Assessing the shape and topology of allometric relationships with body mass: a case study using testes mass allometry

A Revision of the Traditional Analysis Method of Allometry to Allow Extension of the Normality-Borne Complexity of Error Structure: Examining the Adequacy of a Normal-Mixture Distribution-Driven Error Term

Huxley’s model of simple allometry provides a parsimonious scheme for examining scaling relationships in scientific research, resource management, and species conservation endeavors. Factors including biological error, analysis method, sample size, and overall data quality can undermine the reliability of a fit of Huxley’s model. Customary amendments enhance the complexity of the power function-conveyed systematic term while keeping the usual normality-borne error structure. The resulting protocols bear multiple-parameter complex allometry forms that could pose interpretative shortcomings and parameter estimation difficulties, and even being empirically pertinent, they could potentially bear overfitting. A subsequent heavy-tailed Q-Q normal spread often remains undetected since the adequacy of a normally distributed error term remains unexplored. Previously, we promoted the advantages of keeping Huxley’s model-driven systematic part while switching to a logistically distributed error term to improve fit quality. Here, we analyzed eelgrass leaf biomass and area data exhibiting a marked size-related heterogeneity, perhaps explaining a lack of systematization at data gathering. Overdispersion precluded adequacy of the logistically adapted protocol, thereby suggesting processing data through a median absolute deviation scheme aimed to remove unduly replicates. Nevertheless, achieving regularity to Huxley’s power function-like trend required the removal of many replicates, thereby questioning the integrity of a data cleaning approach. But, we managed to adapt the complexity of the error term to reliably identify Huxley’s model-like systematic part masked by variability in data. Achieving this relied on an error term conforming to a normal mixture distribution which successfully managed overdispersion in data. Compared to normal-complex allometry and data cleaning composites present arrangement delivered a coherent Q-Q normal mixture spread and a remarkable reproducibility strength of derived proxies. By keeping the analysis within Huxley’s original theory, the present approach enables substantiating nondestructive allometric proxies aimed at eelgrass conservation. The viewpoint endorsed here could also make data cleaning unnecessary.

Assessment of a Takagi-Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

Background

The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley’s model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability.

Methods

Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space.

Results

Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley’s power model involving covariate depending parameters. Huxley reported a breakpoint in the log–log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley’s data could be validated.

Conclusions

Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.

Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots

Conservation of eelgrass relies on transplants and evaluation of success depends on nondestructive measurements of average leaf biomass in shoots among other variables. Allometric proxies offer a convenient way to assessments. Identifying surrogates via log transformation and linear regression can set biased results. Views conceive this approach to be meaningful, asserting that curvature in geometrical space explains bias. Inappropriateness of correction factor of retransformation bias could also explain inconsistencies. Accounting for nonlinearity of the log transformed response relied on a generalized allometric model. Scaling parameters depend continuously on the descriptor. Joining correction factor is conceived as the partial sum of series expansion of mean retransformed residuals leading to highest reproducibility strength. Fits of particular characterizations of the generalized curvature model conveyed outstanding reproducibility of average eelgrass leaf biomass in shoots. Although nonlinear heteroscedastic regression resulted also to be suitable, only log transformation approaches can unmask a size related differentiation in growth form of the leaf. Generally, whenever structure of regression error is undetermined, choosing a suitable form of retransformation correction factor becomes elusive. Compared to customary nonparametric characterizations of this correction factor, present form proved more efficient. We expect that offered generalized allometric model along with proposed correction factor form provides a suitable analytical arrangement for the general settings of allometric examination.

Contrasting effects of large density changes on relative testes size in fluctuating populations of sympatric vole species

Across species, there is usually a positive relationship between sperm competition level and male reproductive effort on ejaculates, typically measured using relative testes size (RTS). Within populations, demographic and ecological processes may drastically alter the level of sperm competition and thus, potentially affect the evolution of testes size. Here, we use longitudinal records (across 38 years) from wild sympatric Fennoscandian populations of five species of voles to investigate whether RTS responds to natural fluctuations in population density, i.e. variation in sperm competition risk. We show that for some species RTS increases with density. However, our results also show that this relationship can be reversed in populations with large-scale between-year differences in density. Multiple mechanisms are suggested to explain the negative RTS-density relationship, including testes size response to density-dependent species interactions, an evolutionary response to sperm competition levels that is lagged when density fluctuations are over a certain threshold, or differing investment in pre- and post-copulatory competition at different densities. The results emphasize that our understanding of sperm competition in fluctuating environments is still very limited.

The allometry between secondary sexual traits and body size is nonlinear among cervids

Allometric relationships between sexually selected traits and body size have been extensively studied in recent decades. While sexually selected traits generally display positive allometry, a few recent reports have suggested that allometric relationships are not always linear. In male cervids, having both long antlers and large size provides benefits in terms of increased mating success. However, such attributes are costly to grow and maintain, and these costs might constrain antler length from increasing at the same rate as body mass in larger species if the quantity of energy that males can extract from their environment is limiting. We tested for possible nonlinearity in the relationship between antler size and body mass (on a log-log scale) among 31 cervids and found clear deviation from linearity in the allometry of antler length. Antler length increased linearly until a male body mass threshold at approximately 110 kg. Beyond this threshold, antler length did not change with increasing mass. We discuss this evidence of nonlinear allometry in the light of life-history theory and stress the importance of testing for nonlinearity when studying allometric relationships.

The role of gravity in the evolution of mammalian blood pressure

Understanding of the factors involved in determining the level of central arterial blood pressure in mammals has been clouded by inappropriate allometric analyses that fail to account for phylogenetic relationships among species, and require pressure to approach 0 as body size decreases. The present study analyses systolic, mean arterial, and diastolic blood pressure in 47 species of mammal with phylogenetically informed techniques applied to two-parameter equations. It also sets nonlinear, three-parameter equations to the data to remove the assumption of the two-parameter power equation that the smallest animals must have negligible blood pressure. These analyses show that blood pressure increases with body size. Nonlinear analyses show that mean blood pressure increases from 93 mmHg in a 10 g mouse to 156 mmHg in a 4 tonne elephant. The scaling exponent of blood pressure is generally lower than, though not significantly different from, the exponent predicted on the basis of the expected scaling of the vertical distance between the head and the heart. This indicates that compensation for the vertical distance above the heart is not perfect and suggests that the pressure required to perfuse the capillaries at the top of the body may decrease in larger species.

Daily production of spermatophores, sperm number and spermatophore size in two eriophyoid mite species

Under dissociated sperm transfer, (non-pairing) males deposit spermatophores on a substrate, while females seek spermatophores and pick up sperm on their own. Spermatophore expenditures of non-pairing males should be high, due to the increased uncertainty of sperm uptake by a female. In this study I examined spermatophore expenditures in two eriophyoid species that differed in the degree of dissociation between sexes: (1) Aculus fockeui (Nalepa and Trouessart) males rarely visit quiescent female nymphs (QFNs), and mostly deposit spermatophores all over the leaves, whereas (2) Aculops allotrichus (Nalepa) males guard QFNs for many hours and deposit several spermatophores beside them. Males of both species were collected from the field and tested in solitude. Aculus fockeui males deposited on average 19.1 spermatophores per day, whereas A. allotrichus deposited only 3.6 spermatophores per day, and had a very large coefficient of variation. Males and spermatophores of A. allotrichus were significantly smaller and contained less sperm than those of A. fockeui. In both eriophyoids, spermatophore size was fitted to the size of female genitalia and the height of females. The ratio between the diameter of spermatophore head and the width of a female genital coverflap was 0.6, whereas the ratio between the female leg and the length of spermatophore stalk was 0.5. Several factors could be responsible for the discrepancy in spermatophore expenditures between species. Among other factors, the effects of male size, male reproductive strategy and female genitalia size on spermatophore output and size of spermatophores are discussed.

Incorporating parasite systematics in comparative analyses of variation in spleen mass and testes sizes of rodents

Parasite diversity is hypothesized to act on host life-history traits through investment in immunity. In order to incorporate the diversity of the parasite community that an individual host or a host species may face, two indices can be used: Taxonomic Species Richness and Taxonomic Entropy, where the taxonomic information is incorporated with the taxonomic weight. We tested whether these indices correlate with several morphological traits potentially implicated in immune defence and in reproduction, using data on gastrointestinal helminths and their rodent hosts sampled in Southeast Asia. We found no relationship between parasite diversity indices and either spleen mass or testes size at the intraspecific level, i.e. at the level of individuals. At the interspecific level, we found no relationship between the parasite diversity indices and testes size. However, we found that female spleen mass is significantly influenced by the specific species richness of parasites, whereas male spleen mass is influenced by individual mean parasite diversity indices. We concluded that female spleen mass may have evolved in response to gastrointestinal helminth pressure acting at species levels, while in males, the individual spleen mass could be constrained by other factors, such as the blood storage function of the spleen.