Rotational distortion in conventional allometric analyses

Three data sets from the recent literature were submitted to new analyses to illustrate the rotational distortion that commonly accompanies traditional allometric analyses and that often causes allometric equations to be inaccurate and misleading. The first investigation focused on the scaling of evaporative water loss to body mass in passerine birds; the second was concerned with the influence of body size on field metabolic rates of rodents; and the third addressed interspecific variation in kidney mass among primates. Straight lines were fitted to logarithmic transformations by Ordinary Least Squares and Generalized Linear Models, and the resulting equations then were re-expressed as two-parameter power functions in the original arithmetic scales. The re-expressed models were displayed on bivariate graphs together with tracings for equations fitted directly to untransformed data by nonlinear regression. In all instances, models estimated by back-transformation failed to describe major features of the arithmetic distribution whereas equations fitted by nonlinear regression performed quite well. The poor performance of equations based on models fitted to logarithms can be traced to the increased weight and leverage exerted in those analyses by observations for small species and to the decreased weight and leverage exerted by large ones. The problem of rotational distortion can be avoided by performing exploratory analysis on untransformed values and by validating fitted models in the scale of measurement.     

Pollinator size and its consequences: Robust estimates of body size in pollinating insects

Body size is an integral functional trait that underlies pollination‐related ecological processes, yet it is often impractical to measure directly. Allometric scaling laws have been used to overcome this problem. However, most existing models rely upon small sample sizes, geographically restricted sampling and have limited applicability for non‐bee taxa. Allometric models that consider biogeography, phylogenetic relatedness, and intraspecific variation are urgently required to ensure greater accuracy. We measured body size as dry weight and intertegular distance (ITD) of 391 bee species (4,035 specimens) and 103 hoverfly species (399 specimens) across four biogeographic regions: Australia, Europe, North America, and South America. We updated existing models within a Bayesian mixed‐model framework to test the power of ITD to predict interspecific variation in pollinator dry weight in interaction with different co‐variates: phylogeny or taxonomy, sexual dimorphism, and biogeographic region. In addition, we used ordinary least squares regression to assess intraspecific dry weight ~ ITD relationships for ten bees and five hoverfly species. Including co‐variates led to more robust interspecific body size predictions for both bees and hoverflies relative to models with the ITD alone. In contrast, at the intraspecific level, our results demonstrate that the ITD is an inconsistent predictor of body size for bees and hoverflies. The use of allometric scaling laws to estimate body size is more suitable for interspecific comparative analyses than assessing intraspecific variation. Collectively, these models form the basis of the dynamic R package, “pollimetry,” which provides a comprehensive resource for allometric pollination research worldwide.     

Density-dependent habitat selection: evaluating isoleg theory with a Lotka-Volterra model

Contemporary models of density-dependent habitat selection generally focus on long-term evolutionary consequences of intraspecific or interspecific competition and/or patterns of resource use in patchy environments. A primary goal of such studies often is to elucidate evolutionary stable strategies based on steady-state dynamics of population growth. In contrast, we developed a simulation model to explore short-term movements of interspecific competitors among fine-grained habitats of differing attributes, as might result from field manipulations of habitat quality or population densities. In this model, habitat quality is expressed in terms of mean individual fitness, represented by average per capita growth rate calculated according to the Lotka-Volterra equations describing interspecific competition. This model provides a mechanism for quantifying the effects of habitat quality, patterns of resource use and competition on distributions of individuals. Results demonstrate the heuristic value of this model in corroborating predictions derived from the ideal free distribution and isodar theory, and in generating isolegs to test the predictions of isoleg theory. Results indicate that small changes in model parameters have substantial impacts on patterns of habitat use and co-occurrence between species. The model identifies a variety of conditions under which isolegs for a given type of community organization deviate from predictions of contemporary isoleg theory, potentially expanding the universe of possible interspecific behaviors underlying the development of evolutionary stable strategies.     

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non‐linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass‐metabolism allometric exponent b = 0.75, activation energy range 0.2–1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best‐supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 ± 0.105 (mean ± 95% CI). In contrast, the four best‐supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non‐linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.     

Female polymorphism, frequency dependence, and rapid evolutionary dynamics in natural populations

Rapid evolutionary change over a few generations has been documented in natural populations. Such changes are observed as organisms invade new environments, and they are often triggered by changed interspecific interactions, such as differences in predation regimes. However, in spite of increased recognition of antagonistic male-female mating interactions, there is very limited evidence that such intraspecific interactions could cause rapid evolutionary dynamics in nature. This is because ecological and longitudinal data from natural populations have been lacking. Here we show that in a color-polymorphic damselfly species, male-female mating interactions lead to rapid evolutionary change in morph frequencies between generations. Field data and computer simulations indicate that these changes are driven by sexual conflict, in which morph fecundities are negatively affected by frequency- and density-dependent male mating harassment. These frequency-dependent processes prevent population divergence by maintaining a female polymorphism in most populations. Although these results contrast with the traditional view of how sexual conflict enhances the rate of population divergence, they are consistent with a recent theoretical model of how females may form discrete genetic clusters in response to male mating harassment.     

Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those predicted by ideal models such as MST.     

Cephalisation bei Caniden

Cephalisation in Canidae Studied were the intraspecific and interspecific relationships between brain weight and body weight in Canidae. Inclination values of the allometric lines: intraspecific – 0,25, interspecific 0,571. Most of the studied species have nearly the same degree of cephalisation, deviations from the interspecific allometric line are small; the cephalisation of Nyctereutes and Otocyon is less developed than in the other canid species. There is no difference in cephalisation between most canids and felids. Mustelids show a high variability in cephalisation. Criticized were the data of Bauchot (1985) and Gittleman (1986) on brain weight and body weight.     

Mating with the wrong species can be right

The evolutionary importance of interspecific hybridisation has been a controversial issue for quite some time. Some view mating between different species as a maladaptive process; others stress the adaptive value of choosing heterospecific mates under ecological conditions that favour hybrids. A recent paper by Pfennig is the first study to make a priori predictions of how adaptive choice between con- and heterospecific partners should vary with ecological conditions, and then testing these predictions experimentally.     

Life-history variation and allometry for sexual size dimorphism in Pacific salmon and trout

Allometry for sexual size dimorphism (SSD) is common in animals, but how different evolutionary processes interact to determine allometry remains unclear. Among related species SSD (male : female) typically increases with average body size, resulting in slopes of less than 1 when female size is regressed on male size: an allometric relationship formalized as 'Rensch's rule' . Empirical studies show that taxa with male-biased SSD are more likely to satisfy Rensch's rule and that a taxon's mean SSD is negatively correlated with allometric slope, implicating sexual selection on male size as an important mechanism promoting allometry for SSD. I use body length (and life-history) data from 628 (259) populations of seven species of anadromous Pacific salmon and trout (Oncorhynchus spp.) to show that in this genus life-history variation appears to regulate patterns of allometry both within and between species. Although all seven species have intraspecific allometric slopes of less than 1, contrary to expectation slope is unrelated to species' mean SSD, but is instead negatively correlated with two life-history variables: the species' mean marine age and variation in marine age. Second, because differences in marine age among species render SSD and body size uncorrelated, the interspecific slope is isometric. Together, these results provide an example of how evolutionary divergence in life history among related species can affect patterns of allometry for SSD across taxonomic scales.     

Universal scaling in the branching of the tree of life

Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and can be extended down to intra-specific relationships. Here we examine the topological properties of a large set of interspecific and intraspecific phylogenies and show that the branching patterns follow allometric rules conserved across the different levels in the Tree of Life, all significantly departing from those expected from the standard null models. The finding of non-random universal patterns of phylogenetic differentiation suggests that similar evolutionary forces drive diversification across the broad range of scales, from macro-evolutionary to micro-evolutionary processes, shaping the diversity of life on the planet.     

Fitting statistical models in bivariate allometry

Several attempts have been made in recent years to formulate a general explanation for what appear to be recurring patterns of allometric variation in morphology, physiology, and ecology of both plants and animals (e.g. the Metabolic Theory of Ecology, the Allometric Cascade, the Metabolic‐Level Boundaries hypothesis). However, published estimates for parameters in allometric equations often are inaccurate, owing to undetected bias introduced by the traditional method for fitting lines to empirical data. The traditional method entails fitting a straight line to logarithmic transformations of the original data and then back‐transforming the resulting equation to the arithmetic scale. Because of fundamental changes in distributions attending transformation of predictor and response variables, the traditional practice may cause influential outliers to go undetected, and it may result in an underparameterized model being fitted to the data. Also, substantial bias may be introduced by the insidious rotational distortion that accompanies regression analyses performed on logarithms. Consequently, the aforementioned patterns of allometric variation may be illusions, and the theoretical explanations may be wide of the mark. Problems attending the traditional procedure can be largely avoided in future research simply by performing preliminary analyses on arithmetic values and by validating fitted equations in the arithmetic domain. The goal of most allometric research is to characterize relationships between biological variables and body size, and this is done most effectively with data expressed in the units of measurement. Back‐transforming from a straight line fitted to logarithms is not a generally reliable way to estimate an allometric equation in the original scale.     

Body size establishes the scaling of avian postnatal metabolic rate: an interspecific analysis using phylogenetically independent contrasts

The avian postnatal metabolic rate literature is reviewed using power equations, Y = aM^b, to describe the relation between postnatal resting metabolic rate (RMR) and chick body mass (M) for 25 species. In altricial species, the relation between RMR and M from hatching to fledging can be described by a single power equation, whereas in most nonaltricial species two such equations are needed, one for chicks weighing less than about 25% of mature mass ( M _a) and a second for larger chicks. For altricial chicks and larger nonaltricial chicks, the body-mass exponent, b, of 25 intraspecific power equations ranged from 0.25 to 1.67 and varied inversely with M _a. The scaling of postnatal RMR is thus unlike that of either adult or hatchling metabolism in that it is size dependent. We examined the relationship between intraspecific b and M _a using Felsenstein's independent contrasts method to control for statistical complications due to the hierarchical nature of phylogenetic relationships. This "phylogenetic regression" technique yielded the relation b = 1.6 M _a^-015, in which mature mass explained 38% of the variation in b. The mass exponent of this equation (-0.15) did not differ significantly from that determined by nonphylogenetic methods (-0.17).
In altricial chicks and larger nonaltricial chicks, the scaling coefficient, a, of the interspecific power equations varied with adult mass according to the phylogenetically determined relation a (kj/h) = 0.0052M_a^0.65and was higher in fed than in fasted chicks. Equations derived in this analysis permit one to estimate the RMR of a growing chick from its mass and adult body mass and provide a basis for evolutionary and ecological comparisons.     

Evolutionary disarmament in interspecific competition.

Competitive asymmetry, which is the advantage of having a larger body or stronger weaponry than a contestant, drives spectacular evolutionary arms races in intraspecific competition. Similar asymmetries are well documented in interspecific competition, yet they seldom lead to exaggerated traits. Here we demonstrate that two species with substantially different size may undergo parallel coevolution towards a smaller size under the same ecological conditions where a single species would exhibit an evolutionary arms race. We show that disarmament occurs for a wide range of parameters in an ecologically explicit model of competition for a single shared resource; disarmament also occurs in a simple Lotka-Volterra competition model. A key property of both models is the interplay between evolutionary dynamics and population density. The mechanism does not rely on very specific features of the model. Thus, evolutionary disarmament may be widespread and may help to explain the lack of interspecific arms races.     

Population variation in brain size of nine-spined sticklebacks (Pungitius pungitius) - local adaptation or environmentally induced variation?

Background  

Most evolutionary studies on the size of brains and different parts of the brain have relied on interspecific comparisons, and have uncovered correlations between brain architecture and various ecological, behavioural and life-history traits. Yet, similar intraspecific studies are rare, despite the fact that they could better determine how selection and phenotypic plasticity influence brain architecture. We investigated the variation in brain size and structure in wild-caught nine-spined sticklebacks (Pungitius pungitius) from eight populations, representing marine, lake, and pond habitats, and compared them to data from a previous common garden study from a smaller number of populations.     

Optimal hibernation theory

Hibernation has received considerable attention from physiologists and natural historians, but theoretical and ecological treatments of hibernation are rarer. There is ample recent evidence that costs associated with hibernation affect the degree to which hibernation is expressed in nature, but we currently lack a quantitative framework under which to make predictions about how the costs and benefits of hibernation interact under various environmental conditions. Here, we attempt the first steps towards building an optimal hibernation theory for making specific predictions about the expression of hibernation (i.e. the depth and duration of torpor bouts), metabolic functioning, and the total period of hibernation in mammals and birds. Our current understanding of the costs associated with hibernation do not allow for parameterisation of optimal hibernation theory, but we hope this work provides a roadmap for physiologists and ecologists to collect the necessary data in the future.     

The community and ecosystem consequences of intraspecific diversity: a meta‐analysis

Understanding the relationships between biodiversity and ecosystem functioning has major implications. Biodiversity–ecosystem functioning relationships are generally investigated at the interspecific level, although intraspecific diversity (i.e. within‐species diversity) is increasingly perceived as an important ecological facet of biodiversity. Here, we provide a quantitative and integrative synthesis testing, across diverse plant and animal species, whether intraspecific diversity is a major driver of community dynamics and ecosystem functioning. We specifically tested (i) whether the number of genotypes/phenotypes (i.e. intraspecific richness) or the specific identity of genotypes/phenotypes (i.e. intraspecific variation) in populations modulate the structure of communities and the functioning of ecosystems, (ii) whether the ecological effects of intraspecific richness and variation are strong in magnitude, and (iii) whether these effects vary among taxonomic groups and ecological responses. We found a non‐linear relationship between intraspecific richness and community and ecosystem dynamics that follows a saturating curve shape, as observed for biodiversity–function relationships measured at the interspecific level. Importantly, intraspecific richness modulated ecological dynamics with a magnitude that was equal to that previously reported for interspecific richness. Our results further confirm, based on a database containing more than 50 species, that intraspecific variation also has substantial effects on ecological dynamics. We demonstrated that the effects of intraspecific variation are twice as high as expected by chance, and that they might have been underestimated previously. Finally, we found that the ecological effects of intraspecific variation are not homogeneous and are actually stronger when intraspecific variation is manipulated in primary producers than in consumer species, and when they are measured at the ecosystem rather than at the community level. Overall, we demonstrated that the two facets of intraspecific diversity (richness and variation) can both strongly affect community and ecosystem dynamics, which reveals the pivotal role of within‐species biodiversity for understanding ecological dynamics.     

Inferring evolutionarily significant units of bacterial diversity from broad environmental surveys of single-locus data

By far the greatest challenge for diversity studies is to characterize the diversity of prokaryotes, which probably encompasses billions of species, most of which are unculturable. Recent advances in theory and analysis have focused on multi-locus approaches and on combined analysis of molecular and ecological data. However, broad environmental surveys of bacterial diversity still rely on single-locus data, notably 16S ribosomal DNA, and little other detailed information. Evolutionary methods of delimiting species from single-locus data alone need to consider population genetic and macroevolutionary theories for the expected levels of interspecific and intraspecific variation. We discuss the use of a recent evolutionary method, based on the theory of coalescence within independently evolving populations, compared with a traditional approach that uses a fixed threshold divergence to delimit species.     

Models projecting the fate of fish populations under climate change need to be based on valid physiological mechanisms

Some recent modelling papers projecting smaller fish sizes and catches in a warmer future are based on erroneous assumptions regarding (i) the scaling of gills with body mass and (ii) the energetic cost of ‘maintenance’. Assumption (i) posits that insurmountable geometric constraints prevent respiratory surface areas from growing as fast as body volume. It is argued that these constraints explain allometric scaling of energy metabolism, whereby larger fishes have relatively lower mass‐specific metabolic rates. Assumption (ii) concludes that when fishes reach a certain size, basal oxygen demands will not be met, because of assumption (i). We here demonstrate unequivocally, by applying accepted physiological principles with reference to the existing literature, that these assumptions are not valid. Gills are folded surfaces, where the scaling of surface area to volume is not constrained by spherical geometry. The gill surface area can, in fact, increase linearly in proportion to gill volume and body mass. We cite the large body of evidence demonstrating that respiratory surface areas in fishes reflect metabolic needs, not vice versa, which explains the large interspecific variation in scaling of gill surface areas. Finally, we point out that future studies basing their predictions on models should incorporate factors for scaling of metabolic rate and for temperature effects on metabolism, which agree with measured values, and should account for interspecific variation in scaling and temperature effects. It is possible that some fishes will become smaller in the future, but to make reliable predictions the underlying mechanisms need to be identified and sought elsewhere than in geometric constraints on gill surface area. Furthermore, to ensure that useful information is conveyed to the public and policymakers about the possible effects of climate change, it is necessary to improve communication and congruity between fish physiologists and fisheries scientists.     

Metabolic rate of neonate goannas (Squamata: Varanidae)

At 35°C, the standard and maximal metabolic rates for neonates of four species of goannas (Varanus brevicauda, V. eremius, V. tristis and V. gouldii) are consistently higher than predicted by intraspecific equations for adults. However, this is difficult to demonstrate statistically. The consequence of this is that the data for neonates probably should be excluded from the data used to establish intraspecific allometric regression equations for adults. From an interspecific perspective, neonate V. mertensi have a lower standard (0.16 ml O₂ g⁻¹ per h) and maximal (1.18 ml g⁻¹ per h) metabolic rate than neonate V. brevicauda (0.22 ml g⁻¹ per h), V. eremius (0.28 and 2.94 ml g⁻¹ per h, respectively), V. tristis (0.33 and 3.43 ml g⁻¹ per h) and V. gouldii (0.29 and 5.24 ml g⁻¹ per h) at 35°C. Such interspecies differences need to be accounted for in interspecific allometric analysis.     

Concordance between stabilizing sexual selection,intraspecific variation,and interspecific divergence in Phymata

Empirical studies show that lineages typically exhibit long periods of evolutionary stasis and that relative levels of within‐species trait covariance often correlate with the extent of between‐species trait divergence. These observations have been interpreted by some as evidence of genetic constraints persisting for long periods of time. However, an alternative explanation is that both intra‐ and interspecific variation are shaped by the features of the adaptive landscape (e.g., stabilizing selection). Employing a genus of insects that are diverse with respect to a suite of secondary sex traits, we related data describing nonlinear phenotypic (sexual) selection to intraspecific trait covariances and macroevolutionary divergence. We found support for two key predictions (1) that intraspecific trait covariation would be aligned with stabilizing selection and (2) that there would be restricted macroevolutionary divergence in the direction of stabilizing selection. The observed alignment of all three matrices offers a point of caution in interpreting standing variability as metrics of evolutionary constraint. Our results also illustrate the power of sexual selection for determining variation observed at both short and long timescales and account for the apparently slow evolution of some secondary sex characters in this lineage.