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Sex-differential effects of inbreeding on overwinter survival, birth date and mass of bighorn lambs

2010; Oxford University Press; Volume: 24; Issue: 1 Linguagem: Inglês

10.1111/j.1420-9101.2010.02154.x

1420-9101

Elise Rioux-Paquette, Marco Festa‐Bianchet, David W. Coltman,

Animal Behavior and Welfare Studies

Journal of Evolutionary BiologyVolume 24, Issue 1 p. 121-131 Free Access Sex-differential effects of inbreeding on overwinter survival, birth date and mass of bighorn lambs E. RIOUX-PAQUETTE, E. RIOUX-PAQUETTE Département de biologie, Université de Sherbrooke, Sherbrooke, QC, Canada Centre d'Études Nordiques, Université Laval, Québec, QC, CanadaSearch for more papers by this authorM. FESTA-BIANCHET, M. FESTA-BIANCHET Département de biologie, Université de Sherbrooke, Sherbrooke, QC, Canada Centre d'Études Nordiques, Université Laval, Québec, QC, CanadaSearch for more papers by this authorD. W. COLTMAN, D. W. COLTMAN Department of Biological Sciences, University of Alberta, Edmonton, AB, CanadaSearch for more papers by this author E. RIOUX-PAQUETTE, E. RIOUX-PAQUETTE Département de biologie, Université de Sherbrooke, Sherbrooke, QC, Canada Centre d'Études Nordiques, Université Laval, Québec, QC, CanadaSearch for more papers by this authorM. FESTA-BIANCHET, M. FESTA-BIANCHET Département de biologie, Université de Sherbrooke, Sherbrooke, QC, Canada Centre d'Études Nordiques, Université Laval, Québec, QC, CanadaSearch for more papers by this authorD. W. COLTMAN, D. W. COLTMAN Department of Biological Sciences, University of Alberta, Edmonton, AB, CanadaSearch for more papers by this author First published: 02 November 2010 https://doi.org/10.1111/j.1420-9101.2010.02154.xCitations: 35 Elise Rioux-Paquette, Département de biologie, Université de Sherbrooke, 2500 boul. de l'Université, Sherbrooke, QC, Canada J1K 2R1.Tel.: 819 821 8000; fax: 819 821 8049; e-mail: elise.rioux-paquette@usherbrooke.ca AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Although it is generally expected that inbreeding would lower fitness, few studies have directly quantified the effects of inbreeding in wild mammals. We investigated the effects of inbreeding using long-term data from bighorn sheep on Ram Mountain, Alberta, Canada, over 20 years. This population underwent a drastic decline from 1992 to 2002 and has since failed to recover. We used a pedigree to calculate inbreeding coefficients and examined their impact on lamb growth, birth date and survival. Inbreeding had a substantial effect on female survival: for a given mass in September, the probability of overwinter survival for inbred female lambs was about 40% lower than that of noninbred ones. Contrary to our expectations, inbred female lambs were born earlier than noninbred ones. Earlier birth led to inbred female lambs being heavier by mid-September than noninbred ones. There was a nonsignificant trend for inbred female yearlings to weigh more than noninbred ones. A stronger mass-dependent viability selection for inbred compared to noninbred female lambs may explain why surviving inbred females were heavier than noninbred ones. Survival of male lambs was not affected by inbreeding. Sex-differential effects of inbreeding may be a general pattern in sexually dimorphic mammals, because of sex-biased maternal care or sexual differences in early development strategies. Introduction Inbreeding occurs when an individual's parents are related. Compared to the population average, inbred individuals have a greater chance of inheriting identical alleles at a given locus, increasing their homozygosity (Keller & Waller, 2002). Inbreeding can reduce a population's genetic variability and an individual's fitness (Frankham et al., 1999). Decreases in values of fitness-related traits are called inbreeding depression (Keller & Waller, 2002; Snustad & Simmons, 2003). In natural populations, the occurrence of inbreeding is related to population size: when populations decline, the probability of mating with relatives increases. Therefore, inbreeding is a concern for endangered species (Frankham et al., 2002). Many studies of captive and domestic mammals found negative effects of inbreeding on traits ranging from juvenile survival and adult fertility (Sausman, 1984; Hass, 1989; Alados & Escòs, 1991) to mass at birth (Cassinello & Alados, 1996), and even to behaviour (Mariette et al., 2006). In domestic sheep, inbreeding reduces conception rate at the first oestrus, litter weight, litter size, lamb survival and ewe survival (Ercanbrack & Knight, 1991; Wiener et al., 1992a,b,c). Numerous studies found that inbreeding reduced birthweight of sheep (Boujenene & Chami, 1997; Analla et al., 1999; Rzewuska et al., 2005). In cows, it decreases survival, milk production and reproductive performance (Hodges et al., 1979; Hudson & Van Vleck, 1984; Hermas et al., 1987), but it has little effect on morphological traits (Nelson & Lush, 1950; Thomson & Freeman, 1967; Hudson & Van Vleck, 1984). Joron & Brakefield (2003), however, pointed out that the fitness effects of inbreeding can be underestimated in captivity because animals are constrained in their behaviour, interactions with the environment are rare, resources are not limited, and mortality is reduced compared to natural situations. Accordingly, Crnokrak & Roff (1999) found that reported effects of inbreeding were generally higher in wild populations than in captivity. To quantify the role of inbreeding in evolution and in population dynamics, it is therefore important to study wild populations, where environmental factors may interact with the expression of deleterious recessives alleles (Szulkin & Sheldon, 2007). Studies of inbreeding in the wild are rare, however, because they require detailed pedigrees and data on fitness-related traits for most of the study population. Even with a relatively complete pedigree, the detection of inbreeding depression in the wild remains difficult (Keller & Waller, 2002) because kin-recognition mechanisms can reduce the frequency of inbreeding events and so lower the sample size of inbred individuals. Furthermore, although drastic reductions in population size can result in increasing levels of inbreeding, they can also purge recessive deleterious alleles from the population (Frankham et al., 2002). Inbreeding depression has been documented in the wild (Keller & Waller, 2002). For example, in song sparrows (Melospiza melodia), survival was reduced by inbreeding in years when environmental stress was severe (Keller et al., 1994). Amos et al. (2001) used data on grey seals (Halichoerus grypus), long-finned pilot whales (Globicephala melas) and three species of albatross (Diomedea exulans, Thalassarche chrysostoma and Thalassarche melanophris) to show that individuals born from more genetically distant parents had higher reproductive success. Coltman et al. (1999) showed that Soay sheep (Ovis aries) that were more homozygous at microsatellite loci had more parasites and reduced winter survival. Inbreeding can also affect development early in life: heterozygous harbour seal (Phoca vitulina) pups are heavier at birth (Coltman et al., 1998). A few studies reported severe inbreeding depression in the wild (Kruuk et al., 2002; Szulkin et al., 2007) and even extinction because of inbreeding (Saccheri et al., 1998). The loss of genetic variability that should accompany high levels of inbreeding is of concern for the conservation of biodiversity (Frankham et al., 2002) and it is important to understand how inbreeding may affect population dynamics. Recently, an increasing number of studies reported a sex-differential effect of inbreeding in a variety of taxa: insects (Tran & Credland, 1995; Saccheri et al., 2005; Fox et al., 2006), birds (Reid et al., 2007) and mammals (Sausman, 1984; Coulson et al., 1999 but see Slate & Pemberton (2002); Charpentier et al., 2006). In all studies except for Saccheri et al. (2005), females were more likely than males to be affected by inbreeding. Reid et al. (2007) found that the sex-differential effect was inconsistent for different traits associated with immune response. Many mechanisms have been proposed to explain why inbreeding can affect one sex more than the other: nonrandom mortality early in life (Fox et al., 2006), sex-linked deleterious alleles with gender-specific expression (Fox et al., 2006), sex-differential trade-offs in allocation of resources (Fox et al., 2006; Reid et al., 2007), gender-dependent maternal investment (Charpentier et al., 2006), gender differences in food acquisition (Charpentier et al., 2006) or sex-differential early growth strategies (Coulson et al., 1999). Our understanding of sex-differential effects of inbreeding remains limited and more studies are required. Pedigrees can be used to calculate an index of inbreeding based on mating between individuals that share common ancestors (Keller & Waller, 2002). Most studies of inbreeding in wild mammals, however, used proxies based on multilocus heterozygosity and information on allele size or frequency (Coulson et al., 1999; Balloux et al., 2004; Pemberton, 2004; Slate et al., 2004). Correlations between inbreeding measured from pedigrees and these indices, however, tend to be very low regardless of how many loci are used (Balloux et al., 2004; Slate et al., 2004). Our study population of bighorn sheep offers a unique opportunity to evaluate the effects of inbreeding in the wild using a pedigree. Coefficients calculated from pedigrees remain the best estimator for detecting inbreeding depression (Pemberton, 2004). This small population is isolated and has a polygynous breeding system (Hogg, 1987), likely increasing the strength of any effect of inbreeding and therefore our ability to detect them (Komers & Curman, 2000). The population underwent a severe decline, partly because of high predation (Festa-Bianchet et al., 2006) and in 2002–2006, it included on average only 18 females of breeding age. Despite many years at low density, the population continued to show very low recruitment. Inbreeding may have contributed to its poor performance. Here, we first compared the rate of inbreeding with population size, then tested for inbreeding effects on lamb birth date. We finally tested the hypothesis that inbred lambs would show reduced mass and survival compared to noninbred individuals. We chose to investigate the effect of inbreeding on these particular traits because they have an important implication for the dynamic of this population. Birth date influences mass of lambs (Feder et al., 2008), and heavy lambs have high survival overwinter (Festa-Bianchet et al., 1997). If inbreeding affects these traits, it could possibly prevent the expected increase in lamb survival at low population density (Portier et al., 1998). Material and methods Study area and bighorn sheep population Ram Mountain, Alberta, is a mountainous complex (elevation 1080–2170 m) 30 km east of the Canadian Rockies (52°N, 115°W), with 38 km2 of alpine and subalpine habitat used by sheep. The population is isolated: between 1988 and 2008, only three known immigrant males contributed to reproduction. The population has been monitored from late May to late September each year since 1972. Sheep are repeatedly captured in a corral trap baited with salt. More than 98% of the population is marked, so that its exact size and sex-age structure are known each year. Since 1975, the only unmarked animals have been immigrant males and a few lambs not captured in the year of birth. We suspect that immigrants are from the nearby population on Shunda Mountain, across the North Saskatchewan River. From 1972 until 1981, the population was maintained at about 30 adult females by yearly removals of ewes (Jorgenson et al., 1997). When removals stopped, the population increased, peaking at 103 females in 1992. A combination of density-dependent effects on recruitment (Festa-Bianchet et al., 1995; Portier et al., 1998) and high cougar (Puma concolor) predation in 1997–2001 (Festa-Bianchet et al., 2006) led to a decline. The population was reduced to between 15 and 20 ewes in 2002–2008 and failed to recover despite the cessation of high predation. Introductions of sheep from another population in 2004 and 2007 have so far had only a minor impact on the population genetic structure. By July 2009, there were 53 residents, eight introduced sheep and only two that were born to one introduced ewe. Pedigree building and inbreeding estimation Maternal links were established from observations of marked lambs suckling from marked ewes. Paternal links were determined using microsatellites. Tissue collection for DNA analyses began in 1988, with blood sampling of each individual captured until 1993. Sampling resumed in 1997 with the collection of hairs. From 1998 onwards, a tissue sample from the ear was obtained for all captured sheep. Polymerase chain reaction amplification was performed at 32 ungulate-derived loci (Coltman et al., 2005). No evidence of linkage disequilibrium at these loci was found (Coltman et al., 2005). Paternities were assigned using CERVUS version 3.0 (Marshall et al., 1998) at a > 95% confidence level (Coltman et al., 2002). Some individuals were identified as paternal half-siblings using COLONY version 2.0 (Wang, 2004) even though their father was not sampled because it died before we began tissue collections. Of 524 lambs born since 1988, paternity was known for 350 (67%). Most lambs of unknown paternity died soon after birth and were not captured. The available pedigree in 2008 contained 1017 individuals and extended up to seven generations. We calculated the inbreeding coefficient f (Wright, 1922; Keller & Waller, 2002), the probability that two alleles at a given locus in an individual are identical by descent (Crow & Kimura, 1970), using Pedigree Viewer version 5.5 (http://www-personal.une.edu.au/~bkinghor/pedigree.htm). To ensure that for every individual we could calculate a minimum inbreeding coefficient f of 0.125 or higher (Marshall et al., 2002), we followed Kruuk et al. (2002) and Szulkin et al. (2007) and included in our analyses only lambs for which we knew both parents and at least one grandparent. Immigrant males were assumed to be noninbred. To analyse the effects of inbreeding on lamb mass, survival and birth date, we coded individuals as 'noninbred' when f = 0 and as inbred when f > 0 because of the nonlinear effect of inbreeding and to maximize statistical power. There were 6 (10%) lambs with an inbreeding coefficient inferior to 0.008 among the inbred ones. To avoid the erroneous classification as noninbred of lambs with only 1–3 known grandparents, analyses included as 'noninbred' only those for which all four grandparents were known. Despite this additional criterion, we had more noninbred (n = 94) than inbred lambs (n = 60), which included lambs with both known parents and at least one known grandparent to maximize sample size. Although these data-selection criteria mean that the level of inbreeding may have been underestimated for some inbred lambs, of 60 lambs with f > 0, none had only 1 known grandparent, only one had two known grandparents, 12 had three known grandparents and all four grandparents were known for 47. We excluded from these analyses sheep that were first sampled when aged 1 year or older, to avoid possible biases resulting from differential survival over the first year according to level of inbreeding. Definition and collection of variables Mass Seventy-five per cent of lambs were weighed at least twice between June and September. Almost all ewes were weighed 2–7 times each summer. Lamb mass was adjusted to June 15 and to September 15 using a linear mixed model (Pelletier et al., 2007). Female mass was adjusted to June 5 and September 15 using the same procedure. Lamb mass was not adjusted to June 5 because some lambs were not yet born by that date, leading to very low or negative adjusted mass on June 5 (Festa-Bianchet et al., 1996). Absolute summer mass gain was the difference between estimated mass in September and in June. Birth date Estimated by field observations of ewes with newborn lambs with a precision of ± 5 days (Feder et al., 2008). Lamb survival Only lambs that survived to September were included in analyses, because almost none of those that died earlier were captured and therefore we did not know their fathers. We measured lamb survival from September to the following June. Resighting probability is over 99% for ewes and yearlings (Jorgenson et al., 1997), and no lamb thought to have died was ever sighted in a subsequent year. Neonatal mortality When ewes are captured in late May or early June, their lactation status is determined through udder examination. Lactating ewes never seen with a lamb were assumed to have lost their lamb at birth. Sex and paternity of these lambs were unknown. We calculated the proportion of neonatal mortality among all lambs born each year. This measure was used to take into account differences in environmental factors that could explain variation in yearly mass and survival. Previous reproductive status Previous reproductive status was a binomial variable coded 0 if the ewe did not wean a lamb the previous year and 1 if her lamb survived to September 15 (Feder et al., 2008). Mothers that did not wean a lamb the previous year may have had lower energy expenditure and this may affect the condition of their lambs the year after (Martin & Festa-Bianchet, in press). Population size The number of ewes aged 2 years and older in June each year. Faecal crude protein A measure of summer forage quality (Blanchard et al., 2003) also used in other ungulates studies (Leslie & Starkey, 1985; Côté & Festa-Bianchet, 2001) that may influence mass and survival of lambs. Higher faecal crude protein indicates better forage quality. We estimated faecal crude protein in summer as the area under a smoothed cubic spline relating the natural logarithm of faecal crude protein to date, derived from faecal samples collected from late May to late September (Blanchard et al., 2003). Weather We used weather records from the Environment Canada station in Nordegg (elevation 1320 m, about 20 km west of Ram Mountain). 'Summer' mean temperature and total precipitation were from May 15 to June 15 and 'winter' mean temperature and total snowfall were from December 1 to March 31, following Portier et al. (1998). Feder et al. (2008) previously reported an effect of weather on birth date. When snowfall was heavier during the rut, lambs were born later the following spring. Statistical analyses We used generalized linear mixed models to test the effects of inbreeding on lamb mass in June and September, summer mass gain and birth date using a Gaussian error structure. To test for the effects of inbreeding on survival, we used a binomial error structure. Because some mothers produced lambs in multiple years, we included mother identity and year as random factors. The significance of random terms was tested with a likelihood ratio test of models including and excluding random factors and testing the change in deviance against a χ2 distribution with one degree of freedom (Pinheiro & Bates, 2000). In all models, we included the inbreeding coefficient and kept it in the final model selected to assess its effect (see Table 1 for a description of variables used in models). All analyses were conducted in r 2.8.1 (R Development Core Team 2008). Models were fitted using the lmer function and the maximum-likelihood (ML) estimation procedure developed in the lme4 and matrix libraries. ML was used for the selection of final models. Parameter estimates for final models were obtained with restricted maximum-likelihood following Hox (2002). We used a stepwise method to select the final model following McCullagh & Nelder (1989). Model selection using Akaike information criterion (AIC), a numerical value representing the maximum log-likelihood and penalized by two times the number of parameters included in the model (Burnham & Anderson, 2002), led to similar results. Inspection of residuals for models with a normal error distribution was used to check assumptions of normality and homoscedasticity. Birth date was log-transformed to respect those criteria. Sample sizes varied between models because of gaps in the data. Table 1. Variable abbreviations used in models shown in Tables 2 and 3. Abbreviation Description bdate Lamb birth date Sex Lamb sex F Lamb inbreeding coefficient mlj Lamb mass in June mls Lamb mass in September mmps Maternal mass the previous September mmj Maternal mass in June gmm Maternal mass gain during summer mage Maternal age PRS Previous reproductive status snowP Total amount of snowfall previous winter prec Total precipitation during summer TPw Mean temperature previous winter Ts Mean summer temperature Tw Mean temperature the following winter FCPPs Faecal crude protein previous summer FCPs Faecal crude protein during summer popsize Number of adult ewes in June neo Yearly neonatal mortality Results Occurrence of inbreeding vs. population size Of 331 lambs for which we could calculate an inbreeding coefficient because they had at least one known grandparent, 60 (18.1%) had an f > 0. Only 3.6% (12) had a coefficient of 0.125 or more. Coefficients > 0 ranged from 0.00195 to 0.13184 (Fig. 1). The mean inbreeding coefficient of lambs with four known grandparents varied among cohorts (F1,17 = 2.187, P = 0.007; Fig. 2a). To account for a possible increase in inbreeding with time because of the increasing depth of the pedigree, we fitted a linear regression of the mean inbreeding coefficient with year (t16 = 2.315, r = 0.501, P = 0.034). We then assessed the Spearman rank correlation of the residuals of this regression with either the number of males aged 5 years and more or the number of breeding-age ewes, because residuals were not normally distributed. The numbers of breeding-age ewes and of rams aged 5 years and more were correlated (t16 = 4.808, r = 0.769, P < 0.001). Males aged 5 years and more obtained more than 80% of known paternities since 1988. The adjusted mean inbreeding coefficient of lambs, obtained by the regression explained previously, was negatively correlated with the number of males aged 5 years and older during the previous rut (S = 1553, rS = −0.604, P = 0.008, Fig. 2b) but not with the number of breeding-age ewes (S = 1252, rS = −0.292, P = 0.239). This result held when using the mean inbreeding coefficient of lambs with at least one known grandparent. Figure 1Open in figure viewerPowerPoint Distribution of inbreeding coefficients > 0 for bighorn lambs with at least one known grandparent on Ram Mountain, Alberta, 1988–2008. Figure 2Open in figure viewerPowerPoint (a) Number of adult bighorn ewes aged 2 years and older and mean inbreeding coefficient of lambs with four known grandparents on Ram Mountain, Alberta, 1988–2008. (b) Mean inbreeding coefficient, adjusted for yearly variability, of lambs with four known grandparents compared to the number of rams aged 5 years and older during the previous rut. Inbreeding effects on birth date and lamb mass For birth date, the selected model included population size and an interaction between lamb sex and inbreeding coefficient (Table 2), with year (variance = 0.048, variance ratio (variance divided by the sum of residual variance and variance associated with random factors) = 37.5%, χ2 = 20.331, P < 0.001) as a random factor; mother identity (variance = 0.019, variance ratio = 15.3%, χ2 = 1.378, P = 0.241) was not significant. In years with many ewes, births were delayed and there was a strong tendency for female lambs to have later birth dates than male lambs (Table 2). Inbreeding had a sex-differential effect on birth date of lambs, but contrary to our expectations, inbred females were born on average 9 days earlier than noninbred ones (Fig. 3). The final model explained 11.3% of the variance. Table 2. Parameter estimates of fixed effects for the determinants of mass in June and September, summer mass gain and birth date of bighorn lambs on Ram Mountain, Alberta, 1988–2008. Estimates 95% CI P-value Birth date (n = 91) Full model: mmPs + F + sex × F + mage + PRS + FCPPs + snowP + TPw Final model Intercept 0.754 0.474–1.035 < 0.001 Population size 0.006 0.001–0.012 0.013 Lamb sex (female) 0.210 0.005–0.410 0.055 Inbreeding (f > 0) 0.171 −0.025 to 0.387 0.124 Lamb sex (female): inbreeding (f > 0) −0.292 −0.549 to −0.031 0.039 Lamb mass in June (n = 91) Full model: bdate + mmPs + F + sex × F + sex + mage + PrevRS + snowP + TPw + FCPPs + popsize Final model Intercept 4.183 0.633–7.042 0.041 Birth date −0.113 −0.134 to −0.092 < 0.001 Maternal mass previous fall 0.063 0.021–0.108 0.022 Inbreeding (f > 0) −0.255 −0.809 to 0.333 0.312 Lamb mass in September (n = 91) Full model: bdate + sex + mmj + F + sex × F + mage + PRS + prec + Ts + FCPs + popsize Final model Intercept 14.214 5.089–20.434 0.005 Birth date −0.252 −0.303 to −0.207 < 0.001 Lamb sex (male) 2.908 1.899–4.183 < 0.001 Maternal mass in June 0.241 0.129–0.388 0.004 Inbreeding (f > 0) −0.609 −1.766 to 0.878 0.497 Lamb mass gain (n = 154) Full model: sex + ml + popsize + Ts + F + sex × F + mmPs + mage + PRS + bdate + FCPs + prec Final model Intercept 10.068 8.97–11.748 < 0.001 Lamb sex (male) 2.012 1.666–2.531 < 0.001 Lamb mass in June 1.169 1.162–1.258 < 0.001 Population size −0.038 −0.058 to −0.024 < 0.001 Inbreeding (f > 0) 0.059 −0.614 to 0.525 0.497 The variable 'inbreeding' was kept in all models even if it was not significant to show its effect size. Year and mother identity were included as random effects for all models except that for birth date, where only year was included. Male lambs and an inbreeding coefficient f of 0 (noninbred lambs) were used as references. Analyses used restricted maximum-likelihood linear mixed models. CI, confidence interval. Figure 3Open in figure viewerPowerPoint Mean birth dates of bighorn lambs on Ram Mountain, Alberta, 1988–2008 according to sex and inbreeding status. Sample sizes for noninbred females, inbred females, and noninbred males and inbred males are respectively 15, 26, 24 and 26. Asterisk shows significant difference in mean birth dates between inbred and noninbred females. Lamb mass in June increased with maternal mass the previous September and with earlier birth date (Table 2), with random effects of year (variance = 0.506, variance ratio = 31.8%, χ2 = 10.162, P = 0.001) and mother identity (variance = 0.412, variance ratio = 25.9%, χ2 = 7.183, P = 0.007). Fixed effects explained 61.4% of variance. Inbreeding did not explain any additional variance. For lamb mass in September, fixed effects of the selected model explained 60.5% of the variance and included birth date, sex and maternal mass in June (Table 2), with year (variance = 3.228, variance ratio = 33.8%, χ2 = 15.687, P < 0.001) and mother identity (variance = 2.921, variance ratio = 30.6%, χ2 = 7.129, P = 0.008) as random variables. Lamb mass increased with earlier birth date and with larger maternal mass. Males were about 2.9 kg (or 10%) heavier than females, but there was no effect of inbreeding. There was no interaction between inbreeding and sex (estimate: −0.259, 95% CI: −2.329–2.376, P = 0.875). Birth date explained 50% and 46.1% of variance in lamb mass adjusted to June and September, respectively. Because inbreeding affected birth date of female lambs and birth date has an important effect on mass in September, we examined a possible indirect effect of inbreeding on mass. To do so, we excluded birth date from the final model in Table 2. We obtained a significant interaction between sex and inbreeding status (estimate: 2.395, 95% CI: 0.060–5.195, P = 0.041, n = 154) suggesting an indirect positive effect of inbreeding on female lambs' mass in September. Estimates for all other explicative variables were similar to those of the model including birth date. Inbred females were 1.9 kg (about 8%) heavier than noninbred ones (t80 = −2.023, P = 0.046; Fig. 4), and the result held after removing outliers (t78 = −2.361, P = 0.021; Fig. 4). Mass in September was strongly correlated with mass in mid-June (t80 = 11.839, r = 0.798, P < 0.001). Inbred female yearlings (n = 17) were 1.0 kg (about 4%) heavier than noninbred ones (n = 29) but the difference was not significant (t44 = −1.149, P = 0.257; Fig. 4). Figure 4Open in figure viewerPowerPoint Distribution of mass for female bighorn sheep on Ram Mountain, Alberta: noninbred and inbred lambs in September (1988–2008) and yearlings in June (1989–2009). Box shows 25th to 75th percentiles, and moustaches show the first and last 25 percentiles. Mean and median are similar in this boxplot. Empty circles are outliers. Asterisk shows significant difference in mass between inbred and noninbred females. For absolute lamb summer mass gain, fixed effects of the selected model explained 61.2% of the variance (Table 2), with year (variance = 2.027, variance ratio = 54.8%, χ2 = 80.590, P < 0.001) and mother identity (variance = 1.142, variance ratio = 30.9%, χ2 = 11.739, P < 0.001) as random variables. Males gained about 2.0 kg (or 9%) more than females, and mass gain was positively correlated with mass in June. Summer mass gain decreased with population size and, as previously reported (Feder et al., 2008), w