Taxonomic variation in size-density relationships challenges the notion of energy equivalence

The relationship between body mass and abundance is a major focus for research in macroecology. The form of this relationship has been suggested to reflect the partitioning of energy among species. We revisit classical datasets to show that size-density relationships vary systematically among taxonomic groups, with most variation occurring at the order level. We use this knowledge to make a novel test of the 'energy equivalence rule', at the taxonomic scale appropriate for the data. We find no obvious relationship between order-specific exponents for abundance and metabolic rate, although most orders show substantially shallower (less negative) scaling than predicted by energy equivalence. This finding implies greater energy flux among larger-bodied animals, with the largest species using two orders of magnitude more energy than the smallest. Our results reject the traditional interpretation of energy equivalence as a predictive rule. However, some variation in size-density exponents is consistent with a model of geometric constraints on foraging.     

Allometric scaling of maximum population density: a common rule for marine phytoplankton and terrestrial plants

A primary goal of macroecology is to identify principles that apply across varied ecosystems and taxonomic groups. Here we show that the allometric relationship observed between maximum abundance and body size for terrestrial plants can be extended to predict maximum population densities of marine phytoplankton. These results imply that the abundance of primary producers is similarly constrained in terrestrial and marine systems by rates of energy supply as dictated by a common allometric scaling law. They also highlight the existence of general mechanisms linking rates of individual metabolism to emergent properties of ecosystems.     

Measurement of body size and abundance in tests of macroecological and food web theory

1. Mean body mass (W) and mean numerical (N) or biomass (B) abundance are frequently used as variables to describe populations and species in macroecological and food web studies. 2. We investigate how the use of mean W and mean N or B, rather than other measures of W and/or accounting for the properties of all individuals, can affect the outcome of tests of macroecological and food web theory. 3. Theoretical and empirical analyses demonstrate that mean W, W at maximum biomass (W(mb)), W when energy requirements are greatest (W(me)) and the W when a species uses the greatest proportion of the energy available to all species in a W class (W(mpe)) are not consistently related. 4. For a population at equilibrium, relationships between mean W and W(me) depend on the slope b of the relationship between trophic level and W. For marine fishes, data show that b varies widely among species and thus mean W is an unreliable indicator of the role of a species in the food web. 5. Two different approaches, 'cross-species' and 'all individuals' have been used to estimate slopes of abundance-body mass relationships and to test the energetic equivalence hypothesis and related theory. The approaches, based on relationships between (1) log(10) mean W and log(10) mean N or B, and (2) log(10) W and log(10) N or B of all individuals binned into log(10) W classes (size spectra), give different slopes and confidence intervals with the same data. 6. Our results show that the 'all individuals' approach has the potential to provide more powerful tests of the energetic equivalence hypothesis and role of energy availability in determining slopes, but new theory and empirical analysis are needed to explain distributions of species relative abundance at W. 7. Biases introduced when working with mean W in macroecological and food web studies are greatest when species have indeterminate growth, when relationships between W and trophic level are strong and when the range of species'W is narrow.     

Scale-dependent mechanisms in the population dynamics of an insect herbivore

A multiscale approach has lead to significant advances in the understanding of species population dynamics. The scale-dependent nature of population processes has been particularly clearly illustrated for insect herbivores. However, one of the most well-studied insect herbivores, the galling sawfly Euura lasiolepis, has to date been examined almost exclusively at fine spatial scales. The preference-performance, plant vigour and larval survival hypotheses are well supported by this species. Here, we test these hypotheses at a spatial scale larger than that previously considered, i.e. across a landscape in northern Arizona represented by an altitudinal gradient encompassing a series of drainages. We also develop a qualitative model for understanding the population dynamics of E. lasiolepis based on patterns of survival and mortality found in this study and previous ones. Gall density was highly variable across the altitudinal gradient, not explained by host plant variables, and thus a poor surrogate fot population abundance. These findings for the first time fail to support the plant vigour and preference hierarchy hypotheses for E. lasiolepis. Dispersal limitation most likely explains the lack of support for these hypotheses at this scale. By contrast, sawfly survival, gall abortion, parasitism and larval mortality were well explained by host plant quality variables and altitude. The larval survival hypothesis was well supported and is thus comparatively scale-invariant. A qualitative model developed here highlighted the importance of both willow water status and disturbance in determining host plant quality, as well as an apparent trade off between shoot length and plant moisture status in determining vital rates across the altitudinal gradient. This study thus demonstrated for the first time the scale-dependent nature of mechanisms underlying the population dynamics E. lasiolepis, and identified the interaction between parasitism and altitude as a novel mechanism underlying spatial patterns in the survival and mortality patterns of this species.     

Variation in scorpion metabolic rate and rate-temperature relationships: implications for the fundamental equation of the metabolic theory of ecology

The fundamental equation of the metabolic theory of ecology (MTE) indicates that most of the variation in metabolic rate are a consequence of variation in organismal size and environmental temperature. Although evolution is thought to minimize energy costs of nutrient transport, its effects on metabolic rate via adaptation, acclimatization or acclimation are considered small, and restricted mostly to variation in the scaling constant, b(0). This contrasts strongly with many conclusions of evolutionary physiology and life-history theory, making closer examination of the fundamental equation an important task for evolutionary biologists. Here we do so using scorpions as model organisms. First, we investigate the implications for the fundamental equation of metabolic rate variation and its temperature dependence in the scorpion Uroplectes carinatus following laboratory acclimation. During 22 days of acclimation at 25 degrees C metabolic rates declined significantly (from 127.4 to 78.2 microW; P = 0.0001) whereas mean body mass remained constant (367.9-369.1 mg; P = 0.999). In field-fresh scorpions, metabolic rate-temperature (MRT) relationships varied substantially within and among individuals, and therefore had low repeatability values (tau = 0.02) and no significant among-individual variation (P = 0.181). However, acclimation resulted in a decline in within-individual variation of MRT slopes which subsequently revealed significant differences among individuals (P = 0.0031) and resulted in a fourfold increase in repeatability values (tau = 0.08). These results highlight the fact that MRT relationships can show substantial, directional variation within individuals over time. Using a randomization model we demonstrate that the reduction in metabolic rate with acclimation while body mass remains constant causes a decline both in the value of the mass-scaling exponent and the coefficient of determination. Furthermore, interspecific comparisons of activation energy, E, demonstrated significant variation in scorpions (0.09-1.14 eV), with a mean value of 0.77 eV, significantly higher than the 0.6-0.7 eV predicted by the fundamental equation. Our results add to a growing body of work questioning both the theoretical basis and empirical support for the MTE, and suggest that alternative models of metabolic rate variation incorporating explicit consideration of life history evolution deserve further scrutiny.     

A cure for the plague of parameters: constraining models of complex population dynamics with allometries

A major goal of ecology is to discover how dynamics and structure of multi-trophic ecological communities are related. This is difficult, because whole-community data are limited and typically comprise only a snapshot of a community instead of a time series of dynamics, and mathematical models of complex system dynamics have a large number of unmeasured parameters and therefore have been only tenuously related to real systems. These are related problems, because long time-series, if they were commonly available, would enable inference of parameters. The resulting ‘plague of parameters’ means most studies of multi-species population dynamics have been very theoretical. Dynamical models parametrized using physiological allometries may offer a partial cure for the plague of parameters, and these models are increasingly used in theoretical studies. However, physiological allometries cannot determine all parameters, and the models have also rarely been directly tested against data. We confronted a model of community dynamics with data from a lake community. Many important empirical patterns were reproducible as outcomes of dynamics, and were not reproducible when parameters did not follow physiological allometries. Results validate the usefulness, when parameters follow physiological allometries, of classic differential-equation models for understanding whole-community dynamics and the structure–dynamics relationship.     

Long‐distance call evolution in the Felidae: effects of body weight,habitat, and phylogeny

Long‐distance calls used for mate attraction and territorial spacing are distinctive signals in the felid vocal repertoire. Their evolution is subject to natural and sexual selection, as well as various constraints. Body size is an important morphological constraint, with the scaling of the spectral characteristics of a species' vocalizations with its body size being established for several vertebrate groups. Alternatively, the structure of long‐distance calls may have been optimized for transmission in species' habitats (acoustic adaptation hypothesis). The present study assessed whether the mean dominant frequency of long‐distance calls in the Felidae (approximately 70% of all species incorporated) is influenced by the species' body size and/or conforms to the acoustic adaptation hypothesis. After controlling for phylogenetic relationships, we found a significant correlation between mean dominant frequency of a taxon's long‐distance calls and conditions for sound transmission in its habitat type (‘open/heterogeneous’ versus ‘dense’), although no significant influence of body size. Taxa living in more open habitat types have long‐distance calls with significantly lower mean dominant frequencies than those living in dense habitats. The result obtained in the present analysis is fairly robust against random removal of single or few taxa from the data, and also against the use of different branch‐length transformation models in phylogenetic regression. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 487–500.     

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.     

An information-theoretic approach to evaluating the size and temperature dependence of metabolic rate

The effects of body mass and temperature on metabolic rate (MR) are among the most widely examined physiological relationships. Recently, these relationships have been incorporated into the metabolic theory of ecology (MTE) that links the ecology of populations, communities and ecosystems to the MR of individual organisms. The fundamental equation of MTE derives the relation between mass and MR using first principles and predicts the temperature dependence of MR based on biochemical kinetics. It is a deliberately simple, zeroth-order approximation that represents a baseline against which variation in real biological systems can be examined. In the present study, we evaluate the fundamental equation of MTE against other more parameter-rich models for MR using an information-theoretic approach to penalize the inclusion of additional parameters. Using a comparative database of MR measurements for 1359 species, from 11 groups ranging from prokaryotes to mammals, and spanning 16 orders of magnitude in mass and a 59°C range in body temperature, we show that differences between taxa in the mass and temperature dependence of MR are sufficiently large as to be retained in the best model for MR despite the requirement for estimation of 22 more parameters than the fundamental equation of MTE.     

The allometry of metabolism in southern African millipedes (Myriapoda: Diplopoda)

Abstract. We determined standard metabolic rate at 25°C in forty-eight species of millipede from southern Africa and compared these data with confident measures of standard metabolic rate previously published for other arthropod groups.Metabolic rate in millipedes was not significantly different from that in beetles, ants or spiders once body mass effects had been accounted for, but was significantly higher than that in ticks.The exponent for the mass scaling of metabolic rate did not vary significantly between the five arthropod orders.Our best estimate for the relationship between standard metabolic rate (μl O₂ h^-1) and body mass (mg) in non-tick arthropods was 0.86 mass^0.73.     

Structured population dynamics: continuous size and discontinuous stage structures

A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.      

Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals

Metabolic rate is traditionally assumed to scale with body mass to the 3/4-power, but significant deviations from the '3/4-power law' have been observed for several different taxa of animals and plants, and for different physiological states. The recently proposed 'metabolic-level boundaries hypothesis' represents one of the attempts to explain this variation. It predicts that the power (log-log slope) of metabolic scaling relationships should vary between 2/3 and 1, in a systematic way with metabolic level. Here, this hypothesis is tested using data from birds and mammals. As predicted, in both of these independently evolved endothermic taxa, the scaling slope approaches 1 at the lowest and highest metabolic levels (as observed during torpor and strenuous exercise, respectively), whereas it is near 2/3 at intermediate resting and cold-induced metabolic levels. Remarkably, both taxa show similar, approximately U-shaped relationships between the scaling slope and the metabolic (activity) level. These predictable patterns strongly support the view that variation of the scaling slope is not merely noise obscuring the signal of a universal scaling law, but rather is the result of multiple physical constraints whose relative influence depends on the metabolic state of the organisms being analysed.