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Midterm 2 Results

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Midterm 2 Results

Highest grade: 43.5

Lowest grade: 12

Average: 30.9

Greenhouse whitefly

Parasitoid wasp

A fly and its wasp predator:

Laboratory experiment

(Burnett 1959)

spider mite on its own

with predator in simple habitat

Spider mites

with predator in complex habitat

(Laboratory experiment)

Predatory mite

(Huffaker 1958)

Azuki bean weevil and parasitoid wasp

(Laboratory experiment)

(Utida 1957)

collared lemming

stoat

(Greenland)

lemming

stoat

(Gilg et al. 2003)

Wood mouse

(field observation: England)

Tawny owl

(Southern 1970)

prey boom

predator boom

Predator bust

prey bust

Possible outcomes of predator-prey interactions:

- The predator goes extinct.
- Both species go extinct.
- Predator and prey cycle:

- Predator and prey coexist in stable ratios.

Putting together the population dynamics:

Predators (P):

Victim consumption rate -> predator birth rate

Constant predator death rate

Victims (V):

Victim consumption rate -> victim death rate

Logistic growth in the absence of predators

Choices, choices….

- Victim growth assumption:
- exponential
- logistic

- always proportional to victim density (Holling Type I)
- Saturating (Holling Type II)
- Saturating with threshold effects (Holling Type III)

The simplest predator-prey model

(Lotka-Volterra predation model)

Exponential victim growth in the absence of predators.

Capture rate proportional to victim density (Holling Type I).

Isocline analysis:

Predator density

Victim isocline:

Predator isocline:

Victim density

Predator density

Victim isocline:

Predator isocline:

Victim density

dV/dt < 0

dP/dt < 0

dV/dt < 0

dP/dt > 0

dV/dt > 0

dP/dt > 0

dV/dt > 0

dP/dt < 0

Show me dynamics

Predator density

Victim isocline:

Predator isocline:

Victim density

Predator density

Victim isocline:

Preator isocline:

Victim density

Predator density

Victim isocline:

Preator isocline:

Victim density

Neutrally stable cycles!

Every new starting point has its own cycle, except the equilibrium point.

The equilibrium is also neutrally stable.

Logistic victim growth in the absence of predators.

Capture rate proportional to victim density (Holling Type I).

r

a

r

c

Predator density

Victim density

Predator isocline:

Victim isocline:

Show me dynamics

P

V

Stable Point !

Predator and Prey cycle move towards the equilibrium with damping oscillations.

Exponential growth in the absence of predators.

Capture rate Holling Type II (victim saturation).

r

kD

Predator density

Victim density

Victim isocline:

Predator isocline:

Show me dynamics

Unstable Equilibrium Point!

Predator and prey move away from equilibrium with growing oscillations.

P

V

P

V

Unstable Equilibrium Point!

Predator and prey move away from equilibrium with growing oscillations.

No density-dependence in either victim or prey (unrealistic model, but shows the propensity of PP systems to cycle):

P

V

P

Intraspecific competition in prey:

(prey competition stabilizes PP dynamics)

V

P

Intraspecific mutualism in prey (through a type II functional response):

V

Predators population growth rate (with type II funct. resp.):

Victim population growth rate (with type II funct. resp.):

Predator density

Predator isocline:

Victim isocline:

Victim density

Rosenzweig-MacArthur Model

Predator density

Predator isocline:

Victim isocline:

Victim density

Rosenzweig-MacArthur Model

At high density, victim competition stabilizes: stable equilibrium!

Predator density

Predator isocline:

Victim isocline:

Victim density

Rosenzweig-MacArthur Model

At low density, victim mutualism destabilizes: unstable equilibrium!

Predator density

Predator isocline:

Victim isocline:

Victim density

Rosenzweig-MacArthur Model

At low density, victim mutualism destabilizes: unstable equilibrium!

However, there is a stable PP cycle. Predator and prey still coexist!

The Rosenzweig-MacArthur Model illustrates how the variety of outcomes in Predator-Prey systems can come about:

- Both predator and prey can go extinct if the predator is too efficient capturing prey (or the prey is too good at getting away).
- The predator can go extinct while the prey survives, if the predator is not efficient enough: even with the prey is at carrying capacity, the predator cannot capture enough prey to persist.
- With the capture efficiency in balance, predator and prey can coexist.
- a) coexistence without cyclical dynamics, if the predator is relatively inefficient and prey remains close to carrying capacity.
- b) coexistence with predator-prey cycles, if the predators are more efficient and regularly bring victim densities down below the level that predators need to maintain their population size.