Models of the Growth of Organisms under
Nutrient Limiting Conditions
P. R. PAYNE, and ERICA F. WHEELER
With 3 Figures
Abstract
Mathematical models of the growth of animals have been based on consideration of possible internal factors which regulate and limit metabolism so that
the resultant growth equations contain only so-called genetic growth constants.
In most practical situations, however, the growth of animals can be influenced by
changing the relative proportions of essential nutrients in the diet. Two growth
equations are described: (1) one which applies to the growth when the diet fed
has a correct balance of essential nutrients and growth is limited only by the total
intake of metabolizable energy; (2) the other, when the ratio of utilizable protein
to energy in the diet is the factor deciding growth rate and maximum body size.
Since the beginning of this century, numerous authors have attempted
to express their ideas about the nature of animal growth in the form of
mathematical models. Most of these have been based on a consideration of
the growth process as the interaction between an early self-accelerating
phase, and a later self-inhibiting phase, both of which are regarded as being
under the control of genetically determined factors. Thus BRODY [2] used
the two equations:
Weight (W) = a e k1t
and W = W max - b e- k2t
to describe the two phases of growth, where t stands for time and kl' k2
and W max were regarded as genetic growth constants. These constants are
of great importance in the study of the comparative physiology of growth.
However, under most practical conditions both phases of growth are
influenced not only by genetic factors but also by the quality of the food
supply; this includes both the proportions of essential nutrients in the diet
and the total quantity of food consumed. Thus no mathematical description
of growth will be complete unless it takes into account nutritional factors
as well as internal regulatory mechanisms.
One simple example of a growth process which appears to be controlled
principally by the total supply of nutrients is the growth of the foetus. This
is accurately described by a model in which foetal growth rate is taken to be
Nutrient Limiting Conditions
P. R. PAYNE, and ERICA F. WHEELER
With 3 Figures
Abstract
Mathematical models of the growth of animals have been based on consideration of possible internal factors which regulate and limit metabolism so that
the resultant growth equations contain only so-called genetic growth constants.
In most practical situations, however, the growth of animals can be influenced by
changing the relative proportions of essential nutrients in the diet. Two growth
equations are described: (1) one which applies to the growth when the diet fed
has a correct balance of essential nutrients and growth is limited only by the total
intake of metabolizable energy; (2) the other, when the ratio of utilizable protein
to energy in the diet is the factor deciding growth rate and maximum body size.
Since the beginning of this century, numerous authors have attempted
to express their ideas about the nature of animal growth in the form of
mathematical models. Most of these have been based on a consideration of
the growth process as the interaction between an early self-accelerating
phase, and a later self-inhibiting phase, both of which are regarded as being
under the control of genetically determined factors. Thus BRODY [2] used
the two equations:
Weight (W) = a e k1t
and W = W max - b e- k2t
to describe the two phases of growth, where t stands for time and kl' k2
and W max were regarded as genetic growth constants. These constants are
of great importance in the study of the comparative physiology of growth.
However, under most practical conditions both phases of growth are
influenced not only by genetic factors but also by the quality of the food
supply; this includes both the proportions of essential nutrients in the diet
and the total quantity of food consumed. Thus no mathematical description
of growth will be complete unless it takes into account nutritional factors
as well as internal regulatory mechanisms.
One simple example of a growth process which appears to be controlled
principally by the total supply of nutrients is the growth of the foetus. This
is accurately described by a model in which foetal growth rate is taken to be