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(b) Over a unit interval, a certain portion (say
g
) of group E moves to
the group of infectious I.
VI. PREDATOR-PREY INTERACTIONS
We now investigate what may happen to the sizes of populations when
one species preys upon another. One might conjecture several different
possible outcomes. The predator may eliminate the prey, and, unless
it finds something else to eat, the predator would then follow its prey
into extinction. The prey may evade the predator, and the predator
would then starve. Finally, predator and prey may exist in a balance,
with each population exerting some control over the other in a manner
that maintains both populations.
As an example, let us consider the laboratory experiments conducted by
the Russian microbiologist Georgii Frantsevich Gause (1910-1986). When
Gause combined populations of Paramecium caudatum, a ciliated
protozoan, and Didinium nasutum, a predatory protozoan, in a sediment-
free medium, the Didinium ate all of the Paramecium and then starved to
death. However, when he combined the two protozoans in a medium
with sediment, the Paramecium were able to hide from the Didinium
and the Didinium starved. Finally, if Gause periodically added
Paramecium to the sediment-free medium, he was able to maintain
populations of both predator and prey that would continue rising and
falling for a few cycles (Gause [1934]). The last experiment was of
particular interest because it indicated that predator and prey
populations could coexist in a laboratory setting under careful control.
A later experiment by Luckinbill (1973) demonstrated that by increasing
the viscosity of the medium (which decreased the encounter rate
between predator and prey), it is possible to obtain prolonged
coexistence without the periodic ''immigrations'' of Paramecium.
Figure 2-15 shows the population levels of Paramecium aurelia and
D. nasutum in a water medium with methylcellulose added for increased
viscosity. Here again, it is clear that coexistence involves cycles in the
population sizes of both predator and prey.
The sustained oscillations observed in the population levels should not
be surprising at a heuristic level. High prey levels naturally stimulate
the growth of the predator population, which, in turn, causes a decline in
the prey population and a subsequent decrease in the predator
population due to the shortage of food resources. The low level of
predators then allows for the prey population to increase, and the cycle
repeats itself. We next present two more examples illustrating that
coexistence of predator and prey populations involves cycles in the
population numbers.
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