Stem and crown allometry in four congeneric species of dioecious tropical trees

Key message

Congeneric species showed similar stem and crown allometry, but differed in crown dimensions indicating that crown size is adaptive and variable despite mechanical restrictions.

Abstract

Morphological adaptations favor differential use of the space in tropical trees, but the variability in stem and crown allometry can be constrained by phylogenetic and mechanical factors. In addition, dioecious species show marked differences in their energy requirements related to reproduction, but little information is available about the role of shape and allometry on differential acquisition of energy between the sexes. We studied the stem and crown dimensions of congeneric dioecious trees to determine if there are: (i) differences in the allometry between the sexes, (ii) different average sizes among sympatric species, and (iii) differences in stem and crown allometry between sympatric and allopatric species. Two pairs of sympatric Virola (Myristicaceae) in Brazil and Costa Rica were studied. SMA regression models were used to investigate allometric relationships between diameter at breast height (DBH) and tree height, and between DBH and crown volume (CV). No sexual dimorphism in stem and crown morphology was observed in this study, indicating that differences in resource allocation for reproduction between the sexes do not impact the stem and crown structure in these species. Overall, low variability among the species was observed. Only one species differed in stem allometry and none differed in crown allometry. CV differed between sympatric species. Stem and crown allometry are related to structural stability and our results support similar mechanical restriction for these species. The ecological significance of differences in CV among canopy species remains to be explored.

     

Body size and scaling of the hands and feet of prosimian primates

The hands and feet of primates fulfill a variety of biological roles linked with food acquisition and positional behavior. Current explanations of shape differences in cheiridial morphology among prosimians are closely tied to body size differences. Although numerous studies have examined the relationships between body mass and limb morphology in prosimians, no scaling analysis has specifically considered hand and foot dimensions and intrinsic proportions. In this study, we present such an analysis for a sample of 270 skeletal specimens distributed over eight prosimian families. The degree of association between size and shape was assessed using nonparametric correlational techniques, while the relationship between each ray element length and body mass (from published data and a body mass surrogate) was tested for allometric scaling. Since tarsiers and strepsirrhines encompass many taxa of varying degrees of phylogenetic relatedness, effective degrees of freedom were calculated, and comparisons between families were performed to partially address the problem of statistical nonindependence and "phylogenetic inertia." Correlational analyses indicate negative allometry between relative phalangeal length (as reflected by phalangeal indices) and body mass, except for the pollex and hallux. Thus, as size increases, there is a significant decrease in the relative length of the digits when considering all prosimian taxa sampled. Regression analyses show that while the digital portion of the rays scales isometrically with body mass, the palmar/plantar portion of the rays often scales with positive allometry. Some but not all of these broadly interspecific allometric patterns remain statistically significant when effective degrees of freedom are taken into account. As is often the case in interspecific scaling, comparisons within families show different scaling trends in the cheiridia than those seen across families (i.e., lorisids, indriids, and lemurids exhibit rather different allometries). The interspecific pattern of positive allometry that appears to best characterize the metapodials of prosimians, especially those of the foot, parallels differences found in the morphology of the volar skin. Indeed, relatively longer metapodials appear to covary with flatter and more coalesced volar pads, which in turn slightly improve frictional force for animals that are at a comparative disadvantage while climbing because of their larger mass. Despite the essentially isometric relationship found between digit length and body mass across prosimians, examination of the residual variation reveals that tarsiers and Daubentonia possess, relative to their body sizes, remarkably long fingers. Such marked departures between body size and finger length observed in these particular primates are closely linked with specialized modes of prey acquisition and manipulation involving the hands.     

Limb morphology of domestic and wild canids: the influence of development on morphologic change

Biomechanical hypotheses are often invoked to explain the characteristic scaling of limb proportions. Patterns of static allometry and morphologic diversity, however, may also reflect the developmental mechanisms underlying morphologic change. In this study I document the importance of such developmental influences on the evolution of limb morphology in the extremely polymorphic domestic dog and in wild canid species. I use bivariate and discriminant function analyses to compare the limb morphology of adult dogs and wild canid species. I then compare ontogenetic allometry of four dog breeds with static allometry of domestic and wild canids. Results reveal, first, that there is considerable similarity between dogs and wild canid species; many wolf-like canids cannot be distinguished from domestic dogs of equivalent size. However, all dogs are consistently separated from fox-sized, wild canids by subtle but evolutionarily significant differences in olecranon, metapodial, and scapula morphology. Second, in domestic dogs the pattern of static allometry is nearly identical to that of ontogenetic allometry. This finding can be attributed to simple heterochronic alterations of postnatal growth rates. Apparently the diversity of limb proportions among adult domestic dogs and the observed difference between dogs and wild canids are somewhat predetermined, as they directly reflect the diversity of limb proportions evident during development of the domestic dog.     

Ontogeny, phylogeny, and morphology in anuran larvae: morphometric analysis of cranial development and evolution in Rana tadpoles (Anura: Ranidae)

Comparative studies of chondrocranial morphology in larval anurans are typically qualitative in nature, focusing primarily on discrete variation or gross differences in the size or shape of individual structures. Detailed data on chondrocranial allometry are currently limited to only two species, Rana sylvatica and Bufo americanus. This study uses geometric morphometric and multivariate statistical analyses to examine interspecific variation in both larval chondrocranial shape and patterns of ontogenetic allometry among six species of Rana. Variation is interpreted within the context of hypothesized phylogenetic relationships among these species. Canonical variates analyses of geometric morphometric datasets indicate that species can be clearly discriminated based on chondrocranial shape, even when whole ontogenies are included in the analysis. Ordinations and cluster analyses based on chondrocranial shape data indicate the presence of three primary groupings (R. sylvatica; R. catesbeiana + R. clamitans; and R. palustris + R. pipiens + R. sphenocephala), and patterns of similarity closely reflect phylogenetic relationships. Analysis of chondrocranial allometry reveals that some patterns are conserved across all species (e.g., most measurements scale with negative allometry, those associated with the posterior palatoquadrate tend to scale with isometry or positive allometry). Ontogenetic scaling along similar allometric trajectories, lateral transpositions of individual trajectories, and variable allometric relationships all contribute to shape differences among species. Overall patterns of similarity among ontogenetic trajectories also strongly reflect phylogenetic relationships. Thus, this study demonstrates a tight link between ontogeny, phylogeny, and morphology, and highlights the importance of including both ontogenetic and phylogenetic data in studies of chondrocranial evolution in larval anurans.     

Evidence at hand: Diversity, functional implications, and locomotor prediction in intrinsic hand proportions of diprotodontian marsupials

Knowledge about the diversity, locomotor adaptations, and evolution of the marsupial forelimb is limited, resulting in an underrepresentation of marsupials in comparative anatomical literature on mammalian forelimb anatomy. This study investigated hand proportions in the diverse marsupial order Diprotodontia. Fifty-two measurements of 95 specimens representing 47 species, as well as 6 non-diprotodontian specimens, were explored using principal components analysis (PCA). Bootstrapping was used to assess the reliability of the loadings. Phylogenetically independent contrasts and phylogenetic ANOVA were used to test for correlation with size and functional adaptation of forelimbs for locomotor habit, scored as arboreal vs. terrestrial. Analysis of first principal component (PC1) scores revealed significant differences between arboreal and terrestrial species, and was related to relative slenderness of their phalangeal elements. Both locomotor groups displayed allometry along PC1 scores, but with different intercepts such that PC1 discriminated between the two locomotor habits almost completely. PC2 separated some higher-level clades and burrowing species. Analysis of locomotor predictors commonly applied by palaeontologists indicates that ratios between proximal and intermediate phalanges were unsuitable as predictors of arboreality/terrestriality, but the phalangeal index was more effective. From PCA results, a phalangeal slenderness ratio was developed which proved to be a useful discriminator, suggesting that a single unallocated phalanx can be used for an impression of locomotor mode in fossils. Most Diprotodontia are laterally paraxonic or ectaxonic, with the exception of digging species whose hands are medially paraxonic. Our results complement those of studies on placental mammals, suggesting that the demands of arboreality, terrestriality, or frequent digging on intrinsic hand proportions are met with similar anatomical adaptations in marsupials.     

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.     

Tree height–diameter allometry across the United States

The relationship between tree height and diameter is fundamental in determining community and ecosystem structure as well as estimates of biomass and carbon storage. Yet our understanding of how tree allometry relates to climate and whole organismal function is limited. We used the Forest Inventory and Analysis National Program database to determine height–diameter allometries of 2,976,937 individuals of 293 tree species across the United States. The shape of the allometric relationship was determined by comparing linear and nonlinear functional forms. Mixed‐effects models were used to test for allometric differences due to climate and floristic (between angiosperms and gymnosperms) and functional groups (leaf habit and shade tolerance). Tree allometry significantly differed across the United States largely because of climate. Temperature, and to some extent precipitation, in part explained tree allometric variation. The magnitude of allometric variation due to climate, however, had a phylogenetic signal. Specifically, angiosperm allometry was more sensitive to differences in temperature compared to gymnosperms. Most notably, angiosperm height was more negatively influenced by increasing temperature variability, whereas gymnosperm height was negatively influenced by decreasing precipitation and increasing altitude. There was little evidence to suggest that shade tolerance influenced tree allometry except for very shade‐intolerant trees which were taller for any given diameter. Tree allometry is plastic rather than fixed and scaling parameters vary around predicted central tendencies. This allometric variation provides insight into life‐history strategies, phylogenetic history, and environmental limitations at biogeographical scales.     

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. © 1994 Wiley-Liss, Inc.     

Growth and allometry of external morphology in Darwin's finches (Geospiza) on Isla Daphne Major, Galapagos

Seven widely used avian external morphological measurements were examined, mainly in Geospiza fortis and G. scandens on Isla Daphne Major, Galapagos. Geospiza grow more slowly than other "finches", and smaller Geospiza species grow relatively more slowly than larger Geospiza . Weight, wing chord and tarsus grow quickly, while bill characters grow more slowly. This pattern of relative growth (dynamic allometry) is reversed in the static allometry of adults, where bill characters, particularly bill depth in G. fortis , display strong, positive allometry with respect to weight, wing and tarsus. Static allometric patterns help explain differences in the size, shape and relative variability of different characters in adults, as well as the results of multivariate analyses such as principal components or canonical variates. Several different multivariate techniques arrange five Geospiza populations in a consistent two-dimensional morphological space, with a major axis of overall "body-size", and a minor axi of "bill-pointedeness". An alternative analysis of dynamic and static allometry is also provided, based on multivariate techniques.     

Ordinary least squares regression is indicated for studies of allometry

When it comes to fitting simple allometric slopes through measurement data, evolutionary biologists have been torn between regression methods. On the one hand, there is the ordinary least squares (OLS) regression, which is commonly used across many disciplines of biology to fit lines through data, but which has a reputation for underestimating slopes when measurement error is present. On the other hand, there is the reduced major axis (RMA) regression, which is often recommended as a substitute for OLS regression in studies of allometry, but which has several weaknesses of its own. Here, we review statistical theory as it applies to evolutionary biology and studies of allometry. We point out that the concerns that arise from measurement error for OLS regression are small and straightforward to deal with, whereas RMA has several key properties that make it unfit for use in the field of allometry. The recommended approach for researchers interested in allometry is to use OLS regression on measurements taken with low (but realistically achievable) measurement error. If measurement error is unavoidable and relatively large, it is preferable to correct for slope attenuation rather than to turn to RMA regression, or to take the expected amount of attenuation into account when interpreting the data.     

Comparing phylogenetic signal in intraspecific and interspecific body size datasets

Phylogenetic comparative methods have become a standard statistical approach for analysing interspecific data, under the assumption that traits of species are more similar than expected by chance (i.e. phylogenetic signal is present). Here I test for phylogenetic signal in intraspecific body size datasets to evaluate whether intraspecific datasets may require phylogenetic analysis. I also compare amounts of phylogenetic signal in intraspecific and interspecific body size datasets. Some intraspecific body size datasets contain significant phylogenetic signal. Detection of significant phylogenetic signal was dependant upon the number of populations (n) and the amount of phylogenetic signal (K) for a given dataset. Amounts of phylogenetic signal do not differ between intraspecific and interspecific datasets. Further, relationships between significance of phylogenetic signal and sample size and amount of phylogenetic signal are similar for intraspecific and interspecific datasets. Thus, intraspecific body size datasets are similar to interspecific body size datasets with respect to phylogenetic signal. Whether these results are general for all characters requires further study.     

On a polyploid complex of freshwater snails (Planorbidae: Bulinus) in Ethiopia

Allometric growth of the postembryonic stages of Ectobius lapponicus (Linn.) and E. panzeri Stephens is described and analysed. Alternative methods of computing the allometric growth equation are discussed and applied, with the necessary significance tests, to a large number of skeletal structures in all developmental stages of each sex. The validity of Dyar's Law and its modifications are assessed quantitatively.  

Summary:

The growth in linear dimensions of 74 exosketetal structures has been studied quantitatively in all instars of both sexes of Ectobius lapponicus and E. panzeri.
Almost all the investigated structures show some statistically significant degree of allometric growth, but relatively few of them grow by simple allometry. Some possible reasons for this are indicated.
Well-defined growth gradients exist in the appendages and along the main axis of the body. Allometric growth contours, showing sexual and specific differences, express the temporal and spatial variations in the allometric growth ratio.
The limitations of Dyar's Law and Przibram's Rule are discussed and it is shown that conformity with Dyar's Law is not improved by allowing for differences in the duration of the instars.
It is emphasized that allometric growth studies should involve the choice of a suitable reference dimension and the selection of an appropriate statistical model to which the growth data are fitted. The estimation of the allometry parameters a and b , as well as the appropriate significance tests, depend on the model chosen, though the two models compared in this study do not yield appreciably different estimates.     

A support vector machine based test for incongruence between sets of trees in tree space

ABSTRACT: BACKGROUND: The increased use of multi-locus data sets for phylogenetic reconstruction has increased the need to determine whether a set of gene trees significantly deviate from the phylogenetic patterns of other genes. Such unusual gene trees may have been influenced by other evolutionary processes such as selection, gene duplication, or horizontal gene transfer. RESULTS: Motivated by this problem we propose a nonparametric goodness-of-fit test for two empirical distributions of gene trees, and we developed the software GeneOut to estimate a p-value for the test. Our approach maps trees into a multi-dimensional vector space and then applies support vector machines (SVMs) to measure the separation between two sets of pre-defined trees. We use a permutation test to assess the significance of the SVM separation. To demonstrate the performance of GeneOut, we applied it to the comparison of gene trees simulated within different species trees across a range of species tree depths. Applied directly to sets of simulated gene trees with large sample sizes, GeneOut was able to detect very small differences between two set of gene trees generated under different species trees. Our statistical test can also include tree reconstruction into its test framework through a variety of phylogenetic optimality criteria. When applied to DNA sequence data simulated from different sets of gene trees, results in the form of receiver operating characteristic (ROC) curves indicated that GeneOut performed well in the detection of differences between sets of trees with different distributions in a multi-dimensional space. Furthermore, it controlled false positive and false negative rates very well, indicating a high degree of accuracy. CONCLUSIONS: The non-parametric nature of our statistical test provides fast and efficient analyses, and makes it an applicable test for any scenario where evolutionary or other factors can lead to trees with different multi-dimensional distributions. The software GeneOut is freely available under the GNU public license.     

Scaling of Sexual Dimorphism in Body Mass: A Phylogenetic Analysis of Rensch's Rule in Primates

We examined the relationship between body mass dimorphism, measured as the natural logarithm of the male/female ratio, and body mass, defined as ln (female mass), with interspecific allometry, phylogenetically independent contrasts, and phylogenetic autocorrelation in 105 primate species. We repeated the analyses for Strepsirhini (N = 23), Haplorhini (N = 82), Platyrrhinii (N = 32), and Catarrhini (N = 47). With independent contrasts, there is statistically significant (p < .05) positive allometry in Primates in general, Haplorhini, and Catarrhini, but not in Strepsirhini or Platyrrhini. The steepest slope (0.134) is for Catarrhini. Results differed when we conducted analyses with traditional interspecific allometry. For example, not only was the Catarrhini slope not statistically significant but also the magnitude of the slope was shallower than that of all other groups, except Strepsirhini. The results indicate that phylogenetic effects influence the scaling of sexual size dimorphism, and that the statistical method used has a large impact on the interpretation of this biological relationship. We discuss issues involved in applying these statistical methods in detail.     

Phylogenetic interpretation of ontogenetic change: sorting out the actual and artefactual in an empirical case study of centrarchid fishes

Hypothesized relationships between ontogenetic and phylogenetic change in morphological characters were empirically tested in centrarchid fishes by comparing observed patterns of character development with patterns of character evolution as inferred from a representative phylogenetic hypothesis. This phylogeny was based on 56–61 morphological characters that were polarized by outgroup comparison. Through these comparisons, evolutionary changes in character ontogeny were categorized in one of eight classes (terminal addition, terminal deletion, terminal substitution, non-terminal addition, non-terminal deletion, non-terminal substitution, ontogenetic reversal and substitution). The relative frequencies of each of these classes provided an empirical basis from which assumptions underlying hypothesized relationships between ontogeny and phylogeny were tested. In order to test hypothesized relationships between ontogeny and phylogeny that involve assumptions about the relative frequencies of terminal change (e.g. the use of ontogeny as a homology criterion), two additional phylogenies were generated in which terminal addition and terminal deletion were maximized and minimized for all characters. Character state change interpreted from these phylogenies thus represents the maxima and minima of the frequency range of terminal addition and terminal deletion for the 8.7 × 10³⁶ trees possible for centrarchids. It was found for these data that terminal change accounts for c. 75% of the character state change. This suggests either that early ontogeny is conserved in evolution or that interpretation and classification of evolutionary changes in ontogeny is biased in part by the way that characters are recognized, delimited and coded. It was found that ontogenetic interpretation is influenced by two levels of homology decision: an initial decision involving delimitation of the character (the ontogenetic sequence), and the subsequent recognition of homologous components of developmental sequences. Recognition of phylogenetic homology among individual components of developmental sequences is necessary for interpretation of evolutionary changes in ontogeny as either terminal or non-terminal. If development is the primary criterion applied in recognizing individual homologies among parts of ontogenetic sequences, the only possible interpretation of phylogenetic differences is that of terminal change. If homologies of the components cannot be ascertained, recognition of the homology of the developmental sequence as a whole will result in the interpretation of evolutionary differences as substitutions. Particularly when the objective of a study is to discover how ontogeny has evolved, criteria in addition to ontogeny must be used to recognize homology. Interpretation is also dependent upon delimitation within an ontogenetic sequence. This is in part a function of the way that an investigator ‘sees’ and codes characters. Binary and multistate characters influence interpretation differently and predictably. The use of ontogeny for determining phylogenetic polarity as previously proposed rests on the assumptions that ancestral ontogenies are conserved and that character evolution occurs predominantly through terminal addition. It was found for these data that terminal addition may comprise a maximum of 51.9% of the total character state change. It is concluded that the ontogenetic criterion is not a reliable indicator of phylogenetic polarity. Process and pattern data are collected simultaneously by those engaged in comparative morphological studies of development. The set of alternative explanatory processes is limited in the process of observing development. These form necessary starting points for the research of developmental biologists. Separating ‘empirical’ results from interpretational influences requires awareness of potential biases in the course of character selection, coding and interpretation. Consideration of the interpretational problems involved in identifying and classifying phylogenetic changes in ontogeny leads to a re-evaluation of the purpose, usefulness and information conveyed by the current classification system. It is recommended that alternative classification schemes be pursued.     

Phylogenetic analysis of sexual dimorphism and eye-span allometry in stalk-eyed flies (Diopsidae)

Eye stalks and their scaling relationship with body size are important features in the mating system of many diopsid species, and sexual selection is a critical force influencing the evolution of this exaggerated morphology. Interspecific variation in eye span suggests there has been significant evolutionary change in this trait, but a robust phylogenetic hypothesis is required to determine its rate and direction of change. In this study, the pattern of morphological evolution of eye span is assessed in a phylogenetic framework with respect to its function in the sexual system of these flies. Specifically, we examine within the family Diopsidae the pattern of increase and decrease in sexual dimorphism, the morphological coevolution of eye span between males and females, and the evolutionary flexibility of eye-span allometry. Based on several different methods for reconstructing morphological change, results suggest a general pattern of evolutionary flexibility, particularly for eye-span allometry. Sexual dimorphism in eye span has evolved independently at least four times in the family and this trait also has undergone several reductions within the genus Diasemopsis. Despite most species being dimorphic, there is a strong phylogenetic correlation between males and females for mean eye span. The coevolution between the sexes for eye-span allometry, however, is significantly weaker. Overall, eye-span allometry exhibits significantly more change on the phylogeny than the other morphological traits. The evolutionary pattern in eye-span allometry is caused primarily by changes in eye-span variance. Therefore, this pattern is consistent with recent models that predict a strong relationship between sexual selection and the variance of ornamental traits and highlights the significance of eye-span allometry in intersexual and intrasexual signaling.     

Hydraulic architecture and the evolution of shoot allometry in contrasting climates

We used pairs of congeneric shrub species from contrasting habitats to test for repeated evolutionary divergence in leaf-stem allometry and shoot hydraulic architecture in response to water availability. Allometric relationships and mean ratios between leaf size (individual and total area and mass per shoot) and stem cross-sectional area were compared between habitats using six species pairs representing three genera (Arctostaphylos, Baccharis, Ceanothus). We measured correlations among evolutionary changes in allometric, morphological, and physiological traits using phylogenetic independent contrasts. Allometric analysis revealed habitat differences: slopes were homogeneous among species (=1.46), but the more mesic-adapted species generally supported more leaf area at a common stem cross-sectional area. Reducing bivariate allometry to a ratio obscured this pattern because ratios varied with stem size, which was unrelated to habitat. Mean individual leaf size also was not correlated with either water availability or leaf-stem allometry. Stem hydraulic conductivity was generally lower in the xeric-adapted species of each pair, and its evolution mirrored changes in shoot allometry. This study provides evidence for repeated evolutionary divergence in shoot allometry and hydraulic architecture associated with water availability and demonstrates the importance of shoot allometry to water relations, independent of leaf size.     

The significance of differences between means. An empirical study

Three tests of statistical significance: the confidence interval (C), Student's t, and the variance ratio, (F) were applied to 13 homologous sets of 26 differences each between means of groups of six. The C test is shown to be most reliable in separating two distinct populations of values, as significant or not significant, at the 1% level of probability of a larger difference. The other tests are less reliable in that neither makes a distinct separation in these terms. The t test is the least rigorous, and the F test the most, in terms of proportion of total number of differences judged significant by these tests, and of a separation of distinct populations of values in terms of magnitude of the difference.     

Composition chimique elementaire des populations naturelles de Sphaeroma hookeri (Crustace: Isopode Flabellifere). Aspect spatio-temporel

1. Elemental chemical composition of Sphaeroma hookeri Leach of different natural populations from Camargue (Rhône delta) and from the Bassin de Berre (near Marseilles), was studied on samples taken the same day in different populations and on samples collected at different seasons in the same population.
2. Individual analyses of carbon, hydrogen and nitrogen were performed with a Perkin Elmer elemental analyzer. Total inorganic content was obtained for each specimen by weighing the residue after the output of the analyzer.
3. Relative growth in ash, carbon, hydrogen and nitrogen content of the different populations samples was compared by means of Reeve's statistical method.
4. Chemical allometry lines of each population are given. Variability of growth coefficients or mean values in a given population appears from several samples taken in the course of the year.
5. The differences in slope and position have been tested and their significance stated.
6. Growth coefficients of ash, carbon, hydrogen and nitrogen contents show a certain variability among the different populations. But these differences are not always significant owing to the dispersion of the data, a result of the wide individual variation within a population.
7. Much greater significant differences appear from relative positions of the growth lines, and these seem to be due to some ecological factors, among which, for instance, nutriment can lead to a large difference in carbon content.
8. Within a given population no significant difference appears in the growth coefficients of ash, carbon, hydrogen or nitrogen content and therefore the obtained values characterize each population.