Quantitative genetic variation in static allometry in the threespine stickleback

The common pattern of replicated evolution of a consistent shape-environment relationship might reflect selection acting in similar ways within each environment, but divergently among environments. However, phenotypic evolution depends on the availability of additive genetic variation as well as on the direction of selection, implicating a bias in the distribution of genetic variance as a potential contributor to replicated evolution. Allometry, the relationship between shape and size, is a potential source of genetic bias that is poorly understood. The threespine stickleback, Gasterosteus aculeatus, provides an ideal system for exploring the contribution of genetic variance in body shape allometry to evolutionary patterns. The stickleback system comprises marine populations that exhibit limited phenotypic variation, and young freshwater populations which, following independent colonization events, have often evolved similar phenotypes in similar environments. In particular, stickleback diversification has involved changes in both total body size and relative size of body regions (i.e., shape). In a laboratory-reared cohort derived from an oceanic Alaskan population that is phenotypically and genetically representative of the ancestor of the diverse freshwater populations in this region, we determined the phenotypic static allometry, and estimated the additive genetic variation about these population-level allometric functions. We detected significant allometry, with larger fish having relatively smaller heads, a longer base to their second dorsal fin, and longer, shallower caudal peduncles. There was additive genetic variance in body size and in size-independent body shape (i.e., allometric elevation), but typically not in allometric slopes. These results suggest that the parallel evolution of body shape in threespine stickleback is not likely to have been a correlated response to selection on body size, or vice versa. Although allometry is common in fishes, this study highlights the need for additional data on genetic variation in allometric functions to determine how allometry evolves and how it influences phenotypic evolution.     

Life-history variation and allometry for sexual size dimorphism in Pacific salmon and trout

Allometry for sexual size dimorphism (SSD) is common in animals, but how different evolutionary processes interact to determine allometry remains unclear. Among related species SSD (male : female) typically increases with average body size, resulting in slopes of less than 1 when female size is regressed on male size: an allometric relationship formalized as 'Rensch's rule' . Empirical studies show that taxa with male-biased SSD are more likely to satisfy Rensch's rule and that a taxon's mean SSD is negatively correlated with allometric slope, implicating sexual selection on male size as an important mechanism promoting allometry for SSD. I use body length (and life-history) data from 628 (259) populations of seven species of anadromous Pacific salmon and trout (Oncorhynchus spp.) to show that in this genus life-history variation appears to regulate patterns of allometry both within and between species. Although all seven species have intraspecific allometric slopes of less than 1, contrary to expectation slope is unrelated to species' mean SSD, but is instead negatively correlated with two life-history variables: the species' mean marine age and variation in marine age. Second, because differences in marine age among species render SSD and body size uncorrelated, the interspecific slope is isometric. Together, these results provide an example of how evolutionary divergence in life history among related species can affect patterns of allometry for SSD across taxonomic scales.     

Allometric relations in three species of finches (Aves: Fringillidae)

Static nestling, adult and ontogenetic allometry were analysed in three species of finches. Static nestling allometry was very similar across age in early ontogeny and among species and could be approximated by a single matrix of phenotypic variances and covariances. The first eigenvector of this matrix showed negative allometry of bill and tarsus to mass, but positive for wing length to mass. Adult static allometry was also very similar among species, but differed from nestling pattern. In adults the bill had a positive allometry in relation to tarsus and wing, but negative to mass, while tarsus and wing were unrelated to mass. The ontogenetic allometry in each species was very similar to nestling static allometry. Viewed in relation to final size, bill characters grew more slowly than body characters, but for a longer time, which created the difference between adult and nestling allometric patterns. There were differences among species both with regard to elevation and slope of allometric coefficients, suggesting that the differences among species came about by changes in the three fundamental ontogenetic parameters namely growth rate, onset of growth and offset of growth.     

Variation in the ontogenetic allometry of horn length in bovids along a body mass continuum

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.     

Evolution of brain–body allometry in Lake Tanganyika cichlids

Brain size is strongly associated with body size in all vertebrates. This relationship has been hypothesized to be an important constraint on adaptive brain size evolution. The essential assumption behind this idea is that static (i.e., within species) brain–body allometry has low ability to evolve. However, recent studies have reported mixed support for this view. Here, we examine brain–body static allometry in Lake Tanganyika cichlids using a phylogenetic comparative framework. We found considerable variation in the static allometric intercept, which explained the majority of variation in absolute and relative brain size. In contrast, the slope of the brain–body static allometry had relatively low variation, which explained less variation in absolute and relative brain size compared to the intercept and body size. Further examination of the tempo and mode of evolution of static allometric parameters confirmed these observations. Moreover, the estimated evolutionary parameters indicate that the limited observed variation in the static allometric slope could be a result of strong stabilizing selection. Overall, our findings suggest that the brain–body static allometric slope may represent an evolutionary constraint in Lake Tanganyika cichlids.     

The allometric pattern of sexually size dimorphic feather ornaments and factors affecting allometry

The static allometry of secondary sexual characters is currently subject to debate. While some studies suggest an almost universal positive allometry for such traits, but isometry or negative allometry for nonornamental traits, other studies maintain that any kind of allometric pattern is possible. Therefore, we investigated the allometry of sexually size dimorphic feather ornaments in 67 species of birds. We also studied the allometry of female feathers homologous to male ornaments (female ornaments in the following) and ordinary nonsexual traits. Allometries were estimated as reduced major axis slopes of trait length on tarsus length. Ornamental feathers showed positive allometric slopes in both sexes, although that was not a peculiarity for ornamental feathers, because nonsexual tail feathers also showed positive allometry. Migration distance (in males) and relative size of the tail ornament (in females) tended to be negatively related to the allometric slope of tail feather ornaments, although these results were not conclusive. Finally, we found an association between mating system and allometry of tail feather ornaments, with species with more intense sexual selection showing a smaller degree of allometry of tail ornaments. This study is consistent with theoretical models that predict no specific kind of allometric pattern for sexual and nonsexual characters.     

Relationships among ontogenetic,static, and evolutionary allometry

The relationship between ontogenetic, static, and evolutionary levels of allometry is investigated. Extrapolation from relative size relationships in adults to relative growth in ontogeny depends on the variability of slopes and intercepts of ontogenetic vectors relative to variability in length of the vector. If variability in slopes and intercepts is low relative to variability in length, ontogenetic and static allometries will be similar. The similarity of ontogenetic and static allometries was tested by comparing the first principal component, or size vector, for correlations among 48 cranial traits in a cross-sectional ontogenetic sample of rhesus macaques from Cayo Santiago with a static sample from which all age- and sex-related variation had been removed. The vector correlation between the components is high but significantly less than one while two of three allometric patterns apparent in the ontogenetic component are not discernable in the static component. This indicates that there are important differences in size and shape relationships among adults and within ontogenies. Extrapolation from intra- or interspecific phenotypic allometry to evolutionary allometry is shown to depend on the similarity of genetic and phenotypic allometry patterns. Similarity of patterns was tested by comparing the first principal components of the phenotypic, genetic, and environmental correlation matrices calculated using standard quantitative genetic methods. The patterns of phenotypic, genetic, and environmental allometry are dissimilar; only the environmental allometries show ontogenetic allometric patterns. This indicates that phenotypic allometry may not be an accurate guide to patterns of evolutionary change in size and shape.     

Morphological scaling of body form in four shark species differing in ecology and life history

Body form can change across ontogeny, and can influence how animals of different sizes move and feed. Scaling data on live apex predatory sharks are rare and, therefore, we examined patterns of scaling in ontogenetic series of four sympatric shark species exhibiting a range of sizes, ecologies and life histories (tiger, bull, blacktip, and nurse shark). We evaluated 13 linear morphological variables and two areas (caudal and dorsal) that could influence both animal condition and locomotor performance. These measurements included dimensions of the dorsal, pectoral, and caudal fins, as well as several dimensions of body circumference, and of the head. For all four species, the body axis (eye‐to‐eye, lateral span, frontal span, proximal span) scaled close to isometry (expected slope of 1.0). The two largest sharks (tiger and bull sharks) also showed significant negative allometry for elements of the caudal fin. We found significant negative allometry in the lengths of the upper lobe of the caudal fin (caudal fin 1) and the overall height of the caudal fin (caudal fin 2) in tiger and bull sharks, with slopes ranging from about 0.60 to 0.73. Further, tiger sharks showed negative allometry in caudal fin area. These results suggest that in terms of overall body dimensions, small sharks are roughly geometrically similar to large sharks, at least within the species we examined. However, juvenile tiger (and to a lesser extent bull sharks) are notable in having proportionately larger caudal fins compared to adult sharks. As the caudal fin contributes to generating thrust during forward locomotion, this scaling implies differences among adult and juvenile sharks in locomotor ability. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 114 , 126–135.     

Allometric analysis of dental variation in a human population

There exists an extensive literature that deals with interspecific allometry, eg, brain size-body size relationships among species. Yet comparatively little attention has been paid to intraspecific or static adult allometry. An intraspecfic allometric analysis was conducted on the complete permanent dentition of a prehistoric American Indian population (N = 156). Mesiodistal and buccolingual measurements were logarithmically transformed and regressed on log transformations of femur length, an estimate of body size. When measurements of antimeric teeth were introduced together into common regressions on femur length, 20 of the 32 slopes were significantly different from zero. Thirty-one of the slopes ranged between zero and one and clustered between 0.2 and 0.4. Hence, negative allometry describes the tooth size-body size association, ie, taller individuals in general possess absolutely but not relatively larger teeth than shorter individuals. In addition, no significant sex differences for the regression slopes were observed. Though significantly correlated, tooth size and body size variables are too weakly associated to permit accurate predictons from regression equations. Evolutionary implications of intraspecfic dental allometry are discussed.     

ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.     

Does allometry account for shape variability in <Emphasis Type="Italic">Ephedrus persicae</Emphasis> Froggatt (Hymenoptera: Braconidae: Aphidiinae) parasitic wasps?

We analysed linear measurements on various parts of the body and the configuration of 11 landmarks on the wing in a large sample of Ephedrus persicae that had emerged from 13 aphid host species, to assess whether static allometry (a measure of the scaling relationship between traits in a population of individuals at the same ontogenetic stage) accounts for variation in body shape. The analysed specimens came from several localities in Europe, Asia Minor, Japan and South America, and cover a large portion of the distribution area of E. persicae. We found that allometry accounts for variation in body shape among different biotypes within the E. persicae group. The allometric slopes for head size (HD), petiolus width (PETW), mesoscutum width (MSC), and ovipositor sheath length (OVPL) diverged significantly among biotypes, indicating biotype-specific allometries. The analysis of allometric variation in wing shape showed that the pattern and direction of allometric changes also differed among individuals that had emerged from different hosts. Our results (observed divergences in the directions of allometric slopes of particular morphometric traits and wing shape) suggest that allometric relations within E. persicae are not conserved, so that allometry itself changes, evolving differently in aphid parasitoids that emerge from different hosts.     

Walk the line: 600000 years of molar evolution constrained by allometry in the fossil rodent Mimomys savini

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.     

The static allometry of sexual and nonsexual traits in vervet monkeys

Sexual traits vary tremendously in static allometry. This variation may be explained in part by body size‐related differences in the strength of selection. We tested this hypothesis in two populations of vervet monkeys, using estimates of the level of condition dependence for different morphological traits as a proxy for body size‐related variation in the strength of selection. In support of the hypothesis, we found that the steepness of allometric slopes increased with the level of condition dependence. One trait of particular interest, the penis, had shallow allometric slopes and low levels of condition dependence, in agreement with one of the most consistent patterns yet detected in the study of allometry, namely that of genitalia exhibiting shallow allometries. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2015, 114 , 527–537.     

Allometric scaling of mortality rates with body mass in abalones

The existence of an allometric relationship between mortality rates and body mass has been theorized and extensively documented across taxa. Within species, however, the allometry between mortality rates and body mass has received substantially less attention and the consistency of such scaling patterns at the intra-specific level is controversial. We reviewed 73 experimental studies to examine the relationship between mortality rates and body size among seven species of abalone (Haliotis spp.), a marine herbivorous mollusk. Both in the field and in the laboratory, log-transformed mortality rates were negatively correlated with log-transformed individual body mass for all species considered, with allometric exponents remarkably similar among species. This regular pattern confirms previous findings that juvenile abalones suffer higher mortality rates than adult individuals. Field mortality rates were higher overall than those measured in the laboratory, and the relationship between mortality and body mass tended to be steeper in field than in laboratory conditions for all species considered. These results suggest that in the natural environment, additional mortality factors, especially linked to predation, could significantly contribute to mortality, particularly at small body sizes. On the other hand, the consistent allometry of mortality rates versus body mass in laboratory conditions suggests that other sources of mortality, beside predation, are size-dependent in abalone.     

Modes of ontogenetic allometric shifts in crocodylian vertebrae

During postnatal ontogeny of vertebrates, allometric trends in certain morphological units or dimensions can shift drastically among isometry, positive allometry, and negative allometry. However, detailed patterns of allometric transitions in certain timings have not been explored well. Identifying the presence and nature of allometric shifts is essential for understanding the patterns of changes in relative size and shape and the proximal factors that are controlling these changes mechanistically. Allometric trends in 10 selected vertebrae (cervical 2–caudal 2) from hatchlings to very mature individuals of Alligator mississippiensis (Archosauria, Crocodylia) are reported in the present study. Allometric coefficients in 12 vertebral dimensions are calculated and compared relative to total body length, including centrum, neural spine, transverse process, zygapophysis, and neural pedicle. During the postnatal growth, positive allometry is the most common type of relative change (10 of the 12 dimensions), although the diameter of the neural canal shows a negative allometric trend. However, when using spurious breaks (i.e. allometric trends subdivided into growth stages using certain growth events, and key body sizes and/or ages), vertebral parts exhibit various pathways of allometric shifts. Based on allometric trends in three spurious breaks, separated by the end of endochondral ossification (body length: approximnately 0.9 m), sexual maturity (1.8 m), and the stoppage of body size increase (2.8 m), six types of ontogenetic allometric shifts are established. Allometric shifts exhibit a wide range from positive allometry restricted only in the early postnatal stage (Type I) to life‐long positive allometry (Type VI). This model of ontogenetic allometric shifts is then applied to interpret potential mechanisms (causes) of allometric changes, such as (1) growth itself (when allometric trend gradually decreases to isometric or negative allometric change: Type II–IV allometric shift); (2) developmental constraint (when positive allometry is limited only in the early growth stage: Type I allometric shift); and (3) functional or biomechanical drive (when positive allometry continues throughout ontogeny: Type VI allometric shift).     

Allometry for sexual size dimorphism: testing two hypotheses for Rensch's rule in the water strider Aquarius remigis

Within any given clade, male size and female size typically covary, but male size often varies more than female size. This generates a pattern of allometry for sexual size dimorphism (SSD) known as Rensch's rule. I use allometry for SSD among populations of the water strider Aquarius remigis (Hemiptera, Gerridae) to test the hypothesis that Rensch's rule evolves in response to sexual selection on male secondary sexual traits and an alternative hypothesis that it is caused by greater phenotypic plasticity of body size in males. Comparisons of three populations reared under two temperature regimes are combined with an analysis of allometry for genital and somatic components of body size among 25 field populations. Contrary to the sexual-selection hypothesis, genital length, the target of sexual selection, shows the lowest allometric slope of all the assayed traits. Instead, the results support a novel interpretation of the differential-plasticity hypothesis: that the traits most closely associated with reproductive fitness (abdomen length in females and genital length in males) are "adaptively canalized." While this hypothesis is unlikely to explain Rensch's rule among species or higher clades, it may explain widespread patterns of intraspecific variation in SSD recently documented for many insect species.     

Competition and Allometry in Kochia scoparia

Comparisons between crowded and uncrowded Kochia scoparia individualsdemonstrate pronounced effects of competition on plant allometryas well as on the distributions of different aspects of size.Non-destructive measurements of height and stem diameter and,for a subset of the populations, the number and length of leavesand branches, were taken at three times, and the plants wereharvested after the third measurement. The sequential measurementsafforded the opportunity to obtain information of the effectsof competition on allometric growth trajectories of individuals,as well as on static inter-individual allometric relationships. The distributions of most size measures appeared to be normalfor the uncrowded population. Crowded populations developeda negatively-skewed height distribution and a high-inequalitymass distribution, whereas the diameter distributions remainednormal. Plants grown without neighbours showed simple allometricrelationships between height, diameter and weight. For isolatedplants, the 'static' allometric relationship between plantsof different sizes and the allometric growth trajectory of individualswere similar. Crowded populations showed complex allometry;the static inter-individual relationships between height, diameterand weight were curvilinear (on log-log scale). There were largedifferences in the allometric growth slopes of uncrowded vs.crowded plants. Allometric relationships between stem diameterand plant mass, and between total length of leaves and totallength of branches, did not seem to be altered by competition. The data suggest that height was the most important aspect ofsize influencing future growth of individuals in the crowdedpopulation. Only plants above a certain height were able tocontinue to grow from the second to third measurement in thecrowded population. This supports the hypothesis that asymmetriccompetition for light is the cause of the allometric changesand of the increase in size variability due to competition.Copyright1994, 1999 Academic Press Allometric growth, allometry, competition, growth, Kochia     

ARTIFICIAL SELECTION ON HORN LENGTH-BODY SIZE ALLOMETRY IN THE HORNED BEETLE ONTHOPHAGUS ACUMINATUS (COLEOPTERA: SCARABAEIDAE)

Males of the horned beetle Onthophagus acuminatus Har. (Coleoptera: Scarabaeidae) exhibit horn length dimorphism due to a sigmoidal allometric relationship between horn length and body size: the steep slope of the allometry around the inflection of the sigmoid curve separates males into two groups; those larger than this inflection possess long horns, and those smaller than this inflection have short horns or lack horns. I examined the genetic basis of the allometric relationship between horn length and body size by selecting males that produced unusually long horns, and males that produced unusually short horns, for their respective body sizes. After seven generations of selection, lines selected for relatively long horns had significantly longer horn lengths for a given body size than lines selected for relatively short horns, indicating a heritable component to variation in the allometry. The sigmoidal shape of the allometry was not affected by this selection regime. Rather, selected lines differed in the position of the allometry along the body size axis. One consequence of lateral shifts in this allometric relationship was that the body size separating horned from hornless males (the point of inflection of the sigmoid curve) differed between selection lines: lines in which males were selected for relatively long horns began horn production at smaller body sizes than lines selected for relatively short horns. These results suggest that populations can evolve in response to selection on male horn length through modification of the growth relationship between horn length and body size.     

A Test of Genital Allometry Using Two Damselfly Species does not Produce Hypoallometric Patterns

It is widely admitted that sexual selection is the responsible force behind genital traits. However, the particular mechanisms of genital evolution are still debated. Recently, studies of genital static allometry in insects have been used to elucidate such mechanisms. Insect genital traits are often reported to show negative allometry (i.e., a slope < 1), which has generated a number of ideas on how genital traits are selected. However, many studies that have inferred selection mechanisms have omitted consideration of the function of genital traits, used unreliable indicators of body size, and only rarely included female genitalia in their analysis. We investigated whether negative allometry operates for genitalia in two damselfly species (Protoneura cara and Ischnura denticollis). Damselflies are suitable for genital allometry tests as their genital function and body size indicators (wing length and head width) are relatively well known and established. First, we show that the aedeagus is used to physically remove sperm from both sperm storage organs (bursa and spermatheca) and that wing length and head width correlate positively with other morphological traits for the two study species. Second, we estimated genital allometry by measuring aedeagal length, vaginal length, bursal volume, and spermathecal volume. Our results indicate no consistent allometric pattern. Allometry for aedeagal length and vaginal width was not the same. Thus, there was no support for a negative allometric relationship. We urge researchers investigating allometry to look directly at how genitalia function rather than inferring function from allometric relationships only.     

Genital and body allometry in two species of noctuid moths (Lepidoptera: Noctuidae)

One‐size‐fits‐all and related hypotheses predict that static allometry slopes for male genitalia will be consistently lower than 1.0 and lower than the slopes for most other body parts (somatic traits). We examined the allometry of genitalic and somatic morphological traits in males and females of two species of noctuid moths, Spodoptera exigua (Hübner, [1808]) and Helicoverpa armigera (Hübner, [1808]). The relationship between genitalic traits and body size was generally strongly negative‐allometric in males but with no significant differences from 1.00 in females of the two species examined. However, in females, the slope of genital traits was also lower than the slopes for somatic traits. The relationship between somatic traits and the body size indicator was approximately isometric in most cases in males, except in four traits in S. exigua, in which the slopes showed slight negative allometry, and the hind tibia in H. armigera, in which the slope had positive allometry. However, in females, some somatic traits showed isometric and some other showed negative allometry in both species. The coefficients of variation (CV) for all structures in the males were low, not exceeding 10%. Genitalic traits showed significantly lower CV than somatic traits in males. In females, somatic traits showed lower CV than genitalic traits but with no significant difference in the H. armigera. Our observations of strongly negative allometry for genitalic traits in males are consistent with stabilizing selection on genital size and we suggest that male performance in interactions with females is the source of selection on male genital allometry. The difference in the degree of phenotypic variation between genitalic and somatic traits in the two studied species is attributed to the different developmental‐genetic architectures of these traits. Female genitalia showed a similar trend to the males, although the difference between genital and somatic traits was not significant in females. This finding suggests that selection is acting differently on male and female genitalia. Positive allometry of hind tibia in H. armigera may be a result of secondary sexual function.