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PubMed1991

Multiphasic growth and allometry.

Multiphasic growth assumes increase in body weight, or in other body measures, to be a result of more than one growth phase. Therefore, the concept of allometry can be extended from relation between body measures to relation between phases of growth. For two phases of growth, body weight (W) and tail length (L) can be partitioned into W1 + W2 and L1 + L2. Here, W1 and W2 correspond to phases 1 and 2 of weight and L1 and L2 to phases 1 and 2 of length, where each phase is described by a logistic function. Diphasic functions were applied to growth curves for body weight and for tail length of mice that were progeny of a transgenic male mated to random-bred NMRI females. A group of 20 female and male mice with high body weight at week 12, assumed to be transgenic, and a group of 20 with normal body weight, assumed to be non-transgenic, were selected for comparison. Body weight and tail length were measured about weekly from 3 to 26 weeks of age. Allometric relations between phases for weight (W1 and W2) and tail length (L1 and L2) are presented using predicted values based on estimated parameters of the diphasic growth functions. Differences between ages at maximum gain and ratios of duration of phases were analyzed. Growth in second phase of body weight appeared to be unrelated to growth in first phase of body weight and unrelated to growth in tail length. Growth in each phase of tail length appeared to be close to a simple allometric relation with growth in first phase of body weight. It is now feasible to study multiphasic allometric relations of growth between phases of one body measure and between phases of different body measures by comparing estimates of parameters of the multiphasic growth function.

Animals↗
PubMedDate not supplied

Allometry of hepatic weight growth in human staged fetuses.

The growth of the hepatic weight was correlated to fetal parameters of maturity (gestational age, crown-rump length and weight) in 70 human fetuses ranging from 14 to 39 weeks post-conception using the allometric method. The growth of the hepatic weight presents moderate positive allometry relative to age and C-R length, and isometry relative to fetal weight. The coefficiens of correlation are very high (p less than 0.001, Table 1). This study presents growth curves of the hepatic weight useful in medical branches such as anatomy, forensic medicine, fetopathology, medical imagery, onstetrics and pediatrics.

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PubMedDate not supplied

Brain and body growth and allometry in the Mongolian gerbil (Meriones unguiculatus).

A new four-parameter version of Pütter's curve (Pütter, 1920), recently developed by Jolicoeur and Pirlot (1988), is applied to cross-sectional data on brain and body growth in 127 male and 136 female Mongolian gerbils (Meriones unguiculatus) ranging from birth up to approximately 2 years in postnatal age. The physical development of the gerbil is more rapid than that of the white rat and of the domestic rabbit even though its behavioral development is known to be somewhat slower. Like other recent studies on rats, rabbits and humans, the present analysis indicates that complex allometry (curvature of log-log relationships) is more widespread in the quantitative development of mammals than generally realized.

Age Factors↗
PubMed1989

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus): II. Allometry and heterochrony.

Based on a homogeneous sample of 212 individuals spanning all postnatal periods, we examine the ontogeny of cranial sexual dimorphism in Bornean orang-utans (Pongo pygmaeus pygmaeus) by means of allometric analysis and in terms of heterochrony. The bivariate growth allometries of 20 cranial dimensions against basicranial length yield two major patterns. Confirming the null hypothesis, strong ontogenetic scaling, where growth regressions of both sexes fall along a single ontogenetic continuum, and where shape differences between adult males and females result from the extension of relative growth in the smaller females to larger size in males, is found in 10 cases. Ontogenetic scaling is particularly strong in proportions of (1) the neurocranium directly associated with brain size, (2) the orbital region, and (3) the dental arcade. In terms of heterochrony such a pattern most likely is the result of a process termed "time hypermorphosis", i.e. an extension of the growth period in time in males. The second major pattern seen in the remaining 10 cases shows a departure from ontogenetic scaling, with males exhibiting a significantly steeper slope than females. Departures from ontogenetic scaling, where size and shape are dissociated with adult males being disproportionately larger than adult females, are found in proportions of cranial regions directly associated with secondary sexual character development: prognathism, canine size, and cheek pad area. In terms of heterochrony such a pattern most likely is the result of a process termed "acceleration", i.e. the rate of shape change is increased in males.

Animals↗
PubMed1989

The role of time and size in ontogenetic allometry: I. Review.

Several interconnected issues are a part of most studies of ontogenetic allometry, the relationship between size and shape during growth. One issue is the choice of a model, either linear or one of a series of nonlinear models that have been proposed in the literature. The independent variable, against which growth is assessed, can be a measure of time, e.g., age or a measure of size, e.g., weight. These categories of independent variables have become confused with Medawar's (1945) classification of allometric studies as empirical or deductive. Medawar's distinction may be less useful than Tukey's (1980) between exploratory and confirmatory studies. The "correct" choice for some of these options will be a function of the data set being analyzed. However, an understanding of the implications of these issues is necessary to make the correct choices.

Age Factors↗
PubMed1988

Asymptotic growth and complex allometry of the brain and body in the white rat.

A new four-parameter version of Pütter's growth curve (Pütter, 1920) is obtained by replacing time by a smooth non-negative function which incorporates an initial delay. Fitted through constrained iteratively-reweighted multiplicative least-squares, this curve provides an accurate description of asymptotic growth and complex allometry of brain weight and body length and weight in a cross-sectional sample of forty-four male white rats.

Animals↗
PubMed1985

Static genetic and phenotypic allometry of dental traits in inbred and hybrid house mice.

Static allometric coefficients were estimated by regression and reduced major axis methods for second and third mandibular molar widths scaled on body weight in 42-day-old inbred and hybrid house mice. Phenotypic slopes were calculated by combining inbred and hybrid strains, and genetic slopes were obtained from differences among the strains. It was hypothesized that the genetic scaling, which reflects the expected evolutionary allometry between populations if they have been produced from directional selection on body weight alone, would exceed the phenotypic scaling. The genetic coefficients were generally higher (average regression estimates in inbreds = 0.65) than the phenotypic ones (comparable average = 0.47), but the differences were non-significant. It was concluded that the higher scaling of tooth dimensions in interspecies versus intraspecies comparisons typically found in previous studies therefore could not necessarily be explained as a secondary response to selection for body size, although more information is needed about trends in the scaling of mammalian teeth at different ages.

Animals↗
PubMed1979

Post-hatching growth and allometry of the teleost brain.

The growth of the brain in the rainbow trout follows an S curve: E = 0.04 t3 + 0.26 t2 - 0.06 t + 0.04 with t (time) in days and E (brain weight) in mg. The growth of the brain, relative to the body, can be given, after longarithmic transformation, by: Y = 0.011 + 0.835 X - 0.047 X2 where Y is log brain weight and X log body weight. This formula is consistent with that of every species after necessary changes of origin. The coefficients of allometry corresponding to this curve vary from 0.788 (body weight from 0.01 to 0.1 g) to 0.226 (body weight from 10 to 100 kg), the most common values varying between 0.507 (body weight from 10 to 100 g) and 0.414 (body weight from 100 g to 1 kg).

Animals↗
PubMed1982

Allometry and multivariate growth revisited.

Turner (1978) introduced a class of deterministic models to describe multivariate growth processes along with a least squares fitting procedure. Turner's fitting procedure is shown to be ill founded and the methods of inference associated with it dangerously misleading. An alternative class of stochastic models is introduced; this is largely based on Turner's generalization of allometry and the Lotka-Volterra equations. The associated fitting procedure is the method of maximum likelihood which allows valid inferences to be made. As an example of the superiority of this new class of models in describing multivariate growth processes one of the data sets analysed by Turner is reconsidered here. Some general comments are made on Turner's analysis of the famous lynx and hare data.

Animals↗
PubMed1980

[Allometry and growth functions (author's transl)].

The concept of allometry is traced back to its origin and development during 140 years including opinions of quite different consequences. As a mean topic the allometric relation is regarded in its application to organic growth of parts to that of a body as a whole. For general considerations two simplified growth functions after Janoschek (1957) and the author are submitted to detailed investigation in order to demonstrate the mathematical treatment supported by graphs. Finally the question is raised whether the allometric relation may have a chance when growth procedures do not occur synchronously. For this case mathematical ideas are taken into account which can only be varified or negated by pursuing a broad variety of cases belonging to this category.

Animals↗
PubMed1980

Allometry formula: a cellular model.

The simple allometry formula y = bxk is often used to describe the relative growth of two parts X and Y of an organism. The allometric constant b can be usefully identified with the relative number of cell division centers (germinal centers) of the two parts, and the allometric constant k can be usefully identified with the relative frequency of cell division of the two parts. This approximation leads to experimentally testable predictions: for example, the developing brains of mammals and birds may have germinal centers not present in the developing brains of fish and reptiles, and the developing brains of humans may differ from the developing brains of monkeys in their rates of cell division.

Animals↗
PubMed1978

Allometry and multivariate growth.

Multivariate allometry, and conservative and nonconservative growth models are generalized by a set of global differential equations, preserving the linear trajectory property. Linear least squares methods are exposited for estimation of parameters, comparing special cases and drawing qualitative conclusions. Three classical sets of data are analyzed in detail, illustrating the usefulness and simplicity of the method.

Animals↗
PubMedDate not supplied

Growth allometry of the mandibles of giant transgenic mice: an analysis based on the finite-element scaling method.

Transgenic mice genetically engineered to produce increased levels of growth hormones, accelerated somatic growth, and larger terminal sizes [Palmiter et al., 1982, 1983] offer an intriguing model with which to investigate the genetic and developmental control of skeletal proportions. In this study, form differences in the mandible between giant transgenic mice (MT-rGH) and their normal litter-mate controls are examined using data generated by finite-element scaling analysis (FESA). Finite-element scaling analysis is a tensor based method developed to study morphological differences between forms. The method uses landmark data to provide measures of size and shape differences local to those landmarks of mandibular size and shape differences for 18 landmarks were compared between the two mouse samples. Bivariate and multivariate analyses were completed to ascertain 1) whether the mandible of larger transgenic mice differed significantly from normal controls, and 2) if observed proportion change resulted from the general allometric affects of overall mandibular size increase. Comparisons of local size and shape differences against a measure of total size difference reveal similar trajectories of growth allometry, indicating that proportion differences between adult control and transgenic mice result from ontogenic scaling.

Animals↗
PubMed1998

The effects of muscular dystrophy on craniofacial growth in mice: a study of heterochrony and ontogenetic allometry.

Mechanical loading of muscles on bones at their sites of attachment can regulate skeletal morphology. The present study examined the effects of muscle degeneration on craniofacial growth, using two strains of muscular dystrophic mice, Mus musculus, differing in pathological severity. We collected radiographic and weight data longitudinally and digitized radiographs to obtain distances between anatomical landmarks in different functional regions of the skull. We then quantified heterochronic and allometric differences among genotypes and between sexes. Because growth is nonlinear with respect to time, we first used the Gompertz model to obtain heterochronic growth parameters, which were then tested with ANOVA. Ontogenetic allometric analyses examined the scaling relationships between various measurements with linear regressions. For most measurements the severely dystrophic mice are significantly smaller in final size than both the control and the mildly dystrophic mice, which are statistically indistinguishable. Measures of total growth and the neurocranium exhibit more differences among groups in heterochronic parameters of early ontogeny because growth in these regions is controlled primarily by brain expansion that ceases early in development. In contrast, the face and mandible exhibit more differences in later growth parameters possibly because of the increased influence of muscles on these regions as growth progresses. The severely dystrophic mice have flatter, more elongate skulls and mandibles than those of the other two genotypes, concurrent with an absence of muscular forces to stimulate growth in a superior-inferior direction.

Alleles↗
PubMed1999

Sexual dimorphism and ontogenetic allometry of soft tissues in Rattus norvegicus.

Most studies of sexual dimorphism in mammals focus on overall body size. However, relatively little is known about the differences in growth trajectories that produce dimorphism in organ and muscle size. We weighed six organs and four muscles in Rattus norvegicus to determine what heterochronic and allometric scaling differences exist between the sexes. This cross-sectional growth study included 113 males and 109 females with ages ranging from birth to 200 days of age. All muscle and organ weights were ultimately greater in males than in females, because males grew for a longer period of time, had a greater maximum rate of growth, and spent more time near the maximum rate. No ontogenetic scaling differences existed between the sexes in organ weight except for lungs and gonads. During growth, organ weights were negatively allometric to body weight. No scaling differences relative to body weight existed between the sexes for muscles; however, there was variation in the allometric relations among muscles relative to body weight. Sexual dimorphism in muscles and organs appears to be a size difference resulting from differences in the duration and rates of growth.

Animals↗
PubMed1998

Cranial allometry and geographic variation in slow lorises (Nycticebus)

A series of 20 craniodental measurements was obtained for two sister taxa: Nycticebus coucang (common slow loris) and N. pygmaeus (pygmy slow loris). Multivariate analysis of variance was performed with adult data to describe patterns of subspecific and specific variation in this genus. The geometric mean of adult cranial dimensions was compared to field data on latitudinal coordinates for available specimens to investigate if size variation in Nycticebus is clinal in nature. Ontogenetic series for larger-bodied N. coucang and smaller-bodied N. pygmaeus were compared to test the hypothesis that species and subspecific variation in skull form results from the differential extension of common patterns of relative growth. A MANOVA provides independent support of Groves's [pp. 44-53 in Proceedings of the Third International Congress on Primatology, Vol. 1 (Basel: S. Karger), in 1971)] classification of Nycticebus into two species, with four subspecies in the common slow loris and one form of the pygmy slow loris. Within N. coucang, cranial proportions for all four subspecies are ontogenetically scaled, and size differentiation is mainly clinal (Bergmann's Rule). N. c. bengalensis represents the most northerly disposed and the largest form. N. c. javanicus represents the next-largest form and is located in a southerly direction the next-farthest away from the equator. N. c. coucang and N. c. menagensis are both equatorial; however, the latter subspecies is the smallest. A genetic basis for some of the taxonomic variation between N. c. coucang and N. c. menagensis is supported by such nonclinal variation in body size. Variation in the presence/absence of I2 is not size-related but rather tracks geographic proximity and isolating factors which predate the most recent inundation of the Sunda Shelf. Although they inhabit a nonequatorial environment, pygmy slow lorises are the smallest of all Nycticebus. As N. pygmaeus is sympatric with N. c. bengalensis, the largest slow loris, it appears that the evolution of its smaller body size represents a case of character displacement. Unlike N. coucang, skull size becomes significantly smaller in more northern N. pygmaeus. This may also reflect character displacement between sympatric sister taxa underlain by a cline-dependent ecological factor which is marked in more northerly latitudes. On the other hand, the negative correlation between body size and latitude in N. pygmaeus could be due to the influence of nonprimate fauna, such as predators, which themselves evince a similar clinal pattern. Analyses of relative growth indicate that skull proportions in the two species of Nycticebus are ontogenetically scaled in two-thirds of the cases. All but one of the seven comparisons (interorbital breadth) which do not indicate ontogenetic scaling represent part of the masticatory complex. This likely reflects a reorganization of N. pygmaeus maxillomandibular proportions linked to smaller size and changes in diet.

Animals↗
PubMed1988

Growth allometry of craniomandibular muscles, tendons, and bones in the laboratory rat (Rattus norvegicus): relationships to oromotor maturation and biomechanics of feeding.

This study addressed the problem of how growth of craniomandibular muscles, tendons, and bones influences the acquisition of oromotor skills and biomechanics of feeding in the laboratory rat (Rattus norvegicus). Rats representing a 6.6-fold size range were dissected, and muscles, tendons, and mandibles were weighed. Cross-sectional areas of tendons and bones providing attachment surfaces for muscles were estimated. Ontogenetic scaling of craniomandibular muscles, tendons, and bones was described by using linear regression models, and departures from size-required compensations were used to characterize changes in oromotor function. A two-dimensional model was developed which permitted calculation of mechanical advantages of four masticatory muscles; the model was used to show how mandibular growth and tooth eruption influence the biomechanics of rat feeding. Relative to mandible weight, most jaw muscles scaled either isometrically or positively, tendon cross-sectional areas scaled isometrically or negatively, and bone surfaces scaled negatively. With the exception of the superficial masseter and internal pterygoid muscles, mechanical advantages did not change significantly during mandible growth. Growth patterns of craniomandibular muscles, tendons, and bones contribute significantly to changes in morphology and oromotor function.

Animals↗