Allometric Ratios Research Articles

Evaluating a simple radiation/dry matter conversion model using data from Eucalyptus globulus plantations in Western Australia.

A simple model that describes growth in terms of physical and physiological processes is needed to predict growth rates and hence the productivity of trees at particular sites. The linear relationship expected between absorbed photosynthetically active radiation (phi(pa), MJ m(-2)) and dry mass production (G(t)); i.e., G(t) = epsilonphi(pa), where epsilon is the radiation utilization coefficient, was fitted to three years' data from five Western Australian Eucalyptus globulus Labill. plantations for which monthly growth measurements, leaf area indices, weather data and soil water measurements were available. Reductions in growth efficiency relative to absorbed photosynthetically active radiation were associated with high vapor pressure deficits (D, kPa) so the relationship between monthly aboveground biomass increments and D was used to calculate utilizable phi(pa). Plotting cumulative aboveground growth against utilizable phi(pa) gave strong linear relationships with slope epsilon. Values of epsilon ranged from 0.93 to 2.23 g dry mass MJ(-1) phi(pa). The variation could not be explained either in terms of soil water content in the root zones, because all plantations appeared to have access to groundwater, or in terms of soil chemistry. A value of epsilon approximately 2.2 is considered near the maximum likely to be applicable to Eucalyptus plantations. An interesting peripheral finding was a strong relationship between allometric ratios and soil phosphorus; this, if confirmed elsewhere, will be of considerable value in converting biomass increments to wood production. There was also a strong negative relationship between the average ratio of leaf/total aboveground biomass and soil nitrogen content.

An analysis of the relationship between foliage biomass and crown surface area inPinus sylvestrisin Sweden

An allometric relationship between foliage biomass and crown surface area is investigated in a data set consisting of 54 fertilized and 99 unfertilized Scots pine (Pinus sylvestris L.) trees from 16 stands in Central Sweden. The allometric ratios for the unfertilized trees are shown to be weakly correlated with competition defined as tree height relative to dominant height (r = 0.475), and with crown coverage (r = ‐0.563). A slight level difference in the ratios can be detected between stands of different site moisture index. The overall relationship is nonlinear but becomes linear if the coefficient of proportionality is made dependent on stand average crown coverage. This also improves the percentage of explanation, which suggests that the allometry of the crown is related to the light conditions of the tree. Under fertilization, the relationship between foliage biomass and crown surface area seems less stable, at least if measured shortly after fertilization.

Comparison of constant and variable allometric ratios for predicting foliar biomass of various tree genera

An equation that incorporates a variable allometric ratio (VAR) was compared with the traditional "power function" for estimation of foliage weight for six tree species. The equations were fitted using diameter at breast height (DBH) and diameter at the base of the live crown as predictors. When DBH was used as the independent variable, the VAR explained statistically significant additional variation in three of the six species examined, and in most cases reduced bias. Residual analysis indicated no need for a more complex mathematical expression than the linear VAR. However, the flexibility of the VAR was not necessary when diameter at the base of the live crown was used as the predictor variable. The use of combined variable predictors (DBH × total height) and multiple regression on DBH and total height was also examined.

Comparison of Constant and Variable Allometric Ratios for Estimating Populus tremuloides Biomass

Abstract An allometric model that incorporates a variable allometric ratio (VAR) was fitted to Populus tremuloides biomass data for bolewood, bolebark, live branch, leaf, and current twig stem components. This model was compared to a log-liner transformation of the power function, which imposes a constant allometric ratio (CAR). Although the VAR model did not improve the estimation of bolewood biomass, it significantly improved the estimation of live branch and leaf biomass, and provided less biased estimates of bolebark and current twig weights relative to the CAR model. The VAR model was superior to the power function as a model of allometric relationships that do not remain constant as the organism grows. It allowed for initially large allometric ratios that declined linearly with increasing stem diameter. For. Sci. 33(2):294-300.

Histology of allometric growth in hindlimb muscles of pigs

SUMMARYHindlimbs of pigs were dissected at 4-week intervals from 9 to 29 weeks after birth. Allometric growth ratios of the gluteal muscles, biceps femoris and semitendinosus were calculated relative to gastrocnemius. Relative growth in weight of the proximal limb muscles was greater than that of the distal muscle, gastrocnemius. The greater relative growth of proximal muscles was not due to greater relative growth of muscle fibre diameters, nor to greater relative growth of muscle cross-sectional areas. In biceps femoris and gluteal muscles, growth in the area of musole cross sections did not keep pace with the radial growth of muscle fibres. The relative longitudinal growth of proximal limb bones exceeded that of distal bones, and the relative longitudinal growth of biceps femoris and semitendinosus exceeded that of any of the limb bones. New sarcomeres were added to muscle length at a faster rate in biceps femoris and semitendinosus than in the peroneus longus located distally in the limb.

Total body zinc concentration and allometric growth ratios in Mytilus edulis collected from different shore levels

Body zinc concentrations (on a soft parts dry weight basis) in 18 composite collections of mussels (Mytilus edulis) taken from different shore levels within a single mussel bed on the north shore of the Tyne estuary at Tynemouth, on 25 October, 1980, showed highly significant correlations with 4 allometric, size-related factors. A negative correlation was found between body zinc concentration and a flesh condition (FC) index defined as mg dry flesh wt per g dry shell wt. Positive correlations were found between body zinc concentration and width: height ratio, width: length ratio and shell valve inequality index (SVI) defined as the weight of heavier shell valve/weight of lighter shell valve. Unlike earlier observations on a single population taken from a single habitat, this heterogeneous collection showed no significant relationship between body zinc concentration and body size as determined by soft-parts dry weight. Body zinc concentration and allometric ratios were, however, related to position on the shoreline. It is suggested that, where mussels are collected from different habitats, environmental factors probably have a greater influence on body size than age. Therefore, normalization of trace metal concentrations to a standard body weight may not be appropriate where specimens are collected from a variety of habitats. Allometric ratios are related to age, but are independent of absolute size, and may therefore provide a more suitable basis for normalization of trace metal concentration within a monitoring programme.

Relationship between body zinc concentration and allometric growth measurements in the mussel Mytilus edulis

The frequency distribution of shell lengths in the mussels Mytilus edulis (L.) taken from a site in the Tyne Estuary (UK) in summer, 1980, typically displayed a bimodal shape, with a small peak in the 8 to 20 mm size range and a much broader peak in the 22 to 50 mm region. A collection of mussels was made consisting of two groups, one from each of the above size peaks. The group of larger mussels had a significantly higher mean zinc concentration than the group of smaller mussels, mainly because a few large individuals had very high zinc concentrations. The ratios of shell width:height, width:length and length:height were also significantly higher in larger mussels. However, the ratio of flesh dry wt:shell dry wt (flesh condition) was lower in larger individuals. The whole soft tissue zinc concentration was positively correlated with width:height and width:length, but negatively correlated with flesh wt:shell wt. It was concluded that allometric ratios may provide an attractive alternative to simple size characteristics as a basis for trace metal determinations, particularly in a comparison of metal levels in mussel populations from widely differing habitats where absolute size is a poor indicator of age or growth rate.

Allometric ratios, invariant numbers and the theory of biological similarities.

From the ratio of two allometric equations concerning the relationships among organ weights, functions and body weight, new allometric equations were always obtained.

Allomorphosis and Geography in Insect Populations

In female Tetraopes tetraophthalrntis there is significant heterogeneity in allometric growth ratios of prothoracic tubercle size and prothorax width among different areas of the range. This suggests that different relative growth rates in the formation of the adult prothorax may have been selectively favored in different areas of the range. However, males do not show the effect. Furthermore, the relationship between individual and population allomorphosis is also strikingly different in the two sexes; estimates of growth ratios at these two levels are similar in females, very dissimilar in males. The analysis of allometric size relationships, in particular by means of the allometric growth equation of Huxley (1932), continues to be regarded as a powerful tool in the study of animal evolution. Recent restatements of the context within which the Huxley equation is useful have been generally less sweeping than the original claims made on its behalf, but its value for descriptive purposes has never been in question. It has been possible in both modern and fossil populations to estimate some effects of natural selection by means of comparisons of growth ratios among populationis, and in some studies to compare levels of allomorphosis. Present material, consisting of a large number of contemporaneous populations of a single species, provides an opportunity for a detailed examination of ecogenotypic differences in an allometric relationship; it further provides an opportunity for a comparison of individual and population allomorphosis. MATERIALS AND METHODS The ease with which large samples of the cerambycid beetle Tetraopes tetraophthalmus can be collected over a large area of the United States makes this insect a particularly suitable form for population analysis. Moreover, recent work on its geographic variation, involving many metrical characters (Mason, 1964), brought to light a situation of interest in the study of allometry. Among the characters used in the 1964 study were two measures of the width of the prothorax, one of them across the lateral tubercles which jut out prominently on either side of the thorax, and the second at a point just anterior to these tubercles. This second measurement will be referred to as the "prothorax width" (Ps,), an index of the size of the insect, taken as the independent variable for purposes of the analysis. The difference between the two prothorax width measurements, giving the total length of the two tubercles together, will be referred to as "tubercle size" (T), the dependent variable. Tubercle size showed a very strikingly positive allometric relationship to body size (i.e., to P,), in some populations, but the effect did not seem consistent among samples from different localities. For the purpose of examining this question statistically, thirty males and thirty females were sampled at random from collections made in 1962 at each of 35 localities distributed as evenly as practicable across virtually the entire range of the species. (Conclusions drawn here are thus based on data from a total of 2100 individuals.) Simpson (1953) has recognized five levels of allomorphosis, extending the categories of Huxley and of Westoll (1950). Two of these levels can be readily compared in Tetraopes. Heterauxesis, or ontogenetic allometry, cannot be measured in the present instance, since the adult stage of the beetle is the only one in which the char-

Wool follicle development in the New Zealand Romney and N type sheep. IV. Pre-natal growth and changes in body proportions

Growth, and the relative growth gradients over the body, have been studied in N-type and normal Kew Zealand Romney foetuses. Body weights, and a series of linear measurements taken between different points over the body, have been obtained from a series of foetuses of known ages. Huxley's allometric growth ratios have been calculated from these measurements by using the least squares regression. There are no significant gromth differences between foetuses belonging to the different AT-genotypes of the New Zealand Ronmey. Foetuses belonging to the New Zealand Romney and some British breeds grow at a faster rate than South African Merino foetuses studied by Malan and Curson (1936a) and Cloete (1939). Relative growth gradients over the body are, in general, similar to those of other mammals, but the results do not support the theory of Cloete (1939), that the relative growth rate of a part of the body is solely a function of the age of the part.