Notes on Solberg & Saether (1994): Male traits as life-history variables – annual variation in body mass and antler size in moose (Alces alces)

Study Overview

  • Topic: Annual variation in two sexually selected male traits in moose (Alces alces): carcass mass (body mass) and antler size (number of points).
  • Population: 2,862 male moose collected in autumn over 23 years (1967–1989) in northern Norway (Vefsn Valley, Nordland).
  • Key aim: Decompose sources of annual variation in male genome-wide traits by testing climatic factors, population density, and population sex ratio as potential drivers.
  • Main claim: Variation in sexually selected traits can be understood as life-history traits; climate, density, and sex ratio each contribute, with their relative importance depending on age and sex class.

Key Concepts and Hypotheses

  • Sexually selected traits: Body mass and antler size are crucial for fighting/mighting success and mating in polygynous cervids.
  • Three explanatory hypotheses for variation in male traits:
    • Climate/food availability: Variation in climate affects food quality/quantity and thereby growth and condition (through summer nutrition and phenology).
    • Population density: Density constrains resources; high density reduces body mass due to competition for food.
    • Sex ratio (and timing of rut): Skewed adult sex ratio (often due to hunting) may shorten maturation in males and alter investment in somatic growth; density-related changes in mating competition may shift selection pressures on traits.
  • The study treats male traits as life-history traits with potential trade-offs between current reproduction (rutting) and future growth.

Study Area and Climate

  • Location: Vefsn Valley, municipalities of Vefsn, Grane, and Hattfjelldal, Nordland, northern Norway (65°20'–66°00' N).
  • Climate context: Proximity to sea; mean monthly temperature ~1.3°C; annual precipitation ~1,200 mm.
  • Climate measurements used for analyses: monthly precip., mean temperature, accumulated day degrees > 6°C, and mean snow depth.
  • Reference for climate: described in Solberg (1991) and Saether (1985).

Materials and Measurements

  • Collections: Autumn harvests (Sept–Oct) from 1967–1989; 2,862 males measured.
  • Sampling assumptions: Males treated as a random sample from each age class; no strong bias in size-based hunting selection detected (no significant relationship between kill date and mandibular length).
  • Females: 1,629 hunter-killed females sampled for intersexual comparisons.
  • Measurements:
    • Carcass mass: Used as proxy for live body mass, with carcass mass assumed to be 55% of total live weight in autumn: 55% × live weight = carcass mass. (Langvatn, 1977; Markgren, 1982).
    • Antler size: All antler points >2 cm counted; age of individuals determined by dental methods (tooth replacement for young; dentine layers for older animals).
  • Age classes: Individuals categorized into age groups (e.g., 1.5, 2.5, 3.5, 4.5, 5.5–8.5 years). In analyses, data for <5 years were pooled where appropriate.
  • Population density proxy: Hunter-observer forms used to estimate relative moose density; density index based on moose observed during the first two weeks of hunting season. In some later years (when hunting started earlier in parts of the area), density estimates used two- to three-week windows to adjust observations.
  • Sex ratio proxy: Calculated as males per female (males: females) observed during the first two weeks of the hunting season; notes indicate this may overestimate males (males more conspicuous) but is assumed to reflect relative changes in population structure over time.

Data Analysis Methods

  • Statistical approaches:
    • Pearson correlation analyses to explore relationships between carcass mass/antler points and climate, density, and sex ratio.
    • One-way ANOVA to test year-to-year (annual) variation in mean carcass mass and mean antler points across age groups.
    • ANCOVA to separate effects of fixed covariates (e.g., age) from other predictors.
    • Multiple regression with stepwise inclusion of independent variables; significance threshold α = 0.05.
    • Sequential Bonferroni correction applied when multiple tests were performed (Rice 1989).
  • Significance interpretation: P-values reported after sequential Bonferroni adjustments where applicable.
  • Software/approach: Standard regression and ANCOVA procedures as described by Sokal & Rohlf (1981).

Results: Age-Specific Patterns (1967–1989)

  • General finding: All age groups of males (>1 year) showed a significant autumn decline in carcass mass with the day of kill, but most of the variation was not explained by the linear model alone (1–9% explained; 91–97% unexplained by linear trend).
  • Mid-season adjustment: A mid-season weight (Oct 10) was used to control for within-season mass decline when calculating subsequent analyses.
  • Age-related growth patterns (Fig. 1):
    • Males reach maximum mean carcass mass around age 6–8 years; older individuals (>9 years) show smaller mean carcass mass than the 6–8 year group.
    • Antler points increase with age up to about 5 years, but older than 5 show a decline in age-specific mean number of points.
    • Females show similar age-related increase in mass up to about age 5, with no clear age-related decline thereafter.
  • Within-cohort relationships (Table 2): Within a single cohort, mean mass of the youngest males predicted a significant portion of the variance in mass in the following year; no such relationship detected for yearlings or 3–4-year-olds (P > 0.05).
  • Across-age covariation: A significant covariation existed between annual mean mass of adjacent age groups (2.5 vs. 3.5, 3.5 vs. 4.5, etc.). This indicates synchronous fluctuations in body size across ages, likely driven by shared environmental or density-related factors.

Results: Population Density Effects

  • Long-term trend: Population density index (based on moose observations during hunting) increased significantly over the 23-year study period (x from 1 to 23; y = 32.5x + 102, r² = 0.69, P < 0.001).
  • Density impact on males (adults 2–8 years): Mean carcass mass decreased over time with increasing density; density explained a significant portion of the variation in mass among adult males (2–8 years).
    • Regression fit (Fig. 2): Annual mean carcass mass vs density index; the decline varied by age (e.g., from about 0.8 kg/year for 2-year-olds to about 1.44 kg/year for 5–8-year-olds).
    • ANCOVA: The density-dependent decrease did not significantly increase with age (F = 0.25; d.f. = 3, 80; P > 0.05).
  • Density effect on females: Mean carcass mass for females did not show a similar density-related decline, except for yearlings where density did relate to mass.
  • Density effect on mass vs sex ratio: The study notes a significant co-variation between density, sex ratio, and mass, making disentangling their separate contributions challenging.

Results: Sex Ratio Effects

  • Sex ratio trend: A significant decline in the male: female ratio occurred over the study (R = -0.64, P < 0.01), from roughly 0.96:1 in 1971 to 0.39:1 in 1988.
  • Relationship with density: The decline in sex ratio was negatively correlated with population density (R = -0.57, P < 0.01); higher density corresponded with fewer recorded males per female.
  • Sex ratio and mean mass (adults): A significant portion of variation in mean carcass mass among adult male cohorts could be explained by sex ratio, particularly for certain age classes (as shown in Table 3 below).
  • Mass-sex ratio coupling: In yearlings and 2-year-olds, there was a robust relationship between adult male mass and the mass of females (M–F coupling, r² ≈ 0.50–0.54); among older age classes, this linkage was weaker.

Results: Climate (Summer) Effects

  • Strong climate signal for youngest age classes:
    • For yearlings (1.5 and 2.5 years), mean autumn carcass mass was best predicted by warm-summer indicators: accumulated day degrees > 6°C during June–July (DD>60°C). Standardized coefficient: β= -0.48; R²=0.32; P<0.01.
    • A combined model including DD>60°C, May–June precipitation, and preceding winter snow depth explained more variance (R² = 0.60; P
  • For 2-year-olds: Mean June–July mean temperature was the best predictor (β = -0.49; R² = 0.24; P<0.05).
  • Climate and older moose: For older age groups, late-winter temperatures had a positive effect on autumn carcass mass, indicating thermoregulatory costs during winter and rut exert greater influence on older than younger moose.
  • Mechanistic interpretation: Warmer, wetter summers likely improve forage quality and digestibility, particularly for protein-rich growth in younger animals; late-winter warmth reduces maintenance costs and supports mass recovery.

Results: Antler Size (Points) and Its Relationship with Mass

  • Age-related pattern: Number of antler points increases with age, even after accounting for carcass mass (Table 4 and Fig. 1).
  • Relationship to mass (antler points as a proxy for antler size): A positive association exists between mass and number of points, but the strength of the mass–points relationship varies by age group (Table 4).
    • Regression of log(number of points) on log(carcass mass): slopes are negative across age groups, with age-specific intercepts differing significantly (P < 0.001 for intercept differences; no significant slope differences after accounting for age). This indicates that, after accounting for body mass, older age groups still bear relatively more points.
  • Covariate analysis on antler points (Table 5): When including climate alongside mass, the covariance demonstrates that:
    • For 1.5-year-olds: Mean carcass mass alone explains a substantial portion of point variance (β ≈ 0.51; R² ≈ 0.26; F ≈ 7.17; P < 0.05).
    • For 2.5-year-olds: May temperature becomes a significant predictor in addition to mass (β ≈ 0.44; R² ≈ 0.56; F ≈ 11.91; P < 0.001).
    • For 3.5-year-olds: May temperature remains a strong predictor (β ≈ 0.71; R² ≈ 0.60; F ≈ 14.03; P < 0.001).
    • For older groups (5.5–8.5 years): May temperature and carcass mass together explain substantial variance (β for temperature ≈ 0.64; β for mass ≈ 0.48; R² ≈ 0.52; F ≈ 10.33; P < 0.001).
  • Key takeaway: Antler size (points) tracks mass, but climate also has a direct effect, particularly for older animals; antler size shows a larger degree of independence from body mass than often assumed, suggesting costs of antler development and/or their hormonal/energetic signaling may be affected by May temperatures.

Tables and Figures: Summary of Quantitative Results

  • Table 3 (Multiple regressions of annual variation in mean carcass mass on yearling mass and sex ratio; standardized coefficients):
    • Age 1.5: Day degrees >60°C in June–July: β = -0.59; May–June precipitation: β = -0.38; R² = 0.50; F = 9.0; P < 0.01
    • Age 2.5: Mean mass as yearling: β = 0.63; R² = 0.40; F = 13.5; P < 0.01
    • Age 3.5: Sex ratio: β = 0.65; R² = 0.43; F = 12.0; P < 0.01
    • Age 4.5: Sex ratio: β = 0.54; R² = 0.30; F = 7.6; P < 0.01
    • Age 5.5–8.5: Sex ratio: β = 0.62; Mean temperature in March–April: β = 0.46; R² = 0.60; F = 12.0; P < 0.001
  • Table 4 (Regression of log(number of antler points) on log(carcass mass) by age groups; P < 0.001 for all):
    • Age 1.5: n = 797; slope = -1.90; intercept = 1.11; F = 116.5; R² = 0.13
    • Age 2.5: n = 561; slope = -1.83; intercept = 1.11; F = 93.6; R² = 0.14
    • Age 3.5: n = 375; slope = -1.98; intercept = 1.21; F = 62.9; R² = 0.14
    • Age 4.5: n = 242; slope = -1.02; intercept = 0.83; F = 26.8; R² = 0.10
    • Age 5.5–8.5: n = 213; slope = -0.78; intercept = 0.75; F = 21.6; R² = 0.09
  • Table 5 (Multiple regression of annual variation of mean number of antler points on carcass mass and climate; standardized coefficients):
    • Age 1.5: Mass coefficient = 0.51; R² = 0.26; F = 7.17; P < 0.05
    • Age 2.5: May temperature coefficient = 0.44; R² = 0.56; F = 11.91; P < 0.001
    • Age 3.5: May temperature coefficient = 0.71; R² = 0.60; F = 14.03; P < 0.001
    • Age 5.5–8.5: May temperature coefficient = 0.64; Mass coefficient = 0.48; R² = 0.52; F = 10.33; P < 0.001

Interpretation and Synthesis

  • All three mechanisms (climate, density, and sex ratio) contribute to annual variation in male moose traits, but their relative importance is age- and sex-specific:
    • Climate is most influential for the youngest age classes, likely through effects on forage quality/availability and phenology that shape growth during summer.
    • Density and sex ratio are stronger predictors for adult males; higher density reduces body mass, and a male-biased sex ratio influences competition and energy allocation during rut, thereby affecting growth trajectories.
    • The decline in sex ratio with density underscores density-dependent selection: in high-density years, competition for mates increases, potentially shifting allocation of resources to reproduction at the expense of somatic growth.
  • Antler size shows a nuanced pattern:
    • Antler points increase with age and are partly determined by body mass, but May temperatures also exert an independent influence, particularly in older males.
    • No detectable direct effect of density or sex ratio on the absolute or relative number of antler points; however, the energetic cost of antlers implies that in higher density/competition environments, smaller males may carry relatively heavier antlers, revealing a potential density-dependent selection on antler traits.
  • Implications for life-history theory:
    • Treating sexually selected characters as life-history traits allows integration of mating competition dynamics with somatic growth and survival trade-offs.
    • The findings align with density-dependent life-history theory: resource limitation and competition can drive trait variation in males, while climate-mediated conditions shape early-life growth, potentially influencing lifetime reproductive success.
    • The observed patterns imply potential low heritability for these traits under strong stochastic environmental influence and density-dependent selection, complicating predictions of evolutionary change.
  • Implications for wildlife management:
    • Hunting practices altering sex ratios could indirectly influence population growth via effects on male maturation timing and somatic growth.
    • Density-dependent reductions in male body mass could impact fitness and competitive ability; management should consider both sex ratio and density to maintain population health.

Key Formulas and Equations (LaTeX)

  • Climate and growth predictors (youngest age group, yearlings):
    • Accumulated day degrees >60°C in June–July: $DD_{>60^ op C}^{(June-July)}$ with standardized coefficient $eta = -0.48$, $R^2 = 0.32$, $P < 0.01$.
    • Combined model: May–June precipitation $P{May-Jun}$ and January–February snow depth $S{Jan-Feb}$ plus $DD_{>60^ op C}^{(June-July)} gives $R^2 = 0.60$, $P < 0.01$.
  • 2-year-olds: Best predictor is mean temperature in June–July: $ar{T}^{(June-July)}$ with $P < 0.05$, $R^2 = 0.24$.
  • Age-class regression results (Table 3, standardized coefficients):
    • Age 1.5: $ eta{ ext{DD}>60} = -0.59,\n eta{ ext{May-Jun precip}} = -0.38,
      R^2 = 0.50,
      F = 9.0,
      P < 0.01$
    • Age 2.5: $ eta_{ ext{Yearling mass}} = 0.63,
      R^2 = 0.40,
      F = 13.5,
      P < 0.01$
    • Age 3.5: $ eta_{ ext{Sex ratio}} = 0.65,
      R^2 = 0.43,
      F = 12.0,
      P < 0.01$
    • Age 4.5: $ eta_{ ext{Sex ratio}} = 0.54,
      R^2 = 0.30,
      F = 7.6,
      P < 0.01$
    • Age 5.5–8.5: $ eta{ ext{Sex ratio}} = 0.62, eta{ ext{March-April temp}} = 0.00?
      (May temperature included, see below),
      R^2 = 0.60,
      F = 12.0,
      P < 0.001$
  • Antler-point regression (Table 4):
    • Age 1.5: $n=797, ext{ slope}=-1.90, ext{ intercept}=1.11, ext{ F}=116.5, ext{ }R^2=0.13$
    • Age 2.5: $n=561, ext{ slope}=-1.83, ext{ intercept}=1.11, ext{ F}=93.6, ext{ }R^2=0.14$
    • Age 3.5: $n=375, ext{ slope}=-1.98, ext{ intercept}=1.21, ext{ F}=62.9, ext{ }R^2=0.14$
    • Age 4.5: $n=242, ext{ slope}=-1.02, ext{ intercept}=0.83, ext{ F}=26.8, ext{ }R^2=0.10$
    • Age 5.5–8.5: $n=213, ext{ slope}=-0.78, ext{ intercept}=0.75, ext{ F}=21.6, ext{ }R^2=0.09$
  • Table 5 (antler points explained by mass and climate; standardized coefficients):
    • Age 1.5: Mass coefficient $=0.51$, $R^2=0.26$, $F=7.17$, $P<0.05$
    • Age 2.5: May temperature coefficient $=0.44$, $R^2=0.56$, $F=11.91$, $P<0.001$
    • Age 3.5: May temperature coefficient $=0.71$, $R^2=0.60$, $F=14.03$, $P<0.001$
    • Age 5.5–8.5: May temperature coefficient $=0.64$, Mass coefficient $=0.48$, $R^2=0.52$, $F=10.33$, $P<0.001$

Notes on Interpretation and Limitations

  • Causality: While significant associations exist, observational data cannot definitively prove causation; multiple interacting factors (climate, density, sex ratio) may co-vary.
  • Density and sex ratio as management levers: The strong link between density/sex ratio and adult male mass suggests that hunting policies that alter sex ratio or population density could indirectly influence male growth, maturation, and mating competition.
  • Antler traits and heritability: The study notes that the heritability of these sexually selected traits may be low due to stochastic environmental components and density-dependent selection; this has implications for predicting evolutionary responses.
  • Ethical/Practical implications: The paper highlights the broader ecological and evolutionary significance of life-history traits under environmental variation and human-influenced population structure, reinforcing the importance of considering ecosystem-wide consequences in wildlife management decisions.

Connections to Foundational Principles and Real-World Relevance

  • Alignment with life-history theory: The work exemplifies how organisms balance resource allocation between growth, survival, and reproduction under variable environmental conditions and competitive contexts.
  • Density dependence in wildlife populations: Echoes findings in other ungulates (e.g., red deer) that male phenotypes can be more strongly affected by density than females due to mating competition and energetic costs of rut.
  • Climate as a driver of phenotypic variation: Demonstrates how climatic variables that influence forage quality and growing season strongly shape growth trajectories, especially in juveniles.
  • Implications for population management: The study provides evidence that shifts in density and sex ratio can alter growth trajectories and potentially reproductive dynamics, informing quotas and harvest strategies.

Summary Takeaways

  • Climate, density, and sex ratio jointly shape annual variation in male moose body mass and antler size, with age- and sex-specific patterns.
  • Young moose are most climate-sensitive for growth; adults show stronger density/sex-ratio effects on mass.
  • Antler size increases with age and mass but also shows climate-linked variation, particularly in older males; antler size appears not to track mass precisely, suggesting independent energetic costs and selective pressures.
  • Treating sexually selected traits as life-history traits provides a framework to understand their ecological and evolutionary dynamics under environmental and anthropogenic pressures.

References (Key Citations Mentioned)

  • Climate–growth links and Bergmann-style patterns in cervids: Langvatn & Albon (1986); White (1983); Saether (1985).
  • Density dependence in ungulates: Clutton-Brock et al. (1982); Albon et al. (1983, 1987); Leader-Williams (1988).
  • Antler development and cost: Goss (1970); Van Ballenberghe (1982); Clutton-Brock (1982).
  • Methodological references: Sokal & Rohlf (1981); Rice (1989).

Quick Reference (Practical Details)

  • Study period: 1967–1989; sample: 2,862 males; age groups: 1.5, 2.5, 3.5, 4.5, 5.5–8.5 years.
  • Key variables: carcass mass (autumn), number of antler points (>2 cm), population density index (moose observed in first 2 weeks), sex ratio (males per female).
  • Main findings by age:
    • Yearlings: climate-driven growth in autumn mass; May–June conditions and preceding winter snow depth matter.
    • Adults: density and sex ratio govern mass declines; climate still relevant but less dominant than density effects.
  • Antlers: Points increase with age; climate (May temperatures) affects points, especially in older age groups; mass explains part of the variance but not all, indicating independent costs of antler production.