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Keywords:

  • animal model;
  • evolutionary response;
  • genetic variability;
  • maternal effect;
  • pedigree;
  • quantitative genetics;
  • Soay sheep

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Using a genealogy containing over 1800 dams and nearly 400 sires (estimated by genetic paternity techniques), combined with maximum likelihood procedures and an ‘animal model’, we have estimated the heritabilities, genetic correlations and variance components of three morphometric traits in the Soay sheep (Ovis aries) on St Kilda, Scotland. This approach allows heritabilities to be estimated in natural populations that violate the assumptions of offspring–parent regression methods. Maternal (or paternal) effects can also be estimated under natural conditions. We demonstrate that all the traits, body weight, hind leg length and incisor arcade breadth, have low but significant heritabilities. Body weight, the trait that experiences the strongest selection, had the lowest heritability but the highest additive genetic coefficient of variation. An evolutionary response to selection is predicted. When maternal effects were not taken into consideration heritabilities were over-estimated, although this effect was only significant in female offspring.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Despite widespread interest in measuring the heritability or ‘evolvability’ of traits within natural populations ( Mousseau & Roff, 1987; Houle, 1992), relatively few studies have succeeded in conducting comprehensive studies of multiple traits within the same population using traditional regression methods. Exceptions among vertebrates tend to come from studies of bird populations, for example in Darwin’s finches (Geospizinae) on the Galápagos islands ( Grant et al., 1976 ; Boag & Grant, 1981; Grant, 1986).

In many species living in the wild, quantitative genetic analyses are hindered by a lack of pedigree information. Several estimates of trait heritabilities have been made in socially monogamous birds, in which parentage can be inferred by field observations of parental care (e.g. Boag & Grant, 1978; van Noordwijk et al., 1988 ). However, in many other species, in which just one or neither parent provides care, pedigree information is much more difficult to infer. In addition, any estimates of additive genetic variation which rely primarily on pedigree relationships that involve parental care are potentially compromised by the effects of shared environment, unless cross-fostering manipulations are possible ( Dhondt, 1982; Griffith et al., 1999 ).

To date, the statistical techniques used to estimate heritabilities in the wild have also been relatively simple, generally involving offspring–parent or sib regression (review by Boag & Grant, 1978; Boag & van Noordwijk, 1987; van Noordwijk et al., 1988 ; Falconer & Mackay, 1996). These regressions use least-squares and make a number of assumptions, many of which are not valid in wild populations ( Cheverud & Dittus, 1992). For example, it is assumed that there is no assortative mating, that populations are in Hardy–Weinberg equilibrium, that there is no inbreeding or selection, that parents are randomly sampled from the population and that genetic means and variances are constant over generations. Furthermore, least-squares methods ideally require data of a balanced design, rare in ecological studies. Despite an awareness of these problems, raised as long ago as the late 1960s ( Hartley, 1967) and reiterated with the advent of maximum-likelihood techniques ( Shaw, 1987), there are few examples in the literature of the use of improved techniques outside the field of plant and animal breeding ( Knott et al., 1995 ; see below).

The discovery of highly polymorphic markers such as microsatellites and the development of new statistical approaches have opened up two new avenues for conducting quantitative genetic studies in natural populations. Firstly, molecular advances allowing parentage testing in the wild should improve both the accuracy and the availability of data for quantitative genetic analysis. In socially monogamous birds, exclusion analysis has shown a variable proportion of young attributable to extra pair copulations ( Birkhead & Møller, 1992). Deleting incorrect pedigree relationships should improve the accuracy of heritability estimates. More importantly, techniques which allow parentage to be assigned from among many candidate parents (e.g. Marshall et al., 1998 ) will allow estimates of heritability that were not previously possible. Furthermore, by identifying noncaring parents, estimates that exclude the potential effects of shared environment can be made.

Secondly, once extensive pedigree links have been established by molecular methods, statistical procedures developed by animal breeders that are more sophisticated than regression can be applied to the data. Restricted maximum likelihood (REML) procedures and the ‘animal model’ approach ( Henderson, 1972; Kennedy, 1989; Meyer, 1991) make fewer assumptions and more efficient use of the data than traditional regression methods. All data, including those from distant relatives and over several generations, can be used to improve the accuracy of the heritability estimates ( Cheverud & Dittus, 1992). By using a multivariate analysis technique, it is also possible to make heritability estimates for several correlated traits simultaneously, and to calculate maternal (or paternal) effects. Utilizing information from all of the traits to obtain estimates for each specific trait yields more accurate results, especially if there are missing data ( Meyer, 1991).

Few field studies have exploited the new quantitative genetic techniques. Exceptions are a study of a population of Toque macaques (Macaca sinica) in Sri Lanka ( Cheverud & Dittus, 1992) and two recent publications, which use both maximum likelihood and an animal model approach. These are an analysis of live weight in a wild bighorn sheep (Ovis canadensis) population in which maternal pedigree links were inferred from behaviour, but no paternal pedigree links were used ( Réale et al., 1999 ), and an analysis of several traits in a red deer (Cervus elaphus) population in which maternal and paternal pedigree links were derived from a mixture of field observation and molecular genetic information ( Kruuk et al., 2000 ).

Alternative, and very different, approaches to estimating variance components have been developed by Ritland (1996) using regression to compare trait similarity and marker-based estimates of relatedness, and by Mousseau et al. (1998 ) using likelihood to infer relationships from marker and phenotypic information. In neither case is a pedigree actually established. Although these techniques are useful where genealogies cannot be determined, the pair-wise approach ( Ritland, 1996) does not weight relationships accurately, leading to high standard errors, and the Mousseau et al. (1998 ) method is prone to bias owing to inclusion of phenotypic information in estimating relationships ( Thomas et al., 2000 ). Although recent developments allow more accurate weighting of family size ( Thomas & Hill, 2000), in general, accurate pedigree information will always allow more accurate estimation of variance components, with lower standard errors, than these pedigree-free methods.

In this study we demonstrate the application of the REML approach to estimate quantitative genetic parameters in a free-living population of Soay sheep (Ovis aries L.) on St Kilda. A recent analysis of phenotypic selection of morphometric traits in the study population ( Milner et al., 1999 ) has shown body weight to experience direct positive selection owing to differential over-winter survival in lambs of both sexes and adult females. Two other correlated traits, hind leg length and incisor arcade breadth, were less strongly selected. By estimating the amount of additive genetic variation in these traits, and genetic correlations between them, we wanted to make predictions about their response to selection.

Although there is no evidence of assortative mating in the Soay sheep ( Paterson & Pemberton, 1997), other assumptions of traditional heritability analyses are violated. As expected of a small, island population, there is some degree of inbreeding, with 5.4% of the sheep having an inbreeding coefficient greater than 0.125 (T. C. Marshall et al., unpublished observation). Furthermore, we know that not all individuals make an equal contribution to the next generation, particularly amongst males ( Coltman et al., 1999 ; Pemberton et al., 1999 ). Consequently the data are unbalanced which, together with over-lapping generations and incompletely nested half- and full-sib progenies, make analysis by traditional least-squares methods virtually impossible ( Shaw, 1987). However, several hundred paternal pedigree links within the population have been inferred by molecular techniques enabling us to use the ‘animal model’ approach.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Study population

Soay sheep, a primitive domestic sheep, may have inhabited the St Kilda archipelago, Scotland (57°49′N 08°34′W), since prehistoric times ( Boyd & Jewell, 1974; Clutton-Brock, 1981). Historically, they have been restricted to the uninhabited and inaccessible island of Soay (99 ha) but, in 1932, 107 sheep were introduced to Hirta, the largest island (638 ha). They increased rapidly until the early 1950s and have since shown dramatic population fluctuations, with counts of between 600 and 1968 individuals ( Jewell et al., 1974 ; Clutton-Brock et al., 1991 ; T. H. Clutton-Brock, B. T. Grenfell, S. D. Albon and J. M. Pemberton, unpublished data). Population crashes occur in winters of high population density ( Clutton-Brock et al., 1991 ; Grenfell et al., 1992 ), especially when combined with wet and windy weather conditions in March ( Grenfell et al., 1998 ).

Within the Village Bay study area (175 ha) on Hirta, life-history records of tagged individuals have been monitored since 1985 through regular censuses taken three times a year ( Clutton-Brock et al., 1991 ). During April and early May each year, lambs were caught and ear-tagged at 2–3 days old. Blood samples and ear-punches were taken for genetic paternity analysis. The mother’s identity was recorded and paternities assigned subsequently (see below).

Morphometric measurements

Measurements of the morphometric traits investigated here were all made on animals caught in August between 1988 and 1997 ( Clutton-Brock et al., 1992 ; Illius et al., 1995 ; Table 1). Faecal samples, from which gastro-intestinal parasite burdens were estimated ( Gulland & Fox, 1992), were collected at the same time. Body weight was the live weight, measured to the nearest 0.1 kg. Hind leg length was measured to the nearest millimetre from the tubercalcis of the fibular tarsal bone to the distal end of the metatarsus. Incisor arcade breadth (measured since 1990) was the distance between the left and right outer edges of the fourth incisor (incisiform canine) measured from dental impressions ( Illius & Gordon, 1987). Many animals (56% of females and 25% of males) have been caught in more than one year, providing repeated measures from the same individual.

Table 1.   Population mean values of the three morphometric traits. These are dependent on the age-structure of the population analysed; for age-specific mean values see Fig. 1. Thumbnail image of

Genetic determination of paternities

Locus-specific protein and microsatellite markers were used to investigate paternity in lambs born between 1987 and 1997 ( Coltman et al., 1999 ; Pemberton et al., 1999 ). Individuals were genotyped at 12–15 loci and candidate fathers, for each lamb, were identified from all tagged rams known to be alive during the preceding rut. Using the parentage-inference software CERVUS 1.0 ( Marshall et al., 1998 ), a log-likelihood ratio, or LOD score, was calculated for each candidate father of each lamb. Criteria for inferring paternity to the ram with the highest LOD score with 95% confidence were obtained through the simulation module of CERVUS 1.0, using relevant parameters of the population, including the number of candidate males, the proportion of candidates genotyped and allele frequencies at the loci used (see Marshall et al., 1998 ; Pemberton et al., 1999 ).

Of 1842 individuals with at least one known parent 1823 had known dams and 383 had sires estimated with 95% confidence. A further 287 ‘base animals’ (individuals of unknown parentage) were also present in the pedigree, through which more distant relationships could be established.

Analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Morphometric model fitting

Nongenetic variation in the three traits was removed as far as possible by fitting fixed effects models for each morphometric trait. General linear modelling (GLM), using a least-squares approach ( McCullagh & Nelder, 1989), was used to determine significant explanatory variables. Analyses were carried out independently for each sex, using Genstat 5, release 3.2 ( Genstat 5 Committee, 1993).

Age was the principal term accounting for variation in the three morphometric traits. Age-specific fitted values for the traits were derived from growth curves fitted through all the available data ( Fig. 1) and used as a proxy for age in the heritability analysis. Exponential growth curves were used for the skeletal measures, hind leg length and incisor arcade breadth, which reached an asymptotic mature size relatively early in life. A Gompertz growth curve was more appropriate for body weight ( Fitzhugh, 1975) where mature size was reached later and in males appeared to continue to change throughout life. The goodness of fit of the growth curves was supported by almost identical fitted values derived when a cubic smoothing spline ( Hastie & Tibshirani, 1990) for age was fitted.

image

Figure 1 Growth curves for the three morphometric traits (a) body weight, (b) hind leg length and (c) incisor arcade breadth in female (– ○ –) and male (– × –) Soay sheep. Fitted points were the observed age-specific population mean values. Body weight was described by the Gompertz curve a + ce–e(–b(age–m)) where a=2.92 and 4.65, c=21.21 and 35.33, b=0.814 and 0.622, and m=– 0.37 and 0.413 for females and males, respectively. Exponential curves, a + brage, were fitted for hind leg length and incisor breadth where for hind leg length a=181.98 and 192.58, b=–23.01 and –28.90, and r=0.241 and 0.389 for female and male hind leg lengths, respectively, and for incisor breadth a=26.19 and 28.37, b=–4.27 and –5.93, and r=0.268 and 0.51. 2 for females and males, respectively.

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Other significant covariates included in the fixed effects models for body weight and male hind leg length were an index of parasite burden (the natural logarithm of the number of strongyle eggs per gram of faeces ( Gulland & Fox, 1992)); catch date, which to some extent controlled for daily weight gain in August ( Milner et al., 1999 ); birth year or ‘cohort’ and year of measurement, which allowed for year to year changes in environmental conditions, measures and population density; birth type (twin or singleton) and coat colour (light or dark). In addition, horn type (polled vs. normal or scurred (deformed) horns) but not catch date explained significant variation in female leg length. The number of missing teeth was a significant covariate in the incisor arcade breadth models, as was horn type in males (normal vs. scurred). Catch date did not affect incisor breadth in either sex and nor did faecal egg count in females. All fixed effects models explained a high proportion of the trait variation (67–88%) and observed phenotypic mean values were in good agreement with fitted lines ( Fig. 1).

Genetic correlations and heritability estimates

A multivariate REML procedure which allowed for unequal design matrices and missing observations was used to estimate genetic correlations and variance components of the three traits simultaneously (PEST and VCE software by Groeneveld, Kovac & Wang, University of Illinois, 1993). In cases of deviations from normality, REML is still efficient and gives estimates with little bias, despite losing some of its optimality properties ( Hoeschele et al., 1987 ). An ‘animal model’ was used, such that the phenotype of the individual was written in terms of its additive genetic value, and other fixed and random effects as follows:

inline image

where y was a vector of the records on individuals, b was a vector of the fixed effects as determined by GLM, a was a vector of the additive genetic effect, c was a vector of the permanent environmental random effect and e was a vector of residual effects. X, Z, and P were design matrices relating records to the appropriate fixed or random effects ( Southwood & Kennedy, 1990). The additive genetic random effect allowed for a related breeding population by using an additive genetic relationship matrix created from the pedigree file. This incorporated information from all known and inferred relatives, of both sexes, correctly weighted for relatedness. The permanent environmental effect grouped repeated measurements from the same individual to determine the environmental variance between individuals that arose from long-term or nonlocalized conditions.

The total phenotypic variance (VT) was partitioned into three components, the additive genetic variance (VA), the environmental variance (VE) and the residual variance (VR) which included nonadditive genetic effects and variance arising from measurement errors:

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Heritabilities (h2) were calculated as the ratio of the additive genetic variance to the total phenotypic variance ( Falconer & Mackay, 1996):

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whilst the ratio of the environmental variance to the total phenotypic variance was c2 ( Henderson, 1972):

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Heritability estimates tend to have an upward bias if maternal (or paternal) effects are ignored because resemblance between parent and offspring owing to the shared environment, maternal genetic effects or the mother’s nutritional condition can be mistaken for resemblance owing to inheritance ( Falconer & Mackay, 1996). Therefore, to investigate the influence of maternal environmental effects on heritability estimates we re-ran the analysis with an additional environmental random effect for dam. This divided the total phenotypic variance into four components, including the variance caused by the maternal effect VM. The data files were restricted to include only those individuals whose dam was known (449 females and 375 males). To test the significance of the maternal effect, the analysis was repeated omitting the dam effect from the model, and the models compared using a likelihood ratio test based on the χ2 distribution, with the number of degrees of freedom equal to the difference in the number of variance components to be estimated.

Genetic correlations between traits, arising chiefly from pleiotropy ( Falconer & Mackay, 1996), were determined by the same analysis package. Phenotypic correlations (rP), the total observed correlation of phenotypic values, were calculated from the phenotypic covariances between traits estimated by VCE as follows:

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where covP was the phenotypic covariance between traits x and y, and σPx and σPy were the phenotypic standard deviation values of traits x and y.

Approximate standard errors of the variance components were also estimated by REML. When sample sizes were small and fewer pedigree connections could be made, some standard error estimates may be unreliable. This also has implications for the significance of heritabilities, which were determined by t-tests. However, standard errors estimated using a larger but less strict pedigree file (see discussion) were similar.

Repeatability

Repeatability gives an index of the constancy of multiple measurements from a single individual ( van Noordwijk et al., 1988 ) by expressing the proportion of the between-individual variance that was due to permanent differences, both genetic and environmental ( Falconer & Mackay, 1996). Repeatability (r) was estimated from the sum of the heritability (h2) and c2, and so represented an upper limit to possible heritability values:

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Coefficients of variation

It has been argued that heritabilities do not provide a good means of comparing genetic variation between traits or populations ( Houle, 1992; Lynch & Walsh, 1998), especially where levels of environmental variation differ between traits ( Kruuk et al., 2000 ). In such cases, standardizing genetic variances by the trait mean values rather than the total phenotypic variance may be more appropriate. The additive coefficient of variation (CVA) was calculated for each trait in each sex as:

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where was the trait mean ( Houle, 1992).

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Correlations between traits

Phenotypic correlations among the three traits were similar in each sex (Table 2) whereas genetic correlations differed. Hind leg length and body weight showed a high degree of phenotypic and genetic correlation in both sexes. This explained the observed indirect selection of hind leg length when direct selection of body weight occurred ( Milner et al., 1999 ). The phenotypic correlations between other trait pairs were lower, as were genetic correlations in females, reflecting less strong linkage.

Table 2.   Phenotypic (above the diagonal) and genetic (below the diagonal) correlations between traits in each sex. Correlations were determined by variance component estimation. Standard errors (in parentheses) are approximate. Thumbnail image of

Heritabilities and repeatabilities

The heritability estimates (h2) for the three traits ranged from 0.18 for body weight in males to 0.39 for hind leg length in males (Table 3). In all cases heritabilities were lower than might have been expected for morphometric traits ( Mousseau & Roff, 1987) but were all significantly different from zero.

Table 3.   Variance components and heritability (h2) estimates for morphometric traits in females and males, using a pedigree containing 2129 individuals. The total phenotypic variance was the sum of (a) three variance components: the additive genetic variance (VA), the permanent environmental variance (VE) and the residual variance (VR), ignoring any maternal effects; and (b) four components (VA), (VE), (VR) and the maternal effects variance (VM), taking the maternal effect (M) into consideration. The repeatability (r) equalled (VA + VE)/VT and c2 = VE/VT. *P < 0.05, **P < 0.01, ***P < 0.001. Thumbnail image of

Neither hind leg length nor incisor breadth showed differences in heritability between the sexes. In the case of body weight, the total phenotypic variance of male body weight was much greater than that of female body weight. This, combined with a lower additive genetic variance in males, led to lower and less significant estimates of the heritability of body weight in males than females.

The repeatability of measures of hind leg length were high and of body weight, reasonably high (Table 3a), indicating low variation in these traits between consecutive measures from the same animal. Incisor breadth had lower repeatabilities and was characterized by the highest residual variance components. This trait would have benefited most from a greater number of multiple measurements.

Coefficients of variation

Additive genetic coefficients of variation were used to compare the amount of genetic variation between traits and sexes. There was little difference between the sexes in CVA values, being 5.95 and 6.18 for body weight, 3.03 and 3.15 for hind leg length, and 2.72 and 2.82 for incisor breadth in females and males, respectively. Coefficients of variation would be expected to be approximately three times larger for volumetric morphological traits than for those of linear dimensions if the traits were perfectly correlated ( Houle, 1992). However, as this is not the case (Table 3), it is difficult to interpret the fact that the CVA’s for body weight were closer to twice rather than three times those of hind leg length and incisor arcade breadth.

Maternal effects

As anticipated, when the maternal environmental effect, M (the ratio of the maternal effect variance to the total phenotypic variance), was taken into consideration, the heritability estimates for both females and males were generally lower (Table 3b). However, the heritability of female body weight remained the same despite a significant maternal effect. Comparing between the sexes, it was apparent that females experienced a strong maternal effect whilst there was no significant effect on traits in male offspring. This was reflected by a significant change in deviance caused by dropping the dam random effect from the female model (χ2=23.8, d.f.=1, P < 0.001) whereas there was no significant change when dam was dropped from the male model (χ2=2.44, d.f.=1, P > 0.1). Examination of the variance components in females (Table 3) revealed that most of the maternal effect variance came from the variance previously attributed to the environmental component.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

Our analysis showed that there was low, but significant, heritable variation in all three morphometric traits in both sexes of Soay sheep. Consistent with our previous analysis of selection ( Milner et al., 1999 ), body weight generally had the lowest heritability, especially in males. The genetic coefficients of variation (CVA) also showed that all traits had some genetic variability but suggested that the heritable genetic variation may be greater in body weight than the other traits.

The low additive genetic variance and high environmental variance of body weight together suggest that the evolutionary response to selection of body weight would be slow. If we assume a mean standardized selection differential for body weight of 0.23 across the whole population and all years of the study ( Milner et al., 1999 ), the predicted evolutionary response would be an increase in mean body weight of approximately 0.02 kg per year. This is insufficient to detect over the period of the study, given the measurement errors of body weight.

Our heritability estimates were low compared with a mean of 0.46 found by Mousseau & Roff (1987) for 570 morphological traits. However, there is considerable variability in heritability estimates of traits such as body weight in sheep, which vary with age and environmental conditions. Published heritabilities of body weight in domestic sheep tend to be biased towards young animals, varying between 0.09 and 0.22 for birth weight and rising to 0.44 at 31 months ( Yazdi et al., 1997 ; Larsgard & Olesen, 1998; Mousa et al., 1999 ). Estimates of the heritability of mature body weight vary between 0.3 and 0.5 ( Näsholm & Danell, 1996). Our results include young animals, which fall within the expected range of results. Equally, they compare well with estimates from bighorn sheep (Ovis canadensis), the only other wild sheep population for which estimates have been made ( Réale et al., 1999 ). In the latter study, heritabilities estimated using REML procedures on maternal links only ranged from 0.00 to 0.81 for different ages and seasons. September weights were more heritable than June weights and heritabilities tended to increase with age ( Réale et al., 1999 ). This highlights how the heritability of body weight may change with age, but small samples, and consequent large standard errors, make interpretation difficult. For these reasons, we did not attempt to estimate age-specific heritabilities in the Soay sheep.

When molecular techniques are used to determine paternities, the level of confidence with which paternities are assigned affects heritability estimates. In our study population, a pedigree file based on paternities in which we had a confidence of 80% contained over 500 more sires, but led to lower estimates of heritability and additive coefficients of variation, especially in males. We would therefore advocate the use of the more accurate pedigree, although we tended to get poorer model convergence and less reliable standard errors with this than the 80% confidence pedigree file (see also Kruuk et al., 2000 ). A trade-off exists between maximizing the accuracy of paternities and maximizing sample size, and the confidence level should be set accordingly ( Marshall et al., 1998 ). In studies where a less accurate pedigree is used, the error in paternity assignment should be included in the estimation procedure.

The relatively low heritabilities of our traits arose from differing combinations of high residual or environmental variance and low additive genetic variance. Heritabilities in small populations have a tendency to be lower than those in large populations owing to gene fixation ( Falconer & Mackay, 1996). However, it has been shown that, despite being small and isolated, the Soay sheep population on St Kilda has remarkably high allozyme heterozygosity ( Bancroft et al., 1995 ). A high environmental variance of all traits was indicated by values for c2, the ratio of the permanent environmental variance to total phenotypic variance, which exceeded the heritabilities. Natural populations have a tendency to have high levels of environmental variation leading to increased total phenotypic variance relative to the additive genetic variance, and so reduced heritabilities ( Ricklefs & Peters, 1981). This highlights the advantage of using additive coefficients of variation (CVA) which scale the heritable genetic variation against the mean rather than total phenotypic variation ( Houle, 1992) when trying to assess the ‘evolvability’ or potential for evolution of traits in natural populations.

Although there was little evidence of a difference in heritability estimates between the sexes, a highly significant maternal effect was found in all three traits in females, whereas no significant maternal effect was detected in males. This reflects differences in the social behaviour of the sexes. Females tend to be hefted within matrilineal groups ( Grubb, 1974) and consequently female offspring grow up under the same environmental conditions as their mothers. By contrast, male offspring disperse from their natal group, usually forming yearling male groups within their mothers’ range at first and then joining all male groups in other parts of the study area ( Grubb, 1974). One would expect the mother’s nutritional condition to affect early development of male and female offspring equally, suggesting that the difference in maternal effects between the sexes arises from shared home ranges in females. A similar situation has been reported in red deer ( Kruuk et al., 2000 ).

An important advantage of our method, which combines a pedigree inferred by molecular techniques and includes noncaring parents, with an animal model, is that maternal (or paternal) effects can be investigated. This has previously only been possible in natural populations by carrying complex manipulations, often impossible in wild mammals.

This study has demonstrated the application of quantitative genetics to estimate variance components and heritabilities in a population that could not have been analysed using traditional methods. This was made possible by bringing together the use of molecular techniques for determining parentage and sophisticated statistical methods. Consequently we have been able to make evolutionary predictions about a wild mammal population. Such an achievement heralds new opportunities to address many previously unanswerable evolutionary questions in ecological studies.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References

We thank the National Trust for Scotland and Scottish Natural Heritage for permission to work on St Kilda and for their assistance in many aspects of the work. Logistical support was provided by the Royal Artillery Range, Hebrides, its St Kilda Detachment and the Royal Corps of Transport. David Green, Tony Robertson, Andrew MacColl, Jill Pilkington and many volunteers collected much of the long-term data. We are grateful to Dave Coltman and Judith Smith for carrying out the genotyping and to David Elston for his statistical advice. We also thank Tim Clutton-Brock, Bryan Grenfell and Adrian Lister for their support and two anonymous referees for their constructive comments on the manuscript. The Soay Sheep Project has been funded by grants from BBSRC, NERC, the Royal Society and the Wellcome Trust.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Analysis
  6. Results
  7. Discussion
  8. Acknowledgments
  9. References
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