Andrew R. Jacobson, Antonello Provenzale, Achaz von Hardenberg, Bruno Bassano, and Marco Festa-Bianchet. 2004. Climate forcing and density dependence in a mountain ungulate population. Ecology 85:1598–1610.

During the 1980s population eruption, the number of yearlings seen during censuses remained more or less stable, while the number of kids and of adults of both sexes increased (Fig. 1a). This observation suggests that the survival of kids to yearling age was lower during the later period than during the earlier part of the study. To examine how survival and weaning success may have varied during the study, we have computed estimates of aggregate vital rates (Fig. E1). We estimate aggregate kid survival, S_K,i, as the ratio of the autumn count of yearlings in year i, to the autumn count of kids in year i – 1:

 

SK,i = Yi / Ki-1.

(E.1)

The adults counted in year i include surviving yearlings from year i – 1. Unfortunately, we can not estimate yearling survival because two-year-old ibex are counted as adults. We therefore construct adult female and adult male aggregate survivals as

 

SF,i = Fi / (Fi-1 + ½Yi-1)	(E.2)
SM,i = Mi / (Mi-1 + ½Yi-1),	(E.3)

where we have assumed that the sex ratio (ratio of males to females) for yearlings is 1.0. Finally, aggregate weaning success is defined as the ratio of kids to adult females in the autumn census,

 

wi = Ki / Fi.

(E.4)

These aggregate vital rates differ significantly from vital rates based on marked individuals in that they are averaged across all members of an age/sex class observed during the census. This difference is apparent in the running mean given by the low-pass filtered adult class aggregate survival rate (Fig. E1c), which has a mean of 0.9 in both genders. This is lower than the (94–97%) annual survival rate reported for individuals from two to 9–10 years of age in another study of Alpine ibex (Toïgo et al. 1997). This difference is at least in part due to the fact that the current results also include yearlings and senescent individuals, which have shown lower survival than prime-aged adults in almost all studies of ungulates (Gaillard et al. 2000).

FIG. E1. Aggregate survival and weaning success rates computed for the age/sex classes of Alpine ibex in the Gran Paradiso National Park, as defined by Eqs. E.1 through E.4. (a) Adult female aggregate survival rate (solid line) and adult male rate (dashed line). (b) Aggregate kid survival (solid line) and aggregate weaning success (dashed line). (c) and (d) are as in (a) and (b), except that the vital rates have been low-pass filtered using the method described in Fig. 4 of the main text. Aggregate vital rates above unity, as in (a), are indicative of errors in the census counts or violation of assumptions such as yearlings being equipartitioned in gender, or that the system is closed to migration.

Ibex are different from other ungulates in showing little if any sex differences in prime-age survival (Girard et al. 1999, Toïgo et al. 1997) and indeed little difference is seen between adult female and adult male aggregate survival rate in this population. Before the eruption, however, adult males tended to have a slightly lower and more variable aggregate survival rate than did the adult females. Both adult females and adult males enjoyed slightly higher aggregate survival during the eruption. The data suggest that during this period, the averaged male aggregate survival rate was greater than that of the females.

The aggregate kid survival rate shows no clear trend in the mean, but its variability changed significantly from before the eruption to after (Fig. E1b,d). Before 1980, the time series is characterized by episodic dips in aggregate survival associated with harsh winters (Fig. 1), but during the 1980s no such episodes are evident. After about 1989, kid survival begins a strong decline, despite the continued lack of harsh winters. This may well be a sign of density-dependent mortality for juveniles.

Aggregate weaning success manifests an apparent slight falling trend across the entire duration of the study, with no clear difference between the pre- and post-1980 time periods (Fig. E1d).

FIG. E2. Adult sex ratio (ratio of males to females) plotted against total adult ibex (r = 0.79). Empty circles represent years with average snow cover at Serrù below the mean of 126 cm; filled circles represent years with average snow cover above the mean. The correlation between sex ratio and adult ibex abundance in years of low snow cover (empty circles) is stronger (r = 0.86) than that for years of high snow cover (filled circles, r = 0.58).

Literature cited

Gaillard, J., M. Festa-Bianchet, N. G. Yoccoz, A. Loison, and C. Toïgo. 2000. Temporal variation in vital rates and population dynamics of large herbivores. Annual Review of Ecology and Systematics 31:367–393.

Girard, I., C. Toïgo, J. Gaillard, D. Gauthier, and J. P. Martinot. 1999. Patron de survie chez le bouquetin des Alpes (Capra ibex ibex) dans le Parc National de la Vanoise. Revue d'Ecologie (La Terre et la Vie) 54:235–251.

Toïgo, C., J. M. Gaillard, and J. Michallet. 1997. Adult survival pattern of the sexually dimorphic Alpine ibex (Capra ibex ibex). Canadian Journal of Zoology 75:75–79.