Species Competition and Predation - Ecological Systems - page 239

Lotka-Volterra competition equations, as discussed above, as direct contributions
to the coefficients of density-dependence a . However, other aspects of the behavior
of organisms are not accounted for well because all resource acquisition rates and
foraging rates are assumed to be linear, i.e., the amount of any resource or prey
consumed or captured by an individual organism per unit time is simply propor-
tional to the abundance of that resource or prey [ 17 ]. One very simple and almost
unavoidable deviation from the linearity of Lotka-Volterra equations occurs
through the simple fact that an individual organism is generally limited in how
much resource can be consumed per unit time, or howmany prey can be captured and
consumed. As a resource or prey becomes very abundant, the rate of consumption
normally plateaus. Such plateaus weaken density-dependent feedback as densities
increase, creating instabilities in population dynamics and promoting population
fluctuations [ 1 ].
There is a vast literature on how these fluctuations might be stabilized and the
extent to which they are indeed responsible for population fluctuations in nature [ 1 ].
Some scenarios involving population fluctuations provide further mechanisms of
coexistence, because they enable population fluctuations to be partitioned by the
various species, as discussed below ( environmental and population fluctuations ).
However, when such nonlinearities are not strong enough to destabilize dynamics,
and even in many cases when they do, the general principles for the Lotka-Volterra
case continue to apply to the extent that they have been studied theoretically. For
instance, a very general development of Levin [ 41 ], though lacking specific detail,
is entirely consistent with the messages from the Lotka-Volterra development on
partitioning resources and predators.
Resource-competition models where the resources do not regenerate in
a Lotka-Volterra manner have also been studied [ 46 ], reproducing much of the
detail, even quantitatively, for the Lotka-Volterra case. For plants, the key resources
are light energy and simple inorganic compounds. Obtaining them in the right
proportions is key to optimum plant growth, which makes the equations not just
nonlinear, but nonadditive in the different resources. Despite these differences, the
qualitative picture given here reappears in a different quantitative form [ 29 , 31 ].
Nonlinear predation for equilibrium scenarios has been studied in limited situations
[ 40 , 47 - 49 ]. Quantitative variations on the results from the Lotka-Volterra case are
found, but again in general the qualitative messages here remain intact. The reason is
the fundamental nature of the requirement for coexistence that a species should
inhibit its own growth more than it inhibits the growth of other species if it is to
coexist with them. Thus, the requirement that intraspecific density dependence be
stronger than interspecific density dependence is a robust requirement [ 15 ]. More
complex nonlinear situations differ only in providing alternative ways of achieving
this outcome. Partitioning of the environment, in one form or another, remains
common among these alternative models. The major exception is for complex
behaviors that lead to frequency dependence, as discussed next.
Some of the strongest effects occur when the per capita rates of foraging depend
on the relative abundances of the species. The linear rates assumed in the
Lotka-Volterra development mean that the fraction that any particular prey species