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Little is known about the effects of environmental variation on allometric relationships of condition‐dependent traits, especially in wild populations. We estimated sex‐specific static allometry between horn length and body mass in four populations of mountain ungulates that experienced periods of contrasting density over the course of the study. These species displayed contrasting sexual dimorphism in horn size; high dimorphism in Capra ibex and Ovis canadensis and low dimorphism in Rupicapra rupicapra and Oreamnos americanus. The effects of density on static allometric slopes were weak and inconsistent while allometric intercepts were generally lower at high density, especially in males from species with high sexual dimorphism in horn length. These results confirm that static allometric slopes are more canalized than allometric intercepts against environmental variation induced by changes in population density. [ABSTRACT FROM AUTHOR]

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass. [ABSTRACT FROM AUTHOR]

Metabolic rate (MR) often scales with body mass (BM) following a power function of the form MR = aBMb, where b is the allometric exponent (i.e. slope on a log-log scale). The variational properties of b have been debated, but very few studies have tested for genetic variance in b, and none have tested for a genotype-by-environment (G_E) interaction in b. Consequently, the short-term evolutionary potentials of both b and its phenotypic plasticity remain unknown. Using 10 clones of a population of Daphnia magna, we estimated the genetic variance in b and assessed whether a G×E interaction affected b. We measured metabolic rate on juveniles of different sizes reared and measured at three temperatures (17, 22 and 28°C). Overall, b decreased with increasing temperature. We found no evidence of genetic variance in b at any temperature, and thus no G_E interaction in b. However, we found a significant G_E interaction in size-specific metabolic rate. Using simulations, we show how this G_E interaction can generate genetic variation in the ontogenetic allometric slope of animals experiencing directional changes in temperature during growth. This suggests that b can evolve despite having limited genetic variation at constant temperatures. [ABSTRACT FROM AUTHOR]

Allometry studies describe how phenotypic traits increase relative to the increase of the size of the organism. Given that the increase in size of an organism is attributable to growth, a multiplicative process, allometric relationships are often analysed on a proportional scale (e.g. a log–log scale) to account for the multiplicative nature of the data. Nonetheless, the logarithmic transformation of the data when estimating allometric relationships has been the subject of debate. In a series of replies to various case studies of allometry, G. C. Packard has repeatedly criticized this approach under the premise that the logarithmic transformation of the data alters the estimate of the allometric exponent and obscures the biological meaning of the allometric parameters. Recently, Packard (2018) reanalysed data from our study on horn length allometry in bovids (Tidière et al. 2017) and reached conclusions that contrasted with those reported in our original study. Echoing many authors before us, we argue here that logarithmic transformation of the data in allometric studies is justified by the expected distribution of the residual variation in ontogenetic, static and evolutionary allometry. We also point out that allometric slopes thus obtained have a direct biological interpretation in terms of elasticities. Finally, we show that Packard's criticism is based on qualitative and not quantitative assessment of the models fitted on different scales, and his conclusions disregard statistical and biological evidence supporting models fitted on a log–log scale. [ABSTRACT FROM AUTHOR]

The allometric-constraint hypothesis states that evolutionary divergence of morphological traits is restricted by integrated growth regulation. In this study, we test this hypothesis on a time-calibrated and well-documented palaeontological sequence of dental measurements on the Pleistocene arvicoline rodent species Mimomys savini from the Iberian Peninsula. Based on 507 specimens representing nine populations regularly spaced over 600 000 years, we compare static (within-population) and evolutionary (among-population) allometric slopes between the width and the length of the first lower molar. We find that the static allometric slope remains evolutionary stable and predicts the evolutionary allometry quite well. These results support the hypothesis that the macroevolutionary divergence of molar traits is constrained by static allometric relationships. [ABSTRACT FROM AUTHOR]

Morphological allometry refers to patterns of covariance between body parts resulting from variation in body size. Whether measured during growth (ontogenetic allometry), among individuals at similar developmental stage (static allometry), or among populations or species (evolutionary allometry), allometric relationships are often tight and relatively invariant. Consequently, it has been suggested that allometries have low evolvability and could constrain phenotypic evolution by forcing evolving species along fixed trajectories. Alternatively, allometric relationships may result from natural selection for functional optimization. Despite nearly a century of active research, distinguishing between these alternatives remains difficult, partly due to wide differences in the meaning assigned to the term allometry. In particular, a broad use of the term, encompassing any monotonic relationship between body parts, has become common. This usage breaks the connection to the proportional growth regulation that motivated Huxley's original narrow-sense use of allometry to refer to power-law relationships between traits. Focusing on the narrow-sense definition of allometry, we review here evidence for and against the allometry-as-a-constraint hypothesis. Although the low evolvability and the evolutionary invariance of the static allometric slope observed in some studies suggest a possible constraining effect of this parameter on phenotypic evolution, the lack of knowledge about selection on allometry prevents firm conclusions. [ABSTRACT FROM AUTHOR]