Ecological Archives E096-191-A2

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 B. Riparian browse availability model structure and parameter estimates.

Browse availability in the riparian zone was modeled in two steps: 1) as a binomial response variable with browse either present (1) or absent (0); and 2) as the loge of browse volume (m³) for the cases where browse was present. This approach is recommended as a simple alternative where standard transformations do not produce a normal error distribution in a zero-inflated data set (Fletcher et al. 2005). A benefit of this method is that we can first investigate the determinants of when total browse depletion occurs, and then conduct a more subtle assessment of variation in browse availability when it is present. Browse was considered to be present if the plot-level canopy volume estimate within each 10 cm height interval was > 5 % of the maximum canopy volume recorded at that level for that species. Five species were included in the models (Euclea pseudebenus, Maytenus linearis, Searsia pendulina, Tamarix usneoides and Ziziphus mucronata); each occurred at three or more of the five sites and together constituted ~80 % of the total sampled canopy volume. Goat density in the preceding four weeks (animals∙ha (Tree)^-1), year (2008 or 2009) and forage accessibility to goats were fitted as fixed effects. Forage accessibility was scored as a three-level factor representing the ease with which goats could reach forage at different canopy heights above ground (easy: < 1.3 m, medium: 1.3 – 1.7 m and hard: > 1.7 m). Species was fitted as a random effect to account for differences in abundance and animal feeding preferences, with height above ground nested within species to describe variation in canopy structure among species. Repeat measures at each study site were accounted for by including plot nested within site as a random effect. Finally, to account for stochastic region-wide differences in environmental conditions among sampling intervals (e.g., river flooding, rainfall × temperature variation), sampling trip was fitted as a random effect.

Browse presence model:

lmer(Browse.presence ~ Density + Accessibility + Year + Density:Accessibility + (1|Species/Height) + (1|Site/Plot) + (1|Sampling trip), family="identity")

Browse volume model:

lmer(Browse.volume ~ Density + Accessibility + Year + Density:Accessibility + (1|Species/Height) + (1|Site/Plot) + (1|Sampling trip), family="binomial")

Table B1. Parameter estimates for browse models. Statistical support for parameter estimates is indicated as follows: *** p < 0.001; ** p < 0.01; * p < 0.05; . p < 0.01.

Literature cited

Fletcher, D., D. I. MacKenzie, and E. Villouta. 2005. Modelling skewed data with many zeros: a simple approach combining ordinary and logistic regression. Environmental and Ecological Statistics 12:45–54.

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