Predation (Chapter 18)

1
Predation (Chapter 18)

1. Predator-prey cycles
2. Models of predation
3. Functional vs. numeric responses
4. Stability in predator-prey models

2
Two big themes

• Predators can limit prey populations.
• This keeps populations below K.

3

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

4
(No Transcript)
5
(No Transcript)
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 dont 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
removal of prey by predators
rate of change in the prey population
intrinsic growth rate of the prey
11

• 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
Predators are stable when Prey are stable
when
Number of Predators (P)
Number of prey (R)
16
Prey are stable when
Prey Isocline
Number of Predators (P)
r/c
d/ac
Number of prey (R)
17
Predators are stable when
Predator 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)

1. Finish Lotka-Volterra model
2. Functional vs. numeric responses
3. Stability in predator-prey cycles

20
Number of predators depends on the prey
population.
Predator 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)
22
(No Transcript)
23
(No Transcript)
24

• Changing the number of prey can cause 2 types of
  responses
• Functional response relationship between an
  individual predators 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

29
(No Transcript)
30

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

31
(No Transcript)
32
(No Transcript)
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

34
(No Transcript)
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

• Huffakers 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
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 gt death rate population
  increases

A
44

• Point A stable equilibrium population
  increases below A and decreases above A

A
45

• Between A B predators reduce population back
  to A

A B
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

B
49

• Point C stable equilibrium

B
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
52
(No Transcript)