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.

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Midterm 2 Results

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Midterm 2 results

Midterm 2 Results

Highest grade: 43.5

Lowest grade: 12

Average: 30.9


Midterm 2 results

Greenhouse whitefly

Parasitoid wasp

A fly and its wasp predator:

Laboratory experiment

(Burnett 1959)


Midterm 2 results

spider mite on its own

with predator in simple habitat

Spider mites

with predator in complex habitat

(Laboratory experiment)

Predatory mite

(Huffaker 1958)


Midterm 2 results

Azuki bean weevil and parasitoid wasp

(Laboratory experiment)

(Utida 1957)


Midterm 2 results

collared lemming

stoat

(Greenland)

lemming

stoat

(Gilg et al. 2003)


Midterm 2 results

Wood mouse

(field observation: England)

Tawny owl

(Southern 1970)


Midterm 2 results

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.


Midterm 2 results

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


Midterm 2 results

Choices, choices….

  • Victim growth assumption:

    • exponential

    • logistic

  • Functional response of the predator:

    • always proportional to victim density (Holling Type I)

    • Saturating (Holling Type II)

    • Saturating with threshold effects (Holling Type III)


  • Midterm 2 results

    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).


    Midterm 2 results

    Isocline analysis:


    Midterm 2 results

    Predator density

    Victim isocline:

    Predator isocline:

    Victim density


    Midterm 2 results

    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


    Midterm 2 results

    Predator density

    Victim isocline:

    Predator isocline:

    Victim density


    Midterm 2 results

    Predator density

    Victim isocline:

    Preator isocline:

    Victim density


    Midterm 2 results

    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.


    Midterm 2 results

    Logistic victim growth in the absence of predators.

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


    Midterm 2 results

    r

    a

    r

    c

    Predator density

    Victim density

    Predator isocline:

    Victim isocline:

    Show me dynamics


    Midterm 2 results

    P

    V

    Stable Point !

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


    Midterm 2 results

    Exponential growth in the absence of predators.

    Capture rate Holling Type II (victim saturation).


    Midterm 2 results

    r

    kD

    Predator density

    Victim density

    Victim isocline:

    Predator isocline:

    Show me dynamics


    Midterm 2 results

    Unstable Equilibrium Point!

    Predator and prey move away from equilibrium with growing oscillations.

    P

    V


    Midterm 2 results

    P

    V

    Unstable Equilibrium Point!

    Predator and prey move away from equilibrium with growing oscillations.


    Midterm 2 results

    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


    Midterm 2 results

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

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


    Midterm 2 results

    Predator density

    Predator isocline:

    Victim isocline:

    Victim density

    Rosenzweig-MacArthur Model


    Midterm 2 results

    Predator density

    Predator isocline:

    Victim isocline:

    Victim density

    Rosenzweig-MacArthur Model

    At high density, victim competition stabilizes: stable equilibrium!


    Midterm 2 results

    Predator density

    Predator isocline:

    Victim isocline:

    Victim density

    Rosenzweig-MacArthur Model

    At low density, victim mutualism destabilizes: unstable equilibrium!


    Midterm 2 results

    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!


    Midterm 2 results

    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.


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