A recent model, designed with stream systems in mind, suggested that p
rey exchange (movement of prey among patches) tends to reduce predator
impacts on prey density; that is, rapid prey im migration into a patc
h with predators can swamp local effects of predators on prey density.
The previous model, however, included two assumptions that influence
the model's qualitative predictions. First, it assumed that the system
's focal patches are surrounded by an environment that has no predator
s and a constant prey density. More importantly, it assumed that prey
do not alter their per capita emigration rates in response to the pres
ence of predators. We extended the earlier model by relaxing these ass
umptions. Specifically, we: (1) addressed predator impacts in patches
surrounded by background environments that do not have predators, (2)
allowed the background environment to have a constant or decreasing pr
ey density (i.e., we examined situations in which predators deplete pr
ey), and (3) accounted for the fact that prey per capita emigration ra
tes are often altered by the presence of predators. Our most interesti
ng results concerned the profound effects of prey emigration behavior
on the relationship between prey exchange and predator impact. If prey
do not alter their emigration rates in response to predators, then, a
s predicted by the earlier model, high prey exchange should result in
very low predator impact. If, however, prey disperse out of patches in
response to the presence of predators (i.e., if prey per capita emigr
ation rates are higher out of patches with predators than out of preda
tor-free patches), then even very high prey exchange rates cannot swam
p predator impact; instead, prey emigration adds to predator impact. T
hus, depending on prey emigration behavior, increased overall prey exc
hange can either decrease or increase predator impact. Predators can a
lso suppress prey emigration (e.g., if prey hide in refuges so effecti
vely that they disperse at low rates from predator patches). In that c
ase, high prey exchange rates tend to result in ''negative predator im
pacts'' (i.e., higher prey density in patches with predators). The det
ails of the above relationships are influenced by whether or not the b
ackground environment has predators. If the background has predators,
but predators do not deplete prey (e.g., if predation is offset by rec
ruitment), then predator impact depends only on the ratio of per capit
a emigration rates out of predator and predator-free patches; that is,
attack rates do not influence predator impact. In contrast, if predat
ors can deplete prey, then attack rates influence predator impact. In
that situation, if attack rates are high relative to prey emigration r
ates out of predator-free patches, then predator impact steadily incre
ases over time. A literature review suggested that prey alterations in
per capita emigration rates in response to the presence of predators
can potentially explain some surprising natural phenomena, including t
he existence of ''negative predator impacts,'' and the apparent tenden
cy for invertebrate predators (primarily, stoneflies) to have stronger
impacts on prey than vertebrate predators (primarily, fish). Finally,
we discussed possible adaptive links between prey escape success, ref
uge use, dispersal behavior, and predator impacts. This discussion rai
sed a ''paradox of danger'': that due to their effects on prey exchang
e, more dangerous predators might often have unexpectedly weak effects
on local prey density. In this context, we suggest a framework for st
udying relationships between prey behavior, prey exchange, and predato
r impacts.