Mathematical model determines reaction between new predator and microbe competitor when the competitor is the predator's sole nutrient resource. The model utilizes differential equations to describe the interactions with the specific growth rates, and analyzes these growth rates as they are affected by population density and nutrient concentration

Weston, C. R.

Yang, J. N.

English

Mathematical model of predator effect on bacteria growt

NASA Technical Reports Server

A mathematical model of the effect of a predator on species diversity

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September 1970	 Brief 70-10006 
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P1MA ICH BRIEF 
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NASA Tech Briefs announce new technology derived from the U .S. space program. They are issued to encourage commercial 
application. Tech Briefs are available on a subscription basis from the Clearinghouse for Federal Scientific and Technical 
Information, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
A Mathematical Model of the Effect of a Predator on Species Diversity 
One of the striking features of terrestrial soils is the 
presence of a diversity of microbial species, many of 
which have overlapping nutritional requirements. 
Even a partial overlap in nutrient needs, between two 
microbes, predator and consumer, challenges the 
competitive exclusion principle—an ecological gen-
eralization that no two species can coexist indefinitely 
when they require a common limiting resource. 
A mathematical model has been developed to de-
termine what occurs when a predator is introduced, 
which has the normally successful microbe competitor 
as the sole nutrient resource. The conclusions derived 
from this model can be applied to other, more ad-
vanced ecological problems, e.g., wildlife population 
control. 
The analysis of the interactions of the predator and 
consumer populations and their resources is con-
sidered in two parts: first, the development of a basic 
set of differential equations which describe the inter-
actions with the specific growth rates (treated as 
undefined variables); second, a description of the 
specific growth rates as they are affected by popula-
tion density and nutrient concentration. 
Based upon the assumptions and the general test 
conditions, there is a theoretical expectation that (1) 
the level of resource concentration rises when the 
consumer population is reduced by predation, and (2) 
an additional consumer can coexist with the originai 
consumer utilizing the resources released by preda-
tion. These two conclusions are in full agreement with 
previous conclusions cited in the literature. Moreover, 
from this model it is found that the presence of the
second consumer stabilizes a predator-prey associa-
tion which otherwise might oscillate. 
These conclusions suggest that predators play an 
important role in maintaining species diversity, since 
predators reduce the number of individual prey 
organisms in a population to the level where they 
cannot fully exploit their potential resources. It can 
be reasoned that resources never limit population 
growth in the presence of the predators. The further 
implication is that another species which would have 
been excluded in competition for the resource may 
enter the environment and exist on an unexploited 
residue of resource. 
Note: 
The following documentation may be obtained 
from:
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Single document price $3.00 
(or microfiche $0.65) 
Reference: 
NASA-CR-101669 (N69-30085), A 
Mathematical Model of the Effect of 
a Predator on Species Diversity 
Patent status: 
No patent action is contemplated by NASA. 
Source: Jann Nan Yang and Charles R. Weston of 
Caltech/JPL 
under contract to 
NASA Pasadena Office 
(N PO- l 1230) 
Category 05 
{his document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person 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 such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19700000006 2020-03-17T00:01:27+00:00Z


A mathematical model of the effect of a predator on species diversity

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