1. FW364 Ecological Problem Solving
Class 19: Predation
November 11, 2013

2. Moving from populations of single species to community interactions
Outline for Today
Shifting focus:
Moving from populations of single species to community interactions
Objectives for Today:
Introduce coupled predator-prey interactions
Introduce basic predator-prey equations
Objectives for Next Three (lecture) Classes:
Application of calculus to predator-prey dynamics
Develop predator-prey models using different assumptions
No more textbook!
No multiple-species interactions in text

3. Previous Focus – Single Species
So far, we have mostly looked at examples of single-species dynamics:
Each population was considered in isolation from other populations
in the community in which it resides…
NEW FOCUS: Considering effects of predators and competitors

4. Survival - Predation Link
We have not completely ignored the effects of other species
Predation:
Using survival rates in models
SOME of this mortality may be caused by predators
For example
Many ways a leopard frog can die:
Predation from fish and other organisms
Starvation
Genetic defects
Desiccation
Heat stress

5. Survival - Predation Link
We have not completely ignored the effects of other species
Predation:
Using survival rates in models
SOME of this mortality may be caused by predators
For example
Harvest
 a special kind of predation
(but important differences in “predator” behavior)

6. Ecosystem Management
Recent shift from historical single-species management
to ecosystem management
Ecosystem management:
“management driven by explicit goals, policies, protocols, and practices,
and made adaptable by monitoring and research based on our
best understanding of the ecological interactions and processes
necessary to sustain ecosystem composition, structure, and function.”
Christensen et al. (1996)
Exciting merge of a large body of ecological research with management
Ecosystem management is critical!
We can make incorrect predictions if we ignore species linkages
Models are essential to doing ecosystem management!

7. Linked Populations From here on out: linked populations
I.e., explicit connection of the mortality, fecundity or net population growth rate of one population to the dynamics of other species in the ecosystem
So far models have referred implicitly to connections
 This is the crucial difference
We will examine two types of interactions:
Linked predator-prey populations
Linked competitor populations

8. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Sea lamprey in Great Lakes

9. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Sea lamprey in Great Lakes

10. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Nile perch in Lake Victoria (introduced: 1950s)
Caused extinction or near-extinction of several hundred native species (e.g., cichlids)

11. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Dingo in Australia
(introduced: 3500 years ago)
Caused extinction or near-extinction
of several endemic mammals
Tasmanian tiger
(extinct)
Tasmanian devil (Tasmania)

12. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Huge problem for sheep industry
Dingo in Australia
(introduced: 3500 years ago)
World’s longest fence (~3,500mi) built to restrict dingos (1885)

13. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Early 1900s: Moose colonized
~ 1949: Wolves colonized
 Wolf-moose cycles
Isle Royale
Examples of native predators
Wolves

14. Predator-Prey Interactions
Do predator-prey interactions matter in natural resource management?
(may seem like a silly question now, but not historically)
Some examples
Examples of native predators
Wolves
 wolves are the only predator of moose, and moose are almost exclusively the only prey for wolves, allows for precise research on predator-prey relationships, and of the fluctuation of the two populations.

15. Management Strategies
Clearly, predation is important for natural resource management…
How do we incorporate predation into the systems we manage?
Two examples of managed herbivores:
Elk in Yellowstone National Park
White-tailed deer in Michigan

16. Management Strategies
Elk in Yellowstone National Park
“Natural regulation” strategy
currently popular with the National Park Service
 Controversial “hands-off” policy
Allowing elk populations to fluctuate naturally
 there is no “right” number of elk for the range (i.e., no strict management target)
What effect might natural regulation have on an ecosystem?
Depends on, e.g., predation and type of density dependence
Multiple predators (wolves, mountain lions, coyotes, eagles, bears…)
Except during breeding season, elk have scramble density dependence
(so prone to overshoots and crashes)

17. Management Strategies
White-tailed deer in Michigan
Challenge Question:
Would a natural regulation be a good strategy
for deer management in Michigan?
Think about:
Strength of predation
Type of density dependence
Spread of diseases
And other desirable and undesirable aspects of natural regulation

18. Management Strategies
White-tailed deer in Michigan
Challenge Question:
Would a natural regulation be a good strategy
for deer management in Michigan?
Some thoughts
Natural regulation would probably be a poor management strategy for white-tailed deer in Michigan
Lack of predators (might lead to overgrazing / starvation at high density)
Likely scramble density dependence, so would have undesirable population fluctuations
Spread of tuberculosis / CWD at high density would be undesirable
Deer-vehicle collisions at high density would be undesirable

19. Management Strategies
Elk in Yellowstone National Park
White-tailed deer in Michigan
Challenge Question:
How would management models for elk in Yellowstone
differ from deer in Michigan?
Assumptions:
Wolves are the major predator of elk in Yellowstone
Hunting is the major “predator” on deer in Michigan
Think about type of models we have used previously vs. predator-prey models

20. Management Strategies
Management scenarios are actually pretty different
White-tailed deer:
Single-species model including
Harvest
Density dependence (scramble)
Age-structured model
Elk:
Predator-prey model!
Understand linkage between abundance of elk and wolves

21. Predator-Prey Models How do we model predator-prey interactions?
Types of interactions that fall under predator-prey:
Herbivore – Plant
Parasite – Host
Carnivore – Animal Prey
More generally: Consumer – Resource
Consumer
Resource

22. Predator-Prey Models How do we model predator-prey interactions? Key:
Linked dynamic interaction between predator and prey populations
Interaction is consumption; looking at effects on birth rates, death rates, and population growth of predator and prey
Predator
Prey
Prey dynamics influence predator
Predator dynamics influence prey
Looking at interactions through time
Predator birth rate directly depends on prey population dynamics
Prey death rate directly depends
on predator population dynamics

23. Predator-Prey Models How do we model predator-prey interactions?
Predator-prey interactions are modeled differently from hunting!
i.e., effect of hunting on prey is different from predation
With hunting:
Prey (e.g., deer) death rate is directly dependent on hunting activity
BUT, hunting activity is not directly tied to prey population dynamics
(e.g., more deer may not lead to more hunting)
Let’s start building our models

24. Predator-Prey Models
Start with mass balance for both predators and prey
Prey
Births
Deaths
Population size of prey at some future time depends on
current population size plus number of births minus number of deaths
Predator
Births
Deaths
Population size of predator at some future time depends on
current population size plus number of births minus number of deaths

25. Predator-Prey Models Remember this equation? Nt+1 = Nt + B - D Births
Deaths
Prey
Population size of prey at some future time depends on
current population size plus number of births minus number of deaths
Victim, V
Vt+1 = Vt + Bv - Dv
Births
Deaths
Predator
Population size of predator at some future time depends on
current population size plus number of births minus number of deaths
Predator, P:
Pt+1 = Pt + Bp - Dp

26. Predator-Prey Models Victim, V: Vt+1 = Vt + Bv - Dv Predator, P:
Pt+1 = Pt + Bp - Dp
V: Number of victims (prey) B: Number of births per unit time
P: Number of predators D: Number of deaths per unit time
Subscripts: t: time
v: victim
p: predator
Note: We are only going to deal with closed systems
(no immigration, emigration, or harvest)
Key: Equations are linked!
Death of prey could be due to predators
Growth of predators could be due to prey

27. Which in a natural system look like:
Predator-Prey Models
Victim, V:
Vt+1 = Vt + Bv - Dv
Predator, P:
Pt+1 = Pt + Bp - Dp
Dynamics go like this:
Prey go up…
Predators go up…
Prey go down…
Predators go down…
 predators go up
 prey go down
 predators go down
 prey go up
Which in a natural system look like:

28. Predator-Prey Models Victim, V: Vt+1 = Vt + Bv - Dv Predator, P:
Pt+1 = Pt + Bp - Dp
Over next three predation lectures:
Develop equations that include explicit linkages of dynamics
e.g., link predator growth rate to prey
link prey death rate to predators
Make the move to continuous time
… Use all that calculus training again

29. More Predator-Prey Excitement
Looking Ahead
In Lab tomorrow:
Return Midterm II
More Predator-Prey Excitement