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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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Observed litter size frequencies with fitted distributions with ΔAIC ≤6.The top two panels show for a range of sample sizes (of litters sampled), mean litter size, and carnivore families. The third panel from the top shows three populations of Vulpes vulpes with litter size determined by placental scars and the bottom panel illustrates three different methods for determining litter size of a Bristol population of V. vulpes (Harris, unpublished data). (A) Lycaon pictus, n = 36 [53]; (B) Crocuta crocuta, n = 108 [54]; (C) Panthera tigris altaica, n = 16 [55]; (D) Ursus arctos, n = 303 [56]; (E) Meles meles, n = 37 [57]; (F) Lontra canadensis, n = 9 [58]; (G) V. vulpes, n = 112 [59]; (H) V. vulpes, n = 506 [60]; (I) V. vulpes, London, n = 158 (Harris, unpublished data); (J) V. vulpes, placental scars, n = 340; (K) V. vulpes, embryos, n = 60; (L) V. vulpes, direct counts, n = 191. See Table S1 for details of datasets. Distribution abbreviations: observed frequencies (Obs); shifted Poisson (SP); ZT Poisson (ZTP); discretised normal (DN); discretised lognormal (DLN); discretised stretched beta –2 parameter form (DSB2); discretised stretched beta 3 parameter form (DSB3); shifted generalised Poisson (SGP); ZT generalised Poisson (ZTGP); shifted binomial (SB); ZT binomial (ZTB); shifted negative binomial (SNB); ZT negative binomial (ZTNB).
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pone-0058060-g001: Observed litter size frequencies with fitted distributions with ΔAIC ≤6.The top two panels show for a range of sample sizes (of litters sampled), mean litter size, and carnivore families. The third panel from the top shows three populations of Vulpes vulpes with litter size determined by placental scars and the bottom panel illustrates three different methods for determining litter size of a Bristol population of V. vulpes (Harris, unpublished data). (A) Lycaon pictus, n = 36 [53]; (B) Crocuta crocuta, n = 108 [54]; (C) Panthera tigris altaica, n = 16 [55]; (D) Ursus arctos, n = 303 [56]; (E) Meles meles, n = 37 [57]; (F) Lontra canadensis, n = 9 [58]; (G) V. vulpes, n = 112 [59]; (H) V. vulpes, n = 506 [60]; (I) V. vulpes, London, n = 158 (Harris, unpublished data); (J) V. vulpes, placental scars, n = 340; (K) V. vulpes, embryos, n = 60; (L) V. vulpes, direct counts, n = 191. See Table S1 for details of datasets. Distribution abbreviations: observed frequencies (Obs); shifted Poisson (SP); ZT Poisson (ZTP); discretised normal (DN); discretised lognormal (DLN); discretised stretched beta –2 parameter form (DSB2); discretised stretched beta 3 parameter form (DSB3); shifted generalised Poisson (SGP); ZT generalised Poisson (ZTGP); shifted binomial (SB); ZT binomial (ZTB); shifted negative binomial (SNB); ZT negative binomial (ZTNB).

Mentions: Variance-mean ratios of observed litter size frequencies (mean  = 0.41, SD ±0.40) indicated that empirical distributions tend to be underdispersed (Table S1). While the majority of datasets each represented one population (96%), most data were pooled over multiple years (97%) (Table S1). Best fitting distributions differed substantially between datasets (Tables 2 and S2), although all distributions with ΔAIC ≤6 provided fits consistent with the empirical data (Table S3). For 97% of all datasets, several of the 12 candidate distributions (mean  = 6.54, SD ±3.38) could not be discounted based on their AIC values (Table S2 and Fig. 1A–F for examples). The most widely applicable distribution was the discretised normal, with ΔAIC ≤6 for 95% of datasets; all other distributions were selected for between 22% and 87% of datasets. The “right shifted” method consistently performed better than zero-truncation for all distributions (Table S2), being on average 1.32 (SD ±0.16) times more likely to have a ΔAIC ≤6. While there was little support for intraspecific differences between red fox populations, distinct probability distributions best described litter size data determined by pre- and post-birth methods (Appendix S1 and Table S1).


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)

Observed litter size frequencies with fitted distributions with ΔAIC ≤6.The top two panels show for a range of sample sizes (of litters sampled), mean litter size, and carnivore families. The third panel from the top shows three populations of Vulpes vulpes with litter size determined by placental scars and the bottom panel illustrates three different methods for determining litter size of a Bristol population of V. vulpes (Harris, unpublished data). (A) Lycaon pictus, n = 36 [53]; (B) Crocuta crocuta, n = 108 [54]; (C) Panthera tigris altaica, n = 16 [55]; (D) Ursus arctos, n = 303 [56]; (E) Meles meles, n = 37 [57]; (F) Lontra canadensis, n = 9 [58]; (G) V. vulpes, n = 112 [59]; (H) V. vulpes, n = 506 [60]; (I) V. vulpes, London, n = 158 (Harris, unpublished data); (J) V. vulpes, placental scars, n = 340; (K) V. vulpes, embryos, n = 60; (L) V. vulpes, direct counts, n = 191. See Table S1 for details of datasets. Distribution abbreviations: observed frequencies (Obs); shifted Poisson (SP); ZT Poisson (ZTP); discretised normal (DN); discretised lognormal (DLN); discretised stretched beta –2 parameter form (DSB2); discretised stretched beta 3 parameter form (DSB3); shifted generalised Poisson (SGP); ZT generalised Poisson (ZTGP); shifted binomial (SB); ZT binomial (ZTB); shifted negative binomial (SNB); ZT negative binomial (ZTNB).
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pone-0058060-g001: Observed litter size frequencies with fitted distributions with ΔAIC ≤6.The top two panels show for a range of sample sizes (of litters sampled), mean litter size, and carnivore families. The third panel from the top shows three populations of Vulpes vulpes with litter size determined by placental scars and the bottom panel illustrates three different methods for determining litter size of a Bristol population of V. vulpes (Harris, unpublished data). (A) Lycaon pictus, n = 36 [53]; (B) Crocuta crocuta, n = 108 [54]; (C) Panthera tigris altaica, n = 16 [55]; (D) Ursus arctos, n = 303 [56]; (E) Meles meles, n = 37 [57]; (F) Lontra canadensis, n = 9 [58]; (G) V. vulpes, n = 112 [59]; (H) V. vulpes, n = 506 [60]; (I) V. vulpes, London, n = 158 (Harris, unpublished data); (J) V. vulpes, placental scars, n = 340; (K) V. vulpes, embryos, n = 60; (L) V. vulpes, direct counts, n = 191. See Table S1 for details of datasets. Distribution abbreviations: observed frequencies (Obs); shifted Poisson (SP); ZT Poisson (ZTP); discretised normal (DN); discretised lognormal (DLN); discretised stretched beta –2 parameter form (DSB2); discretised stretched beta 3 parameter form (DSB3); shifted generalised Poisson (SGP); ZT generalised Poisson (ZTGP); shifted binomial (SB); ZT binomial (ZTB); shifted negative binomial (SNB); ZT negative binomial (ZTNB).
Mentions: Variance-mean ratios of observed litter size frequencies (mean  = 0.41, SD ±0.40) indicated that empirical distributions tend to be underdispersed (Table S1). While the majority of datasets each represented one population (96%), most data were pooled over multiple years (97%) (Table S1). Best fitting distributions differed substantially between datasets (Tables 2 and S2), although all distributions with ΔAIC ≤6 provided fits consistent with the empirical data (Table S3). For 97% of all datasets, several of the 12 candidate distributions (mean  = 6.54, SD ±3.38) could not be discounted based on their AIC values (Table S2 and Fig. 1A–F for examples). The most widely applicable distribution was the discretised normal, with ΔAIC ≤6 for 95% of datasets; all other distributions were selected for between 22% and 87% of datasets. The “right shifted” method consistently performed better than zero-truncation for all distributions (Table S2), being on average 1.32 (SD ±0.16) times more likely to have a ΔAIC ≤6. While there was little support for intraspecific differences between red fox populations, distinct probability distributions best described litter size data determined by pre- and post-birth methods (Appendix S1 and Table S1).

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