Allometry and size in ontogeny and phylogeny

Heterozygosity and morphological variability of chum salmon (Oncorhynchus keta) in southern British Columbia

We compared variability in two meristic and six morphometric characters with heterozygosity within and among 27 populations of chum salmon (Oncorhynchus keta) in southern British Columbia. Among individuals, there was no relationship between levels of heterozygosity at 10 electrophoretic loci and degree of meristic or morphometric variation. Decreased morphological variance was not associated with increased heterozygosity. Morphological variance and heterozygosity did not change with age for chum salmon maturing at three to five years of age. Among populations of chum salmon, increased levels of average heterozygosity were not associated with decreased variance of morphometric or meristic characters. Our results do not support the hypothesis that more heterozygous individuals show less phenotypic variability than more homozygous ones due to a canalization of morphology during development. Genetic distances between pairs of chum salmon populations were significantly correlated with pairwise Mahalanobis distances derived from meristic, but not from morphometric characters. Chum salmon are morphometrically adapted to the natal stream environment, whereas biochemical and meristic characters in these populations may be less affected by local selective forces.

Allometry between length and cross-sectional dimensions of the femur and tibia in Homo sapiens sapiens

Allometric equations relating length and cross-sectional geometric properties of the femur and tibia are generated using skeletal remains from three recent human population samples. Approximate isometry, or geometric similarity, is found both within and between samples. Cross-sectional areas scale to approximately length2, while second moments of area scale to approximately length4. It is shown that this is consistent with the maintenance of equivalent mechanical stress in long bones of different length under dynamic loadings in vivo. Other evidence indicates that bending and torsional loadings are more critical than axial loadings in the determination of lower limb bone cross-sectional dimensions.

Quantitative genetics and developmental constraints on evolution by selection

It has often been argued that the principles of random mutation and selection are insufficient to account for macroevolutionary phenomena, such as the origin of morphological novelty and directionality in evolution. A third, epigenetic, principle is said to be required and this principle is thought not to be included in microevolutionary theory. The third principle has most recently been identified as internal selection and/or non-random phenotypic effects of mutation. It is shown that the genetic variance/covariance matrix of quantitative genetic theory measures developmental constraints due to internal selection and non-random mutation. The genetic variance/covariance matrix causes the response to selection to deviate from the optimal rate and direction as specified by the selection gradient, which measures direct selection on the phenotypes. Therefore, microevolutionary theory takes account of developmental constraints on evolution by natural selection through the genetic variance/covariance matrix. Theories for predicting the pattern of genetic variance and covariance from stabilizing selection and the phenotypic effects of mutation are discussed.

The Timm-stained hippocampus of the European hedgehog: a basal mammalian form

A quantitative and qualitative description has been made of the components of the Timm-stained hippocampus of the European hedgehog. While the laminar organization and the relative size of the major subdivisions of the hippocampus (i.e., area dentata, Ammon's horn, and subiculum) are similar to those of the albino laboratory rat, the relative proportions and the staining characteristics of some of the components of the subdivisions are different. The differences are particularly evident in Ammon's horn where regions are poorly differentiated along the dentatosubicular axis and the mossy fiber zone is relatively extensive. The description characterizes a hippocampal form that can be used as a basal reference in comparative studies of the mammalian hippocampus.

Comparative morphometry of mammalian otolith organs

The endolymphatic volume of the utricle and the saccule and the surface area of the saccular macula were measured in eight mammalian species, including humans. The results confirmed that all measurements increased slowly but consistently correlating with increases in body weight. However, differences in these endolymphatic volumes or macular surface areas might also be influenced by functional characteristics among different species rather than simply reflecting geometrical comparability.

The effect of selection on brain and body size association in rats

Changes in brain size, body size and their co variance are reported from a long-term replicated directional selection experiment on body weight gain in rats. Two strains had been selected for increased and two for decreased weight gain between 3 and 9 weeks of age, and there were two randomly selected control lines. Selection produced significant changes in body weight in all selected lines. Divergence from the controls occurred in brain size in those strains selected for increased weight gain; no significant divergence was found for the strains selected for decreased weight gain. Divergence among unselected control lines suggests that genetic drift occurred in expression of brain size. Sexual dimorphism in response to selection results from sex differences in heritabilities and genetic correlations in relevant traits. In spite of considerable change in body size and brain size, no significant change in their covariation occurred either between the selection lines or between sexes. The relevance of these results to a brain and body size ‘scaling effect’ during evolutionary divergence is discussed.

Ontogenetic and interspecific organ weight allometry in Old World monkeys

The importance of allometry as an analytic tool is well recognized in the literature of primate morphology. However, a number of recent studies have illustrated how interpretive difficulties can arise when researchers confound different types of allometric data. Such confusion is due less to carelessness than to uncertainty about how different types of allometry are related. The present study examines the relationship between two types--ontogenetic and interspecific allometry--in the case of organ weight scaling in six species of Old World monkeys. Accepting the interpretation of interspecific allometry as a reflection of functional scaling constraints, the results of this analysis indicate how ontogenetic patterns have been modified in different-sized species to maintain compliance with these constraints. Specifically, for the heart and lungs it appears that vertical transpositions of individual species' ontogenies are dictated by isometric interspecific allometry, while in the case of the kidneys and liver, the relation of negative allometry across species entails alteration of the relative growth coefficients of the individual species. While these conclusions can at present only be applied to organ weight scaling, the approach of examining interspecific patterns in light of developmental differences between species should prove very helpful in our efforts to understand the phenomena of size and scaling.

An allometric network model of craniofacial growth

This study of cranial skeletal growth kinematics details the conceptual principles underlying the development of an allometric network model of such growth. This model is tested by the analysis of longitudinal rat and cross-sectional human growth data and by comparison of this model with a previously described allometric centered model. It is shown that the network model is superior to the centered model in three ways: (1) The allometric network model permits growth prediction when allometric constants are known; (2) the network model has significantly smaller errors than the centered model; and (3) the network model is capable of displaying growth kinematics of both the neural and facial skulls while in time there are marked transformations, such as relative rotations of two sets of cranial anatomic points.

Scaling of antipyrine intrinsic clearance of unbound drug in 15 mammalian species

The intrinsic clearance of unbound drug (CLuint) for antipyrine in 15 mammalian species was characterized by an equation of the form, CLuint = theta 1 (body weight) theta 2 (brain weight) theta 3, where thetas are constants. Maximum lifespan potential in mammals can also be characterized by an equation of this form. It is suggested that the set of genetic mechanisms regulating longevity and other constitutional characteristics in species is also linked to rates of drug metabolism. The ability to scale interspecies data in pharmacokinetics is taken as an expression of this design principle.

Paedomorphosis and neoteny in the pygmy chimpanzee

The strongly paedomorphic skull form in the pygmy chimpanzee results from the heterochronic process of neoteny. This cranial paedomorphosis and neoteny in Pan paniscus may be related to reduced sexual dimorphism in morphology and behavior. The interspecific differences in form result from shifts in the rate and timing of similar patterns of development.

Allometry and heterochrony in the African apes

In this work allometry and heterochrony are integrated in an analysis of ontogenic and interspecific morphological patterns in the African apes. The relationship between the interspecific differences in adult morphology and the differences in underlying patterns of growth allometries, body weight growth rates, and developmental chronologies is investigated. Results indicate that rate hypermorphosis, or the extension of ancestral allometries into new size/shape ranges with no increase in the duration of ontogeny, underlies many of the interspecific differences in form among the African apes. In addition, the need for further clarification of the processes of heterochrony is stressed by distinguishing between rate and timing differences. These distinctions and processes are illustrated and discussed using the morphological data on the African apes.

The measurement of form and variation in form: an application of three-dimensional quantitative morphology by finite-element methods

D'Arcy Thompson developed a method of coordinates which allowed for a geometrical presentation of form and form change. While his grid transformations have received much attention, little work in the geometry of form and form change has occurred since. We present a three-dimensional nonhomogeneous finite-element scaling method which allows for the mathematical and geometrical measurement of form change in addition to the graphical representation of these deformations as D'Arcy Thompson grids. This allows a reconciliation between geometrical and statistical methods for analyzing form. The method involves quantification of the transformation of one form into another in three dimensions without special registration and contains algorithms for obtaining a mean form. The method is applied to an analysis of variation in cranial form among adult male rhesus macaques from the Cayo Santiago skeletal collection. Variation was greatest in the superior-inferior direction, followed by the anterior-posterior and medial-lateral directions. The upper facial region is particularly variable. An analysis of allometry relative to local size variation shows that the larger any particular region is, the relatively greater its height, narrower its width, and shorter its length. An analysis of allometry relative to overall size showed that the upper face is positively allometric, the occipital region is strongly negatively allometric, and the other regions are isometric. After within-group variation is characterized, as described here, between-group studies, such as growth series and phylogenetic series, can be performed.

Relative brain size and metabolism in mammals

Comparisons of the relation between brain and body weights among extant mammals show that brain sizes have not increased as much as body sizes. Interspecific increases in brain and body size appear to occur at the same rate, however, when the amount of available energy is taken into account. After this adjustment, brains of primates are slightly larger than expected from the overall mammalian data, but primates also use a larger proportion of their total energy reserves for their brains. Analyses of relative brain size must take into account the requirements that the metabolically active brain has for the body.

Body size, mortality, and longevity

The body-size dependent relationships of mortality and longevity are examined for birds and eutherian mammals. Differences between mass exponents for maximum recorded longevity and survival times for fractions of original adult populations confirm the age-dependence of mortality in both classes and a size-dependency of population-age distribution. The potential number of offspring produced by a surviving fraction of a mammalian population appears to be a size-independent ecological constant. Social structure would be more likely in larger animals since greater continuity would be provided when a higher proportion of the population consisted of senior, experienced animals, as described by the ratio of time for survival of 1 in 1000 to maximum potential lifespan: t0.001/tmax = 0.91 m0.32/2.94 m0.20 = 0.31 m0.12, that is, the expected lifespan approaches the maximum as size increases.

Effects of saltwater feeding and reduced food intake on femurs of domestic ducklings

Seven-day-old domestic ducklings were assigned to groups and fed freshwater and food ad libitum (control), 1% NaCl and food ad libitum (stressed), or freshwater and only as much food as the stressed group ate (starved). Tissues were sampled after 3 and 7 days. Other groups of ducklings were fed freshwater and food ad libitum for 9 days (control), 1% NaCl and food ad libitum for 7 days followed by freshwater for 2 days (de-stressed), or freshwater and the same amount of food as the de-stressed group for 7 days followed by food ad libitum for 2 days (de-starved). Body weights were recorded and the femurs were analyzed. Univariate, multivariate, and allometric analyses clearly demonstrate that stressed and starved regimens influence femoral morphology differently. Stressing for 3 days reduced femoral ash and by 7 days had retarded femoral linear growth. Three days of starvation produced no apparent effect on the femur, but starvation for 7 days reduced the amount of femoral ash/femoral length. Furthermore, major differences between stressed and starved ducks disappeared after de-stressing for 2 days. Studies of bone growth and metabolism may benefit by using this avian model.

Principal components of craniofacial growth for white Philadelphia males and females between 6 and 22 years of age

Three principal components, explaining 83 percent of the common variation for 999 males and females between 6 and 22 years of age, describe ontogenetic patterns of relationship for seven facial dimensions, including sella-nasion, sella-basion, nasion-prosthion, infradentale-menton, articulare-gnathion, gonion-gnathion, and articulare-gonion. Accounting for 65 percent of the variation, a general component associated with both size and shape defines size-required changes in proprotion during growth. Independent patterns of regional variation associated with alveolar remodeling (second component) and condylar growth (third component) describe specific sources of facial modification. Mean multivariate component scores reveal that sexual dimorphism, which progressively favors males over females with age, results from accumulating differences in size and related proportional changes in shape. The timing of the condylar growth spurt, as evident from variation in ramus height, produces secondary dimorphism which diminishes following the adolescent phase in males. Significant age effects are indicated for alveolar remodeling and mandibular growth of the condyle.

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.

Scaling in Tensile "Skeletons": Structures with Scale-Independent Length Dimensions

Skeletal structures that resist only tensile forces can scale differently than compression resisting structures that fail in bending or buckling. The tensile structures examined scalelike simple ropes: length and diameter of the structure are not correlated, and in three of four cases, length is independent of scale or load, but diameter is dependent on scale. These relations suggest that similarity in stress rather than strain, or deformational behavior, is the basis for mechanical adaptation in the gross dimensions of these tensile structures.

Differential long bone growth of children between two months and eleven years of age

Diaphyseal lengths of the humerus, radius, femur and tibia of upper-middle class While children between two months and 11 years of age show positive allometric growth, indicating substantial shape or proportional change. The segments of the lower extremity display greater allometric increase than the humerus and radius; variation in relative growth within each extremity is small and inconsistent. Sex differences are consistent, with slightly greater proportional increases demonstrated for boys. The results suggest that absolute intralimb variation in growth, following a disto-proximo growth or maturity gradient, is due to initial differences in size or scale and not to differences in patterns of growth. Developmental variation between extremities is due to scaling plus variation in relative growth patterns.

Allometric scaling in the dentition of primates and prediction of body weight from tooth size in fossils

Tooth size varies exponentially with body weight in primates. Logarithmic transformation of tooth crown area and body weight yields a linear model of slope 0.67 as an isometric (geometric) baseline for study of dental allometry. This model is compared with that predicted by metabolic scaling (slope = 0.75). Tarsius and other insectivores have larger teeth for their body size than generalized primates do and they are not included in this analysis. Among generalized primates, tooth size is highly correlated with body size. Correlations of upper and lower cheek teeth with body size range from 0.90-0.97, depending on tooth position. Central cheek teeth (P44 and M11) have allometric coefficients ranging from 0.57-0.65, falling well below geometric scaling. Anterior and posterior cheek teeth scale at or above metabolic scaling. Considered individually or as a group, upper cheek teeth scale allometrically with lower coefficients than corresponding lower cheek teeth; the reverse is true for incisors. The sum of crown areas for all upper cheek teeth scales significantly below geometric scaling, while the sum of crown areas for all lower cheek teeth approximates geometric scaling. Tooth size can be used to predict the body weight of generalized fossil primates. This is illustrated for Aegyptopithecus and other Eocene, Oligocene, and miocene primates. Regressions based on tooth size in generalized primates yield reasonable estimates of body weight, but much remains to be learned about tooth size and body size scaling in more restricted systematic groups and dietary guilds.

Organ scaling in mammals: the liver

1. Values for liver weight, in growing and adult male and female mammals, both terrestrial and aquatic, as well as values for hepatic blood flow, blood volume and oxygen consumption are submitted to linear (log-log) regression analysis. 2. The slope of the regression line for liver weight on adult body weight in adult mammals was found to be 0.886. No statistically significant difference was found between male and female, nor between terrestrial and aquatic mammals (at the 1% confidence level). 3. Over about four orders of magnitude there is (on present evidence) a tendency for the mammalian liver to grow as about the 0.94 power of body weight (pre- and post-natal). 4. The slopes of the regression lines for hepatic blood flow, blood volume and oxygen consumption were found to be 0.91, 0.86 and 0.69, respectively. 5. The mean hepatocyte size in fixed tissue of rats was found to be 7400 micrometers 3. 6. It is argued that the slope of the regression line for hepatic oxygen consumption in mammals generally is likely to fall in the range of 0.67-0.77.

Relative growth of the limbs and trunk in the African apes

Examination of relative growth and allometry is important for our understanding of the African apes, as they represent a closely related group of species of increasing body size. This study presents a comparison of ontogenetic relative growth patterns of some postcranial dimensions in Pan paniscus, Pan troglodytes, and Gorilla gorilla. Interspecific proportion differences among the three species are also analyzed. It is stressed that reliable ontogenetic information can only be obtained if subadults are examined-growth data cannot be inferred from static adult scaling. Results indicate that some postcranial relative growth patterns are very similar in the three species, suggesting differential extrapolation of a common growth pattern, whereas for other proportion comparisons the growth trends differ markedly among the species, producing distinct shape differences in the adults. Interspecific shape changes among the three species are characterized by positive allometry of chest girth and negative allometry of body height and leg length. It is suggested that relative decrease of leg length with increasing body size among the African pongids might be expected on biomechanical grounds, in quadrupedal terrestrialism. Relative to body weight or trunk length, the limbs of the bonobo (Pan paniscus) are longer than in the common chimpanzee or the gorilla, with a lower intermembral index. This may most closely resemble the primitive condition for the African apes.

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 intraspecific 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 predictions from regression equations. Evolutionary implications of intraspecific dental allometry are discussed.

An allometric study of the area dentata in the rat and mouse

The volumes of the hilus, stratum granulosum, stratum moleculare and the zones of the stratum moleculare corresponding to the terminal fields of the perforant paths and the ipsilateral-commissural projections have been estimated in the area dentata of Wistar rats and DBA/2J mice, stained according to the Timm technique. The density of granule cells in the stratum granulosum and synaptic contacts in the stratum moleculare have been estimated from low power electron micrographs using stereological techniques. The volume and density parameters have been used to calculate the total number of granule cells and synaptic contacts in the fasciae dentatae of these two species. It is concluded that the number of synaptic contacts is proportional to the volume of the fascia dentata while the number of granule cells is proportional to the surface area of the fascia dentata and that the fasciae dentatae in these two species are isometric forms. The implications of these relationships are discussed with regard to the effect of the size of the fascia dentata on information processing in this structure. A significant difference existed between the ratio of the volumes of the hila and the ratio of the volumes of the fasciae dentatae in the two species studied. However, the volume of the deep zone of the stratum moleculare fasciae dentatae, the terminal zone of the hilar afferents was proportional to the volume of the hilus. The same density of synaptic contacts in the deep zone of the strata molecularia of both species, therefore, indicates a proportionality between the volume of the hilus and the number of synaptic contacts made by the hilar afferents. These observations are discussed with respect to the manner by which the maintenance of the observed proportionalities and the relative differences in the size and number of neurons in the subregions of the area dentata may be involved in the modification of the form and function of this region during phylogenesis.

Postnatal growth allometry of the extremities in Cebus albifrons and Cebus apella: a longitudinal and comparative study

Cebus albifrons and Cebus apella, partially sympatric capuchin monkeys from South America, are known to differ substantially in adult body mass and bodily proportions. C. apella possesses a robust, stocky build in contrast to the more gracile, relatively longer limbed body design of C. alblfrons. Average birth weights and adult body lengths of these two congeners, however, are remarkably similar and do not serve to distinguish them. This study examines longitudinal growth rates and patterns of ontogenetic scaling in the extremities (humerus, radius, hand, femur, tibia, foot) in order to document the nature and magnitude of skeletal changes associated with increasing age and body mass. Our data indicate that the growth rates of the six skeletal components of the limbs differ only slightly and somewhat inconsistently between the two species. Body mass, however, increases at a consistently faster rate in C. apella. Relative to body mass, therefore, the extremities of C. albifrons scale much faster than those of C. apella. This implies that at any given postnatal body mass, C. alblfrons is longer limbed that C. apella. Conversely, C. apella is heavier than C. albifrons at any given limb length or age. We suggest that such differences in body mass distribution are causally related to differences in locomotor behavior and foraging strategies. Specifically, the relatively long-limbed C. albifrons is probably more cursorial and tends to travel longer distances each day than C. apella. C. apella is a much more deliberate quadruped and is also characterized by especially vigorous and powerful foraging and feeding behaviors. We also compare our results to other (mostly cross-sectional) studies of skeletal growth allometry in nonhuman primates.