The role of phenotypic plasticity in responses of hunted thinhorn sheep ram horn growth to changing climate conditions


John Loehr, Department of Biological and Environmental Sciences, University of Helsinki, PO Box 56 (Viikinkaari 9), 00014, Finland.
Tel.: +35 850 436 6672; fax: +35 891 915 7694; e-mail:


When phenotypic change occurs over time in wildlife populations, it can be difficult to determine to what degree it is because of genetic effects or phenotypic plasticity. Here, we assess phenotypic changes over time in horn length and volume of thinhorn sheep (Ovis dalli) rams from Yukon Territory, Canada. We considered 42 years of horn growth from over 50 000 growth measurements in over 8000 individuals. We found that weather explained a large proportion of the annual fluctuation in horn growth, being particularly sensitive to spring weather. Only 2.5% of variance in horn length growth could be explained by an individual effect, and thus any genetic changes over the time period could only have had a small effect on phenotypes. Our findings allow insight into the capacity for horn morphology to react to selection pressures and demonstrate the overall importance of climate in determining growth.


Wildlife can exhibit rapid phenotypic changes, and assessing to what degree these are genetic or because of plasticity can be daunting (Postma, 2006; Kuparinen & Merilä, 2007; Marshall & McAdam, 2007; Gienapp et al., 2008; Teplitsky et al., 2008; Ozgul et al., 2009). Nonetheless, understanding what factors influence morphology on shorter timescales is important to both the study of evolution and the management of wildlife. Here, we assess whether phenotypic plasticity might explain phenotypic changes over time in the horn growth of thinhorn sheep (Ovis dalli, Nelson, 1884) rams. In doing so, we assess the possible contributions of climate and selective hunting to changes in horn growth.

We expect that horn growth is affected by climatic factors. In recent years, our understanding of the influence of climate on wildlife has progressed because of the insight that climatic processes can operate on decadal or interdecadal timescales (Sinclair & Gosline, 1997; Hik & Carey, 2000; Gedalof et al., 2002; Klvana et al., 2004). In particular, the usefulness of climate indices such as the North Atlantic Oscillation (NAO) and Pacific (inter)Decadal Oscillation (PDO) to describe the environmental conditions has been recognized (Mantua et al., 1997; Stenseth & Mysterud, 2005). PDO has affected the environment and ecosystems of north-western North America since at least the 17th century (Gedalof et al., 2002) and in the recent past, interdecadal oscillations have occurred, with a warm phase 1925–1946, followed by a cold phase 1947–1976, and another warm phase beginning in 1977. These large-scale climate shifts affect coastal sea temperatures and continental surface air temperatures (Mantua et al., 1997). Biological repercussions of environmental conditions in the north Pacific have been found in salmon abundance in coastal Alaska, USA (Mantua et al., 1997), tree ring growth in north-western Canada and USA (Gedalof & Smith, 2001), and wapiti (Cervus elaphus L.) population growth rates (Hebblewhite, 2005) in inland populations in Alberta, Canada.

An alternative explanation for changes in horn growth could be the harvesting system in place in the focal population. Harvesting policy is based on ram horn size, with individuals with relatively faster growing horns attaining legal hunting status at a younger age than those with slower growth (Loehr et al., 2007). Evidence from both experimental (Reznick et al., 1990; Conover & Munch, 2002) and field (e.g. in Atlantic cod, Gadus morhua L.; Olsen et al., 2004, and bighorn sheep Ovis canadensis, Shaw; Coltman et al., 2003) systems shows that selective harvest regimes may have evolutionary consequences for harvested species. Biased harvesting based on horn growth may result in a response visible at the phenotypic level (Coltman et al., 2003), and we wished to assess whether a response to selection is likely to be found in thinhorn sheep horn growth.

Here, we assess temporal trends and patterns in horn growth over a 42-year time period. Our analysis constitutes the first large-scale assessment of the environmental factors affecting horn growth in the Ovis genus. Two aspects of the dataset make it an excellent resource to assess the capacity for genetic factors or phenotypic plasticity to affect horn growth. First, we have repeated measures of horn growth over the lifetime of individuals, and we can gauge the maximum amount that genetic factors affect growth by assessing the proportion of variance in growth that the individual effect explains. Second, the data are composed of a large sample of growth segments from many individuals that overlap in time. Thus, we are able to estimate the effect of the year of growth and separate it from the effect of the individual.


We used data from thinhorn sheep rams harvested between 1973 and 2005 (a time span that includes the 1963–2001 cohorts, see online appendix S1) from four mountain blocks encompassing the sheep’s distribution (Southern lakes, Pelly Mountains, Ruby Range, and Ogilvie/Mackenzie) in the Yukon Territory, Canada (Online appendix S2). Territorial regulations dictate that all hunted sheep horns must be brought for measurement and the insertion of an identification plug. At this time, the length of annual growth and horn circumference at each annulus was measured (to the nearest mm) with a flexible tape measure by conservation officers and Yukon Department of Environment biologists and technicians. All horn length measurements were taken beginning in 1973, and circumferences (necessary for the calculation of horn volume) were taken for the second and third annuli from 1973 to 1977, and thereafter, all annuli circumferences were measured. We assessed the repeatability of this method by comparing scores of three Yukon Department of Environment technicians. Both within-observer repeatability (= 126 segments, one observer; R = 0.981; length; R = 0.996, circumference) and between-observer repeatability (= 135 circumferences, three observers; R = 0.977, length; R = 0.998, circumference) were high. The age of individuals was determined by counting annual growth segments (Geist, 1966a).

All growth segments were used in the analysis except for the first two (which can be worn down throughout the sheep’s lifetime) and the last (which may be affected by the date that an individual was harvested). For analysis, horn volume for each growth segment was calculated as a conical frustum (Heimer & Smith, 1975).

Weather variables

Monthly values for PDO and sea surface temperature (SST) were obtained with permission from the University of Washington’s Joint Institute for the Study of the Atmosphere and Oceans ( These values are derived as the leading principal component of monthly SST anomalies in the North Pacific Ocean, poleward of 20°N. We divided the PDO monthly values into seasonal time periods that could affect horn growth. Preliminary analysis indicated that spring (April–May) conditions had the greatest correlation with horn growth, and we focussed our analysis on these months.

For April and May, the mean monthly temperature and total monthly precipitation as snow or rain were taken from Environment Canada weather stations near Whitehorse, Watson Lake, Burwash, Dawson City, and Mayo (appendix S2). Regional indices were created by removing the mean, and then a composite index was created to represent all stations in one variable.

Hunter harvesting

Similarly to bighorn sheep (Coltman et al., 2003), the thinhorn sheep harvest system results in rams with rapid horn growth being shot at a younger age than those with slower growth (Loehr et al., 2007). Rams can be harvested legally when their horns have described a ‘full curl’ or when they are 8 years of age or older. In the Yukon, rams are harvested prior to the rut, very occasionally at 4 years of age but usually at 8 or 9 years of age. To assess the harvest rate of legal rams, we compared the number of full-curl (legal) rams counted in the aerial surveys (n = 2 884) to the number harvested from the same game management subzones in the same years (n = 769), which yielded a harvest rate of about 27%.

Because our data are composed of hunted sheep, they do not represent a random sample of available sheep. This is a concern for our estimate of individual effects if our data do not contain a large proportion of the actual horn growth rates in the population (for example, it is conceivable that individuals with consistently slow growth are not present in the data). However, recent work on a hunted population of bighorn sheep (Bonenfant et al., 2008) found that natural mortality and horn growth rates were not correlated before harvesting commences (except for yearlings where a marginally positive relationship was found), and no correlation between horn growth and natural mortality in older age groups was found. It was also found that rams with greater early horn growth were more frequently harvested, whereas rams with poor early growth were also harvested once they became older (see Bonenfant et al. Fig. 4). Thus, although our data may contain some bias in the frequency with which certain growth rates are harvested, more important to our conclusions is that the data are likely to contain the full range of growth rates that exist.

Statistical analyses

Firstly, to determine which environmental variables were best correlated with horn growth, we surveyed the relationship between the PDO climate index, local weather variables, and horn growth. In addition to the temperature, rain, snow, and PDO indices, we used Principal Component Analysis to combine variables. Analysis produced one PC that explained 53% of variance with the following scores: Temperature: 0.85; Rain: 0.56; Snow: 0.72; and PDO: 0.75.

A linear mixed model (LMM) was fitted to the length and volume of each horn segment (i.e. one year’s growth in horn length), with the following predictors as fixed or random effects: growth segment (GS, fixed), age at death (AD, fixed), population (POP, random), individual (ID, random), cohort year (COH, random), year of growth (YG, random), and April–May PC (AMPC, continuous covariate). For analysis, we used the following maximal models:


where (A|B) denotes variable A is random over the levels of factor B (A = 1 is the intercept, i.e. a classic random effect), A/B means B nested within A, and A*B means A and B and their interaction (e.g. O’Hara, 2009). The optimal model was chosen by comparing the Akaike Information Criterion (AIC) for different maximum likelihood models, adding or subtracting a single term at each iteration until no improvement could be found.

We also wished to assess to what extent the individual effect varied over different growth segments. This was not possible to do for each growth segment, and thus we performed a separate analysis and grouped the growth segments into four separate categories (3rd to 5th, 6th to 8th, 9th to 11th, and > 11). This model used the same variables as selected by AIC analysis with the addition of an interaction between ‘individual’ and ‘growth segment’.

The residuals of the LMM for horn growth were screened for heteroscedasticity and normality. As a result, the dependent variable in the LMM, annulus length, was square root transformed. A Q-Q plot of residuals revealed some departures from normality. However, the large sample size and robustness of LMM to non-normal data suggested that this would not affect our results (for a short discussion of this point, see Läärä, 2009).

‘Population’ was defined according to predefined game management subzones in the Yukon Territory. We did not have information on density for all populations in the study, so it was not easy to include this in the model. However, any effects of density, as well as other environmental variables that affect annual growth, would be included in the ‘year of growth’ factor.

Records of horn length were first taken in 1973. Therefore, the first cohorts were represented by individuals that were older than average, and the last cohorts were represented by individuals younger than average individuals (see online appendix S1). We know that age at death and horn volume growth are negatively correlated in hunted individuals (Loehr et al., 2007), and thus any trends in the data may be biased by the relationship between growth and age at death. We tested whether including age at death in models predicting length affected analysis of cohort trends present in the data. In this case, with horn length as our response variable, it is technically not correct to include ‘age at death’ as a predictor variable because age at death cannot be causal, as death occurs after horn growth. Nonetheless, we included ‘age at death’ in our model to account for the pattern in the time series.

In the above analysis, we wanted to be certain that the negative relationship between age at death and horn length did not affect the interpretation of temporal trends in cohorts. However, we also wanted to properly test whether horn length grown at a young age predicted age at death. To do so, we used LMM analysis for the following model:


In this analysis, we separately tested whether horn length grown at 2, 3, or 4 years of age predicts age at death. We chose these horn segments because these are all grown before any sheep becomes legal to hunt, and because they are typically the longest segments they should have the greatest bearing on when the sheep becomes legal to hunt. Tests produced similar results, and we present analysis from the fourth growth segment.

To test for a trend over time in cohorts for horn length, we added ‘Cohort’ as a continuous fixed factor to the full model (where environment is controlled) and also to a model where environmental variables (‘Year’ and ‘April–May PC’) were not included.

Statistical analyses were performed using r 2.9.0 (R Development Core Team, 2009) for the LMM analyses and spss 10 (SPSS Inc., Chicago, Illinois, USA) for correlations.


The LMM models fitted to predict horn growth are shown in Table 1. For length and volume analyses, respectively, there were 55 565/50 546 growth measurements from 8 417/8409 individuals in 243 populations, with 42 years of horn growth represented for forty-one cohorts.

Table 1.   Models fitted for analyses of horn growth and accompanying AIC scores.
iModel descriptionLength ΔAICVolume ΔAIC
  1. GS, growth segment; AD, Age at death; ID, individual; POP, population; COH, cohort; AMPC, April–May PC; YG, Year of horn growth.

1GS + AD + ID + POP + COH + AMPC + AMPC*ANN + YG00
2GS + AD + ID + POP + COH + AMPC + YG8421
3GS + AD + ID + POP + COH + YG10127
4GS + AD + ID + POP+ AMPC + YG227109
5GS + AD + ID + POP + YG244115
6GS + AD + ID + POP + AMPC36753371
7GS + AD + ID + POP + COH64115626
8GS + AD + ID + POP67475746

The final model for growth in horn length and volume was arrived at based on AIC scores (Table 1). Age-dependent growth segment (annulus) patterns differed for volume and length measurements (Fig. 1). After the growth segment pattern is accounted for, the percentage of remaining variance described by the variables of interest are presented in Table 2. Growth in horn length was best described by ‘Year’ (6.3% of variance) and ‘April–May PC’ (4.1%), and to a lesser extent by ‘individual’ (2.5%), ‘population’ (1.3%) and ‘cohort’ (1.2%). AIC analysis suggested that the interaction between ‘April – May PC’ and ‘growth segment’ should be included in the length model; however, this term only explained 0.03% of variance, therefore, it was not considered further. Horn volume was best predicted by ‘individual’ (7.9% of variance), ‘year’ (5.8%), and ‘population’ (5.1%), and to a lesser extent by ‘cohort’ (0.7%) and ‘April–May PC’ (0.8%). Similar to horn length, AIC analysis suggested that the interaction between ‘April – May PC’ and ‘growth segment’ should be included in the volume model, however, because of the low amount of variance explained (0.03%), it was not considered further.

Figure 1.

 Mean horn growth (± 1 SD) for volume and length for growth segments 3–15, from hunted thinhorn sheep rams in Yukon Territory, Canada.

Table 2.   Variance explained by independent variables influencing horn growth in thinhorn sheep rams from Yukon Territory, Canada. The pattern of growth in growth segments (Fig. 1) explained 80% (length) and 46% (volume) of variance in the model. We were interested in what proportion of the remaining variance could be explained by the variables of interest after the growth segment growth patterns were explained. Therefore, for the other variables, we calculated the variance explained for each variable from the total remaining variance.
EffectVariancePercentage of variance explained (excluding annulus effect)
  1. AMPC, April–May PC.

 Individual0.036 (0.030–0.042)2.5 (2.4–2.7)
 Population0.018 (0.009–0.031)1.3 (1.2–1.4)
 Year0.090 (0.056–0.142)6.3 (5.6–7.4)
 Cohort0.018 (0.010–0.031)1.2 (1.0–1.4)
 AMPC0.27 (0.17–0.38)4.1 (3.1–5.2)
 Individual1.01 (0.94–1.08)7.9 (7.7–8.1)
 Population0.65 (0.51–0.82)5.1 (4.7–5.5)
 Year0.73 (0.46–1.21)5.8 (4.8–6.8)
 Cohort0.09 (0.05–0.17)0.7 (0.6–0.9)
 AMPC0.39 (0.12–0.72)0.8 (0.4–1.4)

For length, the individual effect was highest for the 6th to 11th growth segments, and there is no effect of the individual for the 3rd to 5th and ≥ 12th segments (Table 3). This contrasted with the individual effect for volume, which was strongest for the 3rd to 5th growth segments and gradually declined thereafter. Within-individual correlations between length and volume showed that these measurements are least correlated for the 3rd to 5th growth segments, after which the measurements become very highly correlated (Table 4).

Table 3.   Estimates for individual level variance components for subsets of the data limited to groups of growth segments.
MeasurementAll segments3rd to 5th6th to 8th9th to 11th≥ 12th
Length0.036 (0.030–0.042)0.0004 (0–0.012)0.032 (0.022–0.042)0.034 (0.018–0.048)0.00007 (0–0.0066)
Volume1.01 (0.94–1.08)1.83 (1.71–1.95)0.49 (0.40–0.58)0.25 (0.11–0.38)0.0004 (0–0.064)
Table 4.   Pearson correlation coefficients of individual horn volume and length for growth segments 3–14.
Growth segment34567891011121314

A small amount of variance in horn length (1.2%) could be attributed to cohort. We found an increasing trend in cohort horn growth when ‘year of growth’ and ‘April–May PC’ were not included in the model (Variance Estimate (VE) = 0.007, SE = 0.002, = 4.2, Fig. 2), but no trend over time was found when the environmental variables were included (VE = −0.009, SE = 0.005, = −1.6, Fig. 2). The trend in horn growth can thus be fully explained by the environmental variables.

Figure 2.

 Plots of horn growth of thinhorn sheep in Yukon Territory, Canada. Time series of cohort effect for horn growth. Black circles: estimates are best linear unbiased predictions (BLUPs) from ‘cohort’ effect from model with no environmental covariates or yearly effect (i.e. model 7 in Table 1). Grey diamonds: estimates for ‘cohort’ effects from model with environmental covariates and growth year effects (i.e. model 1 in Table 1).

Age at death could be predicted by horn length growth: VE = −0.0022 (CI = −0.0025 to −0.0019) explaining 6.8% of total variance; year: VE = 0.16 (CI = 0.14–0.18) explaining 16% of total variance; and population: VE = 0.056 (CI = 0.14–01.8) explaining 6.7% of total variance.


Plasticity in horn growth was evident in both horn length and volume; annual variation in growth (variables ‘Year’ and ‘April–May PC’) accounted for 10% of growth in length and 6.6% of growth in volume (Table 2). The effect of the individual differed sharply between horn length and volume (Table 3). For horn length, only 2.6% of growth was explained by an individual effect, and some of these variations may be because of environmental effects on the individual. We were not able to assess heritability of horn growth, but 2.6% provides an upper bound for the amount of variation in horn growth that can be accounted for by additive genetic variance. Thus, any selection that may have been acting on horn length (e.g. directly from hunting or indirectly because of environmental change) was unlikely to have caused major genetic changes in horn length over the time period assessed. The individual effect was greater for horn volume and explained 7.9% of variance, indicating the possibility that volume has a greater genetic component. The higher value for volume is at least partially because of nonindependence of horn circumference annuli over an individual’s lifetime (i.e. horn circumference grown in year x + 1 must be as great or greater than that grown in year x). Horn volume is more dependent on the size of the bone upon which the horn grows, which is also likely to result in an increase of the individual effect.

Our data suggest a very small role for additive genetic variance to affect horn length, which contrasts with earlier results from the closely related bighorn sheep for which h2 estimates calculated using Animal Model had varied between 0.69 ± 0.10 (Coltman et al., 2003) and 0.39 ± 0.13 (Coltman et al., 2005). The fact that differences between previous research and ours exist is not necessarily surprising, given that heritability of traits can vary widely depending on the relative influence of nongenetic factors on a population (e.g. Hoffman & Merilä, 1999). Wilson (2008) also pointed out that heritability estimates based on Animal Model analyses are not comparable across studies because estimates are highly model specific. For example, Wilson (2008) used simulated data and found that horn growth h2 was increased from 0.12 to 0.55 by including fixed factors in analysis. When considering the overall significance of our results, a strength is that we take multiple populations into account, thus providing a result that can be more easily generalized to other thinhorn populations.

It is interesting that horn length and volume differ both in the amount of variance that the individual effect explains (Table 2) and in what stage of growth the individual effect is the strongest (Table 3). The contrast is the strongest for the third to fifth growth segments, and the within-individual correlations between length and volume were correlated least for these same segments (Table 4). It is also clear that the pattern in horn growth differs between volume and length (Fig. 1). For length, there is a gradual decline in growth over segments, while volume shows an increase in volume growth up until the fifth segment and then declines thereafter.

Populations of thinhorn sheep in the Yukon are highly genetically structured (Worley et al., 2004), and so there is potential for populations to diverge in genetic-determined characters at a regional level. We found that horn length varied little between populations, while the effect of population was more evident for volume (Table 2). This trend at the population level appears to reflect the very low amounts of variance explained by the individual for length and somewhat higher values for volume.

Effects of climate on horn growth

Annual variation, which accounted for a combined 10% of growth in length and 7% of growth in volume, was predicted by weather in April–May. Horn length was best predicted by the April–May PC (about 46% of annual variation), while horn volume variation was predicted to a lesser extent (18%) by the environment. We used a combination of local weather variables and the PDO climate index, which outperformed any single one of variables if they were entered into the model (analysis not presented). Recent research has frequently found that climate indices such as NAO and PDO predict population dynamics, variation in demographic rates, and phenotypic traits better than local weather variables (Post & Stenseth, 1999; Stenseth & Mysterud, 2005). However, it has been suggested that this counterintuitive trend may be because of a lack of sufficient knowledge about which aspects of local weather affect the variable in question (Hallett et al., 2004; Morrison & Hik, 2007). In general, it appears that conditions in the North Pacific Ocean are the driving force behind local weather in Yukon Territory (Mantua et al., 1997); thus, it is not a surprise that a combination of local weather and PDO climate index produces the most accurate prediction of horn growth.

Our results from climate data and horn growth appear to be in basic agreement with factors affecting forage production on the bighorn sheep range. Stelfox (1975) found that forage production on bighorn sheep range was most influenced by spring precipitation and soil moisture, while soil temperature and winter precipitation (snow) had a lesser effect. Horn growth begins at the end of April and, like tree rings, much of the total horn growth occurs early in the growing season (Hemming, 1969; Bunnell, 1978). Improved environmental conditions (probably manifested as a greater abundance and quality of forage) during the primary time of horn growth probably lead to a greater amount of growth, as demonstrated by Hoefs & Nowlan (1997) for captive rams.

We did find an increasing trend in length growth over time, but this only explained a small amount of the variance, as the cohort effect (which will include any temporal variations between individuals) was small (1.2% of variance). This effect could adequately be explained by changes in the environment, as measured through the April–May PC effect. Although we cannot rule out a genetic response to the environment, the small individual effect for horn length growth suggests a limited role for genetic variation in affecting length. The fluctuations in horn growth that occur in cohorts over the space of a few years are also indicators of the capacity for phenotypic plasticity to explain cohort differences in horn growth (see Fig. 2).

Age at death and horn growth

Horn length grown at an early age predicted age at death, either because of the selective harvest policy or a natural trade-off between growth and longevity (e.g. Geist, 1966b; Robinson et al., 2006; Loehr et al., 2007; but see Bonenfant et al., 2008) or both. (Hunting regulations appear to be a likely contributor to this trend; however, it would still be visible in hunted sheep data only because of a natural trade-off between growth and longevity, because there would be a reduced probability of harvesting old sheep with rapid early horn growth.) About seven percentage of variance in age at death could be attributed to horn length growth, which is similar to that found previously for horn volume (Loehr et al., 2007). The effect on lifetime fitness of the trade-off (either natural or imposed by hunting) between early horn growth has not yet been measured in thinhorn sheep. At Ram Mountain, in a heavily hunted population of bighorn sheep, nonsignificant relationships were found between male lifetime reproductive success and horn length (= −0.13) and horn circumference (= −0.07) (Coltman et al., 2005).

Although the actual strength of selection is unknown for our study, there appears to be little potential for selection to produce a response in horn length over the time period studied because of the following factors: (i) the small individual effect found in horn length growth, and (ii) the finding that the early growth segments (which have the greatest effect on what age a sheep will become legal to harvest) contain none of the individual effect (Table 3). It is possible that an effect of hunting could have been visible in the data if a decrease in horn growth of cohorts was present in the full model; however, the opposite trend was found with slightly increasing horn growth over time (Fig. 2). This result contrasts with an earlier finding from bighorn sheep (Coltman et al., 2003). This previous study differs from ours in that the bighorn population studied showed a considerable effect of additive genetic variance on horn length. In addition to this, it was an isolated population, with relatively heavy hunting pressure.

Horn volume grown at a young age is also negatively correlated with longevity (Loehr et al., 2007), and for volume, the individual effect explained about 8% of total variance in horn growth. For volume, the individual effect was strongest for horn grown early in life (Table 3). Thus, there is a possibility that horn volume could react more swiftly to selection. However, we caution that it is not known what proportion of the individual effect can be attributed to additive genetic variance. Only 0.6% of variance in horn volume could be attributed to the cohort variable, indicating very little change over time.


Individual genotype appears to play only a limited role in determining horn length in thinhorn sheep, while the effect of the individual was greater for horn volume, indicating the possibility that horn volume could react more swiftly to selection. Our results emphasize the importance of the environment, and in particular spring weather, in determining horn length. Thus, a warming climate that has resulted in a small increase in horn growth over four decades is unlikely to be accompanied by a genetic change. Recently, much emphasis has been rightfully placed on investigating the evolutionary consequences of harvesting or climate change on wildlife. While in many harvested or climate-affected species human-induced evolution may first appear to be a likely contributing factor to phenotypic change, our results, and other recent work (e.g. Teplitsky et al., 2008; Ozgul et al., 2009), emphasize the importance of also considering nonevolutionary factors.


This study is presented in honour of Manfred Hoefs, who established the horn measuring protocol in 1973. Without his dedication and foresight, none of these analyses would have been possible. This work was supported by research grants (nos. 205371 and 202324) from the Academy of Finland, and the University of Helsinki research funds, and the research funding programme ‘LOEWE – Landes-Offensive zur Entwicklung Wissenschaftlich-ökonomischer Exzellenz’ of Hesse’s Ministry of Higher Education, Research, and the Arts. We thank P. Merchant and all the Yukon conservation officers and other wildlife officials who have taken the horn measurements necessary for this research. We thank G.X. Ludwig, R. Tiilikainen, A. Kuparinen, J. Merilä, and two anonymous referees for comments that improved the manuscript.