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Published byHilda Allen Modified over 3 years ago

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Midterm 2 Results Highest grade: 43.5 Lowest grade: 12 Average: 30.9

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**A fly and its wasp predator:**

Greenhouse whitefly Parasitoid wasp Laboratory experiment (Burnett 1959)

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**(Laboratory experiment)**

spider mite on its own with predator in simple habitat Spider mites with predator in complex habitat (Laboratory experiment) Predatory mite (Huffaker 1958)

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**(Laboratory experiment)**

Azuki bean weevil and parasitoid wasp (Laboratory experiment) (Utida 1957)

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collared lemming stoat (Greenland) lemming stoat (Gilg et al. 2003)

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**(field observation: England)**

Tawny owl Wood mouse (field observation: England) (Southern 1970)

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**Possible outcomes of predator-prey interactions:**

The predator goes extinct. Both species go extinct. Predator and prey cycle: prey boom Predator bust predator boom prey bust Predator and prey coexist in stable ratios.

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**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

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**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) DEFINE ISOCLINE pt where prey pop at equilibrium (b - d = 0) Describe Trivial versus nontrival solution (for victims r = 0, V = 0 = trivial) First row answers are trivial Second row answers are nontrivial One nontrivial solution for both victim and predators For victim recall a = capture efficiency of predator For predator recall B = capture and conversion efficiency q instant death rate

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**The simplest predator-prey model (Lotka-Volterra predation model)**

DEFINE ISOCLINE pt where prey pop at equilibrium (b - d = 0) Describe Trivial versus nontrival solution (for victims r = 0, V = 0 = trivial) First row answers are trivial Second row answers are nontrivial One nontrivial solution for both victim and predators For victim recall a = capture efficiency of predator For predator recall B = capture and conversion efficiency q instant death rate Exponential victim growth in the absence of predators. Capture rate proportional to victim density (Holling Type I).

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Isocline analysis: DEFINE ISOCLINE pt where prey pop at equilibrium (b - d = 0) Describe Trivial versus nontrival solution (for victims r = 0, V = 0 = trivial) First row answers are trivial Second row answers are nontrivial One nontrivial solution for both victim and predators For victim recall a = capture efficiency of predator For predator recall B = capture and conversion efficiency q instant death rate

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**Predator density Victim density Victim isocline: Predator isocline:**

How to conduct a Phase-plane analysis. 1.Determine nontrival solution to equations = isocline Plot the isocline 3. Find the equilibrium (intersection of the two isoclines) 4. Determine the signs(+/-) of the RATE OF CHANGE for Victims and Predators Relative to the isocline and in the four quadrates 5. Use arrows to indicate direction of pop change in phase plane 6. Goal is to determine the fate of INTERACTING POPULATIONS 7. Do this by add vectors to determine simultaneous direction of change in both species Arrows = direction of change in numbers for victim and predators Victim isocline = that number of predators at which the prey pop does not grow If # predators above isocline then Prey #’s decrease If # predators less than isocline # prey go up Predator isocline = that # prey at which Pred pop does not increase

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**Predator density Victim density Victim isocline: Predator isocline:**

dV/dt < 0 dP/dt < 0 dV/dt < 0 dP/dt > 0 dV/dt > 0 dP/dt > 0 Work through “how to do” with students to illustrate steps. dV/dt > 0 dP/dt < 0 Show me dynamics

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**Predator density Victim density Victim isocline: Predator isocline:**

Describe meanings stable = spiral to equil unstable = spiral away from equil Neutrally stable = cycle but not approach equil.

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Victim density Predator density Victim isocline: Preator isocline:

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**Neutrally stable cycles!**

Victim density Predator density Victim isocline: Preator isocline: Neutrally stable cycles! Every new starting point has its own cycle, except the equilibrium point. The equilibrium is also neutrally stable.

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**Logistic victim growth in the absence of predators. **

DEFINE ISOCLINE pt where prey pop at equilibrium (b - d = 0) Describe Trivial versus nontrival solution (for victims r = 0, V = 0 = trivial) First row answers are trivial Second row answers are nontrivial One nontrivial solution for both victim and predators For victim recall a = capture efficiency of predator For predator recall B = capture and conversion efficiency q instant death rate Logistic victim growth in the absence of predators. Capture rate proportional to victim density (Holling Type I).

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**r a r c Predator density Victim density Predator isocline:**

1. Equil is stabilized by density dependent pop growth of prey 2. Equil is still approached in oscillatory manner 3. #’s pred can drop to very low values in some cycles (Thus stochastic flucuations could drive system to extinction) [CF fig 8.8 Hastings] Predator isocline: Victim isocline: r c Show me dynamics

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Stable Point ! Predator and Prey cycle move towards the equilibrium with damping oscillations. P V

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**Exponential growth in the absence of predators. **

DEFINE ISOCLINE pt where prey pop at equilibrium (b - d = 0) Describe Trivial versus nontrival solution (for victims r = 0, V = 0 = trivial) First row answers are trivial Second row answers are nontrivial One nontrivial solution for both victim and predators For victim recall a = capture efficiency of predator For predator recall B = capture and conversion efficiency q instant death rate Exponential growth in the absence of predators. Capture rate Holling Type II (victim saturation).

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**r kD Predator density Victim density Victim isocline:**

Predator isocline: Show me dynamics

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**Unstable Equilibrium Point!**

Predator and prey move away from equilibrium with growing oscillations. P V

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**Unstable Equilibrium Point!**

Predator and prey move away from equilibrium with growing oscillations. P V

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No density-dependence in either victim or prey (unrealistic model, but shows the propensity of PP systems to cycle): P V Intraspecific competition in prey: (prey competition stabilizes PP dynamics) P V Intraspecific mutualism in prey (through a type II functional response): P V

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

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

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**Rosenzweig-MacArthur Model**

Victim density Predator density Predator isocline: Victim isocline:

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**Rosenzweig-MacArthur Model**

Victim density Predator density Predator isocline: At high density, victim competition stabilizes: stable equilibrium! Victim isocline:

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**Rosenzweig-MacArthur Model**

Victim density Predator density Predator isocline: At low density, victim mutualism destabilizes: unstable equilibrium! Victim isocline:

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**Rosenzweig-MacArthur Model**

Victim density Predator density Predator isocline: At low density, victim mutualism destabilizes: unstable equilibrium! Victim isocline: However, there is a stable PP cycle. Predator and prey still coexist!

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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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