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.     

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

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass.     

Postnatal long bone growth in terrestrial placental mammals: Allometry,life history,and organismal traits

The ontogenetic allometry of long bone proportions is poorly understood in Mammalia. It has previously been suggested that during mammalian ontogeny long bone proportions grow more slender (positive allometry; length ∝ circumference^>1.0), although this conclusion was based upon data from a few small‐bodied taxa. It remains unknown how ontogenetic long bone allometry varies across Mammalia in terms of both taxonomy and body size. We collected long bone length and circumference data for ontogenetic samples of 22 species of mammals spanning six major clades and three orders of magnitude in body mass. Using reduced major axis bivariate regressions to compare bone length to circumference, we found that isometry and positive allometry are the most widespread patterns of growth across mammals. Negative allometry (i.e., bones growing more robust during ontogeny) occurs in mammals but is largely restricted to cetartiodactyls. Using regression slope as a proxy for long bone allometry, we compared long bone allometry to life history and organismal traits. Neonatal body mass, adult body mass, and growth rate have a negative relationship with long bone allometry. At an adult mass of roughly 15–20 kg, long bone growth shifts from positive allometry to mainly isometry and negative allometry. There were no significant relationships between ontogenetic long bone allometry and either cursoriality or basal metabolic rate. J. Morphol. © 2012 Wiley Periodicals, Inc.     

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.     

Ontogeny,function, and scaling of the mandibular symphysis in papionin primates

In vivo study of mastication in adult cercopithecine primates demonstrates a link between mandibular symphyseal form and resistance to “wishboning,” or lateral transverse bending. Mechanical consideration of wishboning at the symphysis indicates exponentially higher stresses along the lingual surface with increasing symphyseal curvature. Lengthening the anteroposterior width of the symphysis acts to resist these higher loads. Interspecific adult cercopithecine allometries show that both symphyseal curvature and symphyseal width exhibit positive allometry relative to body mass. The experimental and allometric data support an hypothesis that the cercopithecine mandibular symphysis is designed to maintain functional equivalence—in this case dynamic strain similarity—in wishboning stress and strain magnitudes across adult cercopithecines. We test the hypothesis that functional equivalence during masticatory wishboning is maintained throughout ontogeny by calculating relative stress estimates from morphometric dimensions of the mandibular symphysis in two cercopithecine primates, Macaca fascicularis and M. nemestrina. Results indicate no significant differences in relative stress estimates among the two macaque ontogenies and an interspecific sample of adult papionin primates. Further, relative stress estimates do not change significantly throughout ontogeny in either species. These results offer the first evidence for the maintenance of functional equivalence in stress and strain levels during postnatal growth in a habitually loaded cranial structure. Scaling analyses demonstrate significant slope differences for both symphyseal curvature and width between the ontogenetic and interspecific samples. The distinct interspecific cercopithecine slopes are realized by a series of ontogenetic transpositions in both symphyseal curvature and width. Throughout papionin ontogeny, symphyseal curvature increases with less negative allometry, while symphysis width increases with less positive allometry versus the interspecific pattern. As symphyseal curvature and width are inversely proportional to one another in estimating relative stresses, functionally equivalent stress levels are maintained both ontogenetically and interspecifically, because the relatively slower rate of allometric increase in symphyseal curvature during growth is compensated for by a slower rate of allometric increase in symphyseal width. These results indicate the primacy of maintaining functional equivalence during growth and the need for ontogenetic data in understanding the evolutionary processes that affect form–function relations as well as the interspecific patterning of adult form across a clade. J. Morphol. 235:157–175, 1998. © 1998 Wiley-Liss, Inc.     

Evolution of post-weaning skull ontogeny in New World opossums (Didelphidae)

Quantification of mammalian skull development has received much attention in the recent literature. Previous results in different lineages have shown an effect of historical legacy on patterns of skull growth. In marsupials, the skull of adults exhibits high variation across species, principally along a size axis. The development keys of the marsupial skull are fundamental to understanding the evolution of skull function in this clade. Its generally well-resolved phylogeny makes the group ideal for studying macroevolution of skull ontogeny. Here, we tested the hypothesis that ontogenetic similarity is correlated with phylogeny in New World marsupials, so that developmental patterns are expected to be conserved from ancestral opossums. We concatenated our previously published ontogenetic cranial data from several opossum species with new ontogenetic sequences and constructed an allometric space on the basis of a set of comparable cranial linear measurements. In this ontogenetic space, we determined the degree of correspondence of developmental patterns and the phylogeny of the group. In addition, we mapped ontogenetic trajectories onto the opossum phylogeny, treating the trajectories as composite, continuously varying characters. Didelphids differed widely in the magnitude of skull allometry across species. Splanchnocranial components exhibited all possible patterns of inter-specific variation, whereas mandibular variables were predominantly allometrically “positive” and neurocranial components were predominantly allometrically “negative.” The distribution of species in allometric space reflected the compounded effect of phylogeny and size variation characteristic of didelphids. The terminal morphology of related species differed in shape, so their ontogenetic trajectories deviated with respect to that of reconstructed common ancestors in varying degree. Phylogeny was the main factor structuring the allometric space of New World marsupials. Didelphids inherited an ancestral constellation of allometry coefficients without change and retained much of it throughout their lineage history. Conserved allometric values on the nodes splitting placental outgroups and marsupials suggest a developmental basis common to all therians.     

A PATH-ANALYTIC MODEL FOR THE MEASUREMENT OF SELECTION ON MORPHOLOGY

This paper describes a path model for the analysis of phenotypic selection upon continuous morphological characters. The path-analysis model assumes that selection occurs on unmeasured general size and shape allometry factors that summarize linear relations among sets of ontogenetically, phylogenetically, or functionally related traits. An unmeasured factor for general size is considered the only aspect of morphometric covariance matrices for which there is an a priori biological explanation. Consequently, selection coefficients are derived for each measured character by holding constant only a general size factor, rather than by using multiple regression to adjust for the full covariance matrix. Fitness is treated as an unmeasured factor with loadings, representing directional selection coefficients, computed as the covariances of the size-adjusted characters with the measured fitness indicator. The magnitudes and signs of the selection coefficients, combined with biological insight, may suggest hypotheses of selection on one or more shape allometry factors. Hypotheses of selection on general size and shape allometry factors are evaluated through cycles of measurement, analysis, and experimentation, designed to refine the path diagram depicting the covariances among the measured characters, the measured indicator of fitness, and unmeasured factors for morphology and fitness. The path-analysis and multiple-regression models were applied to data from remeasurement of Lande and Arnold's (1983) pentatomid bugs and to Bumpus's (1899) data on house sparrows. The path analysis suggested the hypothesis that variation in bug survivorship was an expression of directional selection on wing loading. Bumpus's data are consistent with a hypothesis of stabilizing selection on general size in females and directional selection for small wing size relative to body size in males.     

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus) as detected by principal-components analysis

The ontogeny of cranial sexual dimorphism in the Bornean orang-utan (Pongo pygmaeus pygmaeus) is examined by means of principal-components analysis (PCA). Normalized first components are called allometry vectors or vectors of relative growth and show that sexual dimorphism is present at all stages of growth. Two patterns of sexual dimorphism are present: (1) sexual differences at age groups 2 and 3 are the result primarily of differences in principal component II scores, reflecting mainly shape-related differences, and (2) age groups 5, 6, and 7 show a trend of stronger size-related shape differences with increasing age in the allometry vector along with decreasing differences in principal component II scores, reflecting an increase in size-related shape differences between the sexes. Age group 4 shows a combination of both patterns. Our results support Shea's hypothesis (1985a) that when using multigroup PCAs in closely related taxa, the allometry vector will generally estimate the shape variation resulting from the extension of common growth allometry patterns (ontogenetic scaling). The second and subsequent components summarize shape variation from slope and intercept differences between the groups, provided that ontogenetic scaling is not solely responsible for all the shape differences present. Subanalyses of those dimensions previously found to show ontogenetic scaling and acceleration follow this pattern well. The total sample provides a pattern whereby ontogenetically scaled dimensions possess a stronger influence over accelerated dimensions but still generally follow Shea's hypothesis. Finally, variously derived coefficients provided several interesting findings: (1) strong evidence was found against multivariate isometry for both the pooled and the separate samples, (2) multivariate allometric coefficients for both sexes follow the general growth pattern of negative scaling in neurocranial dimensions and positive scaling in the viscerocranium, and (3) multivariate slopes have a very high correlation with bivariate slopes relative to the same independent X variable, thereby lending further support to Jolicoeur's (1963a, b) allometry generalization.     

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.     

HETEROCHRONY AND ALLOMETRY: LESSONS FROM THE WATER STRIDER GENUS LIMNOPORUS

Heterochrony and allometry both deal with evolutionary modifications of ontogenies. Although data about both morphology and age are required to identify heterochronic processes, age data are not needed to study allometry. Using a simple graphical model, we show that allometric patterns cannot be used to infer the underlying heterochronic processes. We present a case study of the water strider genus Limnoporus Stål (Heteroptera: Gerridae) to illuminate the distinct roles that allometry and heterochrony play in integrated studies of the evolution of form. Multivariate analyses reveal several evolutionary modifications of growth trajectories (changes in direction, lateral transposition, and ontogenetic scaling), which are fairly consistent with the hypothesized phylogeny of the genus. Because there is no positive correlation between instar durations and size increments, size cannot be used as a proxy for age data in studies of heterochrony. In fact, a measure of overall size itself shows a remarkable variety of heterochronic changes among the six species. Mixtures of several heterochronic processes predominate over the more unitary reflections of “pure” processes. Heterochronic changes in different branches of the phylogeny, apparently independent of size scaling, suggest considerable potential for adaptive evolution. “Local” differentiation of ontogenetic traits within small clades may be at least as important as “global” evolutionary trends in large clades and will often be missed in “global” analyses.     

Quantification of ontogenetic allometry in ammonoids

Ammonoids are well‐known objects used for studies on ontogeny and phylogeny, but a quantification of ontogenetic change has not yet been carried out. Their planispirally coiled conchs allow for a study of “longitudinal” ontogenetic data, that is data of ontogenetic trajectories that can be obtained from a single specimen. Therefore, they provide a good model for ontogenetic studies of geometry in other shelled organisms. Using modifications of three cardinal conch dimensions, computer simulations can model artificial conchs. The trajectories of ontogenetic allometry of these simulations can be analyzed in great detail in a theoretical morphospace. A method for the classification of conch ontogeny and quantification of the degree of allometry is proposed. Using high‐precision cross‐sections, the allometric conch growth of real ammonoids can be documented and compared. The members of the Ammonoidea show a wide variety of allometric growth, ranging from near isometry to monophasic, biphasic, or polyphasic allometry. Selected examples of Palaeozoic and Mesozoic ammonoids are shown with respect to their degree of change during ontogeny of the conch.     

Stochastic ontogenetic allometry: the statistical dynamics of relative growth

Background

In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, , where and are the logarithmic sizes of two traits at any given time t. Realistically, however, stochasticity is an inherent property of ontogenetic allometry. Due to the inherent stochasticity in both and , the ontogenetic allometry coefficients, and k, can vary with t and have intricate temporal distributions that are governed by the central and mixed moments of the random ontogenetic growth functions, and . Unfortunately, there is no probabilistic model for analyzing these informative ontogenetic statistical moments.

Methodology/Principal Findings

This study treats and as correlated stochastic processes to formulate the exact probabilistic version of each of the ontogenetic allometry coefficients. In particular, the statistical dynamics of relative growth is addressed by analyzing the allometric growth factors that affect the temporal distribution of the probabilistic version of the relative growth rate, , where is the expected value of the ratio of stochastic to stochastic , and and are the numerator and the denominator of , respectively. These allometric growth factors, which provide important insight into ontogenetic allometry but appear only when stochasticity is introduced, describe the central and mixed moments of and as differentiable real-valued functions of t.

Conclusions/Significance

Failure to account for the inherent stochasticity in both and leads not only to the miscalculation of k, but also to the omission of all of the informative ontogenetic statistical moments that affect the size of traits and the timing and rate of development of traits. Furthermore, even though the stochastic process and the stochastic process are linearly related, k can vary with t.     

Sexual dimorphism of Dall's porpoise and harbor porpoise skulls

To evaluate and quantify sexual dimorphism of skull shape and assess the ontogenetic background for differences, samples of 134 harbor porpoise (Phocoena phocoena) and 85 Dall's porpoise (Phocoenoides dalli) were compared in terms of cranial shape and shape ontogeny using three-dimensional geometric morphometrics. After correction for allometry, no sexual differences were detected in harbor porpoise, while Dall's porpoise showed statistically significant sexual dimorphism of skull shape. Since no sex-specific differences were detected in the directionalities of the ontogenetic vectors, we cannot reject that the dimorphism is innate. Based on the different mating systems of the two species and the lack of sexual dimorphism in the harbor porpoise, the dimorphism in Dall's porpoise is most likely a result of sexual selection in relation physical competition for mates given that male skulls provide room for larger neck muscles with a more favorable lever arm.     

Weapon allometry varies with latitude in the New Zealand giraffe weevil

Animal body size commonly shows a relationship with latitude to the degree that this phenomenon is one of the few ‘rules’ discussed in evolutionary ecology: Bergmann's rule. Although exaggerated secondary sexual traits frequently exhibit interesting relationships with body size (allometries) and are expected to evolve rapidly in response to environmental variation, the way in which allometry might interact with latitude has not been addressed. We present data showing latitudinal variation in body size and weapon allometry for the New Zealand giraffe weevil (Lasiorhynchus barbicornis). Males display an extremely elongated rostrum used as a weapon during fights for access to females. Consistent with Bergmann's rule, mean body size increased with latitude. More interestingly, weapon allometry also varied with latitude, such that lower latitude populations exhibited steeper allometric slopes between weapon and body size. To our knowledge, this is the first study to document a latitudinal cline in weapon allometry and is therefore a novel contribution to the collective work on Bergmann's rule and secondary sexual trait variation.     

Allometry of reaching and contact structures in Kukulcania hibernalis (Araneae: Filistatidae)

Large part of the morphological diversity observed across taxa is attributed to the effect of sexual selection; and the static allometry of these structures vary largely from highly positive to negative, depending on their function, and position on the animal's body. In arthropods, information of how sexually selected contact and reaching male structures use during courtship scale on body size is scarce. We tested two complementary hypotheses: the reaching structure hypothesis and the contact‐function hypothesis, in the spider Kukulcania hibernalis. We used the length of the proximal segments of the male pedipalp to test the reaching structure hypothesis, and claw features to test the contact‐function hypothesis. Our results support both hypotheses. Small males have disproportionally longer pedipalps (highly negative allometry) than large males, increasing the probability of small‐bodied males to inseminate even large females. We also found that both distal contact and noncontact homologous structures scaled shallow (slope < 1) on body size, but allometry was significantly shallower for contact than for noncontact distal structures, providing support to the contact‐function hypothesis, and allowing teasing apart the effect of sexual selection on distal contact structures with dual functions.     

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.     

When size makes a difference: allometry, life-history and morphological evolution of capuchins (Cebus) and squirrels (Saimiri) monkeys (Cebinae, Platyrrhini)

Background

How are morphological evolution and developmental changes related? This rather old and intriguing question had a substantial boost after the 70s within the framework of heterochrony (changes in rates or timing of development) and nowadays has the potential to make another major leap forward through the combination of approaches: molecular biology, developmental experimentation, comparative systematic studies, geometric morphometrics and quantitative genetics. Here I take an integrated approach combining life-history comparative analyses, classical and geometric morphometrics applied to ontogenetic series to understand changes in size and shape which happen during the evolution of two New World Monkeys (NWM) sister genera.

Results

Cebus and Saimiri share the same basic allometric patterns in skull traits, a result robust to sexual and ontogenetic variation. If adults of both genera are compared in the same scale (discounting size differences) most differences are small and not statistically significant. These results are consistent using both approaches, classical and geometric Morphometrics. Cebus is a genus characterized by a number of peramorphic traits (adult-like) while Saimiri is a genus with paedomorphic (child like) traits. Yet, the whole clade Cebinae is characterized by a unique combination of very high pre-natal growth rates and relatively slow post-natal growth rates when compared to the rest of the NWM. Morphologically Cebinae can be considered paedomorphic in relation to the other NWM. Geometric morphometrics allows the precise separation of absolute size, shape variation associated with size (allometry), and shape variation non-associated with size. Interestingly, and despite the fact that they were extracted as independent factors (principal components), evolutionary allometry (those differences in allometric shape associated with intergeneric differences) and ontogenetic allometry (differences in allometric shape associated with ontogenetic variation within genus) are correlated within these two genera. Furthermore, morphological differences produced along these two axes are quite similar. Cebus and Saimiri are aligned along the same evolutionary allometry and have parallel ontogenetic allometry trajectories.

Conclusion

The evolution of these two Platyrrhini monkeys is basically due to a size differentiation (and consequently to shape changes associated with size). Many life-history changes are correlated or may be the causal agents in such evolution, such as delayed on-set of reproduction in Cebus and larger neonates in Saimiri.     

Taylor's law and related allometric power laws in New Zealand mountain beech forests: the roles of space,time and environment

Taylor's law says that the variance of population density of a species is proportional to a power of mean population density. Density–mass allometry says that mean population density is proportional to a power of mean biomass per individual. These power laws predict a third, variance–mass allometry: the variance of population density of a species is proportional to a power of mean biomass per individual. We tested these laws using 10 censuses of New Zealand mountain beech trees in 250 plots over 30 years at spatial scales from 5 m to kilometers. We found that: 1) a single‐species forest not disrupted by humans obeyed all three laws; 2) random sampling explained the parameters of Taylor's law at a large spatial scale in 8 of 10 censuses, but not at a fine spatial scale; 3) larger spatial scale increased the exponent of Taylor's law and decreased the exponent of variance–mass allometry (this is the first empirical demonstration that the latter exponent depends on spatial scale), but affected the exponent of density–mass allometry slightly; 4) despite varying natural disturbance, the three laws varied relatively little over the 30 years; 5) self‐thinning and recruiting plots had significantly different intercepts and slopes of density–mass allometry and variance–mass allometry, but the parameters of Taylor's law were not usually significantly affected; and 6) higher soil calcium was associated with higher variance of population density in all censuses but not with a difference in the exponent of Taylor's law, while elevation above sea level and soil carbon‐to‐nitrogen ratios had little effect on the parameters of Taylor's law. In general, the three laws were remarkably robust. When their parameters were influenced by spatial scale and environmental factors, the parameters could not be species‐specific indicators. We suggest biological mechanisms that may explain some of these findings.     

Allometry of territory size and metabolic rate as predictors of self-thinning in young-of-the-year Atlantic salmon

1. Self-thinning is a progressive decline in population density caused by competitively induced losses in a cohort of growing individuals and can be depicted as: log₁₀ (density) = c − β log₁₀ (body mass).
2. In mobile animals, two mechanisms for self-thinning have been proposed: (i) the space hypothesis predicts that maximum population density for a given body size is the inverse of territory size, and hence, the self-thinning slope is the negative of the slope of the allometric territory-size relationship; (ii) the energetic equivalence hypothesis predicts that the self-thinning slope is the negative of the slope of the allometric metabolic rate relationship, assuming a constant supply of energy for the cohort.
3. Both hypotheses were tested by monitoring body size, population density, food availability and habitat for young-of-the-year Atlantic salmon ( Salmo salar ) in Catamaran Brook, New Brunswick. The results were consistent with the predictions of the space hypothesis. Observed densities did not exceed the maximum densities predicted and the observed self-thinning slope of −1·16 was not significantly different from the slope of −1·12, predicted by the allometry of territory size for the population under study.
4. The observed self-thinning slope was significantly steeper than −0·87, predicted by the allometry of metabolic rate, perhaps because of a gradual decline in food abundance over the study period. The decline in density was more rapid in very shallow sites and may have been partly caused by a seasonal change in water depth and an ontogenetic habitat shift rather than solely by competition for food or space.
5. The allometry of territory size may be a useful predictor of self-thinning in populations of mobile animals competing for food and space.