Allometric Inference in Morphology

SYNOPSIS. Disparate rates of change in the surfaces and volumesof organisms with change in size combine with the interdependenceof surface-limited and volume-limited functional attributesto define criteria for the size-dependency of shapes. Size contributesto the specification of types of structures required, limitsto their functional range, and the scaling relationships amongcomponents of systems. Size-dependency may be stated in termsof a null hypothesis in morphology, with departures indicativeof special adaptations which may be of particular interest.The study of size-dependency in shape and function is approachinga general theory of form with content comparable in scope toa general theory of diversity.     

Allometric scaling in animals and plants

In this paper we give a derivation for the allometric scaling relation between the metabolic rate and the mass of animals and plants. We show that the characteristic scaling exponent of 3/4 occurring in this relation is a result of the distribution of sources and sinks within the living organism. We further introduce a principle of least mass and discuss the kind of flows that arise from it.     

Allometric neoteny and the evolution of succulence in cacti

With the objective of analysing the role of heterochrony in the evolution of succulence in the cactus family, a comparative study of xylem development in six species with contrasting morphologies was carried out. Two woody leaf-bearing cacti and four succulent cactus species belong to different subdivisions within the family were analysed. In each species and for different ages, vessel-element length was measured, vessel-element lateral wall-pitting described and the percentage of xylem and parenchyma in the stem quantified. In the succulent species it was found that vessel element length did not change between juvenile and adult wood, that wall-pitting in adult plants was similar to that of seedlings, and that the woody tissue in adult plants was organized in vascular bundles as in the primary tissue of seedlingS. Leaf-bearing cacti, in contrast, changed in both vessel element length and wall-pitting when secondary wood was produced, and the secondary woody tissue of adult plants was organized in a continuous cambial cylinder as in most dicotyledonS. An allometric analysis suggests that a retardation in the developmental rate of woody tissues (allometric neoteny) is the main mechanism in the development of succulence in cacti.     

Allometric relations in plant growth

Allometric relations Y = aX^b are shown to exist in phyllotaxis, under the form r = k log R = p ()(m + n) ^–2 , where r = Y is the normalized internode distance in the cylindrical representation of phyllotaxis and R is the plastochrone ratio in the centric representation, p()=a is a constant for every angle of intersection of the opposed parastichies of the visible pair (m, n), for every m and n, and for all possible limit divergence angles corresponding to the Fibonacci-type sequences..., m–n, n, m, m + n=X, 2m + n, ..., and where b=–2. Richards' phyllotaxis index will be deduced.This work was supported by the Natural Science and Engineering research Council Canada, grant A6240     

Allometric Relationships in Field-grown Soybean

Allometric relationships in plants uncover size-correlated variationsin form and development and characterize the relative growthof a part of a plant in comparison with a whole. Stable allometricrelationships in ontogeny can be used as components of cropmodels and to estimate plant parameters that are difficult tomeasure. Our objective was to discover whether stable allometricrelations exist in ontogeny of field-grown soybeans (GlycinemaxL.). We used field data on vegetative stages, plant height,stem weight, and leaf weight of 16 soybean cultivars measuredon farms and on the experiment station of Mississippi StateUniversity during 1993–1995 growing seasons. The numberof observed crops for each cultivar ranged from one to 14. Stemheights displayed linear log-log dependencies on the vegetativestage, before and after the breakpoint stage, which typicallywas between the ‘fourth node’ and ‘sixth node’vegetative stages. Slopes of the log-log dependencies afterthe breakpoint stage were similar in all cultivars. Stem masshad log-log linear dependencies on stem height. Slopes of thesedependencies differed among cultivars grown under the same conditions,and among crops of the same cultivar grown under different conditions.Water stress could be a modifier of these relationships. Theproportion of leaf weights in the total weight of leaves andstems decreased linearly as the vegetative development progressed.Since allometric relations are stable for a specific crop, theycan be used to forecast vegetative development as soon as theyare established.Copyright 1998 Annals of Botany Soybean,Glycine maxL., allometry, vegetative development.     

Allometric disparity in rodent evolution

In this study, allometric trajectories for 51 rodent species, comprising equal representatives from each of the major clades (Ctenohystrica, Muroidea, Sciuridae), are compared in a multivariate morphospace (=allometric space) to quantify magnitudes of disparity in cranial growth. Variability in allometric trajectory patterns was compared to measures of adult disparity in each clade, and dietary habit among the examined species, which together encapsulated an ecomorphological breadth. Results indicate that the evolution of allometric trajectories in rodents is characterized by different features in sciurids compared with muroids and Ctenohystrica. Sciuridae was found to have a reduced magnitude of inter‐trajectory change and growth patterns with less variation in allometric coefficient values among members. In contrast, a greater magnitude of difference between trajectories and an increased variation in allometric coefficient values was evident for both Ctenohystrica and muroids. Ctenohystrica and muroids achieved considerably higher adult disparities than sciurids, suggesting that conservatism in allometric trajectory modification may constrain morphological diversity in rodents. The results provide support for a role of ecology (dietary habit) in the evolution of allometric trajectories in rodents.     

Allometric scaling and seasonality in the epidemics of wildlife diseases

We present a susceptibles-exposed-infectives (SEI) model to analyze the effects of seasonality on epidemics, mainly of rabies, in a wide range of wildlife species. Model parameters are cast as simple allometric functions of host body size. Via nonlinear analysis, we investigate the dynamical behavior of the disease for different levels of seasonality in the transmission rate and for different values of the pathogen basic reproduction number (R(0)) over a broad range of body sizes. While the unforced SEI model exhibits long-term epizootic cycles only for large values of R(0), the seasonal model exhibits multiyear periodicity for small values of R(0). The oscillation period predicted by the seasonal model is consistent with those observed in the field for different host species. These conclusions are not affected by alternative assumptions for the shape of seasonality or for the parameters that exhibit seasonal variations. However, the introduction of host immunity (which occurs for rabies in some species and is typical of many other wildlife diseases) significantly modifies the epidemic dynamics; in this case, multiyear cycling requires a large level of seasonal forcing. Our analysis suggests that the explicit inclusion of periodic forcing in models of wildlife disease may be crucial to correctly describe the epidemics of wildlife that live in strongly seasonal environments.     

An Allometric Modelling Approach to Identify the Optimal Body Shape Associated with,and Differences between Brazilian and Peruvian Youth Motor Performance

Children from developed and developing countries differ in their body size and shape due to marked differences across their life history caused by social, economic and cultural differences which are also linked to their motor performance (MP). We used allometric models to identify size/shape characteristics associated with MP tests between Brazilian and Peruvian schoolchildren. A total of 4,560 subjects, 2,385 girls and 2,175 boys aged 9–15 years were studied. Height and weight were measured; biological maturation was estimated with the maturity offset technique; MP measures included the 12 minute run (12MR), handgrip strength (HG), standing long jump (SLJ) and the shuttle run speed (SR) tests; physical activity (PA) was assessed using the Baecke questionnaire. A multiplicative allometric model was adopted to adjust for body size differences across countries. Reciprocal ponderal index (RPI) was found to be the most suitable body shape indicator associated with the 12MR, SLJ, HG and SR performance. A positive maturation offset parameter was also associated with a better performance in SLJ, HG and SR tests. Sex differences were found in all motor tests. Brazilian youth showed better scores in MP than their Peruvian peers, even when controlling for their body size differences The current study identified the key body size associated with four body mass-dependent MP tests. Biological maturation and PA were associated with strength and motor performance. Sex differences were found in all motor tests, as well as across countries favoring Brazilian children even when accounting for their body size/shape differences.     

Allometric growth and carbon storage in the mangrove Sonneratia apetala

Allometric growth reflects different allocation patterns and relationships of different components or traits of a plant and is closely related to ecosystem carbon storage. As an introduced species, the growth and carbon storage of Sonneratia apetala are still unclear. To derive allometric relationships of the mangrove S. apetala and to estimate carbon storage in mangrove ecosystems, we harvested 12 individual Sonneratia apetala trees from four different diameter classes in the Futian National Nature Reserve, Guangdong, China. Allometric growth models were fitted. The results showed that diameter at breast height (DBH) and wood density were better variables for predicting plant biomass (including above- and below-ground biomass) than plant height. There were significant power function relationships between biomass and DBH, with a mean allometric exponent of 2.22, and stem biomass accounted for 97% of the variation in S. apetala total biomass. Nearly isometric scaling relationships were developed between stem biomass and other biomass components. To better understand the carbon stocks of the S. apetala ecosystem, we categorized all trees into five age classes and quantified vegetation carbon storage. The S. apetala vegetation carbon storage ranged from 96.48 to 215.35 Mg C ha^?1, and the carbon storage significantly increased with stand age. The allometric equations developed in this study are useful to estimate biomass and carbon storage of S. apetala ecosystems.

     

Allometric relations of teeth and jaws in man

Static adult intraspecific allometry of jaws and teeth was investigated in a sample of 100 Negro crania. The relations between tooth area, postcanine surface, incisor surface, and four viscerocranial measures were examined separately for males and females. Our results indicate a marked lack of morphological integration between P-sets within the orofacial subregion and a similar lack of correspondence between jaw size and tooth size. Allometric analyses indicate that mandibular length scales negatively allometric to maxilloalveolar length and to bigonial width, that canine base area scales positively to upper and lower jaw length, and that all the other teeth scale negatively to jaw length. The postcanine surface area was found to be negatively allometric to the canine base area, which in turn scaled isometrically to incisor surface. Hence, any lengthening of the mandible will tend to be associated with a relative shortening of the maxilla, with relatively larger canines and a relative reduction of the cheek teeth.     

Allometric growth in the Praying mantis Stagmatoptera biocellata

The growth of ten exoskeletal structures has been studied throughout the post-embryonic development in Stagmatoptera biocellata. The selection of an appropriate statistical procedure to analyse the data was discussed. In spite of theoretical prediction the least-squares regression technique turned out to be as efficient as the Bartlett (1949) procedure for studying growth. Longitudinal treatment of longitudinal data proved to be the best method for this kind of analysis. All the dimensions investigated showed some statistically significant degree of allometric growth and could be ascribed to certain class of allometry. The adaptative value of some allometric growth patterns was discussed in terms of physiological efficiency. A hypothesis put forth by Balderrama & Maldonado (1973) about the anatomic relationships between the parts involved in the mantis strike, received clear support from this analysis. A quantitative assessment of Dyar's (1890) and Przibram's (1912) rules and their modifications led us to conclude that they are untenable at least for the mantid Stagmatoptera biocellata. However, some periods of constant growth ratio could be identified during the post-embryonic development and the concept of maximum growth period was put forward as a complementary element for typifying structures.     

Allometric plasticity in a polyphenic beetle

Abstract 1. Environmental conditions, such as variation in nutrition, commonly contribute to morphological variation among individuals by affecting body size and the expression of certain morphological traits; however the scaling relationship between a morphological trait and body size over a range of body sizes is generally assumed not to change in response to environmental fluctuation (allometric plasticity), but instead to be constant and diagnostic for a particular trait and species or population. The work reported here examined diet‐induced allometric plasticity in the polyphenic beetle Onthophagus taurus Schreber (1759) (Coleoptera: Scarabaeidae). 2. Male O. taurus vary in body size depending on larval nutrition. Only males above a critical body size threshold express fully developed horns; males smaller than this threshold develop only rudimentary horns or no horns at all. 3. Field populations that naturally utilise two different resources for feeding larvae (horse dung vs. cow manure) exhibited significant differences in the average scaling relationship between body size and male horn length over the same range of body sizes. Males collected from cow manure populations expressed consistently longer horns for a given body size than males collected from horse dung populations. 4. Males reared in the laboratory on horse dung or cow manure also exhibited significant differences in the average scaling relationship between body size and horn length. Differences between laboratory populations reared on horse dung or cow manure were of the same kind and magnitude as differences between field populations that utilise these different resources naturally. 5. These findings suggest that between‐population differences in scaling relationships between horn length and body size can be the product of differences in the quality of resources available to developing larvae. Results are discussed in the context of onthophagine mating systems and recent insights in the developmental and endocrine control of horn polyphenisms.     

Clinal and Allometric Variation in the Skull of Sexually Dimorphic Opossums

Journal of Mammalian Evolution - Three species of sexually-dimorphic opossums are broadly distributed across South America: the habitat generalist Didelphis albiventris, the Atlantic forest-dweller...     

Allometric estimation of metabolic rates in animals

The relationship between body mass (M) and metabolic rate (MR) typically accounts for most (>90%) of the inter-specific variation in MR. As such, when measurement of a species of interest is not possible, its MR can often be predicted using M. However, choosing an appropriate relationship to make such predictions is critical, and the choice is complicated by ongoing debate about the structure of the relationship between M and MR. The present study examines a range of methods including ordinary least squares (OLS), reduced major axis (RMA), and phylogenetically-informed (PI) approaches for estimating log(MR) from log(M), as well as non-linear approaches for estimating the relationship between MR and M without the need for log-transformation. Using data for the basal metabolic rates of mammals, it is shown that RMA regression overestimates the scaling exponent of MR (b, where MR=aM(b)), suggesting that OLS regression is appropriate for these data. PI approaches are preferred over non-PI ones, and the best estimates of log(MR) are obtained by including information on body temperature, climate, habitat, island endemism, and use of torpor in addition to log(M). However, the use of log-transformed data introduces bias into estimates of MR, while the use of non-linear regression underestimates MR for small mammals. This suggests that no single relationship is appropriate for describing the relationship between MR and M for all mammals, and that relationships for more narrow taxonomic groups or body mass ranges should be used when predicting MR from M.