Repeated selection of morphometric traits in the Soay sheep on St Kilda

Authors


J. M. Milner, Institute of Terrestrial Ecology, Hill of Brathens, Kincardineshire AB31 4BY, UK. Fax: 01330 823303. E-mail: j.milner@ite.ac.uk

Abstract

1. Long-term studies allow the outcomes of repeated selection events to be monitored. Here, we investigate phenotypic selection in successive winter mortality events in the Soay sheep of St Kilda, Scotland, between 1985 and 1996. Selection of three quantitative morphometric traits, body weight, hindleg length and incisor arcade breadth, was investigated in different sectors of the population.

2. Evidence from fitness differentials of positive directional selection for large size was repeatedly found in lambs and adult females. Selection in the opposing direction was only found in one year in lambs.

3. Selection gradients showed that in most years when significant selection occurred, body weight was the focus of direct selection, whereas selection of hindleg length and incisor breadth was indirect, arising from their correlation with body weight.

4. Selection was strongest in years of low over-winter survival and almost absent in years when survival was high. Intensity of selection was greatest in lambs, emphasizing the differences in selection pressure experienced by different sectors of the population, in addition to the temporal variation in selection pressure due to population density and environmental conditions.

5. Despite repeated positive selection of body weight, no evidence of a change in the population mean was found over the course of the study.

Introduction

An area of concern to ecologists, evolutionary biologists and conservation biologists alike is how predictable or repeatable selection events are. Given the wide variety of factors affecting over-winter survival; for example, further questions arise as to whether the same sectors of a population and the same phenotypes are always affected, and how selection varies with the severity of mortality.

Long-term studies involving marked individuals provide unique opportunities for monitoring sequential selection events and investigating the course of evolutionary processes. Some of the best examples of natural selection of quantitative traits come from studies of birds (Price & Boag 1987), and in particular from the studies of directional and oscillating selection of beak morphology in Darwin's finches (Geospizinae) of the Galápagos islands (Grant et al. 1976; Boag & Grant 1981; Grant 1986). In an area of contrasting environmental extremes, characterized by a highly variable food supply and strong intra-specific competition, body size, and functional and ecological aspects of beak variation important for foraging, have experienced both positive and negative selection over the course of an El Niño event and two droughts (Boag & Grant 1981; Price et al. 1984; Grant & Grant 1989). By demonstrating that these traits were highly heritable (Boag 1983; Grant 1983) an understanding of the evolution and adaptive radiation of these characters has been gained.

However, phenotypic selection [an association between fitness and phenotype (Endler 1986)] of a heritable morphometric trait may be observed without any evolutionary consequences if a large component of the phenotypic variance is environmental rather than genetic (Falconer & Mackay 1996). This was the case for tarsus length in the collared flycatcher, Ficedula albicollis Temminck (Alatalo, Gustafsson & Lundberg 1990). van Noordwijk et al. 1988) found selection against small body size in great tit (Parus major L.) nestlings acted strongly on the environmental variance that resulted from poor feeding conditions.

In this paper we investigate phenotypic selection in successive winter mortality events in the Soay sheep (Ovis aries L.) on St Kilda over the period 1985–96. These events vary considerably in severity between years due to a number of intrinsic and extrinsic factors, including population density. Within the population there is evidence of density dependent effects on survival (Clutton-Brock et al. 1991; Grenfell et al. 1992), and it is known that survival is influenced by body weight (Stevenson 1994; Clutton-Brock et al. 1996). In addition, population dynamics of large herbivores may be strongly influenced by stochastic environmental variation (Gaillard, Festa-Bianchet & Yoccoz 1998). Climatic conditions, in particular the effect of March gales (Grenfell et al. 1998) and variations in plant productivity are important extrinsic factors that may be highly variable between years, and have a large influence on the scale of over-winter survival.

Previous studies on St Kilda have shown selection of morphometric characters (Illius et al. 1995), proteins and microsatellites (Gulland et al. 1993; Bancroft et al. 1995) in Soay sheep. Other studies have demonstrated density-dependent selection of the polymorphic traits, coat colour and horn type (Moorcroft et al. 1996; Clutton-Brock, Wilson & Stevenson 1997). During a specific mortality event, the population crash in the winter of 1991–92, Illius et al. (1995) showed that differential survival favoured animals with relatively broad incisor arcades and that this character had a greater fitness advantage than body weight.

In this study, we expand on that analysis to assess whether there has been consistent directional selection across successive mortality events and an evolutionary response to selection (Falconer & Mackay 1996). We examine phenotypic selection of three quantitative morphological characters, body weight, hindleg length and incisor arcade breadth. The first two represent aspects of body size, whilst the latter is a trait of functional importance in foraging (Illius & Gordon 1987), as well as a linear measure of size. We explore the fitness differentials of these phenotypes in terms of survival. However, correlations between characters complicate the measurement of phenotypic selection (Lande & Arnold 1983), since direct selection acting on one trait also produces an indirect effect on correlated traits. We have therefore used multivariate techniques to tease apart direct and indirect selection, and determine which characters are important in predicting the survival of different sectors of the population.

Our results suggest that over-winter survival consistently favoured larger size in Soay sheep and that the intensity of selection was linearly related to the proportion of sheep that survived. Of the three characters measured, body weight tended to be the target of selection rather than hindleg length or incisor breadth. However, there has been no detectable change in body weight over the 13 years of the study.

Materials and methods

Study population

The Soay sheep on Hirta (638 ha), St Kilda, have shown dramatic population fluctuations between 600 and 1825 individuals during the periods of intensive monitoring from 1959 to 1968 (Jewell, Milner & Boyd 1974), and from 1985 to the present (Clutton-Brock et al. 1991; unpublished data). Population crashes, during which 50–70% of animals die of starvation, exacerbated by high gastrointestinal parasite burdens (Gulland 1992), occur in late winter (March) when a high sheep population has depleted the standing crop of vegetation (Grubb 1974; Clutton-Brock et al. 1991; Grenfell et al. 1992). These crashes have the potential to be major selection events. Crashes are followed by years of relatively low population density which, due to high winter survival (greater than 90%) and high fecundity (Clutton-Brock et al. 1992), allow the population to increase rapidly.

Data collection

Survival

Life-histories of tagged individuals in the Village Bay area of Hirta (175 ha) have been monitored since 1985 by regular censusing at three times of year and daily mortality searches from February to April (Clutton-Brock et al. 1991). An individual was considered to have survived a winter if it was alive on 15 May the following year. In all cases ‘years’ ran from spring to spring so, for example, the winter of 1985 covered the period from autumn 1985 until spring 1986. Estimates of the study area population size and age/sex structure were made from census results, the population being the number of sheep entering the winter that regularly used the study area (Fig. 1). This number is well correlated with sheep numbers on the whole island and represents approximately a third of the total population (Clutton-Brock et al. 1991).

Figure 1.

Number of sheep by age and sex class, within the Village Bay study area on Hirta, St Kilda, on 1 October each year between 1985 and 1996.

Morphometric measurements

In most years, over half of the study area population was caught in August or September (median proportion 0·56, range 0·18–0·70; Table 2), allowing body measurements, blood and faecal samples to be taken. Body weight was the live weight, measured to the nearest 0·1 kg. It is a composite measure of body size and condition. Gutfill and wetness of fleece are factors influencing weight that cannot be controlled for and therefore contribute to the error in this measure (Illius et al. 1995). Hindleg length, measured to the nearest millimetre from the tubercalcis of the fibular tarsal bone to the distal end of the metatarsus, has been recorded from 1988 onwards. Incisor arcade breadth, measured since 1990, was the distance between the outer left and right edges of the fourth incisor (incisiform canine) (Illius & Gordon 1987) measured from dental impressions of the incisor arcade made using Tenacetin dental modelling wax (Associated Dental Products, Swindon, UK). This is a size measure with functional significance for survival through its relationship with bite size and food intake rate (Gordon, Illius & Milne 1996).

Table 2.  Comparison of body weight (kg) of (a) female lambs, (b) male lambs, (c) adult female and (d) adult male sheep that died with those that survived over-winter mortality. Years denote the year in which winter started, i.e. 1985 represents the winter 1985/86. All measurements were made the preceding August and corrected for catch date. The proportion of the study area population that was caught and therefore weighed, varied between years t-tests were carried out for years in which sample sizes of those surviving and dying both exceeded five. *P≤ 0·05; **P≤ 0·01; ***P≤ 0·001. † Denotes years in which some of the individuals caught were dosed with anthelminthic treatments. These individuals have been excluded from all analyses because of the influence of treatment on survival (Gulland 1992).Thumbnail image of

The period of catching during late summer was a time of considerable daily weight gain (0·12 kg day−1 in lambs, 0·08 kg day−1 in adult females and 0·20 kg day−1 in adult males). Catch date was variable during the 1980s, particularly in 1985 and 1988, whilst throughout the 1990s was restricted to a much shorter period. In an attempt to control for the effects of catch date, body weights (and hindleg lengths in lambs) were standardized to that expected if the animals were caught on a single day.

All three morphometric variables were highly intercorrelated (Table 1), particularly hindleg length and body weight in lambs. In all cases, hindleg length was more closely correlated with body weight than incisor breadth. A lower correlation occurred between incisor breadth, and both body weight and hindleg length in adult females. This arose because a number of females had lost teeth in old age. These individuals were not excluded from the analysis because they could help to discriminate between the effects of body weight and incisor breadth on survival.

Table 1.  Correlations between loge-transformed morphometric characters in three sectors of the population *P < 0·05; **P < 0·01; ***P < 0·001.Thumbnail image of

The associations between body weight, and both hindleg length and incisor breadth are shown in Fig. 2 for lambs and adults, together with the fitted allometric relationships. There were no significant differences between the sexes either in the slopes or in the elevations of the fitted lines, except in the relationship between incisor breadth and body weight in lambs (Fig. 2b). However, males tended to be larger than females. Considerable variation occurred in both hindleg length and incisor breadth, independent of variation in body weight (except in the case of hindleg length in lambs) providing opportunity for selection of either trait to occur. In adult females, a number of individuals had incisor breadths considerably smaller than would have been expected for their body weight for the reasons described above.

Figure 2.

Relationships between morphometric characters measured in August and corrected for catch date, in (a and b) lambs (r2 = 0·76 and 0·36, respectively) and (c and d) adults (r2 = 0·39 and 0·12, respectively), showing fitted values according to the allometric equations given.

Age and sex

Selection in lambs (individuals less than 1 year old) was analysed separately from yearlings (individuals aged 12–23 months) and adults (over 2 years old) because of the particular susceptibility to mortality of animals during their first winter (Clutton-Brock et al. 1992). Differences in survival between yearlings and adults were less marked, and individuals could be grouped together in a single category without affecting the results. Data from males and females were analysed separately because of the differential survival of the sexes, lower survival in males being associated with faster growth and rutting activity (Stevenson & Bancroft 1995).

Analysis

Selection differentials

Standardized selection differentials, S′ (Falconer & Mackay 1996) were used to investigate the degree of selection of quantitative morphometric traits during winter mortality. They were calculated as the change in the population mean of the trait before (b) and after (a) selection, using the following expression:

image

where vb is the variance about the mean, before selection. Morphometric traits were transformed by natural logarithms before all analyses. The significance of S′ was determined by t-tests, comparing the character means of survivors with non-survivors (Endler 1986; Smith 1990). Shifts in character means were also compared between high and low density years when the population was, respectively, above or below a threshold of 400 animals (approximately the median population size).

Selection gradients

In an attempt to determine which of the correlated traits studied was the target of selection, multivariate selection analysis (Lande & Arnold 1983) was used on data from 1990 to 1996, the years when all three characters were measured. Standardized directional selection gradients (β′) were found from the multiple regression of relative survival on each trait, standardized to unit variance, where the relative survival of an individual was calculated as its absolute survival (0 or 1) divided by the mean absolute survival of individuals of that age/sex class [taken as the proportion of survivors (Table 2)]. The partial regression coefficients were a measure of the intensity of selection acting on each character, without phenotypic responses due to selection on other correlated characters (Price et al. 1984). As such, they could be used to determine the relative importance of the traits measured (Endler 1986) and to compare between selection events. In lambs, body weight and hindleg length were too closely correlated (r = 0·87, all other r < 0·60) for both traits to be included in the analysis so hindleg length was dropped (Lande & Arnold 1983; Grant & Grant 1989).

Analyses were carried out using genstat 5, release 3·2 (genstat 5 Genstat, 5 Committee 1993).

Heritabilities

Preliminary estimates of heritability, the ratio of the additive genetic variance to the total phenotypic variance (Falconer & Mackay 1996), have been made for the three traits. Variance components were estimated from an animal model using a restricted maximum likelihood procedure which allowed for unequal design matrices and missing observations (Veerkamp & Brotherstone 1997). Estimates were based on 1777 data records from 963 individuals of known pedigree. The model included the additive genetic random effect and a random effect to take account of repeated measurements from the same individual. Age, sex, catch date, year, parasite burden and cohort were fitted as fixed effects.

Results

Selection differentials

Body weight

Differences in mean body weight between lambs surviving winter and those dying were significant in two-thirds of the years in which sample sizes were large enough for a comparison to be made (Table 2a,b). In both sexes, individuals surviving were larger than those dying in all years except 1990 and 1992, when this trend was reversed, but differences were not significant. This showed that positive directional selection for increased body weight was repeatedly occurring.

In adult females, significant selection on body weight occurred in the same years as in lambs (Table 2c). In no year were individuals surviving significantly lighter than individuals dying, although in 1994 there was a trend in that direction. Adult females therefore also showed repeated positive selection of body weight. By contrast, in adult males there were no significant differences in body weight between survivors and non-survivors in any year, although trends were in the same direction as in other sectors of the population (Table 2d). Unfortunately, in many years sample sizes of adult males were too small for statistical comparison.

Hindleg length

Significant positive selection of hindleg length was found in lambs in the same years as selection of body weight (Table 3a,b). In adult females the same pattern of differential survival favouring larger individuals was found for hindleg length as occurred for body weight, with the exception of 1993 when selection of hindleg length was not significant (Table 3c). In adult males there was again no evidence of selection for size in any year (Table 3d). The differences in leg length between survivors and non-survivors were generally less pronounced than differences in body weight.

Table 3.  Comparison of hindleg lengths (mm) of (a) female lambs, (b) male lambs, (c) adult female and (d) adult male sheep that died with those that survived over-winter mortality. All measurements were made the preceding August and corrected for catch date. t-tests were carried out for years in which sample sizes of both survivors and non-survivors exceeded five *P≤ = 0·05; **P≤ = 0·01; ***P≤ = 0·001.Thumbnail image of

Incisor breadth

There was significant positive selection of incisor breadth in 1991 and 1993 in female lambs, and 1993 only in male lambs, corresponding with some of the years in which selection of the other traits was observed (Table 4a,b). In adults of both sexes, survivors had significantly larger incisor breadths than non-survivors in 1991 (Table 4c,d), in agreement with Illius et al. (1995). This was also true in adult females in 1996. Both these years were years in which significant differences were found in other traits, but only in the case of males in 1991 were differences greater in incisor breadth than either body weight or hindleg length, as shown by the values of the t-test.

Table 4.  Comparison of incisor breadth (mm) of (a) female lambs, (b) male lambs, (c) adult female and (d) adult male sheep that died with those that survived over-winter mortality. All measurements were made the preceding August t-tests were carried out for years in which sample sizes of both survivors and non-survivors exceeded five. *P≤ = 0·05; **P≤ = 0·01; ***P≤ = 0·001.Thumbnail image of

Between-year variation in selection

At low population density over-winter survival was high (Fig. 3–5) and there was no evidence of a shift in any of the character means in lambs or adult males although in adult females there was a positive shift in mean body weight (t = 2·35, d.f. = 372, P = 0·019). By contrast, in high population years, a distinct positive shift in character means could be seen between survivors and non-survivors in all three traits in lambs (body weight t = 6·68, d.f. = 466, P < 0·001; hindleg length t = 6·24, d.f. = 398, P < 0·001; incisor breadth t = 3·12, d.f. = 341, P = 0·002) and in body weight (t = 3·92, d.f. = 693, P < 0·001) and hindleg length (t = 2·39, d.f. = 554, P = 0·017) in adult females. The same was also true of body weight in adult males (t = 2·05, d.f. = 279, P = 0·042), detectable because of the larger sample size resulting from pooling several years’ data.

Figure 3.

Frequency distribution of body weights corrected for catch date of (a) lambs, (b) adult females and (c) adult males during years of low (<400 individuals) and high (>400 individuals) population size. Individuals which died (▪) are distinguished from individuals that survived (□) over-winter mortality.

Figure 4.

Frequency distribution of hindleg lengths of (a) lambs, corrected for catch date, (b) adult females and (c) adult males during years of low (<400 individuals) and high (>400 individuals) population size. Individuals which died (▪) are distinguished from individuals that survived (□) over-winter mortality.

Figure 5.

Frequency distribution of incisor arcade breadths of (a) lambs, (b) adult females and (c) adult males during years of low (<400 individuals) and high (>400 individuals) population size. Individuals which died (▪) are distinguished from individuals that survived (□) over-winter mortality.

The interpretation of this differential survivorship for phenotypic selection was shown by the selection differentials, S′, plotted against population size (Fig. 6). Selection of both body weight and hindleg length increased with population size, but the relationship was not linear. A threshold model, as has been applied to population growth on St Kilda (Grenfell et al. 1992; Grenfell et al. 1998), would explain the relationship better, with no significant selection below a threshold population size of ≈400, and significant selection above the threshold. However, the large variance in selection above the threshold means the nature of the relationship at high population density is difficult to define.

Figure 6.

Selection differentials (S′) for log-transformed morphometric characters in female (□) and male lambs (▪), adult females (○) and adult males (•), in relation to population density.

The correlation between survival and population density, although good in lambs (r = −0·806 in females and r = −0·817 in males), was poor in adults (r = −0·451 in females and r = −0·535 in males) with unexpectedly high survival in several years of high population density. Consequently, selection was more closely related to the proportion of the population surviving than to population density itself (Fig. 7). Selection of all three morphometric traits increased as the proportion of survivors decreased and was significantly stronger in lambs than adults for body weight (F1,39 = 11·0, P = 0·002), but not in hindleg length (F1,29 = 1·34, P = 0·256) or incisor breadth (F1,25 = 0·03, P = 0·854). There were no significant differences in the strength of selection between the sexes in any of the traits in either lambs (S′w: F1,17 = 0·23, P = 0·640; S′h: F1,13 = 0·30, P = 0·593; S′i: F1,10 = 0·37, P = 0·558) or adults (S′w: F1,20 = 0·01, P = 0·905; S′h: F1,14 = 0·03, P = 0·876; S′i: F1,13 = 0·59, P = 0·458).

Figure 7.

Selection differentials (S′) for log-transformed morphometric characters in female (□) and male lambs (▪), adult females (○) and adult males (•), in relation to the proportion of each sector of the population that survived over-winter mortality (p). Fitted lines are shown for significant relationships. Differences between sexes were not significant, allowing a single common regression line to be fitted for each age class.

Selection gradients

Standardized selection gradients, β′, used to distinguish direct from indirect selection, showed that selection of the three traits studied was greatest for body weight in lambs, in 6 out of the 7 years for which comparisons were made (Table 5a). This suggests that body weight, rather than hindleg length or incisor breadth, was the target of direct selection. Significant positive selection for body weight in lambs occurred in 1993 and 1996 (and at the 10% level in 1991 and 1995), whilst in 1990 there was significant negative selection for body weight. In adults, no selection could be measured in 1995 because all individuals caught the previous August survived. Otherwise a similar pattern to that observed in lambs was apparent for females, with selection being greatest for body weight in 5 out of 6 years (Table 5b). By contrast, in adult males there was no significant selection of body weight in any year (Table 5c).

Table 5.  Standardized directional selection gradients (β′ ± standard error) for correlated morphometric characters in (a) lambs, (b) adult females and (c) adult males. Values indicate the relative intensity of selection, comparable between traits and between selection events. In lambs, body weight and hindleg length were too closely correlated for both to be included in the analysis. All characters have been loge transformed HP < 0·10; *P < 0·05; **P < 0·01; ***P≤ 0·001.Thumbnail image of

An interesting feature revealed by the selection gradients was that hindleg length in adult females never experienced significant selection (Table 5b), contrary to the results shown in Table 3b. This suggests that the apparently significant selection of hindleg length observed in lambs may also have arisen indirectly from the selection of the highly correlated trait, body weight. Furthermore, in 1993 and 1996 in adult females, and in 1991 in adult males, the direction of the selection gradient for hindleg length was negative (although not significant), in contrast to the positive results obtained when selection differentials were calculated for hindleg length without taking into account the correlation with body weight.

Similarly, the direction of selection gradients for incisor breadth in all sectors of the population has been negative in most years since 1992, contrary to the direction implied by selection differentials and despite simultaneous positive selection on weight. This highlights the importance of taking correlations between characters into account. Incisor breadth was the principle character under selection in adult males in 1991. This event was the only occasion on which significant selection of any of the traits occurred in the adult male sector of the population.

Selection gradients also showed that, in agreement with the relationship between selection differentials and proportion of survivors established above, years of intense selection, when selection gradients were high, were consistent with years of low survival rates. One exception was the winter of 1994–95 when the intensity of selection in lambs was lower than would have been predicted from the small proportion of the lamb population that survived.

Evolutionary response

Having demonstrated significant positive selection of body weight over a number of years, in both lambs and adult females, with only one significant and less intense selection event in the opposing direction in lambs, one might expect to detect a long-term shift in the population mean of this trait. However, modelling change in body weight against time from 1985 to 1996, no evidence was found to support this (Fig. 8). Once age, sex and population size had been controlled for (F6,2125 = 584·5; P < 0·001) no additional variation in weight could be accounted for by time (F1,2125 = 0·86; P = 0·354). However, a preliminary estimate of the heritability of body weight suggested that it was low and significant at the 5% level (Table 6), whereas heritabilities of the other two traits were both higher and more significant. It therefore appeared that selection was operating on variance that was largely of environmental rather than genetic origin with the consequence that no response was observed over the period of the study.

Figure 8.

Changes in mean body weight (corrected for catch date) in female (□) and male lambs (▪), adult females (○) and adult males (•) during the period 1985–96. Change in body weight (W) is described by the expression W = c − 0·004pop, where c is 14·20 for female lambs, 16·32 for male lambs, 24·01 for adult females and 28·93 for adult males.

Table 6.  Repeatabilities and heritabilities (±SE) of morphometric traits calculated using a restricted maximum likelihood procedure on 1777 records from 963 individuals of known pedigree *P < 0·05; **P < 0·01; ***P≤ 0·001.Thumbnail image of

Discussion

This analysis shows clear, strong evidence for repeated phenotypic selection of body weight in lambs and to a lesser extent in adult female Soay sheep on St Kilda. Standardized selection gradients indicated that, although there was also apparent selection of the correlated traits, hindleg length and incisor breadth, these traits were subject to indirect selection, whilst body weight was the target of direct selection. However, due to the small genetic component of variation in body weight no significant evolutionary response to repeated selection was detected. It may be that over a longer time period a response would be detectable.

The fact that body weight should be important in determining over-winter survival of Soay sheep is neither new (Grubb 1974; Clutton-Brock et al. 1992; Stevenson 1994; Bancroft et al. 1995; Clutton-Brock et al. 1997), nor surprising when one considers fasting endurance theory (Lindsted & Boyce 1985; Millar & Hickling 1990) or energetics models (Searcy 1980; Brown, Marquet & Taper 1993). However, that it should be more important than incisor arcade breadth contradicts the findings of Illius et al. (1995), who argued for the functional importance of incisor breadth in determining food intake rates at times of low forage availability and supported it with evidence of superior survival of relatively large-mouthed individuals after body weight had been controlled for. In the current analysis the only evidence that this might be the case was from adult males in 1991–92 when incisor breadth, not body weight, was the target trait of selection.

However, careful examination of the original 1991–92 data set revealed some misclassifications in the survival outcomes of some individuals. Re-analysis with the corrected data set did not support the initial findings, but showed that although incisor breadth had a strong effect on its own, it was not significant after controlling for body weight. If incisor breadth was more important than body weight in determining survival, we might expect the group of adult females with missing teeth and therefore small incisor arcades relative to their body weight, to show lower levels of survival than other females of similar body weight, but this was not the case.

At times of high sheep population the standing biomass of vegetation is at a minimum (Grubb 1974). The hypothesis presented by Illius et al. (1995) was that individuals with the broadest incisor arcades would be able to maximize their bite size and, hence, food intake rate (Gordon et al. 1996) when grazing on very short swards. However, this theory does not account for the fact that under the heavy grazing pressure associated with high population density, the sward in late winter is very heavily dominated by bryophytes (Gwynne & Boyd 1970; M. J. Crawley, unpublished data) able to exploit a time of competitive release from grass species. Histological analysis of faecal samples from St Kilda shows a peak in bryophyte intake in March, accounting for as much as 30% of epidermal fragments (Milner & Gwynne 1974). A trade-off may therefore exist between large bite size at the expense of high bryophyte intake of low nutritional value (Prins 1981) and smaller bite size with the ability to select more highly nutritious food items (Gordon & Illius 1988). Indeed, in recent years, when population size was high, selection on incisor breadth tended to be negative in all age and sex classes, after controlling for body weight.

Large body size has long been recognized as important in enhancing survival of terrestrial vertebrates during periods of resource shortage in seasonal environments (Millar & Hickling 1990). The fasting endurance hypothesis (Lindsted & Boyce 1985) provides a mechanism to explain the differential survival observed on St Kilda where at the end of winter none of the island's plant communities can provide sufficient nutrients to support the sheep (Milner & Gwynne 1974) and animals die of malnutrition (Gulland 1992). Comparing across species, larger individuals have proportionally greater fat reserves relative to body weight (Calder 1984) and are able to metabolize somatic sources at a lower weight specific rate (Lindsted & Boyce 1985), whilst their daily energy requirements are proportionally lower (Kleiber 1961). If the same holds within a species, during periods of shortage the smallest individuals will deplete their reserves first (Millar & Hickling 1990). However, larger size will only be favoured when losses incurred during fasting can be recouped later and the absolutely greater food requirements of a large body size can be met. When food is generally limited, as may be the case on small islands, individuals of smaller body size may be at an advantage because they are better able to survive and reproduce under such conditions (Lomolino 1985). On St Kilda there was no evidence of a long-term change in body size despite temporal fluctuations in selection pressures caused by short-term perturbations in environmental conditions and population size. This suggests that an optimal body size may have already been reached.

Body weight is composed of two elements, body size and condition. We have no reliable measure or index of condition in live animals because Soay sheep are unusual in depositing little subcutaneous body fat compared with domestic breeds (McClelland, Bonaiti & Taylor 1976). However, indirect evidence suggested that it was the condition element of body weight rather than body size that experienced selection. If body size was under-going selection we would expect hindleg length to have shown equally strong selection as body weight. Furthermore, the lower heritability and repeatability of body weight than hindleg length indicated a larger proportion of environmental variance (including a proportionally greater measurement error) within the body weight phenotypes. This can be attributed to variation in condition (Lindstedt & Boyce 1985) since body fat is the most variable constituent of body mass (Pond 1978). Condition is known to be highly dependent on environmental conditions, in particular food availability (Choquenot 1991), and is often used to explain part of the variability of size from variation in environmental conditions (van Noordwijk et al. 1988). We cannot, however, rule out the possibility that some other fitness trait such as disease resistance, which also has implications for body condition, is the underlying variable under selection.

Morphological traits tend to have high heritabilities (Mousseau & Roff 1987), especially compared with life history traits. Consequently, we may have expected the heritabilities of the traits considered here to be higher. However, it seems likely that body weight has been under selection in the same direction for many generations with the result that little heritable variation remains, heritability of body weight is low and any response to further selection is slow. Little remaining additive genetic variance in body weight may also be compounded by high environmental variance resulting from variable climatic conditions, to limit heritability (Houle 1992). A fuller investigation of the genetic and environmental coefficients of variation is being conducted.

Alternatively the lack of evolutionary response could result from opposing selection occurring at some other phase of the life history or on some other unmeasured trait that is correlated with body weight. Survival is only one component of fitness, but similar analysis conducted on female fecundity data have also shown selection pressures favouring heavier maternal body weights (Clutton-Brock et al. 1997). This would therefore reinforce the trend towards increased body weight rather than counteract it.

Selection was most intense when survival was lowest, both when comparing between sectors of the population and between years. This observation was in agreement with the result of Price et al. (1984) for selection of beak dimensions in Darwin's finches. The differences in selection pressure found between sectors of the population highlights the importance of assessing the responses to selection separately for each age or sex class (Fowler 1987; Gaillard et al. 1998). In particular, lambs were more strongly affected by selection than adults, explained by the greater influence on survival of phenotypic variation within growing animals (Clutton-Brock 1988). This is in keeping with the general rule that juvenile survival is highly sensitive to limiting factors whether caused by population density or by stochastic environmental factors (Gaillard et al. 1998).

Although the strongest selection was detected when population density was high, as found by Moorcroft et al. (1996) and Clutton-Brock et al. (1997) on St Kilda, high population density did not necessarily lead to strong selection if environmental conditions were favourable for survival. This mirrors the relationship between population growth and sheep density in which at high densities the population can increase, decrease or remain constant, depending on environmental conditions (Grenfell et al. 1998) and emphasizes the importance of environmental stochasticity in determining population dynamics (Srther 1997).

This study therefore highlights the temporal variation in intensity of selection due to the effects of density and stochastic environmental variation on survival, as well as the variation between age and sex classes. We have shown that the same phenotypes and same sectors of the population were consistently affected by phenotypic selection, but the implications of this for the evolution of body size were moderated by the low heritability of body weight.

Acknowledgements

We are grateful to 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. The project would not have been possible without the generous assistance and logistical support of the Royal Artillery Range, Hebrides, its St Kilda Detachment and the Royal Corps of Transport. Special thanks go to Tony Robertson, Andrew MacColl and Jill Pilkington for their important contributions to the long-term data collection, and to a number of volunteers for helping them. We are grateful to David Elston of BioSS, for his invaluable statistical advice and to Sue Brotherstone of ICAPB, Edinburgh University, for assistance in determining heritabilities. The work is supported by grants from NERC, BBSRC and the Wellcome Trust.

Received 6 April 1998;revisionreceived 21 July 1998

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