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

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PQ #15

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

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

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

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

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)

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)

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

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

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.

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

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

How would you stabilize an unstable system?

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

(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’

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”

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