M 5.5

1. IDQ #10 – Trees 2. PQ #15 – 14.3 and 14.43. Ch 14 Discussion

Turn in today:Lab 11A; WolvesTurn in Friday:Lab 10BC; Field Lab – HandoutFriday – 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

• 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)

( 𝑑𝑁h

𝑑𝑡 )=𝑟 h𝑁 h−𝑝𝑁 h 𝑁𝑝

Predator Growth

• 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)

( 𝑑𝑁𝑝

𝑑𝑡 )=𝑐𝑝𝑁 h𝑁 𝑝−𝑑𝑝 𝑁𝑝

• p, c, d, r are constants• Ns are variables

( 𝑑𝑁h

𝑑𝑡 )=𝑟 h𝑁 h−𝑝𝑁 h 𝑁𝑝

( 𝑑𝑁𝑝

𝑑𝑡 )=𝑐𝑝𝑁 h𝑁 𝑝−𝑑𝑝 𝑁𝑝

Graph by Dr. K Schmidt, Texas Tech

P

N

Pred(-)

Pred(+)

Host(+)

Host(-)

K

• Hosts can grow when predators shrink, and hosts shrink when predators grow.

• Reproductive lags lead to cycles

In other words:

safetyin #’s

limits to growth

• The predator in this scenario has a straight vertical line: Np is constant.

• The intersection of the two isoclines give us a stable cycle.

P

N

Graph by Dr. K Schmidt, Texas Tech

P

N

Region of pos. DD:expanding oscillations (unstable)

Remember! Predator variation is due to prey variation!

K

Two dysfunctional extremes

Efficient predatorslead to highlyunstable predator-prey interactions

Inefficient predatorslead to extinctionof the predator in variable environments

KK

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

What NOT to do – the Paradox of Enrichment

Kmule deer

mou

ntai

n lio

n

mule deerK

K K’

stable EQ

unstable EQ

(1) Productivity goes into building new predators NOT prey

(2) Instability increases

(3) Populations go extinct

Þ Feed deer (increases K to K’)

N*

P*

Combined response

• 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