Interspecific Allometry Research Articles

Comparisons Among Biomass Allocation and Spatial Distribution Patterns of Some Vine, Pteridophyte, and Gymnosperm Shoots

The interspecific allometry of leaf, stem, and reproductive biomass distal to stem diameter was determined for a total of 12 angiosperm vine, gymnosperm, and pteridophyte species to compare allocation patterns to vegetative and reproductive shoot organs. The allometry of stem diameter in terms of the distance from shoot apices also was determined to quantify the manner in which vines, gymnosperms, and pteridophyte stems tapered along their length. The stems of vine species were found to weigh more than those of arborescent gymnosperm species distal to any point of equivalent stem diameter. Vine species also distribute more of their stem mass to shoot length as opposed to girth than gymnosperm species. Vine stems also supported proportionally larger leaf and reproductive biomass in comparison to gymnosperm stems of equivalent diameter, yet partitioned their total shoot biomass more or less equally between leaf and stem biomass in the same manner as the gymnosperm species examined. The allometry of vine as well as gymnosperm leaf biomass with respect to stem biomass appeared to be slightly anisometric and negative, suggesting that more massive stems had proportionally less leaf biomass than their smaller, less massive counterparts. Vine stems could be approximated as very slender cones; the shape and geometry of gymnosperm stems complied with those of stubby, truncated cones whose top diameter (for those examined), on the average, equaled 28% of the basal diameter. In general terms, the interspecific allometry of vines was most similar to that of pteridophytes. Collectively, these data refute the commonly held notion that vine stems are simply more slender than those of species with self-supporting stems.

Interspecific Allometries of Critical Buckling Height and Actual Plant Height

Size-dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self-supporting stems ranging in diameter between 0.03 cm ≤ D ≤ 3.0m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species (D < 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species (D ≖ 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size-range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric “rule,” Hcrit/H ≈ 4, appears to govern the evolution of plant size.

Interspecific allometries of critical buckling height and actual plant height

Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self‐supporting stems ranging in diameter between 0.03 cm ≤ D ≤ 3.0m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species (D &lt; 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species (D ≖ 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size‐range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric “rule,” Hcrit/H ≈ 4, appears to govern the evolution of plant size.

Allometry of the Long Bones of Closely Related Macaques

In an attempt to investigate the relationships between ontogenetic, static adult and interspecific allometry, long limb bones of closely related macaques (Macaca mulatta, Macaca fascicularis, Macaca fuscata fuscata and Macaca fuscata yakui) were studied. Sex differences of intralimb allometry were also investigated. Principal component analyses were applied to the maximum length of bones to provide multivariate assessments of relationships between ontogenetic and static adult allometries. Static adult and ontogenetic allometries were different in M. fuscata and M. mulatta, but coincided in M. fascicularis. In interspecific comparison of ontogenetic and static adult allometries, M. fascicularis showed a unique allometric tendency. Analyses of bivariate allometries revealed that sexual dimorphism was a result of ontogenetic scaling (time hypermorphosis). The difference between subspecies of Japanese macaques (M. fuscata fuscata and M. fuscata yakui) was also explained by ontogenetic scaling. A vertical transposition was observed in the ontogenetic patterns of interlimb allometries among the three species. This relationship produced an interspecific positive allometry of the hindlimb compared with the forelimb, which differed from the general trend among nonhuman primates.

Degrees of freedom in interspecific allometry: An adjustment for the effects of phylogenetic constraint

The data used in studies of bivariate interspecific allometry usually violate the assumption of statistical independence. Although the traits of each species are commonly treated as independent, the expression of a trait among species within a genus may covary because of shared common ancestry. The same effect exists for genera within a family and so on up the phylogenetic hierarchy. Determining sample size by counting data points overestimates the effective sample size, which then leads to overestimating the degrees of freedom that should be used in calculating probabilities and confidence intervals. This results in an inflated Type 1 error rate. Although some workers (e.g., Felsenstein [1985] Am. Nat. 125:1-15) have suggested that this issue may invalidate interspecific allometry as a comparative method, a correction for the problem can be approximated with variance components from a nested analysis of variance. Variance components partition the total variation in the data set among the levels of the nested hierarchy. If the variance component for each nested level is weighted by the number of groups at that level, the sum of these values is an estimate of an effective sample size for the data set which reflects the effects of phylogenetic constraint. Analysis of two data sets, using taxonomy to define levels of the nested hierarchy, suggests that it has been common for published studies of interspecific allometry to severely overestimate the number of degrees of freedom. Interspecific allometry remains an important comparative method for evaluating questions concerning individual species that are not similarly addressed by the format of most of the newer comparative methods. With the correction proposed here for estimating degrees of freedom, the major statistical weakness of the procedure is substantially reduced.

Relations between song repertoire size and the volume of brain nuclei related to song: comparative evolutionary analyses amongst oscine birds

Song and brain structure are compared amongst 41 species of oscine birds by using the method of independent evolutionary contrasts. We find a significant correlation between the relative volume of the song control centre, the high vocal centre (HVC), and the number of song types typically found in the repertoire. Relative HVC volume is not correlated with the number of different syllable types per song bout. The relative volume of a second song nucleus, area X, is not significantly correlated with either measure. Relative HVC volume is uncorrelated with relative volume of the hippocampus, a brain area involved in other forms of memory. This is the first evidence for repeated independent evolution of an association between complexity of learned song and the relative volume of one of the song control nuclei though to be involved in song learning.

Multivariate allometry of the robust australopithecine zygomatic foramen: Bootstrap approach to confidence limits

The oddly rounded and disproportionate temporal fossa (or zygomatic foramen) in hyper-robust australopithecine fossils has elicited comment. Is this feature a scaled, positively-allometric version of hominoid anatomy in general or a unique adaptation? Multivariate allometry employing log principal component analysis is directed at the question, but confidence limits of the sampling error associated with these estimates are either dependent upon questionable multivariate theory or else unattainable by theory. The bootstrap method is therefore employed to estimate these aspects of dispersion. The size and shape of the hyper-robust australopithecine zygomatic foramen cannot be explained by simple extrapolation of primate interspecific allometries; although the positively and negatively allometric aspects of scaling are similar, the actual coefficients of scaling are significantly larger in the crucial variable in the australopithecines.

Small size and monogamy: spatial organization of Blanford's foxes, Vulpes cana

Interspecific comparisons between canids suggest allometries in the characteristics of neonates, such that species with lower body weights tend to produce relatively heavy neonates, in relatively small litters whose combined weight is relatively low. Canids weighing less than 6 kg have generally been reported as monogamous with occasional polygyny; on the basis of a parental investment hypothesis, the interspecific allometries suggest that the smallest canids have the greatest tendency to be polygynous. This prediction was explored by studying Blanford's foxes, which at ca 1 kg are lighter than any previously studied. Data from 11 radio-tracked foxes studied over 2 years indicated that they were organized as strictly monogamous pairs in territories of about 1·6 km 2 which overlapped minimally. Three out of five territories contained a single non-breeding yearling female during the mating season, but there was no evidence of polygyny. It is suggested that the departure of Blanford's fox from the allometric trends can best be explained in terms of adaptations to its habitat rather than as a direct consequence of small size.

Interspecific allometry of the mandible, dental arch, and molar area in anthropoid primates: Functional morphology of masticatory components

Allometric equations relating the lengths and widths of the mandible and dental arch, and of molar area, were obtained in a wide range of anthropoid primates grouped into four subsets, pongids, cercopithecids, nonmarmoset platyrrhines, and marmosets. Mandibular width is negatively allometric against length across anthropoids but cercopithecids had relatively wider mandibles than nonmarmosets of the same size class. Mandibular length relative to dental arch length was isometric within and between the four groups but dental arch width scaled negatively against all the other dimensions examined in this study, indicating a functional dissociation between the dental arcade and the bony mandible. Molar area showed various scaling patterns relative to mandibular length (isometry) and width (positive). There were no parameters that scaled positively against body weight across groups, except for molar area in cercopithecids (strongly) and nonmarmoset (moderately). Notable functional specializations include relatively long dental arches in cercopithecoids, related to large, elongate bilophodont molars, and the tendency to increase relative jaw length across the range of anthropoid sizes, reflecting negative allometry of the brain (cranial bicondylar width). We caution that various allometry and functional patterns may be masked by generalizing from broad taxonomic comparison involving a large sweep of adaptative patterns.

The functional morphology of weight bearing: limb joint surface area allometry in anthropoid primates

Biomechanical scaling of long bone joint surface areas was investigated in 13 species of anthropoid primates. It was proposed that joint surface areas should scale with positive allometry with respect to body size in order to maintain relatively constant safety factors for joints in small and large animals and that modifications from the overall pattern of scaling may be expected in the limb joints of species exhibiting specialized locomotor behaviours that radically alter limb loading. Within anthropoids, the brachiating primates, white‐handed gibbons (Hylobates lar) and black‐handed spider monkeys (Ateles geoffroyi), were used to test this hypothesis. Total joint surface areas were found to scale with significant positive allometry in 11 of 12 limb joints. The observed pattern of interspecific allometry supports the hypothesis that weight bearing is a major constraint on the design of joints. This positive interspecific allometry is reflected at the intraspecific level as well, with larger joints of larger species showing significant intraspecific scaling. Suspensory species showed no significant deviations from the overall anthropoid pattern, despite their reduced compressive loading of the limb joints, even after controlling for joint mobility. These results suggest that, while evolutionary changes in locomotor behaviour that produce significant increases in loading of a joint may be accompanied by selection for increased joint surface areas, adoption of locomotor repertoires that reduce limb loading may have no selective effect on joint morphology, and joint design in these cases will reflect the biomechanics of the ancestral locomotor condition.

The Interspecific Allometry of Reproduction: Do Larger Species Invest Relatively Less in Their Offspring?

The cumulative amount of energy that a female invests (maternal energy investment, MI) in her young largely determines their survival and her fitness. To date much of the theory addressing the interspecific allometry of MI against body weight in mammals has been on the per unit time basis. However, the allometry of MI across a reproductive event or lifetime provides a more useful theoretical insight into constraints on MI across species of different body sizes. Two theoretical models are presented which describe the interspecific allometry of energy a female mammal allocates to MI per reproductive event and during her lifetime, in relation to her body size. If it is assumed that a female's weight changes little during her reproductive lifespan then these models predict that the energy devoted to MI should scale at approximately 1 with body weight. In contrast to the predictions of previous authors, these models predict that females of larger species invest a similar proportion of their energy to MI as do those of smaller species.

LONG-TERM CORRELATED RESPONSE, INTERPOPULATION COVARIATION, AND INTERSPECIFIC ALLOMETRY.

A model of long-term correlated evolution of multiple quantitative characters is analyzed, which partitions selection into two components: one stabilizing and the other directional. The model assumes that the stabilizing component is less variable than the directional component among populations. The major result is that, within a population, the responses of characters to selection in the short term differ qualitatively from those in the long term. In the short term, the responses depend on genetic correlations between characters, but in the long term they are only determined by the fitness functions of stabilizing and directional selection, independent of genetic and phenotypic correlations. Treating the stabilizing component as a constant and assuming the directional component to vary among populations, I present formulas for the interpopulation covariation and interspecific allometry, which are functions of the intensity matrix of stabilizing selection. Particular attention is paid to the relationship between intra- and interpopulation correlations.

Long-Term Correlated Response, Interpopulation Covariation, and Interspecific Allometry

Long-Term Correlated Response, Interpopulation Covariation, and Interspecific Allometry

Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy-use

Global regressions of ecological population densities on body mass for mammals and for terrestrial animals as a whole show that local population energy-use is approximately independent of adult body mass—over a body mass range spanning more than 11 orders of magnitude. This independence is represented by the slope of the regressions approximating –0.75, the reciprocal of the way that individual metabolic requirements scale with body mass. The pattern still holds for mammalian primary consumers when the data are broken down by geographic area, by broad habitat-type and by individual community. Slopes for mammalian secondary consumers are also not statistically distinguishable from –0.75. For any given body mass temperate herbivores maintain on average population densities of 1.5 to 2.0 times those of tropical ones, though slopes do not differ. Terrestrial animals of all sizes exhibit approximately the same range of population energy-use values. These results agree with those reported for population energy-budgets. It is suggested that rough independence of body mass and the energy-use of local populations is a widespread rule of animal ecology and community structure.

Ecological significance of hypometabolism in nonhuman primates: allometry, adaptation, and deviant diets.

The "Kleiber relationship" describes the interspecific allometry between body size and metabolism. Like other allometric relationships, the Kleiber relationship not only summarizes scaling effects across species but also provides a standard by which species can be compared. One well-noted deviation from the Kleiber relationship is "hypometabolism": metabolic rates below that expected for a given size. It has been suggested in the literature that hypometabolism may be a primitive mammalian trait, a thermoregulatory adaptation, an adaptation to arboreal folivory, or an adaptation to a diet that is deviant for body size. Data on primate physiology and behavior are used to evaluate these hypotheses. Only the deviant-diet hypothesis is supported by the data on nonhuman primates. Indeed, the Jarman-Bell relationship, which is the basis for this hypothesis, provides a more coherent explanation of correlated features of animal physiology and behavior than do the alternative models. Hypometabolism may be an energy-conserving adaptation to a variety of nutritional stresses. The present analysis underscores the point that metabolic rate, like foraging behavior, should be thought of as evolutionarily labile.

Intra- and Interspecific Allometry of Oxygen Consumption in Snakes

where P is energy metabolism per unit time (power), M is body mass, a and b are the mass coefficient and the mass exponent, respectively. Usually, a and b are determined by linear regression of the variables P and M. Comparison between adult representatives of species that differ widely in size yielded an interspecific allometric equation in which b approximated 0.75 (Kleiber, 1932; Brody, 1945; Hemmingsen, 1960). Following Kleiber's (1965) suggestion, the 3 mass exponent has been applied indiscriminately to both intraand interspecific comparisons. Heusner (1982a, b, 1983), challenged the common acceptance of b = 0.75. He questioned both the underlying assumption and the theoretical implication of the regression analysis by which this value was derived, and suggested a mass exponent of % as the appropriate value for intraspecific compari-

Postnatal ontogeny of the musculo‐skeletal system in the Black‐tailed jack rabbit (Lepus californicus)

The ontogeny of 23 postcranial skeletal dimensions, mechanical properties of the third metatarsal and the femur, and the isometric contractile properties of the gastrocnemius muscle were measured in a complete postnatal growth series of the highly cursorial hare Lepus californicus. Newborn hares are handicapped by short limbs, relatively weak muscles and bone tissue, and shorter muscular contractile distances. However, during growth these deficiencies are rapidly overcome. Hind limb length and gastrocnemius contractile distance undergo positive allometry, scaling as (body mass)0·39 and (body mass)0·41, respectively. The mechanical advantage of the gastrocnemius lever system experiences negative allometry (a(body mass)‐0·12), giving young hares larger advantage around their joints. This, combined with initial positive allometry of gastrocnemius contractile force (α(body mass) 1·23) and subsequent negative allometry of contractile force (α(body mass)0·61), results in the production of relatively greater propulsive forces transmitted from the foot to the ground in juveniles than in adults. In addition, the second moment of area of the metatarsal is relatively large in younger animals, and scales in such a way that during the first half of postnatal growth mechanical similarity is maintained between the breaking moment of the bone (α(body mass)1·50) and the moment imposed on the bone by the gastrocnemius (a(body mass)l·54). These ontogenetic changes contribute to the development of a locomotor system which is effective at escape by the time the young hare is only 20% of adult body size, and must forage independently. Differences between the ontogenetic allometry of Lepus, the interspecific allometry of mammals and the ontogenetic allometry of reptiles are noted and considered in a phylogenetic context.

Phyletic size change and brain/body allometry: A consideration based on the African pongids and other primates

A problematic aspect of brain/body allometry is the frequency of interspecific series which exhibit allometry coefficients of approximately 0.33. This coefficient is significantly lower than the 0.66 value which is usually taken to be the interspecific norm. A number of explanations have been forwarded to account for this finding. These include (1) intraspecificallometry explanations, (2) nonallometric explanations, and (3) Jerison’s “extraneurons” hypothesis, among others. The African apes, which exhibit a lowered interspecific allometry coefficient, are used here to consider previous explanations. These are found to be inadequate in a number of ways, and an alternative explanation is proposed. This explanation is based on patterns of brain and body size change during ontogeny and phytogeny. It is argued that the interspecific allometry coefficient in African apes parallels the intraspecific one because similar ontogenetic modifications of body growth separate large and small forms along each curve. In both cases, body size differences are produced primarily by growth in later postnatal periods, during which little brain growth occurs. Data on body growth, neonatal scaling, and various lifehistory traits support this explanation. This work extends previous warnings that sizecorrected estimates of relative brain size may not correspond very closely to our understanding of the behavioral capacities of certain species in lineages characterized by rapid change in body size.

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.

Adaptation and body size in primates

The present paper is concerned with the phenomenon of interspecific allo metry in primates and its relationship to the concept of adaptation. A metrical study of the primate skull was performed to investigate the extent to which particular dimensions of the primate skull (e. g. foramen magnum area, second lower molar length) can be used as indicators of body size and to analyse the allometric relationships involved in the evolution of specific features (e. g. cranial capacity, foramen magnum size, tooth dimensions). Fourteen standard dimensions were taken from the skulls of 48 nonhuman primate species. The logarithmic relationship between these dimensions and body weight was analysed. Most consistent indicators of body size in living primates are skull length, zygomatic width, condylar area, and foramen magnum area. Brain size and foramen magnum area have both increased by adaptive shifts in primate evolution.