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Predation
Community Level Effects
Predation
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Functional
Responses
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As prey density
increases, each
predator can
consume more prey
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Numerical
Responses
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As prey density
increases, predators
increase in number,
and that larger
number of predators
consumes more prey.
Predation
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As an example, consider the work of
Holling in 1959.
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Studied 3 species of small mammal:
Peromyscus leucopus
Blarina brevicauda
Sorex cinereus
Predation
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These 3 species all consume saw-fly
larvae, and each does it in such a way
that it is possible to determine who
consumed what.
Holling sampled his study site to
determine prey (saw-fly larva) density,
and estimated small mammal density.
Predation
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Notice, the number of Blarina and
Peromyscus was basically constant
regardless of pupae density.
Blarina and Peromyscus appear to have
a relatively small numerical response to
increased prey density.
Sorex appears to have a relatively large
numerical response.
Predation
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We could also look at number of pupae
consumed by each species relative to
density of pupae.
This gives us an index of the functional
response.
Predation
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Here we note that the relationships are
opposite of what we saw before.
Blarina has a large functional response,
Peromyscus is intermediate, and Sorex
has the smallest functional response.
What does this tell you about these
predators?
Predation
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We can combine these relationships into
a single graph, by looking at precent
predation relative to prey density.
This is done by multiplying number of
pupae eaten by number of predators
present, and dividing by density of the
pupae (=proportion of pupae eaten).
Predation
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Notice that the proportion of prey eaten
by each species peaks at a different
pupal density. Therefore, as sawfly
density increases, it encounters first
significant Blarina predation, then Sorex
predation, then Peromyscus predation.
This is very different than if all peaked
at the same density.
Predation
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The functional response is a
consequence of the coevolutionary
interaction between predator and prey,
and the reproductive biology of the
predator.
Holling predicted 3 forms of the
functional response.
Functional Responses
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Type I: a linear response between
number of prey consumed and prey
density.
Type II: prey consumption is
asymptotic.
Type III: prey consumption is logistic.
Functional Response
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The asymptotic behavior of Type I and
Type II functional responses is a
consequence of satiation of the
predator, or increased handling time as
prey are consumed at a high rate.
This is important in terms of the effect
the predator has on the prey
population.
Functional Response
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Look at the proportion of prey eaten
over the range of prey densities, for
each kind of functional response.
Functional Response
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The Type I response is density
independent.
Type II response is density dependent,
with, but it is decreasing with increased
prey density.
Type III is density dependent, but in
different directions depending on prey
density.
Functional Response
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Only the Type III functional response is
density dependent in a way that
promotes population regulation.
The Type III functional response is the
one most likely to regulate prey
populations.
Functional Response
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What causes a Type III functional
response?
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Factors that cause low hunting efficiency at
low prey density.
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Failure to develop an appropriate search image
without positive reinforcement.
Presence of prey refugia at low densities.
Functional Response
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Clearly, it is highly unlikely that a
predator will cause the extinction of its
prey.
Just as in parasites, killing your ‘host’
will be selected against.
Predator Prey Coexistence.
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Under what conditions will we see
stable coexistence of a predator and its
prey?
This is very similar to what we did with
2 competing species.
Predator Prey Coexistence
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Our basic strategy is to
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1) write simple differential equations
describing the growth of the 2 populations
2) define equilibrium as the point where
the populations do not change.
3) do a phase plane analysis using the
isoclines for the 2 species.
Predator Prey Coexistence
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Model for the predator population:
dP
dt
 apHP  dP
Predator Prey Coexistence
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Here, dP/dt is the growth rate of the
predator.
a = production efficiency of the
predator (proportion of energy
assimilated by predator that is
converted into new predator biomass.
p=ingestion efficiency of the predator
(proportion of available prey actually
consumed).
Predator Prey Coexistence
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H = density of the prey.
d = death rate of the predator. Notice,
in the absence of prey, the predator
population must certainly decrease.
Predator Prey Coexistence
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For the prey population, we have:
dH
dt
 rH  pHP
Predator Prey Coexistence
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dH/dt = growth rate of the prey
population.
p, H, and P are as in the previous
equation.
r is the birth rate of the prey.
Predator Prey Coexistence
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Note, the births of prey are decreased
by deaths (pHP).
Note also, that encounters between
predator and prey is the product of
their numbers. This is a ‘brownian
motion’ idea.
Predator Prey Coexistence
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At equilibrium,
dP
dH
dt
dt
 0  apHP  dP
 0  rH  pHP
Equilibrium
apHP  dP
rH  pHP
Equilibrium
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Predator isocline:
d
H
aP
Equilibrium
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Prey isocline:
r
P
p
Equilibrium
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As in the case of competing species,
these differential equations have no
explicit solutions. So we simply plot the
isoclines.
This produces the following graph:
Equilibrium
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The behavior of this system is very
intuitive, and very pleasing.
It produces exactly the type of behavior
we see in the moose and wolves of Isle
Royale.
We see this behavior in lynx/showshoe
hare systems. From another view, we
could plot it as:
Equilibrium
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The lags make sense.
It takes time for the predator
population to catch up with they prey.
Predators do not produce new
predators instantaneously. Nor do they
stop reproducing instantaneously.
Equilibrium
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We can make the model more realistic.
We know that there will be a carrying
capacity for the prey population, and
probably for the predator as well.
There will aslo be an Allee effect: some
minimum population size necessary to
sustain the population.
Equilibrium
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New the system becomes much more
interesting. The exact position of the
predator isocline will be very important.
The results will be different for systems
in which the predator isocline is to the
left or right of the ‘hump’ in the prey
isocline.
Unstable equilibrium
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In this first scenario, once the system is
perturbed from the equilibrium point,
the systems spirals out of bounds and
extinction results. Why?
Unstable equilibrium
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Here, the hump is to the right of the
predator isocline, and we get an
unstable system. Why?
The predator population is capable of
growing even at very low prey density the predator is an efficient humter. As
the predator becomes less efficient, the
predator isocline shifts to the right.
Stable equilibrium
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When the ‘hump’ is to the left, the
region in which the predator population
does not grow is larger.
Very high prey densities are necessary
for the predator to increase. This might
be the result of crypsis, or inefficient
foraging by the predator.
An interesting twist
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There was a wonderful paper by
Rosenzweig in Science quite a few years
ago, titled: the paradox of the plankton.
In the paper, Rosenzweig showed that
zoo plankton did not follow the
predictions.
A twist
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The predator isocline was to the left,
but the system persisted and did not
cycle to extinction. It did cycle, but not
to extinction.
What happened?
A twist
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If prey have a refugia, or an escape
from predation, the isocline will look
different:
Equilibrium
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The phytoplankton had a refugia, and
consequently the zooplankton were
unable to exploit the entire prey
population. The result was a cyclical
system as shown.
An important point
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What are the assumptions of these
models?
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First, there is a type I functional response.
Second, there are no stochastic effects.
Nevertheless, the models give us a
basic understanding of how the system
work.