Models of Growth under Nutrient Limiting Conditions
129
If time is measured from the completion of a short lag phase (t'),
associated with the process of implantation,
W = II (t - t'y .
Figure 1 shows how well such an equation describes the growth of the
foetuses of a wide variety of species.
Table 1. Numerical [,a/ues of the parameters of the equation W = a (t-t')3 for foetal
,~rowth of severa! species.
SPECIES
a X 10 6
t'
Chick
4
1·1
i\fouse
1
8·0
Guinea Pig
0.6
15
Pig
1
28
Cow
3.2
56
Rhesus
0.3
29
Man
0.2
36
In order to develop a mathematical description of growth in later life,
we must start from what is known of the efficiency of food utilisation over
short periods of time. MILLER and PAYNE [4] have described two equations
which relate instantaneous growth rates to the balance between gain due to
the anabolism of available nutrients in the diet, and losses due to the catabolism of body constituents. Thus, when the growth limiting factor in the
diet is protein,
dlV
-~ = II (pee - 250 WO. 73 )
dt
where e = intake of metabolisable energy per day (kcals)
(1)
P = protein calories expressed as a percentage of total calories in the
diet
e = efficiency of protein utilisation (NPU), and,
II is a constant relating body weight gain to body nitrogen gain.
When the only dietary factor limiting growth rate is the consumption
of total metabolisable energy (e), we have:
dJli = II (6.8 e - 725 WO.73)
d t
(2)
These two equations give useful predictions of weight gain over short
periods of time for animals, when e, P and e are known. For long term
predictions we need additional information about the relation of caloric
9 3. Symp. Quant. BioI.