130
P. R. PAYNE, and ERICA F. WHEELER
intake to body weight and stage of growth. We have proposed a simple
model which describes the relation between caloric intake C and body
weight Was
Here kl and k2 are constants, characteristic of the particular animal concerned and represent the genetically determined aspects of growth.
When W is small, C::: kl WO.73, which agrees with the observation that
in young animals the maximum observed calorie consumption is a constant
multiple of the basal metabolic rate, which is in turn proportional to WO.73.
KLEIBER [3] has shown that for a number of species the value of kl falls
between 300 and 450 kcal/day/kgo. 73 , and we have taken 400 as a mean
value for all species. The term -k2 W expresses the fact that, as growth
proceeds, calorie intakes per unit of body weight progressively decline
towards a limiting value corresponding to adult maintenance levels. The
minimum calorie intake necessary for weight maintenance is close to 1.5 x
the basal metabolic rate, or::: 107 kcalJday/kgo. 73 [4], hence for any maximum body weight (Wma,J, the value of k2 = 400-107 = 293 W max -0.27
WmaxO.27
The resulting expression for caloric intake
C = 400 WO.73 - 293 W max -0.27W
(3)
is in very good agreement with observed food intakes at different weights
of the rat, the dog and man.
Equation (3) in conjunction with (1) and (2), leads to two differential
growth equations which have exact solutions and are very similar to those
described by VON BERTALANFFY [1].
Where protein content is the limiting dietary factor,
When caloric intake is limiting,
W= (z::r·
7
(1 _e-6.8k2IxlO_6y.7
(5)
Figure 2 shows the general form of these equations using a value of k2
appropriate to the rat. The energy limited curve, derived from (5), forms
an enveloping maximum growth curve and would only be obtained if the
diet contained ideal proportions of all essential nutrients. The lower curves,
derived from equation (4) predict the effects of varying proportions of
utilisable protein (P e) in the diet on growth velocity and maximum body
P. R. PAYNE, and ERICA F. WHEELER
intake to body weight and stage of growth. We have proposed a simple
model which describes the relation between caloric intake C and body
weight Was
Here kl and k2 are constants, characteristic of the particular animal concerned and represent the genetically determined aspects of growth.
When W is small, C::: kl WO.73, which agrees with the observation that
in young animals the maximum observed calorie consumption is a constant
multiple of the basal metabolic rate, which is in turn proportional to WO.73.
KLEIBER [3] has shown that for a number of species the value of kl falls
between 300 and 450 kcal/day/kgo. 73 , and we have taken 400 as a mean
value for all species. The term -k2 W expresses the fact that, as growth
proceeds, calorie intakes per unit of body weight progressively decline
towards a limiting value corresponding to adult maintenance levels. The
minimum calorie intake necessary for weight maintenance is close to 1.5 x
the basal metabolic rate, or::: 107 kcalJday/kgo. 73 [4], hence for any maximum body weight (Wma,J, the value of k2 = 400-107 = 293 W max -0.27
WmaxO.27
The resulting expression for caloric intake
C = 400 WO.73 - 293 W max -0.27W
(3)
is in very good agreement with observed food intakes at different weights
of the rat, the dog and man.
Equation (3) in conjunction with (1) and (2), leads to two differential
growth equations which have exact solutions and are very similar to those
described by VON BERTALANFFY [1].
Where protein content is the limiting dietary factor,
When caloric intake is limiting,
W= (z::r·
7
(1 _e-6.8k2IxlO_6y.7
(5)
Figure 2 shows the general form of these equations using a value of k2
appropriate to the rat. The energy limited curve, derived from (5), forms
an enveloping maximum growth curve and would only be obtained if the
diet contained ideal proportions of all essential nutrients. The lower curves,
derived from equation (4) predict the effects of varying proportions of
utilisable protein (P e) in the diet on growth velocity and maximum body