Ecological Archives E096-191-A4

G. P. Hempson, A. W. Illius, H. H. Hendricks, W. J. Bond, and S. Vetter. 2015. Herbivore population regulation and resource heterogeneity in a stochastic environment. Ecology 96:2170–2180. http://dx.doi.org/10.1890/14-1501.1

Appendix D. Fecundity model structures and parameter estimates.

Variation in recruitment was assessed using binomial general linear models (GLMs; logistic link) fitted to pregnancy, litter size and offspring pre-weaning survival data for animals over 12 months old. The following binary codes were modeled: a) pregnancy: not pregnant (0) or pregnant (1), b) litter size: singleton (0), twins or triplets (1), and c) pre-weaning survival: dead (0) or alive (1) at first sampling trip after birth. In each case the full model included the following fixed effects: age2 (months), goat density (animal∙ha^-1; at either a 0 to 4 week, 5 to 8 week or 9 to 12 week time lag), year and season (two level factor: ‘wet season and early to mid-dry season’ or ‘mid- to late-dry season’). In addition, litter size (two level factor: ‘singleton’ or ‘twin/triplet’) was included in the pre-weaning survival model. Pregnancy data were modelled for the full duration of the study (February 2007 to October 2009), because we could confidently assess the reproductive status of an animal from the beginning of the study. Litter size and pre-weaning survival data were only analysed for February 2008 to October 2009, as there was a marked improvement in the quality of the data reported by herders from that in 2007.

Pregnancy model:

glm(Pregnant  ~ poly(Age,2,raw=TRUE) + Season + Density, family = binomial)

Litter size model:

glm(Litter.size ~ poly(Age,2,raw=TRUE) + Density, family = binomial)

Pre-weaning survival model:

glm(Survival ~ Litter.size + Density, family = binomial)

Table D1. Parameter estimates for fecundity models. Density time lags: pregnancy = 0 to 4 weeks prior to most recent sampling trip; litter size = 9 to 12 weeks and neonate survival = 5 to 8 weeks prior to first sampling trip after parturition. Statistical support for parameter estimates is indicated as follows: *** p < 0.001; ** p < 0.01; * p < 0.05; p < 0.01.

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