Allometry Formula Research Articles

РОСТ И МОРФОФИЗИОЛОГИЧЕСКОЕ СОСТОЯНИЕ ОРГАНОВ ПИЩЕВАРЕНИЯ БРОЙЛЕРОВ ПРИ ИСПОЛЬЗОВАНИИ КОРМОВОЙ ДОБАВКИ «ФАРМАТАН» (БУТИТАН)

The authors studied the growth characteristics (morphophysiological indicators) of broilers’ digestive organs when using Pharmatan in the diet at doses of 0.025; 0.05 and 0.075%. For the study, three medium-weight broiler chickens were selected – on a daily basis for the first three days, then on a weekly basis. The mass of the stomach, individual intestines, the mass of internal organs, and the coefficient of growth rate were determined according to Brody. To study the relative growth rate, the simple allometry formula y = axb was used. It has been established that the most intensive growth of the digestive organs is observed in the first week of broiler life and consists in the stimulated growth of the intestine, especially the cecum. Later on, the growth of the digestive organs in birds of the control group increases and becomes equal to or higher than in broilers of the experimental group. In general, for 42 days of the experiment, the growth rate of the organs of the gastrointestinal tract is practically the same in the birds of the experimental and control groups. The parameters of the regression equations indicate significant differences in the growth of individual organs of the digestive tube during the individual development of broilers. In the experimental groups of broilers, almost all intestinal organs grow quite intensively (b = 1.325–1.783) during the first week of raising, with relatively low values of determination coefficients (cecum – R2 = 0.355; jejunum – R2 = 0.745). High morphological values of 7-day-old birds treated with Pharmatan form the basis for growing broilers with a higher live weight.

Structure analysis of abandoned bamboo stands using forest composition and above ground biomass coupled with allometry formula

Structure analysis of abandoned bamboo stands using forest composition and above ground biomass coupled with allometry formula

Relative growth of hand bone length to width by longitudinal investigation

Although many studies of the hand bone growth have done, there were few reports on their longitudinal study. In this article, the hand bone growth of longitudinal materials was studied from the standpoint of the relative growth.Radiographs of the hand bone of 16 boys and 21 girls were taken from 9 to 15 years of age at 6 month intervals. Lengths and widths of 5 metacarpal and 14 phalangeal bones were measured on the serial radiographs. The relative growth coefficients of length against width were calculated by means of least squares. The allometry formula y=bxa was valid to 19 hand bones for each individual. Each individual relative growth of 19 hand bones was suitable to simple allometry.Mean values and coefficients of variation of relative growth coefficients in the girls were almost larger than those in the boys. On the digit bones the marginal group grew wider than axial group. The growth gradients of the digit and the metacarpal bones within rows was reverse.The rank order correlation analysis of individual numerical order of 19 relative growth coefficients (growth gradient) showed that there are many variations from the person who have many significant correlative pairs to the person who have none. On the individual growth the growth gradient showed a tendency to be more similar in girls than in boys. The growth gradient on the average growth had only a few significant correlation with each individual growth gradient. It was suggested that the growth gradient of a paticular person is better representative of this group than that of average growth.Principal component analysis was accomplished to make individual variations clear. Four principal components whose eigenvalues exceeded unity were obtained from principal component analysis of the correlation matrix. Those were interpreted as the relative growth factors of the hand bone by the highest loadings as follow: F1, a size factor of relative growth coefficient. F2, a factor concerning distal and metacarpal phalanx opposition to middle and proximal phalanx. F3, a factor on marginal bones.From the scatter diagram plotting the 2nd component scores against the 1st component scores, on the 1st component girls' scores were higher than boys. On the contrary boys' component score were higher on the 2nd component. Girls' scores on the both components were more variable. The hand bone growth in girls was more variable in size but less variable in growth gradient than in boys.

Allometry of scent oil accumulation In heteroptera

1. 1. Intraspecies and interspecies comparisons in scent oil composition in Heteroptera bave been made with the aid of the allometry formula y = bx a . 2. 2. Allometry of 4-oxo-oct-2-enal on oct-2-enal is positive ( α > 1) in the two abdominal scent glands of Oncopeltus fasciatus and third abdominal scent gland of Pyrrhocoris apterus. 3. 3. Allometry of scent oil accumulation shows some sensitivity to temperature within the range 20–30°C. 4. 4. A functional difference in the two abdominal scent glands of O. fasciatus reveals itself as a tenfold difference in the magnitude of the proportionality constant b for allomctry of 4-oxo-oct-2-enal on oct-2-cnal.

Allometry of C 6 and C 8 alk-2-enals and alka-2,4-dienals in the metathoracic scent gland of Oncopeltus fasciatus

1. 1. Application of the allometry formula y = bx α to accumulation in the volatile aldehydes of the scent oil from the metathoracic scent gland of Oncopeltus fasciatus (Insecta, Heteroptera) is described. 2. 2. Allometry is positive ( α > 1) for hexa-2,4-dienal on hex-2-enal, for octa-2,4-dienal on oct-2-enal and for the C 6 scent aldehydes on the C 8. 3. 3. Allometry of the scent aldehydes is secondary to changes in the proportions of the scent esters (the C 6 and C 8 alk-2-enyl and and alka-2,4-dienyl acetates) produced by the secretory cells of the gland tubules. 4. 4. Although the rate of total scent oil production is a function of temperature (the Q 10 of this rate probably lies between 2 and 3 over the range 20–30°C) variations in incubation temperature have no effect on the constants of the allometry system.

Allometric nucleo-cytoplasmic volume relations and rotation ellipsoid neuronal bodies of the cat nodosal and superior sympathetic ganglia

Using a Henning and Elias' plot, evidence was obtained for the rotation ellipsoid nature of the three-dimensional shape of neuronal bodies of the nodosal and cervical sympathetic ganglia of the cat. Nucleo-cytoplasmic volume relationships for both types of ganglia neurons obeyed the allometry formula. The allometry coefficient (ratio of logarithms of cytoplasmic and nuclear volumes) was found to be similar in the neurons of both ganglia, its value corresponding to 1.38–1.43.

Age Change of Allometry Coefficients in Japanese

Though allometry formula (y=bxα) is not influenced directly by the age, character of the age group sampled is predicted to be reflected on allometry coefficient. So the age changes of the allometry coefficient of body weight, chest girth and sitting height against stature were analyzed on the both sexes from 6 to 14 year-old. As allometry coefficients in each age were various even within the same stature class and show directional changes with ages, age definition should be required especially in the group of 12-14 yearold, because of marked variation of the coefficients in this period.

Differential phylogenetic development of the acoustic nuclei among chiroptera.

The volumes of the acoustic nuclei of 19 speciesof Chiroptera belonging to 8 families have been compared with those of the basal insectivores by aid of the allometry formula. The progression indices h

Encephalization in Chiroptera

The brain weights of 51 species of Chiroptera belonging to 10 families were compared using the allometry formula and based on the brain weights of some of the most primitive recent Insectivores. Estimates for the degree of encephalization of the various systematic and dietary groups of bats were given in the form of progression indices. A certain amount of between-group overlap was observed.The lowest encephalized group is formed by the Emballonuridae, Molossidae, Vespertilionidae, Rhinolophidae, and Hipposideridae; a median position is occupied by the Nycteridae and Phyllostomatidae; and the highest position by the Desmodontidae and Pteropidae. The Noctilionidae are present in the lowest as well as in the highest groups in relation to differences in feeding habits of the various species. The following ascending order of encephalization was found: insect-eating forms, nectar feeders, frugivorous Microchiroptera, piscivorous species, bloodsuckers, and frugivorous Megachiroptera.The encephalization indices for the Chiroptera do not exceed the upper limit attained by progressive Insectivores while they reach to some extent into the lowest zone of the Prosimians.Before one can ascertain the true nature of the relationship between systematic and dietary groups and encephalization, a detailed investigation of the brain structures in various species must be carried out; this is now being done.

Volumetric Comparisons of Brain Structures in Bats (An Attempt at a Phylogenetic Interpretation)

Bats show, in spite of the unity which they derive from the unique possession of flight-ability, remarkable differences in their encephalization (Pirlot & Stephan, 1970). These differences were found to be more closely related to feeding habits than to systematic relationships. The brains of the insect hunting species show the lowest degree of encephalization when treated with the allometry formula. Then, in ascending order, come the nectarfeeders, the frugivorous Microchiroptera, the fisheaters, the vampires and finally the frugivorous Megachiroptera. The present analysis of a variety of parts of the brain confirm the close relationships between characteristics of the brain and feeding habits. Therefore, in spite of the relatively restricted material, an attempt was made to interpret this surprising interdependence, its possible causes and ways of phylogenetic development.

Fecundity of Atlantic Cod

Fecundity of Atlantic cod from the Newfoundland and Labrador area was investigated in relation to fish length, weight, and age. Variations in fecundity were best explained in terms of size, either length or weight. The fecundity–length relationship was adequately described by the simple allometry formula; fecundity–weight by an arithmetic straight line. Differences in fecundity from north to south are described and discussed in relation to descriptions from other areas. Substantial differences in fecundity of western and eastern Atlantic cod are noted.

Effect of Gibberellic Acid and Kinetin on Growth of the Primary Leaf of Dwarf Bean (Phaseolus vulgaris)

IN the course of experiments on the effect of gibberellic acid on leaf area it was found that this substance accelerated expansion of the primary leaf of dwarf bean (var. Canadian Wonder); but the final area attained was identical with that of leaves receiving no treatment. Kinetin (6-furfurylaminopurine), on the other hand, depressed the rate of leaf expansion. Areas were estimated by use of a regression equation relating to the product of length × breadth calculated from measurements of more than 100 leaves. This equation is: area (cm.2) = 0.8682 (± 0.0196) × p + 3.19, where p is length × breadth in cm.2. The application of the allometry formula indicated that treatment produced no change in shape of leaf, so it is justifiable to apply this regression equation irrespective of treatment. The leaves were sprayed as soon as they had unfolded and assumed a horizontal position (length about 5.0 cm.), and were kept in darkness for about 16 hr. in case kinetin was destroyed by light. The average daily increments in area plotted for the mean period are shown in Fig. 1. Leaves sprayed with gibberellic acid (50 p.p.m.) or gibberellic acid + kinetin (0.1 p.p.m.) at first increased in area at a greater rate than the control. Kinetin alone slightly depressed the rate of leaf expansion. About six days after spraying, the position was reversed and the control and kinetin-sprayed plants increased in area at a greater rate. The final area of the leaves sprayed with gibberellic acid was the same as that of the controls, but kinetin alone depressed final area (Table 1).

The Development of the Runner-bean Leaf with Special Reference to the Relation between the Sizes of the Lamina and of the Petiolar Xylem1

An investigation has been made of the relation between the sizes of the lamina and of the petiolar xylem of both mature and immature leaves of the runner bean (Phaseolus multiflorus Willd.). The ratios xylem area/lamina area and the number of vessels/lamina area are lowest for mature leaves. Immature leaves gave higher but somewhat more variable values for these two ratios. There is a constant growth ratio between the lpminn area and the xylem area, such that k is approximately o·61 in the allometry formula. The significance of the results is briefly considered from the point of view that the xylem area is related to the water requirements of the leaf.

魚個体群に於ける体重-体長関係の統計的取扱法について

Weight-Length relationship in fish population has been dealt with the following two methods: i) Coefficient of fatness (F), F=W/L3…………………………………………(1) ii) Allometric method, W=KLa…………………………………………(2) The first method in the cofficient of fatness (F). however, involves the following limitation and inadequacy: 1) From equations (1) and (2) comes out equation (3), F=KLa-3…………………………………………(3) in equation (3), when α=3, the value of F is constant with no regard to the body-length (L). In this case, therefore, the value of F is significant. But, in case α>3 or α<3, the value of F also becomes a function of the body-length. Therefore, in latter cases, coefficient of fatness (F) is inadequate. 2) The pattern of distribution of the value of coefficient of fatness (F) depends not only on the value of _??_ but on the distribution type of body-length. Therefore, except the case when α=3 and the distribution of F-value is normal, the stochastic treatment of F-value has no significance. 3) When there are flection point and discontinuity in weight-length relationship, the method in coefficient of fatness (F) is in danger of neglecting the biological importance of those factors. Tester (1932) figured the coefficient of fatness (K) by the following equation (4), K=W/La…………………………………………(4) Tester's method is excellent because of obeing able to cover the above-mentioned limitation and inadequacy in coefficient of fatness (F), but his method with the very premise of equation (2), is so complicated and disadvantageous. In this paper, as the starting point, is employed the logarithmic form of equation (2), i.e. log W=log K+α log L. …………………………………(5) or w=k+αl………………………………………………(6) The result of stochastic analysis of allometry formula Y=BXa, or y=b+αx by the author (1951) are applied to the weight-length relationship in fish population, and the test of significancy of “slpe and positional differences” of weight-length lines is used for its comparison of two populations of “Koayu”, plecoglossus altiuelis T. et. S. in Lake Biwa.

A Statistical Analysis of Taxonomic Differences within the Genus Tamandua Gray (Xenarthra).

Summary.1. The ten recognized subspecies of Tamandua tetradactyla (Linn.) are defined mainly by skull proportions. The differences between these subspecies have been analysed with the aid of statistical methods based on the allometry formula, in order to discover how far neglect of the fact that many proportions change with size has led to false conclusions.2. In order to provide a background for the statistical analysis, all available information on the characteristics and distribution of each race is first summarized, and controversial points discussed. The main points are as follows:– (a) Tetradactyla and longicaudata are not clearly defined. The latter seems to be distinct only in fur pattern, lacking the usual striping. (b) Instabilis and quichua show parallel characteristics with races of other mammals from the same localities, suggesting their peculiarities are due to ecological factors.(c) Only longicaudata, quichua, and possibly tetradactyla are distinguishable by their coat characters. (d) Tail‐lengths appear to fall into two size groups, chapadensis and instabilis having shorter tails than the rest. Tail‐length in instabilis is uncorrelated with head and body‐length, suggesting that its short tail is an independent character, not due to its small body‐size.3. Allen's classification of instabilis, chapadensis, mexicana, and chiriquensis into two groups, based on relative nasal length, is found to be erroneous. Instabilis appears to be a small edition of mexicana and chiriquensis in the skull characters studied, while chapadensis differs from the others in having a greater extension of the frontals at the expense of the nasals.4. Study of other skull characters suggests that the status of most of the races is dubious. Skulls from nearly all regions show marked variability in proportions, and there is no clear tendency for proportions to change with geographical position.5. Comparison of ranges and means suggests that only chapadensis and mexicana have any claim to be considered distinct subspecies on the basis of skull proportions. Chiriquensis, punensis, tambensis, and specimens from the Middle Amazons cannot with certainty be distinguished from the British Guiana form, tetradactyla. Sellata is probably identical with mexicana. The latter's sole peculiarity seems to be its relatively narrow rostrum.6. It is clear that proportional differences between two groups of animals cannot be accepted as evidence of taxonomic distinctness, when size differences occur, without further analysis. The tests described have been found satisfactory for the purpose of analysing proportional differences.7. The danger is emphasized of basing taxonomic classifications on small samples. Before subspecies are defined it is necessary to collect large samples from different regions and to study the fluctuational variability. Among mammals this is usually large for all quantitative characters.8. Adequate data for the study of rare animals such as Tamandua will only accumulate if museum taxonomists regularly publish comprehensive measurements of the specimens in their care. It is important to make available the individual measurements, since otherwise statistical analysis is severely restricted.9. All original measurements will be deposited in the library of the British Museum (Natural History), London.

Relative Growth in the Snout of Anteaters. A Study in the Application of Quantitative Methods to Systematica

Summary.1. The aim of the paper has been to show how far differences in proportions may safely be used in systematic grouping. The use of percentage sizes is unsatisfactory since they generally change with absolute size, and Huxley suggested the allometry formula as a basis for analysis. But no study has been made of the best statistical methods for (a) discovering the nature of the growth‐relationship between two organs from small samples, (6) estimating the most probable values of Huxley's growth‐coefficients and comparing these in different samples.2. Difficulties in (a) and (b) are discussed. While it is usually impossible to determine the nature of the growth‐relationship from small samples, the systematist can make use of the allometry formula if the points appear to show a linear trend when plotted on a double logarithmic grid. Reasons are given for supposing the normal regression methods applied to the logarithms of the measurements to be the best way of estimating the values of the growth‐coefficients.3. To illustrate the methods, measurements were made of lengths of maxilla;, nasals, and cranium in samples of the skulls of the three genera of Xenarthrous Anteaters, Myrmecophaga, Tamandua, and Cyclopes. Their adult facial indices and total skull‐lengths are:– Myrmecophaga: facial index=l‐6, skull‐length 36 to 38 cm. Tamandua: facial index=0–80, skull‐length 13 to 14 cm. Cyclopes: facial index =0–5, skull‐length up to 5 cm.The systematic problem is “Do genetic differences directly affecting relative face‐length intervene between the three genera, or are the laws of relative growth in face‐length the same throughout ?”4. Convenient changes in notation are suggested and the regression formulae described. Calculated values of a and their standard errors are given Table I. p. 59. t‐tests applied to these suggest that Myrmecophaga has a higher relative growth‐rate in face length than the other two genera, which do not differ very much. The initial growth index and its standard error are, however, found to be quite useless for purposes of comparison.5. A better method of analysis is proposed. This consists in comparing the fit of a single line, separate lines, and parallel lines to the samples by an analysis of Residual Variance. Comparison of parallel lines through the sample means and separate lines will test differences in slope, and comparison of a single line with parallel lines will test differences in other factors, here termed “positional.”6. These tests show no differences between the two samples of Tamandua measured by different observers. Applied to the three genera they show clearly that allometric differences intervene between them, both slope and positional differences being significantly large. Further tests show no significant differences in slope between Tamandua and Cyclopes, while positional differences between them appear only for the allometry of the maxillaæ. If this means that the snout has the same average relative growth‐rate in both genera, then calculation shows that Tamandua has on the average maxillae 1–36 times and nasals 1–09 times as long as Cyclopes with the same cranium length. Difficulties are discussed in interpreting the test for positional differences when slope differences are significant.7. Size‐increase in the skull of Myrmecophaga compared with Tamandua appears to have been concentrated in length. The former has relatively a much slimmer rostrum and more sharply‐pointed posterior projections to the nasals and anterior projections to the frontals.8. Most of the main differences between the skulls of Cyclopes and the two larger genera are probably the result of the marked size‐differences. The reduction in facio‐cranial flexure and sharpness of the dorsal edges to the orbits, and the loss of the eoronoid process, which occur in the larger genera, may be due to this factor. The systematic value of these differences is therefore doubtful, and the evidence for classifying Cyclopes in a separate subfamily after Winge, or in a separate family after Pocock, is unsatisfactory. A return is proposed to the original classification of the group as three separate genera forming the family Myrmecophagidse.9. These anteaters present the unusual case of a positive correlation between the relative growth‐rate of an allometric organ and final size.

Problems of Growth of the African Migratory Locust

General Growth.Generally, females have higher rates of growth than males. The phases, however, do not show appreciable differences in the rate. The pronotum has for increase in length the highest values which decrease throughout the instars (whereas the constants for the other parts remain fairly stable up to the fifth instar).Dyar's rule was applied for the growth in length of the middle femur and the width of the head, and it was found that the rule holds good for these parts.Przibram's rule, as modified by Bodenheimer, holds true for the growth in length of the different parts and shows the occurrence of latent cell-divisions varying from one (width of head and of pronotum) to four (length of pronotum). The number of latent cell-divisions keeps fairly constant in both phases.For wet weight Przibram's principle is inapplicable, owing to the large percentage of differences between the actual and calculated values.Gregarious males are heavier than solitary males up to the third stadium ; gregarious females are heavier than solitary females up to the third stadium ; fourth, fifth and adult stadia being characterized by higher values in wet weight for solitary females than for gregarious females. Females have higher rates of increase in wet weight than males. No significant differences exist in the rates of increase between gregarious and solitary individuals. In the fifth-adult stadium all the rates decrease except in gregarious females, which show a rise.Gregarious insects have higher values in dry weight than solitary insects, except solitary females in the adult stadium. The coefficients are higher for females than for males.The rates of increase reach the highest values in the second-third stadium of gregarious insects and solitary females, whereas solitary males have their highest value in the fourth-fifth stadium.With the exception of solitary females, all the rates of growth in dry weight decline in the fifth-adult stadium.The rates of growth of the hind legs obtained from the cube-roots of their wet weights are compared with the rates of linear growth of the hind femora. Their variation throughout the instars seems to be in opposite directions. Therefore it is suggested that the rates of growth in wet weight of the hind legs and the rates of growth in length of the respective hind femora are independent of each other.Growth of the parts.The application of the exponential allometry formula y=bxα to the data on dimensions of the parts of Locusta shows the existence of negative, positive and almost isometric growth.The pronotum has the highest value for the growth in length relatively to the growth in length of the middle femur ; the lowest value pertains to the growth in width of the head.Males have higher values than females ; phase gregaria exhibits higher growth-ratios than phase solitaria.With the exception of the hind femur the growth-ratios decline throughout the instars. The greatest decline pertains to the growth in length of the pronotum.A growth-gradient exists in Locusta with the highest value in the pronotum. The middle femur divides the growth-gradient into two parts : an anterior part with values decreasing with the growth of the insect, and a posterior part whose values increase with its growth.Effects of the amputation of the hind tibiae on crowded locusts.The effects obtained by mutilating both hind tibiae of three hundred first instar hoppers of Locusta migratoria migratorioides and placing them in a crowded condition are compared with the effects obtained by crowding a batch of the same number of first instar unoperated insects.The insects with their hind tibiae cut off did not develop as far as those of the control batch ; the differences in dimensions are greater for the hind femur than for the other parts of the body.In the experimental batch the hind femur, as a consequence of its useless condition, became extremely short as compared with the elytra, bringing the ratio E/F to a high value (over 1·950), thus leading to a false interpretation.The occurrence of the black-orange coloration in both batches suggested that both developed towards phase gregaria. This coloration was stronger and more uniform in the control batch than it was in the experimental batch. Thus the control animals developed into a better gregarious type.