Compound growth equation was developed in which the rate of this linear growth process is regarded as proportional to the mass already attained at any instant by an underlying Gompertz process. This compound growth model was fitted to the growth data of a variety of birds and mammals of both sexes

Laird, A. K.

English

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November 1968	 Brief 68-10427 
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the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Compound Equation Developed for Postnatal Growth of Birds and Mammals 
A study, entitled "Postnatal Growth of Birds and 
Mammals," has been reported by Anna K. Laird of 
Argonne National Laboratory, Argonne, Illinois. In 
the work, mathematical models of postnatal growth 
curves of various birds and mammals have been inter-
preted based on the compounding of an exponential 
growth process and a linear growth process. These 
models were then superimposed in the growth data 
from different species for comparison of the growth 
rates and the factors which affect these rates. 
In previous studies, the growth of tumors and of 
embryos and their parts was analyzed using a growth 
equation of the Gompertz type. This equation is based 
on the observation that the specific growth rate tends 
to undergo an exponential decay with time. 
In the postnatal growth of many mammals and 
birds, however the sigmoid curve described by the 
Gompertz equation continues into a straight line 
growth process, which is often extensive in time and 
contributes significantly to the final weight of the 
organism. 
In this study, a compound growth equation has 
been developed in which the rate of this linear growth 
process is regarded as proportional to the mass al-
ready attained at any instant by an underlying Gom-
pertz process. This compound growth model has been 
fitted to the growth data of a variety of birds and 
mammals of both sexes. Within this sample of or-
ganisnis, the linear growth rate differs greatly in 
absolute magnitude, but also, to a much smaller de-
gree, in proportion to the normalized Gompertz 
growth curves. Because the linear growth process 
varies in magnitude and may even be absent in normal 
growth, and because it can be eliminated by experi-
mental means, it seems likely that linear and Gorn-
pertz growth are separate biological processes
In agriculture, this compound growth model may 
be useful for the production of food animals. In 
some cases, for example, the empirical breeding 
methods used thus far actually have involved the 
selection of animals that complete the Gompertzian 
growth more quickly, and have a larger linear growth 
componenh The present mathematical model will 
enable the breeder to deal with these two growth 
processes as separate entities. 
Notes: 
I. Available information includes tables for the 
growth of the various species, results, and a dis-
cussion of the results. 
2. The information may be of value in the control 
and treatment of tumor growth, in studies on nutri-
tion and nutritive substances, and in the identifica-
tion of factors influencing growth rates of dif-
ferent races. 
3. Breeders of birds and, animals, medical and bio-
logical research laboratories, cancer prevention 
groups, and nutritionists may find this study of 
interest. 
4. Reference: Additional details may be found in 
"Growth", 1966, vol. 30, pp. 349-363. 
5. Inquiries concerning this report may be directed 
to:
Office of Industrial Cooperation 
Argonne National Laboratory 
9700 South Cass Avenue 
Argonne, Illinois 60439 
Reference: B68-10427
Source.: A. K. Laird
of the Biological and

Medical Research Division

(ARG-10l92) 
(continued overleafl 4
This document was prepared under the sponsorship of the Atomic 
Energy Commission and/or the National Aeronautics and Space 
Administration. Neither the United States Government nor any per-
son acting on behalf of the United States Government assumes any
liability resulting from the use of the information contained in this 
document, or warrants that the use of any information, apparatus, 
method, or process disclosed in this document may not infringe pri-
vately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19680000427 2020-03-12T06:01:25+00:00Z
Patent status: 
Inquiries about obtaining rights for commercial use 
of this innovation may be made to: 
Mr. George H. Lee, Chief 
Chicago Patent Group 
U.S. Atomic Energy Commission 
Chicago Operations Office 
9800 South Cass Avenue 
Argonne, Illinois 60439 
-	 - 
IS-CAS-42D 
RM. 1313	 KSC HQS. 
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Brief 68-10427	 Category 04


Compound equation developed for postnatal growth of birds and mammals

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