Ecological Archives E096-191-A5

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 96:21702180. http://dx.doi.org/10.1890/14-1501.1

Appendix E. Survival model structures and parameter estimates.

Survival was analyzed at the life stage level for each herd, using a two-step approach to accommodate the zero-inflated data set (Fletcher et al. 2005): 1) as a binomial response where mortality was either zero (0) or greater than zero (1) i.e., the mortality occurrence model, and 2) as the loge of the daily morality rate for cases where mortality was recorded, i.e., the mortality extent model. Life stage (three-level factor: ‘juvenile’, ‘yearling’, ‘adult’), year (three-level factor: ‘2007’, ’2008’, ‘2009’), season (two level factor: ‘wet season and early to mid-dry season’ or ‘mid- to late-dry season’) and goat density (animal∙ha-1; at either a 0 to 4 week, 5 to 8 week or 9 to 12 week time lag) were fitted as fixed effects, and herd and cohort size (no. of individuals per life stage per herd) categories fitted as random effects.

Mortality occurrence model:

glm(Mortality ~ Year + Life.stage, family=binomial)

Mortality extent model:

lmer(log(Daily.mortality) ~ Year + Life.stage+ (1|Herd) + (1|Cohort.size))

Mid- to late-dry season adult mortalities (April to August) were analyzed as a response to estimates of animal body condition, animal densities and environmental conditions in each year, using a GLM with binomial error structure. Individuals were scored as ‘1’ if they survived through to August that year and ‘0’ if they died during the late-dry season interval. The effect of body condition on adult mortalities was approximated by either fitting body mass in April or else the proportional change in body mass from February to April (mid-dry season) as a fixed effect. Animal densities from March to May were fitted to assess the effect of competition for forage on adult mortality levels. The effect of interannual differences in dry season severity was assessed by fitting ‘year’ as a three level factor.

Adult dry season survival model:

glm(Survival ~ Proportional.mass.change + Reproductive.status + Year, family = binomial)

Table E1. Parameter estimates for mortality occurrence and extent models. Statistical support for parameter estimates is indicated as follows: *** p < 0.001; ** p < 0.01; * p < 0.05; p < 0.01.

 

Mortality occurrence

Mortality extent

 

 

 

 

 

 

Fixed effects

 

 

 

 

 

Constant

-0.352 (0.371)

 

 

-6.966 (0.352)

***

 

 

 

 

 

 

Year

 

 

 

 

 

   2007

0

 

 

0

 

   2008

0.287 (0.402)

 

 

-0.191 (0.178)

 

   2009

1.066 (0.396)

**

 

0.412 (0.173)

*

 

 

 

 

 

 

Life stage

 

 

 

 

 

   Juvenile

0

 

 

0

 

   Yearling

-0.938 (0.373)

*

 

-0.209 (0.150)

 

   Adult

-0.455 (0.362)

 

 

-0.394 (0.182)

*

 

 

 

 

 

 

Random effects

 

 

 

 

 

   Herd

 

 

 

0.049

 

   Cohort size

 

 

 

0.232

 

   Residual

 

 

 

0.280

 

 

Table E2. Parameter estimates for adult dry season survival model. Proportional mass change was measured as: (Mass (mid-dry) – Mass (early dry)) / Mass (early dry). Statistical support for parameter estimates is indicated as follows: *** p < 0.001; ** p < 0.01; * p < 0.05; . p < 0.01.

Adult dry season survival

 

 

 

Constant

3.268 (0.610)

***

 

 

 

Proportional change in mass

 

 

  Early- to mid-dry season

6.875 (2.557)

**

 

 

 

Reproductive status

 

 

   Pregnant

 

 

   Lactating

-1.843 (0.922)

*

   Not pregnant

-2.461 (0.906)

**

 

 

 

Year

 

 

   2007

 

 

   2008

-0.714 (0.561)

 

   2009

-1.211 (0.521)

*

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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