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Exploiter-Victim Relationships
Host-Parasite: Host death need not occur, and often does
not; birth rate of host reduced by parasite
Host-Parasitoid: Host death always occurs
Predator-Prey: Death rate of prey increased by predators
Herbivore-Plant: May resemble predation or parasitism
Parasitoids
Weevils and wasps
Lynx and Snowshoe Hare
Orange Mites, simple universe
Orange Mites, increased
patchiness
Orange Mites, complex habitat
Field Studies: Dingoes and kangaroos
Dingoes and Boars
Lamprey and Lake Trout
Fox and Rabbit
Plant-Herbivore
Herbivore-- positive effect?
N-fertilization effects
N-fertilization effects
Big Herbivores
Amboseli Elephants
Elephants not excluded
Elephants Excluded
Baobab
Baobab
Baobab,
Elephant
Damage
Functional Response
Change in predator’s attack behavior
as prey density increases
Basic forms to consider:
Type I: Linear increase in #
attacked with increasing # prey
(insatiable predator)
I
Type II: Gradual levelling off
II
As predators become satiated
Type III: Predators satiable as
in Type II, but hunt
inefficiently at low prey
densities
III
Prey density
Toxorhynchites
Toxorhynchites brevipalpus
Toxorhynchites Functional
Response, sympatric & allopatric
prey:
IL (allopatric)
NC (sympatric)
Fraction killed per predator/time
Type I
Type II
Type III
Prey Density
Type II and III: satiable predators become less effective
at controlling prey as prey become more abundant.
Lotka-Volterra Predator-Prey
Model:
Assume:
1) Random search, producing encounters between prey and
predators (and subsequent attacks) proportional to the
product of their densities (attack rate = a’)
2) Exponential prey population growth in absence of predator,
with constant growth rate, r
3) Death rate of predator is constant = q
4) Birth rate of predator proportional to #prey consumed
Prey growth equation
Prey:
Without predator, dN/dt=rN
If predator searches with attack rate a’, and there are C
Predators, then deaths due to predation = a’CN
dN/dt = rN - a’CN
Predator Growth Equation
dC/dt = (birth rate - death rate)C
Death rate assumed constant = q
Birth rate: #prey consumed x conversion constant, f
= (#prey consumed)x f
# prey consumed = a’CN (see prey equation)
births = a’CNf
birth rate = a’Nf
dC/dt = (a’Nf - q)C
Equilibrium Conditions, Prey
Too many predators
Prey:
dN/dt = rN - a’CN = 0
r-a’C = 0
C = r/a’
C = r/a’
C
Not enough predators
N
Equilibrium conditions, predators
C
N = q/a’f
N = q/a’f
Not enough prey
a’Nf - q = 0
N
More than enough prey
dC/dt = (a’Nf - q)C = 0
Changes in both species:
C
N
The prey curve has a hump
Humped Prey curves
Rotifer density
Change in phytoplankton density at different combinations of
Rotifer density and phytoplankton density
Phytoplankton density
Why the Prey curve has a Hump
1. Resource limits for
prey at high densities
(fewer preds needed to
keep in check)
2. But, predator is most
effective at low prey
densities
Effects of a humped prey curve:
C
N
Increasing oscillation
(unstable)
Damped oscillation
(stable point)
Neutral
stability
Effects of a humped prey curve:
C
N
time
Increasing oscillation
(unstable)
Damped oscillation
(stable point)
Neutral
stability