model provided a good fit to empirical litter size data, there was only a 2% difference in the probability of successful disease control in the rabies model for red foxes (Fig. 2C, D). Likewise, quasi-extinction probabilities for African wild dogs showed only a 1% difference among models that employed different litter size distributions (Fig. 2E, F). When litter size was reduced as a function of group size, to simulate an Allee effect, the influence of the distributions was slightly greater (Fig. 2G, H), with an increase of approximately 4% between quasi-extinction probabilities for the best and worst-fitting distributions. Even in this case, only models employing the worst-fitting distributions differed substantially in their predictions from those of models employing other distributions. The variation in the skew and variance of the fitted distributions (Fig. 2) may be attributed to process and sampling error in the data, as well as properties of the distributions such as the tendency to favour overdispersion, e.g. the negative binomial. However, for all parsimonious distributions, these measures were generally consistent with the empirical distributions for all models except island foxes (Fig. 2). In this latter case, the variation in agreement between distributions with ΔAIC ≤6 and the empirical properties (Fig. 2A, B) is probably due to the small sample size increasing the uncertainty of the observed parameter estimates, translating into the selection of multiple distributions. Despite the widely varying variance, the resultant model outcomes were in general unaltered by the choice of distribution. Coefficients of variation (CV) were small for all model outcomes (Table S4), with the greatest variation in the African wild dog model with an Allee effect; the best-fitting distribution (CV  = 0.712) was 1.07 times more variable than for the worst fitting model (CV  = 0.668).

Bottom Line: Here, we focus on an important form of demographic stochasticity: variation in litter sizes.However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small.Importantly, however, the outcomes of demographic models were generally robust to the distribution used.

View Article: PubMed Central - PubMed

Affiliation: School of Biological and Biomedical Sciences, Durham University, Durham, United Kingdom. e.s.nelson@durham.ac.uk

ABSTRACT

Background: Individual variation in both survival and reproduction has the potential to influence extinction risk. Especially for rare or threatened species, reliable population models should adequately incorporate demographic uncertainty. Here, we focus on an important form of demographic stochasticity: variation in litter sizes. We use terrestrial carnivores as an example taxon, as they are frequently threatened or of economic importance. Since data on intraspecific litter size variation are often sparse, it is unclear what probability distribution should be used to describe the pattern of litter size variation for multiparous carnivores.

Methodology/principal findings: We used litter size data on 32 terrestrial carnivore species to test the fit of 12 probability distributions. The influence of these distributions on quasi-extinction probabilities and the probability of successful disease control was then examined for three canid species - the island fox Urocyon littoralis, the red fox Vulpes vulpes, and the African wild dog Lycaon pictus. Best fitting probability distributions differed among the carnivores examined. However, the discretised normal distribution provided the best fit for the majority of species, because variation among litter-sizes was often small. Importantly, however, the outcomes of demographic models were generally robust to the distribution used.

Conclusion/significance: These results provide reassurance for those using demographic modelling for the management of less studied carnivores in which litter size variation is estimated using data from species with similar reproductive attributes.

Show MeSH
Related in: MedlinePlus