Functional Responses

1
Functional Responses
I
II
III
2
Lecture Goals

• Distinguish between a functional and a numerical
  response
• Define the 3 classic functional responses
• Explain how functional responses can influence
  relationships between populations

3
Definitions
NumericalResponse

• a change in the abundance (numbers) of predators
  due to consumption of prey
• population growth

FunctionalResponse

• the variation in the consumption rate of
  predators as a result of changes in the abundance
  of prey

4
Type I

• Lotka-Volterra assumption
• initially consumption conversion proportional
  to N
• some saturation point (discontinuous rate change)
• example Daphnia consuming yeast (Fig. 9.8)

5

• consumption rate declines with increasing prey
  density until saturation level
• possible result of 'handling time' (Holling)
• opening shells (oystercatchers)
• oviposition (parasitoids)
• mastication
• i.e. a FIXED time per prey item

Type II
6
Type III

• saturation similar to Type II
• early acceleration in predation rate due to
• increasing capture efficiency
• decline in handling time
• learning? switching?
• still saturates at high densities
• sigmoid curve

7
Dynamics and Type II Functional Responses

• creates a 'hump' in the prey isocline
• intermediate prey saturates predation but
  competition among prey is not intense
• hump also could be due to 'Allee effect'
• stability varies with crossing of the predator
  isocline

8
Dynamics and Type III Functional Responses

• less predation (lower rate) at low prey
  densities Stabilizing
• predator learning, refuges from predation, etc.
• Switching?
• generalist predators stabilizing?
• Scandinavian Rodents...

9
Scandinavian Rodents

• Cycles in the North
• few predators
• minmax densities of 1100

Gradient in Dynamics

• No regular cyclic dynamics in the south
• many predators(owls, foxes, cats, etc.)

10
The Role of Models

• Ideas, Concepts models Math makes models more
  explicit
• testable, refutable
• can communicate and build
• Simple predator prey models inadequate
• logical results unlikely in light of observations
  
• then examined predation RATE
• predictions more reasonable

• Developing and testing models requires
  quantitative skills
• analytical (mathematics computers)
• empirical (experimental design in lab and field)
• statistical (testing of hypotheses from above)