Lecture 26

Lecture 26: Predation Models

Reading: Economy of Nature, pp. 462-466.

Plants as Consumers
Plants as predators on heterotrophs
Insectivorous plants

Responses by Herbivores to Carnivores

Escape in space and time
        flight
        group living
                early warning (see Ricklefs, 1996, p 281, Fig. 13.2)
                group defense, mobbing
                selfish herd effects

Mechanical defenses
        armor
        horns
        spines

Crypsis
        camouflage
        cryptic coloration, shape, behavior
                peppered moth

Chemical defenses
        defensive and offensive chemicals (venoms of predators)
                blister beetles
                bombardier beetles
        warning coloration
                aposematism, conspicuous coloration
                snakes, frogs, salamanders
                evolution of warning coloration (kin selection)
        mimicry
                bees, wasps, and flies
                monarch and viceroy butterflies
                moth wing eyes and startle response

Dynamics of Predator-Prey Systems

Lotka-Volterra Model
Lotka (1932) and Volterra (1926)

For prey: without predators

Where: N = number of individual prey (biomass or density)

C = number of individual predators (biomass or density)

r = intrinsic rates of increase for the prey

Reductions in prey number by a predator species are due to the frequency of predator-prey encounters, and the encounter frequency is a function of both C and N.

Predator attack efficiency must also be a factor in the rate of prey removals by predators where a’ is the rate of successful predator attacks (assumed to be constant).

If predator killing and removal of prey from the prey population is a’CN, then a prey population subject to predation will have a growth rate that is reduced by the rate of prey consumption by predators.

So:

For predators: without prey

Where: C = number of individual predators (biomass or density)

q = predator mortality rate in the absence of prey (constant)

Increases in predator population can only occur in the presence of prey, and the rate of prey consumption by predators is a’CN. The predator efficiency of converting prey into predator offspring is f, so the predator birth rate is fa’CN.

So:

Zero Growth Isoclines for Predator and Prey Populations

Predator and prey zero isoclines are shown as constants (straight lines) on separate predator-prey density plots with population growth vectors (after Begon, Harper and Townsend, 1990).

For prey: so: or,

Since r and a’ are constants, the zero growth isocline for prey is a constant, defined by predator numbers.

For predators (consumers): so: or,

Since q and fa’ are constants, the zero isocline for predators is also a constant, defined by prey numbers.