Allometric Scaling Coefficients Research Articles

Stable Allometric Trajectories in Picea abies (L.) Karst. Trees along an Elevational Gradient

The effect of temperature on tree phenology and growth has gained particular attention in relation to climate change. While a number of reports indicate that warming can extend the length of the growing season and enhance tree growth rates, it is still debated whether temperature also affects biomass partitioning. Addressing the question of whether trees grown at different elevations invest similarly in various organs, we established four sites along an elevational gradient (320 to 595 m a.s.l.) in managed Norway spruce (Picea abies (L.) Karts) stands regenerating after clearcuts in central Norway. There, differences in temperature, bud break, tree growth, and allometric scaling were measured in small spruce trees (up to 3 m height). The results showed that bud break and shoot growth are affected by temperature, as lower sites completed the bud break process 5 days earlier than the higher sites did. There was some evidence indicating that the summer drought of 2018 affected tree growth during the season, and the implications of this are discussed. The allometric scaling coefficients did not change for the crown volume (slope value range 2.66–2.84), crown radius (0.77–0.89), and tree diameter (0.89–0.96) against tree height. A slight difference was found in the scaling coefficients of crown length against tree height (slope value range 1.04–1.12), but this did not affect the general scaling of the crown volume with tree height. Our results showed that different local environmental conditions affect both the growth rate and phenology in Norway spruce trees but, on the contrary, that the biomass partitioning among different parts of the tree remains essentially unchanged. This demonstrates that the allometric approach is an important tool for unraveling true vs. apparent plant plasticity, which in turn is an essential awareness for predicting plant responses to environmental changes.

The relationship between eDNA particle concentration and organism abundance in nature is strengthened by allometric scaling.

Organism abundance is a critical parameter in ecology, but its estimation is often challenging. Approaches utilizing eDNA to indirectly estimate abundance have recently generated substantial interest. However, preliminary correlations observed between eDNA concentration and abundance in nature are typically moderate in strength with significant unexplained variation. Here, we apply a novel approach to integrate allometric scaling coefficients into models of eDNA concentration and organism abundance. We hypothesize that eDNA particle production scales nonlinearly with mass, with scaling coefficients <1. Wild populations often exhibit substantial variation in individual body size distributions; we therefore predict that the distribution of mass across individuals within a population will influence population-level eDNA production rates. To test our hypothesis, we collected standardized body size distribution and mark-recapture abundance data using whole-lake experiments involving nine populations of brook trout. We correlated eDNA concentration with three metrics of abundance: density (individuals/ha), biomass (kg/ha) and allometrically scaled mass (ASM) (∑(individual mass0.73 )/ha). Density and biomass were both significantly positively correlated with eDNA concentration (adj. r2 =0.59 and 0.63, respectively), but ASM exhibited improved model fit (adj. r2 =0.78). We also demonstrate how estimates of ASM derived from eDNA samples in "unknown" systems can be converted to biomass or density estimates with additional size-structure data. Future experiments should empirically validate allometric scaling coefficients for eDNA production, particularly where substantial intraspecific size distribution variation exists. Incorporating allometric scaling may improve predictive models to the extent that eDNA concentration may become a reliable indicator of abundance in nature.

Reverse translation: effects of acclimation temperature and acute temperature challenges on oxygen consumption, diffusive water flux, net sodium loss rates, Q10 values and mass scaling coefficients in the rainbow trout (Oncorhynchus mykiss).

Our understanding is limited on how fish adjust the effective permeability of their branchial epithelium to ions and water while altering O2 uptake rate (MO2) with acute and chronic changes in temperature. We investigated the effects of acclimation temperature (8°C, 13°C and 18°C) and acute temperature challenges [acute rise (acclimated at 8°C, measured at 13°C and 18°C), acute drop (acclimated at 18°C, measured at 8°C and 13°C) and intermediate (acclimated at 13°C, measured at 8°C and 18°C)] on routine MO2, diffusive water flux, and net sodium loss rates in 24-h fasted rainbow trout (Oncorhynchus mykiss). In the temperature challenge tests, measurements were made during the first hour. In acclimated trout at all temperatures, allometric mass scaling coefficients were much higher for diffusive water flux than for MO2. Furthermore, the diffusive water flux rate was more responsive (overall Q10 = 2.75) compared to MO2 (Q10 = 1.80) over the 8-18°C range, and for both, Q10 values were greater at 8-13°C than at 13-18°C. The net Na+ flux rates were highly sensitive to acclimation temperature with an overall Q10 of 3.01 for 8-18°C. In contrast, very different patterns occurred in trout subjected to acute temperature challenges. The net Na+ flux rate was temperature-insensitive with a Q10 around 1.0. Both MO2 and diffusive water flux rates exhibited lower Q10 values than for the acclimated rates in response to either acute increases or decreases in temperature. These results fit Pattern 5 of Precht (undercompensation, reverse effect) and more precisely Pattern IIB of Prosser (reverse translation). These inverse compensatory patterns suggest that trout do not alter their rates very much when undergoing acute thermal challenges (diurnal fluctuations, migration through the thermocline). The greater changes seen with acclimation may be adaptive to long-term seasonal changes in temperature. We discuss the roles of aquaporins, spontaneous activity, and recent feeding in these responses.

The allometry of proboscis length in Melittidae (Hymenoptera: Apoidae) and an estimate of their foraging distance using museum collections.

An appreciation of body size allometry is central for understanding insect pollination ecology. A recent model utilises allometric coefficients for five of the seven extant bee families (Apoidea: Anthophila) to include crucial but difficult-to-measure traits, such as proboscis length, in ecological and evolutionary studies. Melittidae were not included although they are important pollinators in South Africa where they comprise an especially rich and morphologically diverse fauna. We measured intertegular distance (correlated with body size) and proboscis length of 179 specimens of 11 species from three genera of Melittidae. With the inclusion of Melittidae, we tested the between family differences in the allometric scaling coefficients. AIC model selection was used to establish which factors provide the best estimate of proboscis length. We explored a hypothesis that has been proposed in the literature, but which has not been tested, whereby body and range sizes of bees are correlated with rainfall regions. We tested this by using body size measurements of 2109 museum specimens from 56 species of Melittidae and applied the model coefficients to estimate proboscis length and foraging distance. Our results from testing differences across bee families show that with the addition of Melittidae, we retained the overall pattern of significant differences in the scaling coefficient among Apoidea, with our model explaining 98% of the variance in species-level means for proboscis length. When testing the relationship between body size and rainfall region we found no relationship for South African Melittidae. Overall, this study has added allometric scaling coefficients for an important bee family and shown the applicability of using these coefficients when linked with museum specimens to test ecological hypothesis.

Is tree age or tree size reducing height increment in Abies alba Mill. at its southernmost distribution limit?

Conventional methods for estimating the current annual increment of stand volume are based on the uncertain assumption that height increment decreases with tree age. Conversely, size, rather than age, should be accounted for the observed senescence-related declines in relative growth rate and, consequently, implemented in silvicultural manuals. Results stem from a study on Abies alba Mill. at its southern limit of distribution. Many factors limit height increment when age and size increase in large-statured tree species. Height–diameter allometric relationships are commonly used measures of tree growth. In this study, we tested if tree age was the main factor affecting the reduction in height increment of silver fir trees (Abies alba Mill.), verifying also whether tree size had a significant role in ecophysiological-biomechanical limitations to tree growth. The study was carried out in a silver fir forest located in Southern Italy, at the southernmost distribution limit for this species. Through a stratified random sampling, 100 trees were selected. All the selected trees were then felled and the total tree height, height increments (internode distances), diameter at breast height, and diameter increments (ring widths) were measured. The analyses of allometric models and scaling coefficients showed that the correlation between tree age and height increment was not always significant. We may conclude that tree age did not statistically explain the decrease in height increment in older trees. Instead, the increase in tree size and related physiological processes (expressed as product between diameter at breast height and tree height) explained the reduction in height increment in older trees and was the main factor limiting height growth trends in marginal population of silver fir.

Size structuring and allometric scaling relationships in coral reef fishes.

Temperate marine fish communities are often size-structured, with predators consuming increasingly larger prey and feeding at higher trophic levels as they grow. Gape limitation and ontogenetic diet shifts are key mechanisms by which size structuring arises in these communities. Little is known, however, about size structuring in coral reef fishes. Here, we aimed to advance understanding of size structuring in coral reef food webs by examining the evidence for these mechanisms in two groups of reef predators. Given the diversity of feeding modes amongst coral reef fishes, we also compared gape size-body size allometric relationships across functional groups to determine whether they are reliable indicators of size structuring. We used gut content analysis and quantile regressions of predator size-prey size relationships to test for evidence of gape limitation and ontogenetic niche shifts in reef piscivores (n=13 species) and benthic invertivores (n=3 species). We then estimated gape size-body size allometric scaling coefficients for 21 different species from four functional groups, including herbivores/detritivores, which are not expected to be gape-limited. We found evidence of both mechanisms for size structuring in coral reef piscivores, with maximum prey size scaling positively with predator body size, and ontogenetic diet shifts including prey type and expansion of prey size. There was, however, little evidence of size structuring in benthic invertivores. Across species and functional groups, absolute and relative gape sizes were largest in piscivores as expected, but gape size-body size scaling relationships were not indicative of size structuring. Instead, relative gape sizes and mouth morphologies may be better indicators. Our results provide evidence that coral reef piscivores are size-structured and that gape limitation and ontogenetic niche shifts are the mechanisms from which this structure arises. Although gape allometry was not indicative of size structuring, it may have implications for ecosystem function: positively allometric gape size-body size scaling relationships in herbivores/detritivores suggests that loss of large-bodied individuals of these species will have a disproportionately negative impact on reef grazing pressure.

Extreme positive allometry of animal adhesive pads and the size limits of adhesion-based climbing

Organismal functions are size-dependent whenever body surfaces supply body volumes. Larger organisms can develop strongly folded internal surfaces for enhanced diffusion, but in many cases areas cannot be folded so that their enlargement is constrained by anatomy, presenting a problem for larger animals. Here, we study the allometry of adhesive pad area in 225 climbing animal species, covering more than seven orders of magnitude in weight. Across all taxa, adhesive pad area showed extreme positive allometry and scaled with weight, implying a 200-fold increase of relative pad area from mites to geckos. However, allometric scaling coefficients for pad area systematically decreased with taxonomic level and were close to isometry when evolutionary history was accounted for, indicating that the substantial anatomical changes required to achieve this increase in relative pad area are limited by phylogenetic constraints. Using a comparative phylogenetic approach, we found that the departure from isometry is almost exclusively caused by large differences in size-corrected pad area between arthropods and vertebrates. To mitigate the expected decrease of weight-specific adhesion within closely related taxa where pad area scaled close to isometry, data for several taxa suggest that the pads' adhesive strength increased for larger animals. The combination of adjustments in relative pad area for distantly related taxa and changes in adhesive strength for closely related groups helps explain how climbing with adhesive pads has evolved in animals varying over seven orders of magnitude in body weight. Our results illustrate the size limits of adhesion-based climbing, with profound implications for large-scale bio-inspired adhesives.

Probability distribution of allometric coefficients and Bayesian estimation of aboveground tree biomass

Allometric biomass equations are widely used to predict aboveground biomass in forest ecosystems. A major limitation of these equations is that they need to be developed for specific local conditions and species to minimize bias and prediction errors. This variability in allometries across sites and species contradicts universal scaling rules that predicts constant coefficients for plants. A large number of biomass equations have been developed over the years, which provides an opportunity to synthesize parameter values and estimate their probability distributions. These distributions can be used as a priori probabilities to develop new equations for other species or sites. Here we found the distribution of the parameters a and b of the allometry between aboveground biomass (M) and diameter at breast height (D), ln(M)=a+bln(D), well approximated by a bivariate normal. We propose a method to develop new biomass equations based on prior information of parameter distributions and apply it to a dataset of tropical trees. The method we propose outperforms the classical statistical approach of least-square regression at small sample sizes. With this method it is possible to obtain similar significant values in the estimation of parameters using a sample size of 6 trees rather than 40–60 trees in the classical approach. Further, the Bayesian approach suggests that allometric scaling coefficients should be studied in the framework of probability distributions rather than fixed parameter values.

Food web complexity and allometric scaling relationships in stream mesocosms: implications for experimentation

1. Mesocosms are used extensively by ecologists to gain a mechanistic understanding of ecosystems based on the often untested assumption that these systems can replicate the key attributes of natural assemblages. 2. Previous investigations of stream mesocosm utility have explored community composition, but here for the first time, we extend the approach to consider the replicability and realism of food webs in four outdoor channels (4 m(2)). 3. The four food webs were similarly complex, consisting of diverse assemblages (61-71 taxa) with dense feeding interactions (directed connectance 0.09-0.11). Mesocosm food web structural attributes were within the range reported for 82 well-characterized food webs from natural streams and rivers. When compared with 112 additional food webs from standing freshwater, marine, estuarine and terrestrial environments, stream food webs (including mesocosms) had similar characteristic path lengths, but typically lower mean food chain length and exponents for the species-link relationship. 4. Body size (M) abundance (N) allometric scaling coefficients for trivariate taxonomic mesocosm food webs (-0.53 to -0.49) and individual size distributions (-0.60 to -0.58) were consistent and similar to those from natural systems, suggesting that patterns of energy flux between mesocosm consumers and resources were realistic approximations. 5. These results suggest that stream mesocosms of this scale can support replicate food webs with a degree of biocomplexity that is comparable to 'natural' streams. The findings highlight the potential value of mesocosms as model systems for performing experimental manipulations to test ecological theories, at spatiotemporal scales of relevance to natural ecosystems.

Survivorship curves and their impact on the estimation of maximum population growth rates

Previous efforts to use the Euler equation to estimate maximum population growth rates (variously symbolized as either r, r(m), or r(max)) have used simplified models of survivorship that neglect differences in survivorship schedules among species. In particular, several recent analyses have used either an exponential model of survivorship or a step function model in which all individuals live until a fixed age of death. Using a flexible alternative based on the beta distribution and a compiled data set of mammalian survivorship curves for 58 species, we explore the influence of survivorship shape and scale on the estimation of r. We show that the Euler equation paired with an exponential model of survivorship can be used to calculate an unbiased estimate of r over a large range of body sizes, whereas the more commonly used step function survivorship model results in severely inflated estimates of r, especially for mammals with large maximum population growth rates. Finally, we demonstrate that, despite producing different absolute estimates of r, the three survivorship models examined yield similar allometric scaling coefficients relating r to biomass. These allometric scaling relationships are highly sensitive to the inclusion or exclusion of bats (Chiroptera), which exhibit life-history traits (long life spans, small litter sizes, and relatively long litter intervals) inconsistent with their small body size.

Male dimorphism in Perdita portalis (Hymenoptera, Andrenidae) has arisen from preexisting allometric patterns

Allometric scaling coefficients were quantified using principal components analysis for eight species of closely related Perdita bees. The coefficients were mapped onto a cladogram and male dimorphism in P. portalis was found to be the derived state, whereas polymorphism was ancestral. The phylogeny explained 87.4 ± 1.1% of the variation in male head allometry among taxa, indicating that the evolution of head allometry is highly congruent with the cladogram. These results were used to place Perdita male head allometry in the context of adaptive phenotypic plasticity. Wheeler's (1991) model for the evolution of discrete alternative castes in ants is applied to the morphometric data in Perdita. We argue that the developmental rules that govern the evolution of caste polymorphism in social insects can be applied to the evolution of alternative male mating tactics in other Hymenoptera.