Predation

Community Level Effects

Predation Functional

Responses

As prey density increases, each predator can consume more prey

Numerical Responses

As prey density increases, predators increase in number, and that larger number of predators consumes more prey.

Predation As an example, consider the work

of Holling in 1959. Studied 3 species of small mammal: Peromyscus leucopus Blarina brevicauda Sorex cinereus

Predation 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 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 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 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 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 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 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 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 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

Look at the proportion of prey eaten over the range of prey densities, for each kind of functional response.

Functional Response 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 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 What causes a Type III functional

response? Factors that cause low hunting

efficiency at low prey density. Failure to develop an appropriate search

image without positive reinforcement. Presence of prey refugia at low densities.

Functional Response 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. 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

Our basic strategy is to 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 Model for the predator population:

dPapHPdtdP

Predator Prey Coexistence 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

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 For the prey population, we have:

pHPrHdtdH

Predator Prey Coexistence 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

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 At equilibrium,

dPapHPdtdP 0

pHPrHdtdH 0

Equilibrium

pHPrH

dPapHP

Equilibrium Predator isocline:

aP

dH

Equilibrium Prey isocline:

p

rP

Equilibrium 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 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 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 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 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

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 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 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 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 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

If prey have a refugia, or an escape from predation, the isocline will look different:

Equilibrium 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 What are the assumptions of these

models? 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.