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.     

Abstracts of papers to be presented at the Fiftieth Annual Meeting of the American Association of physical anthropologists Detroit,Michigan April 22–25, 1981

The critical problem confronting all allometric studies is the choice of an appropriate size variable, especially when body mass or some other measure of total size is unavailable. A method proposed by Jolicoeur (1963a,b) claims to generate an internal size variable by a principal components analysis of the covariance matrix of logarithmically transformed data, from which allometric coefficients can be computed. Despite the current popularity of this method, the precise relationship and degree of compatibility between such multivariate coefficients and the exponent of the bivariate power function (Y = βX^α) is unknown. This study evaluates the comparability and interpretability of allometric values computed by Jolicoeur's procedure and by standard bivariate regressions (least squares and major axis). Two primate data sets with known measures of size were utilized for these purposes: (1) longitudinal growth data from radiographs of two species of capuchin monkeys, Cebus apella and Cebus albifrons; and (2) interspecific osteometric data from a series of adult lemurs, species of prosimians from Madagascar. Consistent differences exist between multivariate and bivariate allometric coefficients for both ontogenetic and static data sets. Multivariate analysis underestimated the coefficients in the former and overestimated them in the latter. The internal size variable generated by principal components analysis is clearly not equivalent to, and hence not a suitable substitute for, known measures of size. Moreover, multivariate coefficients are very sensitive to the composition of variables in a given data set; α values of a variable changed appreciably depending on the other variables included in the analysis. The multivariate coefficients are also sample-specific, and provide misleading biological information when compared between samples (e.g., between species of capuchin monkey). For allometric investigations designed to evaluate scaling parameters relative to total size, alternative analytical solutions to the Jolicoeur method should be considered.     

Allometric disparity in rodent evolution

In this study, allometric trajectories for 51 rodent species, comprising equal representatives from each of the major clades (Ctenohystrica, Muroidea, Sciuridae), are compared in a multivariate morphospace (=allometric space) to quantify magnitudes of disparity in cranial growth. Variability in allometric trajectory patterns was compared to measures of adult disparity in each clade, and dietary habit among the examined species, which together encapsulated an ecomorphological breadth. Results indicate that the evolution of allometric trajectories in rodents is characterized by different features in sciurids compared with muroids and Ctenohystrica. Sciuridae was found to have a reduced magnitude of inter‐trajectory change and growth patterns with less variation in allometric coefficient values among members. In contrast, a greater magnitude of difference between trajectories and an increased variation in allometric coefficient values was evident for both Ctenohystrica and muroids. Ctenohystrica and muroids achieved considerably higher adult disparities than sciurids, suggesting that conservatism in allometric trajectory modification may constrain morphological diversity in rodents. The results provide support for a role of ecology (dietary habit) in the evolution of allometric trajectories in rodents.     

Allometry of egg and hatchling mass in birds and reptiles: roles of developmental maturity, eggshell structure and phylogeny

The factors determining hatchling mass (HM) are investigated in a wide range of birds and reptiles using regression analysis, analysis of covariance and comparative analysis by independent contrasts. In birds, initial egg mass (IEM) at laying is the most important factor affecting HM and phylogenetic relatedness has no significant effects on HM. Developmental maturity of the avian neonates did not affect the proportion of IEM converted into HM. For all reptile species, IEM also significantly affected HM but phylogenetic relatedness did not. By contrast, allometric relationships between IEM and HM in the different orders of reptiles were affected by shell type. The robustness of allometric relationships across taxa in birds and reptiles suggests that there is a physiological link between IEM and HM, which contrasts with that observed for the relationship between egg mass and incubation period. This result has significant implications for the inter-relationships between IEM and embryonic growth, which are discussed for birds and reptiles.     

Evolution of ontogeny in the hippopotamus skull: using allometry to dissect developmental change

Allometry describes the effect of size change on aspects of an organism's form and can be used to summarize the developmental history of growing parts of an animal. By comparing how allometric growth differs between species, it is possible to reveal differences in their pathways of development. The ability to compare and categorize developmental change between species is demonstrated here using morphometric methods. This involves the interspecific statistical comparison of a large number of bivariate relationships that summarize ontogenetic trajectories. These linear ontogenetic trajectories can be modified as they evolve in any of three ways: ontogenetic scaling indicative of change in the duration of growth, lateral shifts indicative of changes in prenatal development, and directional change indicative of novel modes of postnatal growth. I apply this analysis to skulls of the common hippopotamus ( Hippopotamus amphibius ) and the pygmy hippopotamus ( Hexaprotodon liberiensis ). The number of allometric changes falling into each category was statistically determined and Jolicoeur's multivariate generalization of simple allometry was used to provide an overview of cranial variation. For these skulls, directional change was not found to be statistically significant, but ontogenetic scaling and lateral shifts were both common. This indicates that conserved patterns of growth covariance (ontogenetic scaling) can be separated from novel or derived patterns (directional change and/or lateral shifts). This study demonstrates that He. liberiensis is not simply an ontogenetically scaled version of its larger relative. The evolutionary implications of allometric growth variation are discussed in the light of these findings and those of other studies.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 80 , 625–638.     

The effect of allometric partitioning on herbivory tolerance in four species in South China

Herbivory tolerance can offset the negative effects of herbivory on plants and plays an important role in both immigration and population establishment. Biomass reallocation is an important potential mechanism of herbivory tolerance. To understand how biomass allocation affects plant herbivory tolerance, it is necessary to distinguish the biomass allocations resulting from environmental gradients or plant growth. There is generally a tight balance between the amounts of biomass invested in different organs, which must be analyzed by means of an allometric model. The allometric exponent is not affected by individual growth and can reflect the changes in biomass allocation patterns of different parts. Therefore, the allometric exponent was chosen to study the relationship between biomass allocation pattern and herbivory tolerance. We selected four species (Wedelia chinensis, Wedelia trilobata, Merremia hederacea, and Mikania micrantha), two of which are invasive species and two of which are accompanying native species, and established three herbivory levels (0%, 25% and 50%) to compare differences in allometry. The biomass allocation in stems was negatively correlated with herbivory tolerance, while that in leaves was positively correlated with herbivory tolerance. Furthermore, the stability of the allometric exponent was related to tolerance, indicating that plants with the ability to maintain their biomass allocation patterns are more tolerant than those without this ability, and the tendency to allocate biomass to leaves rather than to stems or roots helps increase this tolerance. The allometric exponent was used to remove the effects of individual development on allocation pattern, allowing the relationship between biomass allocation and herbivory tolerance to be more accurately explored. This research used an allometric model to fit the nonlinear process of biomass partitioning during the growth and development of plants and provides a new understanding of the relationship between biomass allocation and herbivory tolerance.     

Early development of marine catfishes (Ariidae): from mouth brooding to the release of juveniles in nursery habitats

The development and allometric growth patterns of the ariid catfishes Cathorops spixii and Cathorops agassizii were studied from neurula embryos to juveniles. The ontogenetic sequence revealed that prior to hatching, embryos of both species are well developed, and their axial and appendicular skeletons are well ossified. Embryos of both species grow slowly longitudinally, but positively allometric growth (growth coefficient, β₁ > 1) was observed in head width and eye diameter. It is hypothesized that these growth patterns might be related to functional priorities for the development of sensory organs, such as the inner ears (otoliths), the Weberian apparatus, eyes and nostrils, during the embryonic period. The first appearance of vertebrae and otoliths, as well as the ossification of otoliths and the Weberian apparatus, occur earlier in embryos of C. agassizii than in embryos of C. spixii. After hatching, mouth‐brooded free embryos of both species grow isometrically. Negatively allometric growth was observed in head width and eye diameter during the yolk‐sac period, which is expected given that the sensory organs are already formed. Free embryos of C. agassizii are distinguishable from those of C. spixii by their larger eyes, longer snouts, longer heads and heavier yolk sacs. The end of the yolk‐sac period is characterized by a direct change from free embryo to juvenile, without a true larval period. The juveniles of the two species can also be distinguished from each other by the larger eyes of C. agassizii compared with C. spixii, as in adult fishes.     

On the vegetative biomass partitioning of seed plant leaves, stems, and roots

A central goal of comparative life-history theory is to derive the general rules governing growth, metabolic allocation, and biomass partitioning. Here, we use allometric theory to predict the relationships among annual leaf, stem, and root growth rates (GL, GS, and GR, respectively) across a broad spectrum of seed plant species. Our model predicts isometric scaling relationships among all three organ growth rates: GL is proportional to GS is proportional to GR. It also provides a conceptual basis for understanding the differences in the absolute amounts of biomass allocated to construct the three organ types. Analyses of a large compendium of biomass production rates across diverse seed plant species provide strong statistical support for the predictions of the theory and indicate that reproductive investments may scale isometrically with respect to vegetative organ growth rates. The general rules governing biomass allocation as indexed by the scaling exponents for organ growth rates are remarkably indifferent to plant size and taxonomic affiliation. However, the allometric "constants" for these relationships differ numerically as a function of phenotypic features and local environmental conditions. Nonetheless, at the level of both inter- and intraspecific comparisons, the same proportional biomass allocation pattern holds across extant seed plant species.     

A morphometric approach to the geographic variation of the terrestrial isopod species Armadillo tuberculatus (Isopoda: Oniscidea)

The terrestrial isopod species Armadillo tuberculatus Vogl, 1876 (Crustacea, Isopoda, Oniscidea) is a widely polymorphic species distributed in the south-central Aegean region (Greece) with a different morph on each island. Variation consists in coloration, size of cuticular tubercules, shape of telson and the shape of the male first pleopod exopodite (secondary sexual character of taxonomic importance). We studied the allometric growth of a cuticular tubercule in 17 populations (for both male and female individuals) and the shape variation of the first male pleopod exopodite in 10 populations using Elliptic Fourier Analysis, in order to test for patterns of intraspecific variation and possible relationships between morphs. In addition, Thin Plate Spline analysis was used for the calculation of the minimum bending energy between different exopodite shapes, which was then used for estimating the minimum spanning network (MSN) connecting them. The different allometric growth rates of the tubercule among island groups were significantly related to island latitude and climatic factors. On the other hand, the clustering of islands and the MSN based on male exopodite shape differences were not related to the palaeogeography of the Aegean region or to the present geographic distances of islands. These results are interpreted as evidence for non-adaptive radiation of the morphs.     

MORPHOLOGICAL EVOLUTION IN MUROID RODENTS I. CONSERVATIVE PATTERNS OF CRANIOMETRIC COVARIANCE AND THEIR ONTOGENETIC BASIS IN THE NEOTROPICAL GENUS ZYGODONTOMYS

Analyses of craniodental measurement data from 15 wild-collected population samples of the Neotropical muroid rodent genus Zygodontomys reveal consistent patterns of relative variability and correlation that suggest a common latent structure. Eigenanalysis of each sample covariance matrix of logarithms yields a first principal component that accounts for a large fraction of the total variance. Variances of subsequent sample principal components are much smaller, and the results of bootstrap resampling together with asymptotic statistics suggest that characteristic roots of the covariance matrix after the first are seldom distinct. The coefficients of normalized first principal components are strikingly similar from sample to sample: inner products of these vectors reveal an average between-sample correlation of 0.989, and the mean angle of divergence is only about eight degrees. Since first principal component coefficients identify the same contrasts among variables as comparisons of relative variability and correlation, we conclude that a single factor accounts for most of the common latent determination of these sample dispersions. Analyses of variance based on toothwear (a coarse index of age) and sex in the wild-collected samples, and on known age and sex in a captive-bred population, reveal that specimen scores on sample first principal components are age- and sex-dependent; residual sample dispersion, however, is essentially unaffected by age, sex, or age × sex interaction. The sample first principal component therefore reflects the covariance among measured dimensions induced by general growth, and its coefficients are interpretable as exponents of postnatal growth allometry. Path-analytic models that incorporate prior knowledge of the equivalent allometric effects of general growth within these samples can be used to decompose the between-sample variance by factors corresponding to other ontogenetic mechanisms of form change. The genetic or environmental determinants of differences in sample mean phenotypes induced by such mechanisms, however, can be demonstrated only by experiment.     

Canonical rules for plant organ biomass partitioning and annual allocation

Here we review a general allometric model for the allometric relationships among standing leaf, stem, and root biomass (M(L), M(S), and M(R), respectively) and the exponents for the relationships among annual leaf, stem, and root biomass production or "growth rates" (G(L), G(S), and G(R), respectively). This model predicts that M(L) ∝ M(S)(3/4) ∝ M(R)(3/4) such that M(S) ∝ M(R) and that G(L) ∝ G(S) ∝ G(R). A large synoptic data set for standing plant organ biomass and organ biomass production spanning ten orders of magnitude in total plant body mass supports these predictions. Although the numerical values for the allometric "constants" governing these scaling relationships differ between angiosperms and conifers, across all species, standing leaf, stem, and root biomass, respectively, comprise 8%, 67%, and 25% of total plant biomass, whereas annual leaf, stem, and root biomass growth represent 30%, 57%, and 13% of total plant growth. Importantly, our analyses of large data sets confirm the existence of scaling exponents predicted by theory. These scaling "rules" emerge from simple biophysical mechanisms that hold across a remarkably broad spectrum of ecologically and phyletically divergent herbaceous and tree-sized monocot, dicot, and conifer species. As such, they are likely to extend into evolutionary history when tracheophytes with the stereotypical "leaf," "stem," and "root" body plan first appeared.     

Ontogenetic allometry of the digital rays of the leopard gecko (Gekkota: Eublepharidae; Eublepharis macularius)

The role of allometry in producing the variation in autopodial morphology observed among the lizards is not well understood. Allometry of metapodial and digit lengths in the manus and pes of the primitively padless gekkotan (Eublepharis macularius) is explored using maximum‐likelihood repeated‐measures ANCOVAs with body length as the covariate. Estimated variance–covariance matrices differed significantly within and between autopodia, and integration was stronger among the metapodials than the digits. The first metapodial and the first digit of each autopodium exhibit the strongest covariances with each of the remaining components in each variance–covariance matrix, suggesting that the lengths of the first rays are important for allometric integration of both manus and pes. Metapodials scale isometrically and digits negatively allometrically; both display allometric heterogeneity among themselves in both autopodia. Both autopodia exhibit changes in proportion over the ontogenetic size range, attributable to variation in scaling among the components of the rays. Allometric coefficients do not vary among pedal digits, despite differences in phalanx number, although phalanx number is associated with differences in slope in the manual digits. This is suggestive of heterogeneity in allometry among the manual phalanges, which thus may be associated with variation in phalanx length within gekkotan digits.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

Comparative methods with sampling error and within-species variation: contrasts revisited and revised

Comparative methods analyses have usually assumed that the species phenotypes are the true means for those species. In most analyses, the actual values used are means of samples of modest size. The covariances of contrasts then involve both the covariance of evolutionary changes and a fraction of the within-species phenotypic covariance, the fraction depending on the sample size for that species. Ives et al. have shown how to analyze data in this case when the within-species phenotypic covariances are known. The present model allows them to be unknown and to be estimated from the data. A multivariate normal statistical model is used for multiple characters in samples of finite size from species related by a known phylogeny, under the usual Brownian motion model of change and with equal within-species phenotypic covariances. Contrasts in each character can be obtained both between individuals within a species and between species. Each contrast can be taken for all of the characters. These sets of contrasts, each the same contrast taken for different characters, are independent. The within-set covariances are unequal and depend on the unknown true covariance matrices. An expectation-maximization algorithm is derived for making a reduced maximum likelihood estimate of the covariances of evolutionary change and the within-species phenotypic covariances. It is available in the Contrast program of the PHYLIP package. Computer simulations show that the covariances are biased when the finiteness of sample size is not taken into account and that using the present model corrects the bias. Sampling variation reduces the power of inference of covariation in evolution of different characters. An extension of this method to incorporate estimates of additive genetic covariances from a simple genetic experiment is also discussed.     

Growth of organ systems of Dentex dentex(L) and Psetta maxima(L) during larval development

Growth in volume of common dentex Dentex dentex and turbot Psetta maxima during larval development was studied by means of a quantitative histological method. A two‐phase pattern of volume increase was recorded for both species, turbot volume being always higher than dentex volume. During the first phase, the increase was small but during the second phase volume rose sharply from 22 days post hatch (dph) and 17 dph onwards in dentex and turbot, respectively. In dentex, the specific growth rate ( G ) of the whole larva as well as that of all the structures studied (nervous tissue, trunk musculature, digestive tract, liver, pancreas, spleen and thymus) was always higher during the second phase, whereas in turbot, only total volume of the larva, trunk musculature and nervous tissue had a higher G during the same period. The pattern of allometric growth of digestive organs was similar for both species. These organs showed an initial positive allometric growth that later became near‐isometric (digestive tract and liver) or negative (pancreas). In dentex, nervous tissue and trunk musculature showed near‐isometry throughout the period studied. In turbot, nervous tissue exhibited negative allometry and trunk musculature changed from negative to positive allometry. In both species studied, the highest allometry coefficients were recorded for digestive organs before the larva switched to strict exotrophy. This would indicate the importance of the development of these organs for survival.     

Patterns of Phenotypic Divergence in Wing Covariance Structure of Calopterygid Damselflies

Comparing species differences in covariance patterns of traits subject to divergent selection pressures can increase our understanding to the mechanisms of phenotypic divergence. Different species of calopterygid damselflies have diverged in the melanized wing patch of males. This trait serves multiple ecological functions and has behavioral consequences in terms of sexual selection, interspecific interactions, reproductive isolation. We compared the phenotypic variance-covariance matrices (P) of wing traits among nine populations of four European species of calopterygid damselflies. We found modest divergence in covariance structure among populations of the same species, but strong divergence between species. Interestingly, the orientation of the first eigenvector of P (P _max ) differed more between closely related species than between distantly related species, although this pattern was absent when overall covariance structures were compared. We also found that distantly related species but geographically closer had converged towards a similar covariance structure. Finally, divergence in covariance structure was correlated with divergence in wing patch length, but not with other wing traits. This last finding suggests that divergent selection on wing patch length might have affected the stability of P. These results indicate that P might not only reflect ancestral developmental pathways but might also be influenced by current ecology.     

Egg mass and incubation period allometry in birds and reptiles: effects of phylogeny

Here we test the hypothesis that the relationship between egg mass at oviposition (IEM) and incubation period ( I _p) is a function of the taxonomic relatedness of bird and reptile species. Allometric relationships between IEM and I _p were examined for 1525 bird species and 201 reptilian species. Treating species as independent data revealed the allometric exponent linking I _p to IEM to be 0.234 for birds and 0.138 for reptiles. However, ANCOVA revealed that within both birds and reptiles the elevation and slope of the regression lines were dependent on the taxonomic order studied, indicating that the exponents were confounded by the phylogenetic relatedness of species. Thus, allometric exponents were recalculated based on the method of comparative analysis using independent contrasts. This technique revealed that the allometric exponent in both birds and reptiles was confounded by phylogeny. In birds the allometric relationship between I _p and IEM was almost halved to 0.122, whereas in reptiles the exponent increased to 0.185. Importantly, the results demonstrate that some results of allometric analyses can be artefacts of the method of analysis of the dataset. That for bird eggs I _p is not determined in large part by egg mass allows new questions to be posed regarding the ecological and physiological factors affecting the length of incubation, and hence rates of embryonic growth, for different taxa and habitats.     

SIZE-DEPENDENT PHOSPHORUS UPTAKE KINETICS AND CELL QUOTA IN PHYTOPLANKTON1

The allometric equation, y = aX^b, described the interspecific variation of phosphate uptake kinetics and cell quota with phytoplankton cell size and showed that smaller cells are superior in uptake rate to large. Species-specific measurements, made by track autoradiography in phosphorus deficient cultures of communities from a phosphorus-limited lake, revealed that eight different species did not differ significantly in the Michaelis-Menten half-saturation constant, K_m. However, both saturated uptake rates (V_max) and the initial slope of the uptake curve (V_max:K_m) decreased per unit biomass with increasing cell size. Biomass-specific cell phosphorus quotas also decreased with increasing cell volume, but less rapidly than did V_max or V_max: K_m. Comparable data from the literature showed that marine species were superior in phosphorus uptake to freshwater species of similar size, but allometric variation of kinetics appeared to exist within both groups. Together with a variable internal stores model of phosphorus-limited growth, the allometric relationships of uptake kinetics and quotas predicted competition to favor smaller cells, with a differential in growth rate diminishing as competitive intensity increased.