Species Competition and Predation - Ecological Systems - page 226

trophic level. Critical to understanding of the ultimate effects of competition is the
extent to which negative feedback of a species on itself limits its ability to increase
and harm other species.
Apparent competition is understood by entirely analogous effects. In this case,
we note that N 2 is preyed upon by P 1 and P 2 . An increase in N 2 benefits both P 1 and
P 2 . These predators may therefore increase in abundance, and as a consequence,
predation on the second trophic level will increase. Again, increasing the density of
a species in the middle trophic level feeds back negatively to itself and to other
species. Thus, in a food web, multispecies density dependence occurs when
changes in the density of a species within a given trophic level feed back to that
trophic level through linkages to other trophic levels, modifying the growth rates of
the species. The term “density dependence” is traditionally used in ecology just for
feedback from a species to itself, but understanding of the joint effects of predation
and competition requires broadening of this concept to interspecific density depen-
dence where increasing the density of one species affects the per capita growth rate
of another species. Consistent with this usage, the traditional density dependence
concept of ecology becomes intraspecific density dependence. Competition and
predation both contribute to intraspecific and interspecific density dependence [ 17 ].
Basic understanding of the role of competition in ecological communities is
usually represented by the Lotka-Volterra competition equations. Using the species
labels to mean also their densities, these equations can be written in the form

!

X

n

1
N i

dN i
dt ¼

r i 1 a ij N j ; i ¼ 1 ; :::; n : (13.1)

j ¼ 1

These equations define the per capita growth rate of each species in the focal guild,
which reflect the average conditions that individuals of each species experience.
The quantity r i is the maximum per capita growth rate of species i , which is reduced
by the terms representing density dependence inside the parenthesis. The coeffi-
cient a ij measures density dependence of species j on species i . It measures how
much the per capita growth rate of species i , as a proportion of its maximum value
r i , is decreased by increasing the density of species j by one unit. This coefficient
measures interspecific density dependence if j is different from i , and intraspecific
density dependence if i = j . The coefficient of intraspecific density dependence
defines the so-called carrying capacity for a species: K i = 1/ a ii . Traditionally, the
Lotka-Volterra competition equations have been parameterized with the competition
coefficients defined as multiples of the carrying capacity, with the carrying capacity
itself appearing explicitly in the equations, but this approach is now known to obscure
the workings of the equations [ 15 ], and so is not done here.
Recent understanding shows that the Eq. 13.1 can also represent apparent
competition, not just competition, and indeed they can represent the combined
effects of competition and apparent competition. To do this, the equations are
derived from a larger set of equations that take account of the direct interactions
of the focal species with other species in the food web [ 17 ]. Thus, these equations