Competition
• Intraspecific
– Between individuals of
the same species
• Interspecific
– Between individuals of
different species
• Which one is
stronger?
Interspecific Competition
Competition
K − N −α N 
dN1
1
12 2
= r1 N1 1

dt
K1


K − N −α N 
dN 2
2
21 1
= r2 N 2  2

dt
K2


• Lotka-Voltera Interspecific
competiton
– Convert individuals of species
1 into species 2 equivalents.
-α12 Amount of spp.1’s niche
overlapped by spp 2’s niche
- α 21 Amount of spp.2’s niche
overlapped by spp 1’s niche
1
Competition
• What happens to
species 1 in the
presence of species 2?
K1/α12
dN1/dt =0
N2
N1
K1
Competition
• What happens to
species 1 in the
presence of species 2?
K1/α12
dN1/dt =0
N2
N1
K1
Competition
• What happens to
species 2 in the
presence of species 1?
K2
dN2/dt =0
N2
N1
K2/α21
2
Competition
• What happens to
species 2 in the
presence of species 1?
K2
N2
dN2/dt =0
N1
K2/α21
Competition
K1/α12
K2
dN1/dt =0
N2
N1
N2
K1
dN2/dt =0
N1
K2/α21
Competition
K2
K1/α12
N2
N1
K1
K2/α21
Species 2 wins
3
Competition
K1/α12
K2
K1/α12
K2
N2
N2
N1
K1
K2/α21
N1
Species 2 wins
K2/α21
K1
Species 1 wins
Competition
K2
N2
K1/α12
N1
K2/α21
K1
Unknown who wins
But somebody loses
Competition
K1/α12
K2
N2
K1/α12
K2
N2
N1
K2/α21
Unknown who wins
But somebody loses
K1
N1
K1
K2/α21
Both species win
Coexistence
4
Competition
• What are the requirements for
K1/α12
coexistence?
– K1/α12 > K 2
K2
• K1 > α12 K 2
– K1 > K2/α21
N
2
• K2 > α21 K 1
– Translation?
N1
K1
K2/α21
Competition
•
What are the requirements
for coexistence?
– K1/α12 > K2
KPH/αPH,MD
• K1 > α12 K2
KMD
– K1 > K2/α21
• K2 > α21 K1
NMD
– Translation?
• Species coexistence occurs
when each species limits its
own population growth more
than its growth is limited by
the other species
Interspecific > Intraspecific?
Interspecific < Intraspecific?
N1
KPH
KMD/αMD,PH
Competition
•
•
Example
Yellowstone ungulates
– KPH > αPH,MD KMD
– KMD > α MD,PH KPH
Pronghorn Antelope
2000
N
Mule Deer
1000
Time
5
Competition
•
•
Example
Yellowstone ungulates
– KPH > αPH,MD KMD
– KMD > α MD,PH KPH
Pronghorn Antelope
2000
N
Mule Deer
1000
KPH = 2000
KMD = 1200
Time
Competition
•
•
Example
Yellowstone ungulates
– KPH > αPH,MD KMD
– KMD > α MD,PH KPH
Pronghorn Antelope
2000
N
Mule Deer
1000
KPH = 2000
KMD = 1200
Time
Resource Use / day
g Grass g Forbs
PH
80
15
MD
20
100
g Shrubs
0
100
Competition
•
•
Example
Yellowstone ungulates
– KPH > αPH,MD KMD
– KMD > α MD,PH KPH
Convert pronghorn into
mule deer αMD,PH :
niche overlap = 35/220 =16%
Convert mule deer into
pronghorn αPH,MD :
niche overlap = 35/95 =37%
Pronghorn Antelope
2000
N
Mule Deer
1000
KPH = 2000
KMD = 1200
Time
Resource Use / day
g Grass g Forbs
PH
80
15
MD
20
100
g Shrubs
0
100
6
Competition
•
•
Example
Yellowstone ungulates
– KPH > αPH,MD KMD
– 2000 > 0.37*1200
– 2000 > 444
– KMD > αMD,PH KPH
– 1200 > 0.16*2000
– 1200 > 320
Pronghorn Antelope
2000
N
Mule Deer
1000
KPH = 2000
KMD = 1200
Time
Convert pronghorn into
mule deer αMD,PH :
niche overlap = 35/220 =16%
Convert mule deer into
pronghorn αPH,MD :
niche overlap = 35/95 =37%
Resource Use / day
g Grass g Forbs
PH
80
15
MD
20
100
g Shrubs
0
100
Competition
Sp.1 survives but
R0=1 ZNGI 1
• Tillman competition
– Resource based
– Graph of the amount of
resources a species needs in
order to survive
Amt. of
resource Y
Sp.1 survives
and reproduces
Sp.1 does not survive
Amount of resource X
Competition
• Tillman competition
– Resource based
– Graph of the amount of
resources a species needs
in order to survive for both
species
– Can both species survive?
ZNGI1
Amt. of
resource Y
Sp.2 survives but
R0=1 ZNGI 2
Sp.2 survives
and reproduces
Amount of resource X
7
Competition
• Tillman competition
– Resource based
– Graph of the amount of
resources a species needs in
order to survive for both
species
– If resources fall anywhere in
area A
ZNGI1
ZNGI2
Amt. of
resource Y
C
• Neither species survives
B
A
Amount of resource X
Competition
• Tillman competition
– Resource based
– Graph of the amount of
resources a species needs in
order to survive for both
species
– If resources fall anywhere in
area A
ZNGI1
ZNGI2
Amt. of
resource Y
C
• Neither species survives
B
– If resources fall anywhere in
area B
• Only species 1 survives
A
Amount of resource X
Competition
•
Tillman competition
– Resource based
– Graph of the amount of resources
a species needs in order to survive
for both species
– If resources fall anywhere in area
A
ZNGI1
ZNGI2
Amt. of
resource Y
• Neither species survives
C
– If resources fall anywhere in area
B
B
• Only species 1 survives
– If resources fall anywhere in area
C
• Only species 1 survives
A
Amount of resource X
8
Competition
ZNGI1
ZNGI2
• But what if the ZNGIs
overlap?
C1
Amt. of
resource Y
– Need to determine
relative consumption
rates of the resources
for each species.
C2
Amount of resource X
Competition
ZNGIPH
ZNGIMD
C
Shrub
density
• But what if the ZNGIs
overlap?
CMD
– It depends on the relative
consumption rate of the
resources for each competitor
– Grass density is more limiting for
pronghorns.
– Shrub density is more limiting
for mule deer.
D
B
E
CPH
F
A
• A - Neither spp. survives
• B - Mule deer win
• F - Pronghorn win
Grass density
Competition
ZNGIPH
ZNGIMD
•
C
Shrub
density
B
• C - Mule deer win
D
– More shrubs available then grass
E
A
But what if the ZNGIs overlap?
– Grass density is more limiting for
pronghorns.
– Shrub density is more limiting for
mule deer.
CMD
F
CPH
• D - Coexistence
– Each species consumes relatively
more of its limiting resource
– The relative availability of the two
resources must be between the two
consumption vectors.
• E - Pronghorn win
– More grass available than shrubs
Grass density
9
Competition
ZNGIPH
ZNGIMD
•
C
Shrub
density
B
But what if the ZNGIs overlap?
– Grass density is more limiting for
pronghorns.
– Shrub density is more limiting for
mule deer.
CMD
• C - Mule deer win
D
– More shrubs available then grass
E
CPH
• D - Unknown who will win but only
one species will survive
• E - Pronghorn win
– More grass available than shrubs
F
A
Grass density
Competition
• Lotka-Voltera
– Implicitly concerned with
resources
– Explicitly concerned with
population sizes
– Provides estimate of
equilbrium size of both
species
– Allows determination of
winning competitor or
coexistence
• Tilman
– Explicitly concerned with
resources
– Implicitly concerned with
population sizes
– Doesn’t provides estimate
of equilbrium size of both
species
– Allows determination of
winning competitor or
coexistence
10