Behavioral Ecology Vol. 15 No. 4: 572-578
Behavioral Ecology vol. 15 no. 4 © International Society for Behavioral Ecology 2004; all rights reserved
Fetal sex ratio variation in the highly polygynous Himalayan tahr: evidence for differential male mortality
a Unite Mixté de Recherche No. 5558, "Biometrie et Biologie Evolutive," Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France, b Arthur Rylah Institute for Environmental Research, 123 Brown Street, Heidelberg, Victoria 3084, Australia, and c 8 Totara Street, Geraldine, New Zealand
Address correspondence to D. M. Forsyth. E-mail: dave.forsyth{at}dse.vic.gov.au
Received 25 February 2002; revised 14 July 2003; accepted 2 September 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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The Trivers and Willard model (TWM) predicts that for polygynous ungulates, females of high phenotypic quality should produce more sons than daughters, whereas females of low phenotypic quality should produce more daughters. Kruuk et al. showed that in red deer the TWM only applied when the population was below carrying capacity, and they suggested that published examples supported their interpretation. More recently, Saltz proposed that mothers' age rather than condition could account for skewed sex ratios observed in ungulate populations. We tested these predictions by using data on maternal age, mass, kidney fat reserves (KFI), and fetal sex ratio in an invading population of Himalayan tahr (n = 252), a highly sexually dimorphic and polygynous ungulate introduced to New Zealand. Differences in the body mass and KFI of female tahr supported the prediction that the populations in areas colonized for less than 15 years were below carrying capacity, whereas those in areas colonized for more than 30 years were at, or near, carrying capacity. There was no trend for mothers either of larger mass or with greater KFI to produce more sons than daughters. There was also no evidence of a quadratic relationship between maternal age and the proportion of male fetuses. However, the proportion of male fetuses declined with increasing sampling date independent of maternal attributes. Among 1193 females checked for pregnancy, pregnancy rates increased to a maxima in mid-July. Thereafter, the proportion of females pregnant declined among the three age classes (1, 2, and 3 or more years). Our results therefore provide support for the idea that males experience greater mortality in utero. The role of differential fetal mortality in determining ungulate birth sex ratios deserves further investigation.
Key words: fetal mortality, Hemitragus jemlahicus, kidney fat index, maternal condition, sex ratios, Trivers–Willard model.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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In an influential article, Trivers and Willard (1973)
proposed that for species in which the reproductive success of males is expected to be more variable than that of females, mothers of high phenotypic quality should produce more sons than daughters, whereas females of low phenotypic quality should produce more daughters than sons (the Trivers–Willard model, or TWM). Until recently, however, the evidence for facultative adjustment of the birth sex ratio in ungulates was "equivocal at best" (Hewison and Gaillard, 1999: 229; see also Palmer, 2000). Kruuk et al. (1999) showed that for red deer (Cervus elaphus) on Rum (Scotland), dominant females produced significantly more sons than daughters, but this relationship disappeared at high population density. Similarly, the proportion of male red deer calves shot in Norway has been shown to decline with increasing density and severity of climate (i.e., as nutritional stress increased; Mysterud et al., 2000). There is thus clear evidence of sex ratio variation in red deer supporting the TWM (for wapiti, see also Kohlmann, 1999). Kruuk et al. (1999) also suggested that published examples of positive associations between maternal quality and the proportion of male offspring born were in populations below carrying capacity. This modification of the TWM is important because it requires investigators to know the population status relative to carrying capacity.
Saltz (2001), based on his work with Asiatic wild ass (Equus hemionus; Saltz and Rubenstein, 1995), recently proposed that maternal age rather than condition would be the most common cause of variation in birth sex ratios among ungulates (but see Hewison et al., 2002). Maternal age is likely to be an index of maternal condition (Hewison et al., 2002). Prime-age mothers should therefore produce an excess of male offspring, whereas young and old mothers should produce mostly females.
In this article we test predictions concerning fetal sex ratio variation in a New Zealand population of Himalayan tahr (Hemitragus jemlahicus), a highly sexually dimorphic and polygynous mountain ungulate. The Himalayan tahr was successfully introduced to the South Island of New Zealand during 1904–1919 and now has a breeding range of approximately 5000 km2 (Forsyth and Tustin, 2001). The dressed carcasses of adult female tahr in New Zealand (3 years or more) weigh about 24 kg, whereas adult males (5 years or more) weigh about 50 kg (Tustin KG et al., unpublished data). Females have small home ranges (approximately 2 km2) that include snow-free cliffs (Tustin and Parkes, 1988; Tustin, 1990). Adult males attempt to maintain exclusive access to estrous females by intimidating other males with displays and occasional chases (Tustin, 1990): their mating system is thus best described as tending (sensu Clutton-Brock, 1989; see also Weckerly, 1998).
The TWM might apply only if three prerequisite conditions are met (Hewison and Gaillard, 1999; Trivers and Willard, 1973). First, a high-quality female is better able to care for her offspring than is a low-quality female. Second, differences between offspring at the end of maternal investment are carried through adulthood. Third, the same difference in phenotypic quality has a greater effect on male reproductive success than on female reproductive success. Although there are no data with which to validate these assumptions for Himalayan tahr, because males are about 10% heavier than females at weaning (Tustin KG, Forsyth DM, Duncan RP, Gaillard J-M, unpublished data), a greater parental care for raising sons can be concluded. We also note that investigators have reported higher variance in the long-term reproductive success of males compared with females among sexually dimorphic polygynous ungulates (e.g., red deer; Pemberton et al., 1992), but that no published data demonstrate that sons are better than are daughters at converting extra investment into reproductive success (for review, see Hewison and Gaillard, 1999).
Assuming that the prerequisite conditions are met, the TWM predicts that Himalayan tahr mothers with a higher phenotypic quality should produce more sons than daughters (Trivers and Willard, 1973). We tested the prediction of the TWM by using two indices of maternal condition: body mass and the kidney fat index (KFI). The KFI is a measure of fat reserves (Torbit et al., 1988) and has been shown to be a significant predictor of fetal sex ratios in wapiti (also Cervus elaphus; Kohlmann, 1999). Maternal mass has been more commonly used as a measure of maternal phenotypic quality in studies of ungulate birth sex ratio (for review, see Hewison and Gaillard, 1999).
Before testing Kruuk et al. (1999)'s hypothesis, we checked whether the populations were at carrying capacity by using an index of population density, namely, the number of years that the area had been colonized by tahr (Caughley 1970a,b,c; see below). Kruuk et al.'s (1999) modification of the TWM predicts that there should be no relationship between phenotypic quality and fetal sex ratio for mothers in populations at carrying capacity.
Saltz's hypothesis predicts a quadratic relationship between maternal age and the number of male fetuses: prime-age tahr mothers should produce significantly more sons, whereas young and old mothers should produce significantly more females.
Several investigators have suggested that males may experience greater mortality than do female fetuses in species in which males are born larger than females (Clutton-Brock and Iason, 1986; McMillen, 1979). Kruuk et al. (1999) postulated that the decline in birth sex ratio of red deer under poor winter conditions was caused by greater mortality of male fetuses. This might be expected because males have higher growth rates and thus would be more adversely affected by nutritional stress (Clutton-Brock et al., 1985). Because our data spanned 105 days of gestation (7 June–20 September; the median date of birth for tahr in New Zealand is 31 November ± 18 days [1 SD]; Caughley, 1971), we also tested whether the proportion of male fetuses declined with sampling date. The maximum north–south distance between sampled mothers was 120 km, and we consider it unlikely that birth dates would vary among populations when the geographic range is so small. If males undergo greater mortality in utero, one would expect to see a decline in the proportion of females pregnant as individuals approach parturition. We tested this prediction by using a large sample of females checked for pregnancy.
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METHODS |
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Data collection
Our data came from Himalayan tahr shot from helicopters in the eastern Southern Alps of the South Island, New Zealand, during June–September 1972–1975. Tahr were shot, processed, and sold as a commercial venture (Parkes et al., 1996
). After shooting a group of tahr from the helicopter, the pilot landed and the animals were eviscerated before being ferried to a processing area (normally a flat area adjacent to a road) by the helicopter (for further detail, see Tustin, 1990). All measurements were made at processing areas by, or under the direct supervision of, K.G.T., and we are therefore confident that no inconsistencies occurred during the data collection process. Of a total of 2646 females sampled, 1163 females were checked for pregnancy. However, because of the difficult sampling conditions, sex was assessed for only 252 fetuses of the 1020 pregnant females (25%). We did not encounter any difficulties sexing fetuses owing to their stage of development (the first pregnant female recorded [on June 7; day 34] had a male fetus). We can therefore consider that the mothers available to us were a random sample of the population.
Sampling date was treated as a continuous variable, beginning with day 1 (5 May, the date the first animal was shot) and ending with day 142 (23 September). Maternal age was determined from the annual growth rings in the longest horn, following the method of Caughley (1965). Maternal mass was the weight of the eviscerated, hocked, and beheaded carcass minus all bleedable blood (±0.05 kg). Following the method of Caughley (1970b), KFI was calculated as 100 times the mass of fat surrounding the kidney divided by kidney mass. Body mass was available for 206 mothers and KFI for 226 of the 252 mothers.
Testing the prediction of Kruuk et al. (1999) for food-limited ungulates requires a measure of population density or relative food availability. Because humans are the only predators of tahr in New Zealand, populations are assumed to be food limited. Caughley (1970a,b,c) tested this hypothesis and concluded that tahr underwent an "irruptive oscillation," with peak densities attained about 15 years after females colonized an area. Time since colonization was related to the rate of population increase (r): in the population sampled approximately 10 years after colonization r was 0.13, whereas in the population sampled approximately 20 years after colonization r was close to zero (Caughley, 1970a). Because the abundance of preferred food species was shown to decline with increasing years of colonization, it was concluded that these demographic changes were caused by nutritional stress (Caughley, 1970a). We therefore used the detailed patterns of colonization in Caughley (1970c) and Parkes and Tustin (1985) to classify the seven areas in which mothers were shot according to the number of years since female tahr colonized that area. Because male tahr often preceded the arrival of females by many years (Caughley, 1970c), we defined colonization as the number of years between the year that females invaded the area and 1972 (the first year of sampling). Mothers were thus classified into two distinct groups. The first group of mothers came from areas colonized for less than 15 years (n = 210), and the second group of mothers came from areas colonized for more than 30 years (n = 42). The latter group of mothers was expected to be at carrying capacity, whereas the former was expected to be below carrying capacity. We compared both the body mass and condition of mothers from areas colonized for less than 15 years and areas colonized for more than 30 years to check the reliability of this dichotomy. Both body mass and condition were expected to be higher in the mothers from areas colonized for less than 15 years.
Statistical analyses
We first tested, using linear models, whether mothers from areas colonized for less than 15 years had significantly greater body mass and KFI than did mothers from areas colonized for more than 30 years. We used all females in the larger data set for which those data were available, with sample sizes as follows: less than 15 years body mass, n = 1126; more than 30 years body mass, n = 432; less than 15 years KFI, n = 1101; and more than 30 years KFI, n = 422. Body mass and KFI were log-and loge-transformed, respectively, for these analyses. Before we tested for an effect of colonization, we controlled for age class, year, and sampling date (Caughley, 1970b).
Mothers were pooled into age classes according to the proportion of female tahr pregnant (n = 1612) and lactating (n = 1799); 0 year (never pregnant or lactating); 1 year (50% pregnant but never lactating); 2 years (more than 80% pregnant and less than 40% lactating); 3 years or more (more than 80% pregnant and more than 60% lactating). In contrast to many other ungulates, there was no evidence of age-related senescence in maternal mass or pregnancy and lactation rates (Tustin KG, Forsyth DM, Duncan RP, Gaillard J-M, unpublished data), probably owing to a relatively small number of females more than 10 years of age. We therefore did not use a senescent age-class (c.f. Gaillard et al., 2000a,b; Mysterud et al., 2000). The frequency of the 252 mothers in the three relevant age-classes were as follows: 1 year, n = 18; 2 years, n = 45; and 3 years or more, n = 189.
We then used parametric logistic regression to determine the relationship between the proportion of male fetuses and the variables: year, maternal age, maternal mass, maternal KFI, and sampling date. Because both maternal mass and body condition were significantly affected by age and sampling date (see below), we used the residuals from the appropriate fitted linear model in our analyses (residual maternal mass, RMM; residual KFI, RKFI). To establish those relationships, we used the full female data set (n = 1827 females for body mass and n = 1467 females for KFI).
We used a quadratic model to test Saltz's prediction that prime-aged females bear significantly more sons relative to both older and younger females. For this analysis we used the actual ages rather than the age classes defined above.
We also used logistic regression to determine which variables best explained variation in the proportion of females pregnant. Because overall pregnancy rates varied with age (see above), we conducted separate analyses for each of the three age classes. We compared linear and quadratic terms for the effect of sampling date on the proportion of females pregnant.
Determining which combination of variables and terms best explain variation in data is problematic: even with a relatively small number of variables, the potential number of models that can be considered is very large (Burnham and Anderson, 1998). Our approach was to first test the specific hypotheses outlined above by constructing the appropriate models. Thus, the TWM models examined only maternal condition (i.e., body mass or KFI), and the Saltz model examined only maternal age. The importance of these models for explaining variation in fetal sex ratio was assessed by analysis of deviance (McCullagh and Nelder, 1989) and by inspection of the parameter estimates and their standard errors (Hosmer and Lemeshow, 1989).
We then used model selection based on Akaike's information criterion (AIC) to determine which of the candidate models "best" explained the data (see Burnham and Anderson, 1998). Models were compared according to the AICc statistic, and the resulting models ranked according to their normalized Akaike weights (AICw). The best model had the largest AICw (Burnham and Anderson, 1998). Results of the model selection process are presented following the recommendations of Anderson and Burnham (2002). All statistical analyses were performed with S-Plus (Venables and Ripley, 1999).
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RESULTS |
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Our model selection procedure indicated that colonization was an important predictor of both female body mass and KFI (Table 1). For mass, the best model (i. e., the model with the largest AICw) included the variables age class, sampling date, and colonization. Mass increased with increasing age but declined with increasing sampling date and years since colonization (Table 2). For KFI, the model with the largest AICw included age class, year, a quadratic term for sampling date, and colonization (Table 1). As for mass, KFI declined with increasing sampling date and years of colonization (Table 2). Body mass and KFI therefore declined with increasing years since colonization, as was expected if the recently colonized areas were below carrying capacity and the long colonized areas were at carrying capacity. The best models (Table 2) explained 78% of the variation in female body mass and 23% of the variation in female KFI. Cook's distance indicated that no outlier influenced the results of these tests; in both analyses, the residuals had approximately constant variance.
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Mothers were aged from 1–15 years, and the overall fetal sex ratio did not differ from parity (122 males/130 females) (Figure 1). Saltz's hypothesis predicts a quadratic relationship based on maternal age. However, there was no relationship between the proportion of sons produced and maternal age using either a quadratic logistic model (logit [proportion of sons] = –0.43 [±0.40] + 0.13 [±0.14] age – 0.01 [±0.01] age2; change in deviance from null model
0.54, df = 1, p 
.46) or a simple logistic model (logit [proportion of sons] = –0.20 [±0.23] – 0.03 [±0.04] age; change in deviance = 0.46, df = 1, p =.496).
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There was a weak positive correlation (r =.325) between RMM and RKFI for the 187 mothers for which both variables were measured. For RMM, there was no evidence that heavier mothers had male fetuses (logit[proportion of sons]= –0.10 [±0.14] + 0.05 [±0.04] RMM, df = 1; change in deviance = 1.23, p =.27). There was no evidence that females with greater RKFI produced more sons (logit[proportion of sons] = –0.07 [±0.14] + 0.002 [±0.004] RKFI, df = 1; change in deviance = 0.32, p =.57).
The model selection procedure requires using only females for which all predictor variables were measured (Burnham and Anderson, 1998; Anderson and Burnham, 2002). Hence, our sample size was reduced to 187 mothers for identifying the best model explaining variation in fetal sex ratio (Table 3). The best model included only one variable, sampling date (model 14 in Table 3): logit[proportion of males] = –2.50 (±0.78) – 0.024 (±0.007) sampling date. There was little evidence that the variables age class, year, body mass, and KFI were important predictors of fetal sex ratio. There was evidence that colonization may have been an important predictor, with model 14 having only a slightly larger AICw than that of model 13. However, there was little support for either multiplicative (model 11) or additive (model 12) effects of these variables, and further inspection revealed that sampling date and colonization were confounded in two ways. First, many more mothers were sampled in the recently colonized areas (n = 210) compared with the longer colonized areas (n = 42). Second, mothers in the recently colonized areas were sampled over a longer period (median = 113 days, SD = 11.6, range = 34–139) than were those in the longer colonized areas (median = 70 days, SD = 14.9, range = 67–139). For the 42 mothers from the longer colonized areas, there was no relationship between fetal sex ratio and sampling date: logit [proportion of males] = –0.81 (±2.12) – 0.022 (±0.030) sampling date. For the mothers in the recently colonized areas, there was a strong relationship: logit[proportion of males] = –3.64 (±1.63) – 0.034 (±0.014) sampling date. Excluding the single male fetus recorded on day 34 (Figure 2) from our analyses did not change the model rankings in Table 3.
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Although the fetal sex ratio differed between years, there was little evidence that year was an important predictor of fetal sex ratio variation (Table 3). The sex ratios by year were as follows: 1972, 1.0 (n = 1 male); 1973, 0.3556 (n = 45); 1974, 1.0 (n = 3); 1975, 0.5771 (n = 175); and 1976; 0.4643 (n = 28).
We analyzed pregnancy rates separately for each of the three age classes (Table 4). Of the six models examined for each age class, model 2 was selected as the best for age classes 1 and 2. That model included year and a quadratic term for sampling date. The best fitted models were as follows: logit[proportion of females1 pregnant] = –6.20 (±2.72) – 1.15 (±0.86) year1973 – 1.86 (±0.96) year1974 + 0.51 (±0.95) year1975 – 2.00 (±1.06) year1976 + 0.16 (±0.06) sampling date – 0.008 (±0.0003) sampling date2; and logit[proportion of females2 pregnant] = –4.13 (±3.78) + 1.17 (±0.82) year1973 + 0.28 (±1.17) year1974 + 9.60 (±14.28) year1975 + 9.04 (±31.50) year1976 + 0.13 (±0.08) sampling date – 0.008 (±0.0004) sampling date2. The next best model for both age classes included those variables plus colonization. For age class 3, the best model included colonization instead of year: logit[proportion of females3 pregnant] = –3.98 (±4.41) + 0.21 (±0.09) sampling date – 0.001 (±0.0004) sampling date2 – 1.21 (±0.64) colonization. The coefficients for the quadratic term were similar for the three age classes. Thus, the first fetus was recorded on 7 June; thereafter the proportion of females pregnant increased, with the maximum pregnancy rate attained in each age-class during 14–23 July (Figure 3). After 23 July, the proportion of females pregnant declined.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Neither maternal mass nor KFI was included in the three highest-ranking models explaining variation in fetal sex ratio (Table 3). Given that the aim of model selection is to identify the most important variables for explaining variation in data (Burnham and Anderson, 1998
), we conclude that maternal mass and KFI were unimportant in explaining fetal sex ratios in Himalayan tahr. Our findings suggest that factors other than maternal condition were more important for explaining the observed variation in fetal sex ratio. In other studies the relationship between maternal condition and offspring sex ratio is often weak, thus requiring very large samples for the effect to be detected (see Kruuk et al., 1999). However, many studies have also failed to find any evidence supporting the TWM in dimorphic and polygynous ungulates (Hewison and Gaillard, 1999), even when the species is known to meet the assumptions of the TWM (for fallow deer, Dama dama, see Birgersson, 1998; for Soay sheep, Ovis aries, Lindström et al. 2002).
We emphasize that the TWM refers to differences among individuals at a given time. The mothers in this study came from areas that had been colonized for less than 15 years and more than 30 years (Caughley, 1970c), and both maternal mass and KFI declined with period of colonization (Tables 1 and 2). Also, after adjusting for the effects of sampling date, females 3 years or more from the area colonized for more than 30 years had lower rates of pregnancy than did those from areas colonized less than 15 years (Table 4). There was thus strong evidence that females in the recently colonized areas were below carrying capacity. Because both mass and condition decreased with density, a light female at low density may correspond to a heavy female at high density. We attempted to control for this possibility by including colonization as a factor in our analyses.
Kruuk et al. (1999) showed that the TWM applied to red deer only when the population was below carrying capacity. However, comparison of plausible models did not support Kruuk et al.'s prediction: the models including the variables RMM, RKFI, and colonization, ranked very low relative to other models (Table 3). Our results thus add to several studies noted by Kruuk et al. (1999) as showing no association between population density/resource availability and offspring sex ratio.
We found no evidence to support Saltz's (2001) prediction of a quadratic relationship between maternal age and the proportion of male fetuses. Also, whereas Côté and Festa-Bianchet (2001) observed an increasing proportion of male mountain goat (Oreamnos americanus) kids with increasing maternal age, there was no such effect in our data (Figure 1). Because the technique of ageing tahr by their horn rings has been found to be a reliable indicator of age (Caughley, 1965), we conclude that there was no relation between maternal age and fetal sex ratio in Himalayan tahr. Lindström et al. (2002) observed no "significant" effect of maternal age on birth sex ratio in Soay sheep (Ovis aries). Hence, there is little evidence supporting the contention that maternal age is the predominant determinant of progeny sex ratio variation (see also Hewison et al., 2002).
The best predictor of fetal sex ratio was sampling date alone (Table 3). The proportion of male fetuses declined with increasing sampling date independently of individual maternal variables (i.e., mass and KFI), age class, and year. Male fetuses may undergo greater mortality than do female fetuses (Clutton-Brock and Iason, 1986; Kruuk et al., 1999; McMillen, 1979). The quadratic relationship between sampling date and the proportion of females pregnant in each age class (Figure 3) supports this hypothesis. However, the decline in the rate of pregnancy occurred only after day 120 in all age classes (Figure 3), whereas the fetal sex ratio appeared to change over a longer period (Figure 2). We note that a far smaller sample size was available for the fetal sex ratio compared with the proportion of females pregnant, and it is unfortunate that our sampling did not continue such that both the fetal sex ratio and pregnancy rate could be estimated to parturition.
Because the maximum proportion of pregnant female tahr 3 years or more exceeded 0.95 between days 100 and 120, nearly all female tahr in that age class must conceive. It would obviously be difficult to detect a relationship between maternal quality and sex ratio at conception if males were subject to greater mortality in utero and the mother did not conceive again (i.e., moved from being pregnant to barren). There is evidence of significant early embryonic mortality in poor-condition caribou (Russell et al., 1998), but we do not know of any studies attempting to assess sexual differences in fetal mortality. Kohlmann (1999) observed that fetal sex ratios in elk were male-biased early in the season, but also that mothers with higher KFI were significantly more likely to have a male fetus. We found evidence only of the former for Himalayan tahr. Although our sample size was smaller than was Kohlmann's, our measures of maternal phenotypic quality, mass, and KFI are all likely to be meaningful measures of maternal quality in Himalayan tahr. Roe deer (Capreolus capreolus) and bighorn sheep (Ovis canadensis) females of larger mass survive longer and consequently wean more offspring than do smaller females (Gaillard et al., 2000a), and annual reproductive success for female bighorn sheep has been shown to be mass dependent (Festa-Bianchet, 1998; Festa-Bianchet et al., 1998). Kidney fat is the penultimate fat depot to be used by ungulates (before the bone marrow; Ransom, 1965) and has been shown to be strongly correlated with total carcass fat in mule deer (Odocoileus hemionus; Torbit et al., 1988).
There is much debate concerning the analysis, interpretation, and publication of data on ungulate birth sex ratio (see Festa-Bianchet, 1996; Hewison and Gaillard, 1999; Saltz, 2001). Although fetal sex ratios have the advantage that they avoid the bias associated with locating and sexing offspring before they die (Hewison et al., 1999), our results suggest that for Himalayan tahr there is significantly greater mortality of male fetuses during gestation. Quantifying in utero mortality for males and females in wild populations will be difficult, but the role of differential fetal mortality in ungulate birth sex ratios deserves investigation.
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ACKNOWLEDGEMENTS |
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We thank all the helicopter crews who allowed K.G.T. to sample the tahr that they recovered. The senior author acknowledges the support of the CNRS during the preparation of this manuscript. Comments by Marco Festa-Bianchet, Mark Hewison, Pierrick Blanchard, and Clare Veltman, as well as constructive reviews by three anonymous referees, greatly improved the manuscript.
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