Download A verbal model of predator

Predator/Prey
Two big themes:
1. Predators can limit prey populations.
This keeps populations below K.
2. Predator and prey populations
increase and decrease in regular
cycles.
K= Carrying Capacity
The maximum population size an
environment can support
A verbal model of predator-prey
cycles:
1. Predators eat prey and reduce their
numbers
2. Predators go hungry and decline in
number
3. With fewer predators, prey survive
better and increase
4. Increasing prey populations allow
predators to increase
And repeat…
Why don’t predators increase at the same
time as the prey?
The Lotka-Volterra Model:
Assumptions
1. Prey grow exponentially in the
absence of predators.
2. Predation is directly proportional to the
product of prey and predator
abundances (random encounters).
3. Predator populations grow based on
the number of prey. Death rates are
independent of prey abundance.
Predator-prey cycles can be unstable
– efficient predators can drive prey to
extinction
– if the population moves away from the
equilibrium, there is no force pulling the
populations back to equilibrium
– eventually random oscillations will drive
one or both species to extinction
Factors promoting stability in
predator-prey relationships
1. Inefficient predators (prey escaping)
– less efficient predators (lower c) allow
more prey to survive
– more living prey support more predators
2. Outside factors limit populations
– higher d for predators
– lower r for prey
3. Alternative food sources for the
predator
– less pressure on prey populations
4. Refuges from predation at low prey
densities
– prevents prey populations from falling too
low
5. Rapid numeric response of predators
to changes in prey population
• Huffaker’s experiment on predator-prey
coexistence
• 2 mite species, predator and prey
• Initial experiments – predators drove
prey extinct then went extinct
themselves
• Adding barriers to dispersal allowed
predators and prey to coexist.
Refuges from predation allow predator and
prey to coexist.
Prey population outbreaks
Per capita
population
growth rate
Population growth curve for
logistic population growth
ro
K
Density of prey population
dR
 rR  cRP
dt
Per capita
death rate
Type III functional response
curve for predators
K
Density of prey population
dR
 rR  (predation )
dt
Multiple stable states are possible.
Below A – birth rate > death rate; population
increases
A
Point A – stable equilibrium; population
increases below A and decreases above A
A
Between A & B – predators reduce population
back to A
A
B
Unstable equilibrium – equilibrium point
from which a population will move to a
new, different equilibrium if disturbed
Point B – unstable equilibrium; below B,
predation reduces population to A; above B,
predators are less efficient, so population
grows to C
B
Between B & C – predators are less efficient,
prey increase up to C
B
Point C – stable equilibrium
B
• Predator-prey systems can have
multiple stable states
• Reducing the number of predators can
lead to an outbreak of prey
Growth rate
Death rate