Environmental Engineering Reference
In-Depth Information
interspecific to intraspecific density dependence by Eq. 13.5 . Defining the case
under consideration in parentheses gives the following chain of inequalities:
R p ;
P p Þrð
R p Þrð
P p Þ
<rð
R p ;
P np Þrð
R np ;
P p Þ<rð
R np ;
P np Þ
(13.7)
¼ rð
R np Þ¼rð
P np Þ¼
:
1
Here R or P indicates the presence of resource competition or apparent competition,
and the subscripts “p” and “np” indicate partitioned and not partitioned interactions.
As smaller values of r mean stronger coexistence, the situations are ranked from
strongest coexistence to no coexistence, from left to right. The approximate equal-
ity of r ( R p ) and r ( P p )in( Eq. 13.7 ) is not a conclusion, but the assumption that
resources and predators are partitioned about equally, specifying the scenario
considered here. The rest of the inequalities and approximations are conclusions.
When P or R is not listed in parentheses, predators or resources may still be present,
but are not important sources of density dependence. For instance, strongly density-
dependent predation can prevent resource competition from occurring even though
resources are still consumed and contribute essentially to fitness.
When competition and apparent competition are both present, the value of r is
intermediate between the values that occur when only one of these is present. Thus,
when they are both partitioned in inequalities ( Eq. 13.7 ), the value of r does not
change much, regardless of whether competition and predation are both present, or
only one is present (e.g., Fig 13.2a vs. 13.2e ). When they are both present, but only
one is partitioned, the value of r is necessarily higher than when they are both
partitioned because then a smaller fraction of all density-dependent interactions are
partitioned, reducing the distinction between interspecific and intraspecific density
dependence ( Fig. 13.2c and d vs. 13.2a ). The reason is that there is less partitioning
overall among the array of density-dependent interactions experienced. No
partitioning leads to a value of r equal to 1 ( Fig. 13.2b ), regardless of which
interactions are present, and therefore no possibility for stable coexistence.
The situation not considered in the inequalities ( Eq. 13.7 ) is when there is
partitioning between predation and competition ( Fig. 13.3 ). In this case, although
there is no partitioning of resources or predators, there is joint partitioning of them
in that some species have strong predator feedback loops, being particularly
susceptible to predation, and some species have strong resource feedback loops
and therefore are particularly susceptible to resource competition [ 40 ]. This is
a predation-competition trade-off. But without partitioning within these
interactions, at most two species can coexist. The predator is selective in this
case, and it is simply the keystone species case once again. It implies
R np ;
P np Þ < rð
R np Þ¼rð
P np Þ¼
1
(13.8)
as illustrated in Fig. 13.3 . Although theoretically interesting in that it leads to
coexistence in the absence of resource partitioning, it is not a serious solution
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