Ecology 8310 Population (and Community) Ecology Competition: the R* approach • Consumer and resource dynamics • A graphical approach • ZNGIs • Consumption vectors • Resource renewal • Putting it together • Tests
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Ecology 8310 Population (and Community) Ecology Competition: the R* approach Consumer and resource dynamics A graphical approach ZNGIs Consumption vectors.
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Ecology 8310Population (and Community) Ecology
Competition: the R* approach
• Consumer and resource dynamics• A graphical approach
• ZNGIs• Consumption vectors• Resource renewal• Putting it together
• Tests
The basics:
0
Resource density (R)
dC
/Cd
tConsumer growth
Mortality
R*
The basics: A chemostat
Consumer demographics; resource
"non-dynamic"
Inflow of resource Loss of resource and consumer
The basics: dynamics
Consumer demographics; resource
"non-dynamic"
Inflow of resource Loss of resource and consumer
The basics:
0
Time
Con
sum
er
or
Reso
urc
e D
en
sity Consume
r
Resource
Set by concentration in
inflow
R*
Introduce consumer
What happens to C* and R* if we increase the flow?
The basics:
0
Resource density (R)
dC
/Cd
t
Consumer growth
Mortality
R*
What if we have two consumers?
Two consumers:
0
Resource density (R)
dC
/Cd
tConsumer 1's growth
Mortality
R* R*
Consumer 2's growth
Synedra Asterionella
From Tilman et al. 1981 (L&O)
Alone:Followed population growthand resource (silicate) when
alone:
Data = points.Lines = predicted from model
In Competition:
Synedra wins
What if we change the environment?
Synedra won at 24oC.
Who will win at 8oC?
Asterionella Synedra
From Tilman et al. 1981 (L&O)
Who will win?
From Tilman et al. 1981 (L&O)
From Tilman et al. 1981 (L&O)
What about changing the mortality rate?
Two consumers:
0
Resource density (R)
dC
/Cd
tConsumer 1's growth
Mortality
Consumer 2's growth
Let's extend this to >1 resource…
We could approach this mathematically, but Tilman advanced an elegant graphical approach (underlain by
explicit math)…
ZNGIs:
0
R1
R2
Zero Net Growth Isocline (ZNGI): all
(R1, R2) combinations at which dC/dt=0
ZNGIs:
R1
R2
R1
R2
R1
R2
R1
R2
Essential Substitutable
Complementary
Switching
ZNGI's tell us when the consumer is at equilibrium.
What about the resources?
Resource equilibrium:
Supply = Consumption
Resource supply: "equable" vs. biotic (logistic) resources