1. Predation (Chapter 18) Predator-prey cycles Models of predation
Functional vs. numeric responses
Stability in predator-prey models

2. Two big themes: Predators can limit prey populations.
This keeps populations below K.

3. Predator and prey populations increase and decrease in regular cycles.

6. A verbal model of predator-prey cycles:
Predators eat prey and reduce their numbers
Predators go hungry and decline in number
With fewer predators, prey survive better and increase
Increasing prey populations allow predators to increase
And repeat…

7. Why don’t predators increase at the same time as the prey?

8. The Lotka-Volterra Model: Assumptions
Prey grow exponentially in the absence of predators.
Predation is directly proportional to the product of prey and predator abundances (random encounters).
Predator populations grow based on the number of prey. Death rates are independent of prey abundance.

9. R = prey population size (“resource”)
P = predator population size
r = exponential growth rate of the prey
c = capture efficiency of the predators

10. rate of change in
the prey population
intrinsic growth
rate of the prey
removal of prey
by predators

11. a = efficiency with which prey are converted into predators
For the predators:
a = efficiency with which prey are converted into predators
d = death rate of predators
death rate of predators
rate of change in the
predator population
conversion of prey
into new predators

12. Prey population reaches equilibrium when dR/dt = 0
equilibrium – state of balance between opposing forces
populations at equilibrium do not change
Prey population stabilizes based on the size of the predator population

13. Predator population reaches equilibrium when dP/dt = 0
Predator population stabilizes based on the size of the prey population

14. Isocline – a line along which populations will not change over time.
Predator numbers will stay constant if R = d/ac
Prey numbers will stay constant if P = r/c.

15. Number of Predators (P) Number of prey (R) Predators are stable when:
Prey are stable when:
Number of
Predators (P)
Number of prey (R)

16. Number of Predators (P) Number of prey (R) Prey are stable when: Prey
Isocline
Number of
Predators (P)
r/c
d/ac
Number of prey (R)

17. Number of Predators (P) Number of prey (R) Predators are stable when:
isocline
Number of
Predators (P)
d/ac
Number of prey (R)

18. equilibrium
Number of
Predators (P)
r/c
d/ac
Number of prey (R)

19. Predation (Chapter 18) Finish Lotka-Volterra model
Functional vs. numeric responses
Stability in predator-prey cycles

20. Number of predators depends on the prey population.
isocline
Number of
Predators (P)
Predators
decrease
Predators
increase
d/ac
Number of prey (R)

21. Number of prey depends on the predator population.
Prey decrease
Prey
Isocline
Number of
Predators (P)
r/c
Prey increase
d/ac
Number of prey (R)

24. Changing the number of prey can cause 2 types of responses:
Functional response – relationship between an individual predator’s food consumption and the density of prey
Numeric response – change in the population of predators in response to prey availability

25. Lotka-Volterra: prey are consumed in direct proportion to their availability (cRP term)
known as Type I functional response
predators never satiate!
no limit on the growth rate of predators!

26. Type II functional response – consumption rate increases at first, but eventually predators satiate (upper limit on consumption rate)

27. Type III functional response – consumption rate is low at low prey densities, increases, and then reaches an upper limit

28. Why type III functional response?
at low densities, prey may be able to hide, but at higher densities hiding spaces fill up
predators may be more efficient at capturing more common prey
predators may switch prey species as they become more/less abundant

30. Numeric response comes from Population growth
(though most predator populations grow slowly)
Immigration
predator populations may be attracted to prey outbreaks

33. Predator-prey cycles can be unstable
efficient predators can drive prey to extinction
if the population moves away from the equilibrium, there is no force pulling the populations back to equilibrium
eventually random oscillations will drive one or both species to extinction

35. Factors promoting stability in predator-prey relationships
Inefficient predators (prey escaping)
less efficient predators (lower c) allow more prey to survive
more living prey support more predators
Outside factors limit populations
higher d for predators
lower r for prey

36. Alternative food sources for the predator
less pressure on prey populations
Refuges from predation at low prey densities
prevents prey populations from falling too low
Rapid numeric response of predators to changes in prey population

37. Huffaker’s experiment on predator-prey coexistence
2 mite species, predator and prey

38. Initial experiments – predators drove prey extinct then went extinct themselves
Adding barriers to dispersal allowed predators and prey to coexist.

39. Refuges from predation allow predator and prey to coexist.

40. Prey population outbreaks
Population growth curve for logistic population growth
Per capita population growth rate ro K
Density of prey population

41. Density of prey population
Type III functional response curve for predators
Per capita death rate K
Density of prey population

42. Multiple stable states are possible.

43. Below A – birth rate > death rate; population increases

44. Point A – stable equilibrium; population increases below A and decreases above A

45. Between A & B – predators reduce population back to A

46. Unstable equilibrium – equilibrium point from which a population will move to a new, different equilibrium if disturbed

47. Point B – unstable equilibrium; below B, predation reduces population to A; above B, predators are less efficient, so population grows to C B

48. Between B & C – predators are less efficient, prey increase up to C

49. Point C – stable equilibrium

50. Predator-prey systems can have multiple stable states
Reducing the number of predators can lead to an outbreak of prey

51. Growth rate
Death rate