Predator-prey models

What is a type 1 functional response?

Assumes that a predator’s feeding rate increases linearly with prey density

What is a type 2 functional response?

Describes a curve that increases at a decreasing rate and smoothly approaches an asymptote equal to the inverse of the handling time (1/h)

What is a type 3 functional response?

A sigmoidal relationship in which feeding rate accelerates over an initial increase in prey density but then decelerates at higher prey density

What type of predators show a type 2 response?

Specialist predators

What type of predators show a type 3 response?

Generalist predators

What are 2 types of numerical responses?

• Aggregative response

• Demographic response

What is an aggregative response?

• Increased immigration

• Reduced emigration

What is a demographic response?

• Increased reproduction

• Reduced mortality

What are numerical responses?

Population responses to variation in prey density

What are functional responses?

Individual responses to variation in prey density

What patterns can predator-prey dynamics have?

• Stable

• Cyclical

• Unstable

What is an example of stable predator-prey dynamics?

Lions and wildebeest

What is an example of cyclical predator-prey dynamics?

Snow owls and lemmings

What is an example of unstable predator-prey dynamics?

Dingos and red kangaroos

What is the Lotka-Volterra model?

• The simplest model describing the population dynamics of a single predator species feeding on a single prey species

• Produces coupled oscillations (cycles) in predator and prey density

• Structurally unstable: any perturbation will cause a change in the amplitude and period of the cycle

What does the Lotka-Volterra model assume?

• The prey population grows exponentially

• Predators have a type 1 functional response

• Predator population growth is independent of predator density

What is the Rosenzweig-MacArthur model?

• Incorporates a carrying capacity to the prey population and a more realistic type 2 predator functional response, which causes the prey isocline to be humped

• If the predator isocline intersects the prey isocline on the left of the hump, the system oscillates in a limit cycle

  • Perturbations cause the amplitude of the oscillation to change, and one or both species may go extinct

• If the predator isocline interrupts the prey isocline to the right of the hump, the system will return to the equilibrium point after a perturbation

What does the Rosenzweig-MacArthur model predict?

• Predator-prey systems are more likely to be stable when the predator is relatively inefficient

• Increasing the prey carrying capacity will decrease the stability of the predator-prey dynamics

What is the paradox of enrichment?

Increasing the prey carrying capacity will decrease the stability of the predator-prey dynamics

What do modifications to the Lotka-Volterra model show?

• Incorporating a carrying capacity acts to stabilize the system

• Incorporating a more realistic functional response stabilizes the system

• Predator-prey systems are more likely to be stable when the predator is relatively inefficient

• The addition of resources that increase K can destabilize a system

• Interference or competition among predators for limiting resources will stabilize the system