## Introduction

Populations of large herbivorous mammals may include 10–15 reproducing cohorts of females (Gaillard *et al*. 2000a). At high density, most populations show consistent changes in vital rates: primiparity is delayed (Jorgenson *et al*. 1993a; Langvatn *et al*. 1996) and juvenile mortality increases (Clutton-Brock *et al*. 1987; Clutton-Brock *et al*. 1996; Gaillard *et al*. 1997; Singer *et al*. 1997; Portier *et al*. 1998). Little is known, however, about the effects of density on adult survival.

Fowler (1987) claimed that nine studies of ungulates reported density dependence in adult female survival. Examination of those studies, however, reveals that they either did not report density dependence specifically for survival of presenescent females (Caughley 1970; Klein & Olson 1960; Grubb 1974; Fowler & Barmore 1979; Hansen 1980; Clutton-Brock, Guinness & Albon 1982; Leader-Williams 1982) or did not account for age or sex differences among adults (Sinclair 1977). Less information is available about changes in adult male survival, but some long-term studies suggest that it may not be strongly density-dependent (Gaillard *et al*. 1993; Clutton-Brock *et al*. 1997a; Jorgenson *et al*. 1997). Clutton-Brock & Lonergan (1994) reported that survival of adult male red deer (*Cervus elaphus* L.) decreased with increasing density, but did not account for possible changes in male age structure.

Whether or not adult ungulates show density-dependent survival is important for two reasons. First, from a theoretical viewpoint, research on ungulate reproductive strategies suggests that females reduce maternal effort when resources are scarce (Albon, Mitchell & Staines 1983; Festa-Bianchet & Jorgenson 1998; Festa-Bianchet, Gaillard & Jorgenson 1998). If adult females allocated resources to maintenance rather than to reproduction when food was scarce, their survival should be density-independent within a certain range of resource availability. Males of dimorphic and polygynous species, on the other hand, adopt a risk-prone reproductive strategy (Clutton-Brock *et al*. 1982; Hogg & Forbes 1997) and may show density dependence in survival, because when resources are scarce they may be unable to recover the energy expended during the rut. Second, from a practical viewpoint, it is important to know whether apparent changes in adult survival at high density (Fowler 1987) are due to density dependence in survival or to changes in age structure. If age structure was mostly responsible for changes in adult survival, increasing density may lower overall ‘adult’ survival in naturally regulated populations but not in harvested populations, where very few animals reach senescence (Langvatn & Loison 1999). Eberhardt (1985) pointed out that substantial errors in the estimate of ‘adult’ survival result when senescence is ignored.

Here we analyse capture–mark–recapture (CMR) data for long-term studies of marked roe deer (*Capreolus capreolus* L.) in France and bighorn sheep (*Ovis canadensis* Shaw) and mountain goats (*Oreamnos americanus* de Blainville) in Canada. Bighorns and mountain goats are capital breeders with strong sexual dimorphism (males weigh about 100–110 kg, females 70 kg) (Festa-Bianchet *et al*. 1996; Festa-Bianchet *et al*. 1998; Côté & Festa-Bianchet 2003). Roe deer are income breeders with limited dimorphism (males weigh about 24 kg, females 22 kg) (Andersen *et al*. 2000). Adult roe deer and bighorn sheep have similar age- and sex-specific survival rates (Loison *et al*. 1999) and show positive relationships between individual mass and longevity (Gaillard *et al*. 2000b). In the roe deer and bighorn study populations, density more than doubled during our studies, partly because of experimental changes in management regimes. The mountain goat population almost doubled. We used recent developments of CMR modelling to quantify the potential effects of density on adult survival when age structure was and was not considered, expecting that density would appear to have a stronger effect if age structure was ignored.

### study areas and methods

Bighorn sheep survival was monitored at Ram Mountain (52° N, 115° W), Alberta, from 1975 to 1997. We previously used the number of adult ewes to measure population density (see Festa-Bianchet *et al*. 1998). Because most other studies of ungulates report population size as the total number of individuals, however, here we measure density as the total number of sheep in June, after lambing. The number of ewes and the total number of sheep were highly correlated during the 22 years considered here (*r =* 0·92). The number of bighorn sheep in June ranged from 94 to 232 (Fig. 1). All adult ewes were marked, and resighting probability was > 99%. Over 98% of adult rams were marked, and annual resighting probability exceeded 95% (Jorgenson *et al*. 1997). From 1972 to 1980, yearly removals of 12–24% of adult ewes (Jorgenson, Festa-Bianchet & Wishart 1993b) kept the population at 94–105 sheep. After 1980, ewe removals were discontinued and the population increased. Some males aged 4 years and older were shot by hunters (average 2·4 year^{−1}, range 0–6), both during and after the period of ewe removals (Jorgenson *et al*. 1993b). Ages of all individuals were known because they were first captured when 4 years or younger (almost all as lambs or yearlings), when age can be accurately determined from horn annuli (Geist 1966). Potential predators of adult bighorns included cougars (*Puma concolor* L.) and wolves (*Canis lupus* L.). We did not include data collected after 1997 because 11 ewes were removed that year and mortality was affected by a subsequent substantial increase in cougar predation (Ross, Jalkotzy & Festa-Bianchet 1997).

Mountain goats were monitored at Caw Ridge (54° N, 119° W), Alberta, from 1989 to 2002. The number of goats in June, after the annual birth pulse, ranged from 81 to 147. Goats were captured in traps and marked with ear tags or canvas collars. The proportion of marked adults increased from 31% to 94% over the study, and was over 70% after 1990. We knew the exact age of all goats born after 1987. For goats first caught as adults, age was determined by the number of horn annuli, a technique reliable up to about 7 years (Côté, Festa-Bianchet & Smith 1998). Individuals included in analyses were aged 6 years or less when first caught. Resighting probability exceeded 98% in males and 99% in females. Mountain goats were preyed upon by cougars, wolves and grizzly bears (*Ursus arctos* L.) (Festa-Bianchet, Urquhart & Smith 1994).

Roe deer were studied at Chizé (46° N, 0° E), France, from 1978 to 1999. The population is in a 26-km^{2} enclosure and about 70% of the adults are marked. Each year, about 50% of adults are captured with drive nets and some unmarked deer are removed for release elsewhere in France (Gaillard *et al*. 1993). Ages of almost all marked roe deer born since 1978 were known because they were caught as fawns, but in the first few years of the study several deer were marked as adults and their exact age was not known. Changes in the number of deer removed led to population estimates varying from 157 to 569 deer older than 1 year in March (excluding fawns born the previous year) (Gaillard *et al*. 1993). There were no predators of adult roe deer. Because roe deer can accurately be aged only if first caught as fawns, we had no known-age deer older than 6 in 1984, when density peaked (Fig. 1). To test for density dependence without accounting for age structure (see below) we therefore examined the survival of all adult roe deer captured during the first 3 years of monitoring (1978–80).

Based on earlier results (Loison *et al*. 1999), we considered three age classes for roe deer and bighorn sheep: yearling (survival from 1 to 2 years), prime-aged (2–7 years), and senescent adults (8 years and older). For mountain goats, we considered a separate class of animals aged 2 and 3 years, the age of all known emigrants. No 2-year-old and only 4% of 3-year-old females produced kids (Coté & Festa-Bianchet 2001). We considered goats aged 4–9 years as ‘prime-aged’, so that ‘prime-age’ lasted 6 years for all species. In addition, for female goats survival senescence appeared to begin about 2 years later than for the other species. Senescent mountain goats were therefore aged 10 years and older*.* Similarly to our previous work, the sexes were analysed separately for each species.

We analysed our data with recent developments of capture–mark–recapture techniques. We first fitted a time-dependent model, the so-called Cormack–Jolly Seber (CJS) model (Lebreton *et al*. 1992). To test whether our data sets met all the assumptions of the CJS model, we used the program u-care (Choquet *et al*. 2001), which examines homogeneity of recapture probabilities independent of capture order, and looks for possible differences in recapture probabilities independent of survival.

All animals that died because of hunting or accidents, or were removed, were excluded from our sample in the year of their death or removal. Emigration was impossible at Chizé because of the perimeter fence, and extremely rare at Ram Mountain (Jorgenson *et al*. 1997; Loison *et al*. 1999). Some young goats of both sexes emigrated from Caw Ridge (Coté & Festa-Bianchet 2003). To assess how age structure of bighorn and mountain goat females varied according to density, we compared the proportion of prime-aged females to total population size each year using logistic regression.

Model notations and biological meanings are summarized in Table 1. To model the effects of density dependence and age structure on survival we first did not account for age structure and fitted a simple model with constant survival. Then, we investigated density dependence by fitting a linear relationship between the survival estimate for each year for all adults combined and population density on a logit scale. For the roe deer analysis, this first step included only adults marked between 1978 and 1980, whose exact age was unknown. In a second step, we took into account two adult age classes, estimated survival separately for each age class, then looked for density dependence in each class. The second step included all years of monitoring but excluded animals first caught as adults (and therefore of unknown age) at the beginning of the study. Recapture probabilities for bighorns and mountain goats were very high (> 0·95) and did not vary among years. For roe deer, recapture probabilities varied during two phases of the study, and therefore two levels of capture probabilities were included as parameters in all models (see Gaillard *et al*. 1993 and Loison *et al*. 1999 for further details).

Model notation | Explanation and biological meaning |
---|---|

DD | Density dependence: linear relationship between survival on a logit scale and population size each year |

Age | Two age classes taken into account for adult survival (prime-age and senescent) |

No age | All adults (2 years and older for both bighorns and roe deer, 4 years and older for mountain goats) pooled into a single class |

Sa | Adult survival (2 years and older for bighorn and roe deer, 4 years and older for mountain goats) |

Sy | Yearling survival |

Spa | Survival of prime-aged adults (2–7 years for bighorn and roe deer, 4–9 years for mountain goats) |

SS | Survival of senescent adults (bighorns and roe deer aged 8 and older, mountain goats aged 10 and older) |

S23 | Survival of mountain goats aged 2 or 3 years |

We used the Akaike Information Criterion (AIC) to select the most parsimonious model (Burnham & Anderson 1992) at each stage of the analysis. Because both steps of the analysis involved the same data set for bighorn sheep and mountain goats but not for roe deer, we could select a general model for the entire analysis only for the first two species. The AIC is calculated as the deviance (−2 Ln(L) where L is the likelihood function) plus twice the number of free parameters in the model. The selected models are those with the lowest AIC. Because all models had less than eight parameters, we had a high information : parameter ratio (> 40). We therefore used AIC instead of AICc (Burnham & Anderson 1998). Models that differ in AIC by less than 2 units cannot be clearly distinguished, therefore in that case we selected the simplest model, as recommended by Burnham & Anderson (1998). To test specific hypotheses among nested models, we also used classical Likelihood-Ratio-Tests. For CMR modelling we used the program surge (Lebreton *et al*. 1992; see http://www.phidot.org/software/surge/guide/html for details about the most recent version). It is important to note that regressions were fitted within the procedure of estimation, and not *a posteriori* on CMR estimates. Thus we fitted a series of CMR models in which survival was consistently logit-transformed (to avoid possible estimates over 1, as recommended by Lebreton *et al*. 1992) and was either constant, age-dependent, or constrained to a logistic linear relationship with population density (Clobert & Lebreton 1985).