It takes two to tango
Species Interaction:Predation
Predator
This interaction shapes:
•Evolution
•Distribution
•Abundance
Prey
Figure 18.10
Hudson’s Bay Fur Records
Lynx
Hares
Lab Experiment Classics 1
G.F. Gause (Russian dude) conducted simple
test-tube experiments with Paramecium
(prey) and Didinium (predator)
Lab Experiment Classics 1
Prey
Predator
Oat medium, no sediment
Oat medium, sediment
Oat medium, no sediment,
immigration
Lab Experiment Classics 1
• G.F. Gause conducted simple test-tube
experiments with Paramecium (prey) and
Didinium (predator):
– in plain test tubes containing nutritive medium, the
predator devoured all prey, then went extinct itself
– in tubes with a glass wool refuge, some prey escaped
predation, and the prey population reexpanded after the
predator went extinct
• Gause could maintain predator-prey cycles in such tubes by
periodically adding more predators
Lab Experiment Classics 2
Huffaker’s mites and oranges
Figure 18.7
Simple systems led to instability
• Like Gause’s study, Huffaker’s
experimental system required careful
“tuning” to generate cycles
– Barriers to predator movement
– Prey refuges
– Enhanced dispersal for prey
Take-Home from early lab
studies
• Unlike the simple theory, it is not very easy
to generate longterm cycles
• Importance of refuges in predator prey
systems
Factors Changing Equilibrium
Isoclines
• The prey isocline increases if:
– r increases or c decreases, or both:
• the prey population would be able to support the
burden of a larger predator population
• The predator isocline increases if:
– d increases and either a or c decreases:
• more prey would be required to support the predator
population
Other Lotka-Volterra Predictions
• Increasing the predation efficiency (c) alone in the
model reduces isoclines for predators and prey:
– fewer prey would be needed to sustain a given capture
rate
– the prey population would be less able to support the
more efficient predator
• Increasing the birth rate of the prey (r) should lead
to an increase in the population of predators but
not the prey themselves.
Check out:
www.whfreeman.com/ricklefs
go to Living graphs and select
Lotka-Volterra
Modification of Lotka-Volterra
Models for Predators and Prey
• There are various concerns with the LotkaVolterra equations:
– the lack of any forces tending to restore the
populations to the joint equilibrium:
• this condition is referred to as a neutral
equilibrium
– the lack of any satiation of predators:
• each predator consumes a constant proportion of the
prey population regardless of its density
Functional Responses
Solomon 1949
C.S. (Buzz) Holling 1959
“ number of prey killed per predator
(kill rate) in relation to prey density”
Linking Prey and Predator
dR/dt = rR – cRP
growth of Resource
Prey consumed by the predator
are converted into predators
dP/dt = acRP – dP growth of Predator
c is a constant expressing efficiency of predation
(per capita capture rate)
3 forms of functional response
Type I
Functional Response
Kill rate
Density of prey
• # prey killed/predator increases linearly
•Proportion of prey population eaten is constant
Type II
• # prey killed/predator increases, but at a ever
decelerating rate
• handling time is major determinant
Proportion of prey population taken:
• continuously decreases as prey increases
Lynx Functional Response
Kills of hare per day per lynx
2
'96
'95
'90
1
'91
'88
'89
'87
'92
'94
'93
0
0
50
100
150
Hare density (per 100 ha)
200
Type III
1. Initially low kill rate
• not profitable to kill prey when scarce
• prey refugia
• predators may use alternate prey species
2. Kill rate increases
• then profitable switch or concentrate
• proportion taken increases
3. Asymptotes
• handling time constraints
• social behaviour
Figure 18.13
The Functional Response
• A more realistic description of predator behavior
incorporates alternative functional responses,
proposed by C.S. Holling:
– type I response: rate of consumption per predator is
proportional to prey density (no satiation)
– type II response: number of prey consumed per
predator increases rapidly, then plateaus with increasing
prey density
– type III response: like type II, except predator
response to prey is depressed at low prey density
Prey/predator
Per capita killed
per predator
Nonregulatory
Nonregulatory
Regulatory
Figure 18.12
The Numerical Response
• If individual predators exhibit satiation
(type II or III functional responses),
continued predator response to prey must
come from:
– increase in predator population through local
population growth or immigration from
elsewhere
• this increase is referred to as a numerical response
Kluane Lake, Yukon
20
3
18
Hares
Lynx
14
2
2
12
10
8
1
6
4
2
0
0
Fall 86Fall 87 Fall 88Fall 89Fall 90Fall 91Fall 92Fall 93Fall 94Fall 95Fall 96
Year
Lynx per 100 km
Hare density / ha.
16
Total predation depends on the
combined functional and numerical
response
Several factors reduce predatorprey oscillations.
• All of the following tend to stabilize predator and
prey numbers (in the sense of maintaining
nonvarying equilibrium population sizes):
– predator inefficiency
– density-dependent limitation of either predator or prey
by external factors
– alternative food sources for the predator
– refuges from predation at low prey densities
– reduced time delays in predator responses to changes in
prey abundance
Destabilizing Influences
• The presence of predator-prey cycles indicates
destabilizing influences:
– such influences are typically time delays in predatorprey interactions:
• developmental period
• time required for numerical responses by predators
• time course for immune responses in animals and induced
defenses in plants
– when destabilizing influences outweigh stabilizing
ones, population cycles may arise
Summary 1
• Predators can, in some cases, reduce prey
populations far below their carrying capacities.
• Predators and prey exhibit regular cycles in the
wild, typically with cycle lengths of 4 years or 910 years.
• Lotka and Volterra proposed simple mathematical
models of predator and prey that predicted
population cycles.
Summary 2
• Increased productivity of the prey should increase
the predator’s population but not the prey’s.
• Functional responses describe the relationship
between the rate at which an individual predator
consumes prey and the density of prey.
• The Lotka-Volterra models incorporate a type I
functional response, which is inherently unstable.
• Type III functional responses can result in stable
regulation of prey populations at low densities.
Summary 3
• Type III functional responses can result from
switching.
• Numerical responses describe responses of
predators to prey density through local population
growth and immigration.
• Several factors tend to stabilize predator-prey
interactions, but time lags tend to destabilize them.
• Predator-prey systems may have multiple stable
points.