Heritability of body mass varies with age and season in wild bighorn sheep

ABSTRACT Heritabilities (_h_2) of body mass at different ages and seasons were estimated using offspring–mother regression and restricted maximum likelihood (REML) methods for bighorn sheep

on Ram Mountain, Alberta. Both methods resulted in similar estimates of _h_2 for adults, but for lambs and yearlings heritability was underestimated by offspring–mother regression relative

to REML, possibly because of higher maternal-effects bias for offspring–mother regression. Heritabilities of body mass in bighorn were similar to published estimates for domestic sheep.

Heritability estimated by offspring–mother regression increased after 2 years of age. The REML method suggested that heritability was moderate for lambs and yearlings, very low at 2 years of

age, and increased afterwards. The increase in heritability with age was attributed to declining negative maternal effects. Very low _h_2 estimates at 2 years of age, obtained with both

methods, appeared to be caused by a combination of high environmental variance and very low genetic variance. Body mass of bighorn sheep has a pronounced seasonal cycle, and _h_2 was lower

in June than in September for 2-year-olds and older sheep, and associated with both lower _V_A and higher _V_E in spring. SIMILAR CONTENT BEING VIEWED BY OTHERS EVALUATION OF ALTERNATIVE

METHODS FOR ESTIMATING THE PRECISION OF REML-BASED ESTIMATES OF VARIANCE COMPONENTS AND HERITABILITY Article 23 February 2022 DISSECTION OF X CHROMOSOME DOSAGE COMPENSATION FOR QUANTITATIVE

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Article Open access 16 December 2022 INTRODUCTION Evolutionary changes in quantitative traits in natural populations depend on the magnitude of heritability of each trait and on the genetic

correlations between traits (Lande, 1979; Falconer & Mackay, 1996; Roff, 1997; Lynch & Walsh, 1998). Quantitative genetic studies applied to evolutionary biology and ecology have

recently multiplied (Roff, 1997; Lynch & Walsh, 1998). However, although there are numerous published studies of the quantitative genetics of plants, invertebrates and small vertebrates

(Roff, 1997), studies of large wild mammals are rare (Cheverud & Dittus, 1992). Here we provide the first estimate of the heritability of body mass at different ages for a wild large

mammal, using a unique long-term data set on marked bighorn sheep (_Ovis canadensis_). We chose body mass because it affects many life-history traits of this species, including survival

(Festa-Bianchet et al., 1997), longevity (Bérubé et al., 1999) and female reproductive success (Festa-Bianchet et al., 1998). Cheverud & Moore (1994) underlined the important

contribution to quantitative genetics that could be made by studies in behavioural ecology based upon long-term monitoring of marked individuals. However, wild animals are normally difficult

to capture, and because juveniles often have low survival, very few studies have accumulated the sample size necessary to estimate quantitative genetic parameters reliably (Klein et al.,

1973). One could measure quantitative traits in the captive-reared offspring of wild-caught parents, but there are serious questions about the reliability of laboratory estimates of

heritability (Riska et al., 1989; Simons & Roff, 1994; but see Weigensberg & Roff, 1996). In addition, only a narrow taxonomic range of species is suitable for laboratory study:

long-lived and large mammals are seldom reared in captivity in sufficient numbers. Consequently, heritability studies of large mammals have been restricted to domestic species (Snyman et

al., 1995; Näsholm & Danell, 1996) or to wild species in captivity (Williams et al., 1994; Jaquish et al., 1997; Vandenberg & Garrick, 1997). An additional obstacle to studies of

heritability in large mammals is the difficulty experienced in determining paternity. In many polygynous or promiscuous mammals, paternity can only be determined by molecular methods (Hogg

& Forbes, 1997). Nevertheless, estimates of heritability can be obtained with mother–offspring relationships or with Restricted Maximum Likelihood (REML) methods that take into account

all the genetic relationships available within an incomplete pedigree (Cheverud & Dittus, 1992; Konigsberg & Cheverud, 1992; Cheverud & Moore, 1994). Because opportunities to

recapture wild animals are rare, most field studies cannot obtain age-specific measures of morphological traits. Measurements are therefore adjusted to some average age to increase sample

size for quantitative genetic analyses (Cheverud & Dittus, 1992; Konigsberg & Cheverud, 1992). Heritability of a trait, however, may change with age (Rutledge et al., 1972; Cheverud

et al., 1983) and therefore information may be lost by adjustments to a common age. Because almost all of our study animals were captured repeatedly each year, we were able to analyse how

heritability of body mass varies with age in a long-lived mammal. Different environmental conditions may also affect heritability of a trait (Hoffmann & Parsons, 1991; Falconer &

Mackay, 1996). For example, in temperate ungulates, mass varies greatly according to season (Festa-Bianchet et al., 1996). Annual fluctuations in body mass are associated with adaptive

seasonal changes in metabolic rate and food requirements (Suttie & Webster, 1995), but could also be affected by weather and by food availability. Because in most field studies it is not

possible to measure animals at different times of the year, little is known about seasonal variation in heritability of morphological traits. Therefore, we examined how estimates of

heritability of body mass may vary seasonally in bighorn sheep. We expected that heritability of body mass would be greater in September than in June: an individual’s mass can vary by as

much as 35% over a year, and September body mass appears to be less influenced by environmental factors than June mass (Festa-Bianchet et al., 1996). MATERIALS AND METHODS The bighorn sheep

population at Ram Mountain, Alberta (52°N, 115°W; elevation 1082–2173 m) has been studied since 1971. Data used in this paper were collected between 1973 and 1997. Until 1981, ewe removals

kept the population stable at 30–33 adult ewes. After removals were ended in 1981, the population increased, peaked at 104 ewes in 1992, then declined to 75 ewes by 1997. In most years, over

80% of the lambs that survived to a few weeks of age were captured and marked before October. All unmarked lambs that survived the winter were marked the following year as yearlings, but at

that age their mothers could no longer be identified. Each summer, adult sheep were captured two to six times and weighed to the nearest 125 g with a Detecto spring scale. Body mass of

individual sheep was adjusted using each individual’s own rate of mass gain obtained from multiple captures. The adjustment dates were 5 June (spring mass: sheep probably started gaining

mass in May) and 15 September (autumn mass: by mid-September adult ewes were near their peak yearly mass). Festa-Bianchet et al. (1996) provide more details on the capture schedule and mass

adjustments. Lambs were more difficult to capture than older sheep, therefore for those captured only once we adjusted mass using the mean rate of mass accumulation for lambs of the same sex

weighed at least twice in that same year. Lamb spring mass was adjusted to 15 June instead of 5 June, because few lambs were caught before 5 June and in some years some lambs were born in

early June. Mother–lamb relationships were determined by observing marked lambs repeatedly suckling from marked females from May to October. Allosuckling has never been observed on Ram

Mountain. Fathers are unknown in this population, therefore we could not estimate heritability by using sire–offspring relationships. Previous studies on dimorphic mammals have shown that

heritability estimated without fathers did not greatly differ from heritability estimates when fathers were considered (Konigsberg & Cheverud, 1992), and that the heritability of body

mass is similar for both sexes (Vandenberg & Garrick, 1997). Ewes always produced singleton lambs, therefore common maternal environmental effects on heritability should be reduced.

Common environmental effects on heritability estimates would be very limited, because bighorns are philopatric, do not form kin groups and all ewes in the population use the same home range

(Festa-Bianchet, 1991), decreasing the possibility that a common early environment would have different effects on different family groups. Heritability (_h_2) was estimated for body mass in

spring and autumn for lambs, yearlings, 2-, 3- and 4-year-olds, and adults (the average of all seasonally adjusted mass measurements for each individual between 5 and 11 years of age).

Estimates were obtained by regressing the mean values for offspring at a given age on maternal values at the same age (Falconer & Mackay, 1996). Heritability was calculated as twice the

slope of the regression, and the standard error is twice the standard error of the slope (Falconer & Mackay, 1996). Analyses were performed with both sexes pooled, to compare our results

with studies on domestic sheep that always report heritability estimates for both sexes pooled (Snyman et al., 1995; Näsholm & Danell, 1996). To obtain more accurate heritability

estimates we controlled statistically for environmental effects on phenotypic variance. To account for sexual dimorphism, data were standardized by subtracting each individual’s mass from

the mean mass of its sex–age class and by dividing it by the standard deviation (Lynch & Walsh, 1998). We then used year-specific residuals of body mass, to eliminate between-year

variations in body mass. These adjustments partly accounted for yearly environmentally induced variability in body mass, but not for potential effects of genotype–environment interactions.

Because we used the same individuals to estimate heritability at different ages, our analyses may suffer to an unknown extent from nonindependence of data, therefore we do not present

statistical tests comparing heritability at different ages. Statistics were performed with STATVIEW (Abacus Concepts, 1992). Heritabilities were also estimated with an animal model by

Derivative Free Restricted Maximum Likelihood (DFREML 3.0; Meyer, 1989, 1997). This method uses all the available kin relationships within a pedigree (Shaw, 1987; Meyer, 1989) and constrains

heritability to between 0 and 1 (Meyer, 1989). The REML method can also partition the phenotypic variance _V_P of a quantitative character into _V_A, _V_E and other effects such as

maternal, common environmental, or permanent environmental effects (Meyer, 1989). Pedigrees were built based on known mother–lamb relationships. Because sires were unknown, fathers were

coded as ‘0’ in the pedigrees. We analysed mass records separately according to season and age. For sheep up to 4 years of age, univariate models were fitted with: where Y is the mass

record; B and A are the vectors of fixed and random additive effects; X and Z are the corresponding incidence matrices relating the effects to Y; and E is the vector of residuals. The fixed

part of the model included sex and years. The convergence criterion was set to 10−8. For sheep aged 5–11 years, between one and seven records were available for each individual depending on

its age at death or in 1997 (the last year of data collection, when some animals were still alive). We therefore fitted two models to the data for sheep aged 5–11 years: the univariate model

presented above and one including permanent environmental effects: where all parameters were as defined above, and M was the vector of individual permanent environmental effects associated

with the incidence matrix Z2. The fixed part of the model included sex and years, and age was included as a covariable. The convergence criterion was set to 10−8. The program estimates _V_A,

_V_E, _V_P, _V_M, _h_2 and _m_2 (Meyer, 1997). Heritability was estimated as Repeatability was calculated for adults only as For sheep aged 5–11 years, models with and without permanent

environmental effects were compared using likelihood ratio tests (Shaw, 1987). The difference between likelihood functions (–2 [log likelihood Model 1 – log likelihood Model 2]) of each

model is assumed to follow a chi-squared distribution with degrees of freedom equal to the difference in parameters between the two models (here d.f.=1). RESULTS The number of families used

in offspring–mother regressions ranged from 60 to 101, with mean number of offspring per ewe between 1.53 and 2.52 (Table 1). Heritability estimates with offspring–mother regressions ranged

from −0.15 to 0.59 depending on age and season (Table 1). Heritability estimates before 3 years of age were not significantly different from 0. Estimates differed significantly from 0 for

body mass in September for 4-year-olds and in June and September for sheep aged 5–11 years. After 3 years of age, there was a consistent trend for higher heritability in September than in

June. The data used for the REML analyses are summarized in Table 2. Body mass of sheep increased with age and was higher in September than in June for all age classes (Festa-Bianchet et

al., 1996). The number of animals with records and number of dams with progeny records decreased with age. For June mass of sheep aged 5–11 years, the inclusion of a permanent environmental

effect significantly improved the fit of the model (likelihood ratio test; _χ_12 = 4.855, _P_ < 0.05). The permanent environmental effect was equal to 0.35 ± 0.17 (SE), and repeatability

was 0.63 (Table 3). A model without permanent environmental effect, however, provided the best estimate of the heritability of body mass adjusted to 15 September, according to a likelihood

ratio test (_χ_12=1.673, _P >_ 0.05). Phenotypic variance (_V_P) increased with age. Additive genetic variance (_V_A) ranged from 0.044 to 31.497 (Table 3). _V_A was moderate for lambs

and yearlings, very low for 2-year-olds, and increased afterwards. Environmental variance (_V_E) first increased with age, peaking in September at age 2, then decreased. Heritability

estimates ranged from 0 to 0.81 depending on age and season. Estimates differed significantly from 0 for lambs in both seasons, yearlings in June, and for 3- and 5–11-year-old sheep in

September. Lack of significance for some age classes was possibly caused by high standard errors associated with heritability estimates. Heritabilities were moderate for lambs and yearlings.

The low heritabilities at 2 years of age were associated with very low _V_A. Heritability estimates increased for older age classes (Table 3). Estimates of heritability were higher in June

than in September for yearlings, but from 3 years of age onwards, estimates were higher in September than in June. DISCUSSION Heritability of body mass is not negligible and varies with age

and season for the Ram Mountain bighorn sheep population. Because of small sample sizes, the standard errors of heritability estimates were high. Consequently, heritability estimates could

be shown to be significantly different from zero only when they were high (Klein et al., 1973). Depending on the method, heritabilities were low to moderate for lambs (Tables 1 and 3.

Heritabilities of birth and weaning mass in domestic sheep vary considerably among breeds (total heritability: 0.04–0.39 for birth mass and 0.09–0.52 for weaning mass (Snyman et al., 1995).

Differences in lamb birth date, which were not considered in this study, increase phenotypic variance of body mass (Bérubé, 1997). Births occur later at high population density

(Festa-Bianchet, 1988), and differences in birth date probably decreased the heritability estimate of lamb body mass, because relatives were born at different times. Heritability was also

low to moderate for yearlings. Our REML estimate at 12 months of age (0.43) is within the range of 0.28–0.48 reported by Snyman et al. (1995). For lambs and yearlings, estimates with

offspring–mother regression were lower than those obtained with REML (Tables 1 and 3. REML estimates may be less sensitive to maternal effects because they take into account pedigree

relationships other than mother–offspring (see below). For sheep 2 years of age and older, both methods produced similar heritability estimates. Heritabilities were very low for 2-year-olds

and increased thereafter (Tables 1 and 3. Our estimates were similar to or higher than the few published heritability estimates of mass for mature domestic sheep, that vary between 0.3 and

0.5 (reviewed in Näsholm & Danell, 1996). The low heritability of mass at 2 years of age is probably caused by high environmental variance resulting from individual differences in

reproductive status at that age (Jorgenson et al., 1993). Reproduction at 2 years of age affects body mass (Festa-Bianchet et al., 1995). However, REML estimates also suggested very low

additive genetic variance in body mass at 2 years of age. Traits closely related to fitness generally have low additive genetic variance and heritability (Fisher, 1930; Gustaffson, 1986;

Mousseau & Roff, 1987). Body mass at 2 years of age may be highly related to fitness at Ram Mountain, or may be genetically correlated with other traits related to fitness, such as

reproductive maturity or lifetime reproductive success (Lande, 1979). Mother–offspring estimates of heritability increased with age, although REML estimates were moderate before 2 years of

age, very low for 2-year-olds and increased thereafter (Tables 1 and 3). To our knowledge, no age-specific heritability estimates are available for other wild ungulates, but an increase in

heritability of body mass with age has been shown in domestic sheep (Näsholm & Danell, 1996; Yazdi et al., 1997). The increase in heritability of morphological characters during ontogeny

is generally associated with declining maternal effects with age (Rutledge et al., 1972; Cheverud et al., 1983; Cheverud, 1984). In most mammals, the direct-maternal genetic correlations

vary with age, being positive and moderate soon after birth, then becoming strongly negative near the time of weaning, and positive afterwards (Cheverud, 1984). Because fathers were unknown,

the number of different types of kin relationships in the pedigree was insufficient to precisely estimate maternal effects and direct-maternal genetic correlations (Meyer, pers. comm.).

However, two lines of evidence suggest that maternal effects explained some of the variation in heritability with age. First, as indicated before, heritabilities were underestimated by the

mother–offspring regression compared to REML, suggesting the presence of negative maternal effects early in life. Secondly, the phenotypic correlation of maternal and offspring mass is very

weak (Festa-Bianchet & Jorgenson, 1998), suggesting that small females have a higher level of maternal expenditure than large females, which allows the lambs of small females to reach a

greater weaning mass than that which may be set by genetic effects alone. As individuals aged, maternal effects probably decreased and additive genetic variance accounted for a greater

proportion of the phenotypic variation in body mass (Table 3). For sheep older than 2 years, heritability of body mass was lower in June than in September. Three different reasons have been

proposed to explain differences in heritability depending on environmental conditions (Hoffmann & Parsons, 1991; Falconer & Mackay, 1996; Merilä, 1997). First, low _V_A should be

responsible for lower heritability under poor environmental conditions. Secondly, _V_E should increase under poor environmental conditions. Thirdly, the genetic correlation between measures

of a trait in the two environments should be less than one, indicating a genotype–environment interaction. In our study, lower heritability in June compared to September corresponded to a

decrease in _V_A and an increase in _V_E, as observed in other empirical studies (Simons & Roff, 1994; Merilä, 1997). In the highly seasonal climate of Ram Mountain, sheep have greater

control over their summer mass gain than over their winter mass loss (Festa-Bianchet et al., 1996). Predictable and plentiful summer forage may limit environmental effects on variation of

body mass in September. On the other hand, harsh winter weather may affect forage availability or increase thermoregulatory costs in an unpredictable way (Festa-Bianchet et al., 1996), and

lower the heritability of mass in early June. Environmental variation has been shown to influence quantitative genetic parameters in birds for individuals that have grown under different

environmental conditions (Van Noordwijk et al., 1988; Larsson, 1993; Merilä, 1997), but most of those comparisons involved skeletal measures that do not change in adults. Our results show

that heritability of a trait can also differ when estimated from the same set of individuals measured at different seasons, regardless of age. Heritability of traits that are phenotypically

plastic is sensitive to heterogeneous environmental conditions (Riska et al., 1989; Simons & Roff, 1994; Weigensberg & Roff, 1996). In conclusion, the results of this study underline

the value of long-term monitoring of natural populations for quantitative genetic studies. REML methods of variance component estimates offer good opportunities to study natural populations

where experimental controlled-breeding designs are impractical and where families are of unequal size. The quantitative genetic approach is a promising avenue for studies of behavioural

ecology because it can estimate the evolutionary potential or previous selection processes for complex traits. Our results caution that factors such as season and age should be accounted for

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Genetic parameters for lamb weight at different ages and wool production in Baluchi sheep. _Anim Sci_. 65: 247–255. Article  Google Scholar  Download references ACKNOWLEDGEMENTS We thank the

many people who trapped and weighed sheep over the last 25 years. D.A. Roff provided advice, encouragement and comments on a previous draft of the paper. K. Meyer kindly allowed us to use

her software DFREML 3.0 and helped with the use of REML. J.W. Shipley and S. Demers provided statistical advice. D. Réale was supported by a postdoctoral fellowship from the Fyssen

foundation (France). Financial support for the Ram Mountain bighorn research was generously provided by the Natural Sciences and Engineering Research Council of Canada, the Alberta Natural

Resources Service, The Foundation for North American Wild Sheep, the Université de Sherbrooke and the Fonds FCAR (Québec). This is contribution number 129 of the Groupe de recherche en

écologie, nutrition et énergétique. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Département de Biologie, Université de Sherbrooke, Sherbrooke, J1K 2R1, Québec, Canada Denis Réale & 

Marco Festa-Bianchet * Department of Environmental Protection, Alberta Natural Resources Service, Suite 201, 800 Railway Avenue, Canmore, T1W 1P1, Alberta, Canada Jon T Jorgenson Authors *

Denis Réale View author publications You can also search for this author inPubMed Google Scholar * Marco Festa-Bianchet View author publications You can also search for this author inPubMed 

Google Scholar * Jon T Jorgenson View author publications You can also search for this author inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to Denis Réale. RIGHTS AND

PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Réale, D., Festa-Bianchet, M. & Jorgenson, J. Heritability of body mass varies with age and season in wild

bighorn sheep. _Heredity_ 83, 526–532 (1999). https://doi.org/10.1038/sj.hdy.6885430 Download citation * Received: 22 October 1998 * Accepted: 10 March 1999 * Published: 01 November 1999 *

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Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative KEYWORDS * body mass * genetic

variance * heritability * mammals * _Ovis canadensis_ * REML