Species interactions: Predatorprey dynamics

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Species interactions Predator-prey dynamics

• 1. What effects do predators have on prey
  populations?
• 2. Do predator-prey interactions cause
  populations to oscillate?
• 3. What factors stabilize predator-prey
  population dynamics?

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Previously seen how fast -growing populations may
have an intrinsic propensity to cycle
If time lags occur (e.g. timing of breeding
season relative to resource availability later in
year) then fluctuations will occur depending on
per-capita growth rate r
Stable limit cycle population cycling of
constant amplitude
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Populations may also cycle in response to dynamic
interactions between predators and prey
Hudson Bay Co. records of fur trappers pelts
What evidence would you use to test hypothesis of
link?
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Synchrony of lynx and hare population density
suggest that predation may be involved in driving
cycling. Not always the case. Look at easier
systems
Huffaker 1956
Cyclamen mite (Tarsonemus) pest of
strawberries Predatory mite (Typhlodromus) feeds
on cyclamen mite and could potentially control
population
Growing house experiment Two treatments 1.
Strawberry plants predator and prey mites 2.
Parathion insecticide (p) kills predator but
not prey
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Predator present
No predator
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Mite predator and prey dynamics mirror
observations in the field
New strawberry fields are over-run by cyclamen
mites first year - then controlled second year.
Prey better dispersers?? Application of
parathion in fields led to cyclamen mite outbreak
(need for integrated pest management)
Why do predators control prey in this system?
2 key features High reproductive rate r of the
predator Alternate food source for predator
(can maintain high pop. density when cyclamen
mite is rare.
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Fluctuating prey densities may indicate time lags
in the predator numerical response to prey
density Time lags result from delay in time to
produce offspring Predator abundance may peak 1-2
years after prey abundace has reached a maximum
Pathogen population cycling is analagous
Fluctuations in pathogen infection rates reflect
dispersal through a susceptible population
followed by the development of immunity
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Dispersal of prey away from predators can also
help stabilize predator-prey dynamics by
preventing prey extinction
Huffakers oranges experiment
Six-spotted mite (prey) Typhlodromus mite
(predator)
Dynamics on arrays of oranges and rubber balls
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Initial experiments Add 20 prey mites
(parthenogenic females) Prey population
increased to 5-8,000 individuals and levelled
off Add 2 predator female mites Predators
increased - prey wiped out. Speed of extinction
depended on dispersion of habitat (oranges)
because takes time for predators to arrival
Under what circumstances could predator and prey
coexist?
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Coexistence achieved by helping prey dispersal
(launch pads), while hindering predators
(vaseline)
Black spots predators. Orange colorlow density
redhigh density of prey mites
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Modeling predator-prey dynamics using
Lotka-Volterra
First consider prey in the absence of
predators dR/dt rR Where R prey (resource)
population Prey in the presence of
predators dR/dt rR - cRP Where cRP is the
number of prey individuals captured Loss to
predators is determined by the product of
predator and victim numbers, RP (assumes
predators and prey move randomly through the
environment) and the capture efficiency, c c is
a measure of the effect of the predator on the
per capita growth rate of prey
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Larger c more the per capita growth rate of the
prey population is depressed by the addition of a
single predator Here cR also represents the
functional response of the predator (this
describes how the rate of prey capture is
affected by prey abundance). In this case, the
functional response is linear - capture rate
increases at a constant rate as prey density
increases.
Now consider the predator In the simplest form
of the model, the predator is specialized on
just one prey species - therefore in the absence
of prey, the predator population declines
exponentially dP/dt -dP where P is the
predator population size, and d is the per
capita death rate
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Positive population growth occurs when prey are
present as follows dP/dt acRP - dP Where a
is the conversion efficiency - the ability of
predators to turn prey into additional per
capita growth rate for the predator Population
(and cRP remember, is the number of prey
captured) When a is high a single prey item is
valuable (killing a Woolly Mammoth). d is the
per capita death rate of the predator population
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Just as with competition models we can find
equilibrium solutions where growth rate0
Starting with the prey population dR/dt rR -
cRP 0 rR - cRP rR cRP notice that prey (R)
fall out of the equation! r cP Equilibrium P
r/c Equilibrium P number of predators to keep
the prey population at zero growth. Number of
predators depends on the ratio of the growth rate
of prey to the capture efficiency of the
predators.
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Now for the predator population dP/dt acRP -
dP 0 acRP - dP acRP dP notice that predators
(P) fall out of equation! acR d Equilibrium R
d/ac Equilibrium R is the number of prey needed
to keep the predator population at zero growth.
How many prey are necessary depends on the
ratio of the per capita death rate of predators
to the conversion efficiency of predators
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Dotted lines are zero growth isoclines
Arrows show direction of trajectory of
populations
PREY
PREDATOR
Pred
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Dotted lines are zero growth isoclines
Arrows show direction of trajectory of
populations
Pred
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Now super-impose graphs
Zero growth Isocline predators
Zero growth Isocline for prey
Predict cyclic behavior - amplitude depends on
starting conditions
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Neutral equilibrium cycle
P
R
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Some assumptions of Lotka-Volterra are unrealistic
Predators cannot be satiated. The predation
term, cRP assumes that rate of prey capture is a
direct proportion of prey density (cR) Type I
functional response
Type II and III allow predator satiation (ie
proportion of the prey population declines as
prey abundance increases
Type III has low predation rate when prey are
rare. Why?
Density of prey
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No prey carrying capacity in absence of predators
dR/dt rR -cRP -bR2
Where b is a constant
Maximum prey population
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Factors stabilizing predator-prey oscillations

• Predator inefficiency (low c) yields higher
  equilibrium levels of prey and predators (rem
  equilibrium predators r/c)
• Density-dependent factors outside the system
  affecting predators or prey
• Diet switching by the predator
• Refuges from predators
• Reduced time lags between predator and prey
  population responses

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