Species Competition and Predation - Ecological Systems - page 230

In other words, a simple fitness ratio greater than 1 is sufficient for one species to
exclude the other. When r < 1, the fitness ratio is discounted by the overlap

measure to determine if exclusion will occur. For example, if the overlap is ½,
a species has to have fitness more than twice as high as the other to exclude it. The
mathematics implies this outcome, but intuitively the idea is that the less species
overlap in their niches, the more difficult it is for one species to exclude the other,
but this can still occur if a species has a strong enough fitness advantage.
It is also worth noting that r is a symmetric measure of the ratio of interspecific
to interspecific density dependence for any pair of species i and j , as formula
( Eq. 13.4 ) implies that

r

a ij
a jj :

a ji
a ii

r ¼ : (13.5)

Thus, r can be thought of as niche overlap, and at the same time as the geometric
mean of the ratios of interspecific versus intraspecific density feedback for any pair
of species. Thus, it measures the potential for stabilization of coexistence without
taking into account the fact the ratio might be different for one species compared
with other and lead to dominance instead of coexistence. The formula ( Eq. 13.4 )
shows how that bias changes as the fitness ratio changes, suggesting, as we shall see
below, how changes in circumstances can change the opportunities for coexistence.

Niches and Species Coexistence Mechanisms

The results of the Lotka-Volterra equations can now be applied to see how a guild
of coexisting species is constrained by trophic relationships. For two species to
coexist, the conditions ( Eq. 13.3 ) together with the formula ( Eq. 13.4 ) imply that

k 1
k 2 <

1
r :

r < (13.6)

Fig. 13.2 (continued) indicate relatively strong linkages compared with thin arrows. A gray arrow
indicates that although the linkage might be important, it is not a strong source of density-
dependent feedback for focal species. (a) Low niche overlap because the strong links to both
resources and predators differ between N 1 and N 2 .(b) High niche overlap because the strength of
the links between N 1 and the various resources and predators has the same pattern as the strength
of the links between N 2 and these resources and predators. Although these two species do
discriminate between these resources and predators, they do so in an identical way. (c) High
niche overlap through resources, but low niche overlap through predators, leading overall to an
intermediate level of niche overlap. (d) Low niche overlap through resources, but high niche
overlap through predators, leading overall to an intermediate level of niche overlap. (e)Asind, but
predation is not strongly density dependent, and so overall niche overlap is low due to the low
overlap through resources. (f)Asind, but resource consumption is not strongly density dependent,
and so overall niche overlap is high due to the high overlap through predators