2. M 5.5 IDQ #10 – Trees PQ #15 – 14.3 and 14.4 Ch 14 Discussion
Turn in today:
Lab 11A; Wolves
Turn in Friday:
Lab 10BC; Field Lab – Handout
Friday – Exam 3, 10 AM

3. 1

4. 2

5. 3

6. 4

7. 5

8. PQ #15

9. Predation Behavioral: diet choice, patch use, optimal foraging (ch 7)
Community: diversity (ch 16)
Population: how do host/predator interactions regulate population numbers? (ch 14)
By availability H → P
By fear P → H
By death P → H

10. Two kinds of responses
Numerical – predators increase after prey increase (lag to due reproductive effort time)
Functional – three types of curves (ch7, p 164)

11. Predator-Host Models
How does the growth of one affect the growth of the other?
We need our logistic growth equation again:
The limiting factor is space available
ΔN = r * N * (K – N)/K

12. Predator-Host Models
But, in P-H models, host N is limited by predation and predator N is limited by access to hosts.

13. Host Growth
𝑑 𝑁 ℎ 𝑑𝑡 = 𝑟 ℎ 𝑁 ℎ −𝑝 𝑁 ℎ 𝑁 𝑝
The rate of increase in the host is equal to the normal growth rate, minus the rate of predation (calculated as a per capita rate)

14. Predator Growth
𝑑 𝑁 𝑝 𝑑𝑡 = 𝑐𝑝𝑁 ℎ 𝑁 𝑝 − 𝑑 𝑝 𝑁 𝑝
The rate of increase in the predator is equal to the conversion factor of the food item to offspring (calculated as predation rate times conversion constant), minus the death rate of the predator (calculated as a per capita rate)

15. p, c, d, r are constants Ns are variables
𝑑 𝑁 ℎ 𝑑𝑡 = 𝑟 ℎ 𝑁 ℎ −𝑝 𝑁 ℎ 𝑁 𝑝
𝑑 𝑁 𝑝 𝑑𝑡 = 𝑐𝑝𝑁 ℎ 𝑁 𝑝 − 𝑑 𝑝 𝑁 𝑝
p, c, d, r are constants
Ns are variables

16. Reproductive lags lead to cycles
Graph by Dr. K Schmidt, Texas Tech
Pred
(-)
Pred
(+) P
Host
(+)
Host
(-) K N
Hosts can grow when predators shrink, and hosts shrink when predators grow.
Reproductive lags lead to cycles

17. In other words:
Graph by Dr. K Schmidt, Texas Tech
safety
in #’s
limits to
growth P N
The predator in this scenario has a straight vertical line: Np is constant.
The intersection of the two isoclines give us a stable cycle.

19. Predator variation is due to prey variation!
Region of pos. DD:
expanding oscillations
(unstable) P N
Remember!
Predator variation is due to prey variation!

20. Two dysfunctional extremes
Inefficient predators
lead to extinction
of the predator in variable
environments
Efficient predators
lead to highly
unstable predator-
prey interactions K K K

21. How would you stabilize an unstable system?

22. Can an unstable system be stabilized?
Complex (natural) environments include barriers to predator dispersal
Refuges become important
Physical
Behavioral/Temporal

23. (1) Productivity goes into building new predators NOT prey
What NOT to do – the Paradox of Enrichment
Feed deer
(increases K to K’)
mountain lion
stable EQ K K
mule deer
mule deer
unstable EQ
(1) Productivity goes into building
new predators NOT prey
(2) Instability increases
(3) Populations go extinct P* N* K K’

24. Combined response
ℎ𝑜𝑠𝑡 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑝𝑟𝑒𝑑𝑎𝑡𝑜𝑟 𝑋 𝑝𝑟𝑒𝑑𝑎𝑡𝑜𝑟𝑠 𝑎𝑟𝑒𝑎 =( ℎ𝑜𝑠𝑡 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑎𝑟𝑒𝑎 )
Gives us percentage of host consumed within an area
Percentage should be lower at high densities. Why?
Predator satiation is a defensive mechanism
“Hosts can reduce their individual probability of being eaten by occurring at very high densities”

25. Next… Ecology of fear Hosts/prey engage in vigilance behavior
Fear is high when
Predators are near
Lethality is high
Fear is low when
Effectiveness of vigilance is low
Feeding opportunities are low
Too much vigilance leads to missing out on food
Too little vigilance leads to being killed