This paper describes generalizations of simple growth equations made by assuming that one or more parameters have a probability distribution in the population. Thus, the product of the parental growth equation and the probability density function when integrated over the range of the parameter produces a compound growth function. In most cases, the resulting equations are more complex than the original function, but the new parameters are interpretable directly in terms of the distribution of the parameter in the population. Despite the frequent need for special functions, an effort has been made here to produce simple mathematical forms. An example is provided using some compound growth functions to describe real growth data. This method appears to be a meaningful and useful way to improve the modeling of growth.
In a sample of 67 litters of genetically uniform BALB/c mice, litter size before weaning, which ranged from 2 to 11 animals, had a strong negative and approximately linear effect on body and brain sizes at 100 days after birth. For both males and females, the difference between litters of 11 and 2 was about 3.7 g body weight and 42 mg brain weight. The difference in brain weights was similar to effects produced by severe protein-calorie undernutrition in the postnatal suckling period. The relationship between body weight and brain weight was approximately linear and the fit was not improved significantly by including a nonlinear term or using the allometric equation. The allometric exponent was approximately .35, which is close to values commonly observed for populations of mice having large genetic variability. Although the slopes of the equations relating brain size to body size were similar for males and females, females had substantially larger brains than their male littermates. When males and females were equated statistically for body weight, the brains of females averaged about 32 mg heavier. Statistical considerations in making these estimates are discussed.
Generalized logistic type and Gompertz type models were applied to the growth of average body weights in savannah baboons. The age scale was adjusted by the estimated age of statistical onset of adolescence. The distance curves could be linearized by an age-transformation. The average weight growth pattern of females was similar to males until about 160 weeks old for males. A turning age of growth was introduced for comparing growth patterns. Females chased the trace of males' growth until the turning age introduced. The turning age of females was near the average age of their menarches. However, the adolescent growth of average weights of males was completely different from of females after passing through the turning age. The velocity curve of average weight growth of females was similar to of males only until the ages of statistical onsets of adolescence.
The long term ingestion of a sugar-rich diet (low fat) caused severe obesity in adult rats. In a separate experiment, the habitual consumption of a fat-rich diet (40% kcal from fat) also caused severe obesity. Severe obesity developed in both groups of animals even though they did not overeat. Voluntary food intake for the sugar-fed rats averaged 28,314 +/- 756 calories/rat per 55 wks which was similar to the value of 28,884 +/- 953 calories/rat per 55 wks for the fat-fed rats. However, both values were lower than that of 32,869 +/- 588 for the control rats eating Purina chow. Despite a lower caloric intake, carcass fat averaged 45 +/- 1% for rats eating the sugar-rich diet and 46 +/- 2% for rats eating the fat-rich diet, but only 33 +/- 2% for rats eating a diet of Purina chow. These results provide evidence that severe obesity can develop in the absence of hyperphagia in animals eating a sugar-rich or fat-rich diet. Finally, a rat model for severe obesity is presented in which carcass fat ranged from 18% (lean) to 61% (severe obesity) using dietary intervention alone at critical stages of the animal's life.
Selection for rapid growth in the quail resulted in a changed growth pattern of the embryo and the extra-embryonic membranes (the yolk sac and allantois). The early part of the incubation period was characterized by a reduced embryo weight and a more rapid early development of the extra-embryonic membranes. These changes were followed by an increased growth rate of the embryo. The increased growth rate was apparently linked to the more rapid early development of the extra-embryonic membranes. Thus, the growth rate was most likely restricted by the capacity to absorb and utilize yolk. It also appears that at least part of the increase in growth rate was made possible by the change in the early embryonic growth pattern.
Four growth curve variables were measured in a population of rats in order to assess their association, if any, with a suite of morphometric characters. The growth curve variables (A = asymptotic weight, R = growth rate, P = percentage of asymptotic size at inflection, and G = time to grow from 10 to 90% of asymptotic size) were derived from Richards' curves applied to longitudinal body weight data, and the morphometric characters (measured in 189-day-old rats) consisted of 4 tooth and 7 bone variables. As assessed by a canonical correlation analysis, there was a significant association between the two sets of variables, especially between A and the skeletal variables. It was hypothesized that associations of the bone characters should be greater with A but less with R compared with those for the tooth characters, and this was shown to be the case. The canonical correlation analysis also showed a strong association of P with G in each sex, although in a factor analysis these two variables associated with R.
The effects of daily evening melatonin injections on serum and pituitary levels of growth hormone (GH) and follicle stimulating hormone (FSH) were investigated in male Syrian hamsters receiving thiourea in the drinking water. Melatonin injections, by themselves, had no significant effect on serum or pituitary GH. Thiourea induced hypothyroidism reduced pituitary GH content but increased serum GH several fold. Daily thyroxin (T4) injections for 3 weeks partially restored pituitary GH content and reduced circulating GH to control values. Melatonin injections prevented T4 from reducing circulating GH levels to normal in hamsters receiving thiourea. As previously reported, FSH levels in serum and pituitary were reduced by melatonin. Thiourea-induced hypothyroidism prevented this effect. Daily T4 injections increased circulating FSH levels above control levels; melatonin injections prevented this increase in serum FSH. These observations show that melatonin and T4 have antagonistic actions on GH and FSH release from the pituitary. We conclude that melatonin influences the release of hypothalamic hormones regulating GH and FSH release from the pituitary. The effects of T4 on the sensitivity to melatonin injections could be accounted for by thyroid hormone regulation of pituitary receptors for hypothalamic hormones. An alternative explanation is that T4 regulates the concentration of melatonin receptors in the central nervous system.
The sex-linked prenatally lethal gene tortoise (Moto), an animal model for the human disorder known as Menkes' Kinky Hair Syndrome (MKHS), was studied in the mouse (Mus musculus). The genetic effects upon reproductive performance, birth weight, preweaning growth, and mortality were evaluated to characterize the debilitating effects of the disorder. Reproductive performance of mice were evaluated in two mating types (dam X sire), mutant female (To/+) X normal male (+/Y) and normal female (+/+) X normal male (+/Y). Litter size was reduced in the To/+ X +/Y mating type as expected due to the death of To/Y offspring in utero. Adjusted birth weight of To/+ and +/Y offspring were identical, and both were greater (P less than 0.05) than +/+ offspring. Within one day, however, the To/+ littermates were smaller (P less than 0.05) than +/+ and +/Y and remained consistently inferior in growth through day 30. Normal females and normal males were similar (P greater than 0.05) in growth from day 1 through day 21. Thereafter, +/Y mice were consistently heavier (P less than 0.05) than +/+ mice through day 30. The To/+ genotype had the greatest (13.8%) preweaning mortality rate; +/+ and +/Y genotypes were comparable as were overall comparisons between parity 1 and 2. It is apparent from this study that the copper deficiency and lethality occurring in the progeny of mottled mice were primarily the result of the gene actions in the heterozygote animals. Progression of the disorder may be prevented by experimental determination of both the timing and targeting of in utero therapy in mottled mice and MKHS fetuses.
Frequently, experiments are conducted in order to investigate the effects of various treatments on an animal's growth rate. The data from these investigations usually consist of each animal's body weight or accumulative weight gain at specific times during the experiment. The most common statistical techniques for analysis of growth rates (increments in body weight over time) consider only terminal body weights or final accumulative weight gain. In this study, we compare growth rates over the duration of the experiment and use standard simultaneous testing procedures in order to accommodate more than two treatment groups. Results obtained by comparison of regression lines randomization analysis of variance, and repeated measures analysis are presented.