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Two populations interacting:
Effect of species 1 density on
species 2 per cap. growth rate
Species 1
interspecific
interactions
Species 2
Effect of species 2 density on
species 1 per cap. growth rate
Effect of species 1
density on its own per
cap. growth rate
(intraspecific interactions)
Effect of species 2 on
its own per cap.
growth rate
Intraspecific interactions are characterized by the form of densitydependence:
dN
Ndt
Density-indendence
 dN 
d

 Ndt   0
dN
N
Negative density-indendence
or competition
 dN 
d

 Ndt   0
dN
N
Positive density-indendence
or cooperation
N
 dN 
d

 Ndt   0
dN
Similarly, one species can have a positive, a negative or
no effect on another species.
+,- or 0
Species 2
Species 1
+,- or 0
Intraspecific interactions are characterized by the form of densitydependence:
dN1
N1dt
Density-indendence
N2
Negative density-indendence
or competition
N2
Positive density-indendence
or cooperation
N2
 dN1 

d 
 N1dt   0
dN 2
 dN1 

d 
 N1dt   0
dN 2
 dN1 

d 
 N1dt   0
dN 2
Two-species interactions table:
Effect of
spc 1 on 2
Effect of
spc 2 on 1
Mutualism
Competition
Exploitation
+
-
+
+
Amensalism
Commensalism
Neutralism
+
0
0
0
0
MUTUALISM (+,+)
+
Example: hummingbird
and a hummingbird
pollinated plant:
Species 2
Species 1
+
Each population has a positive effect on the other.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
COMPETITION (-,-)
-
Example: two or more
annual plants compete for
soil resources in spring:
Species 2
Species 1
Each population has a negative effect on the other.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
EXPLOITATION (+,-)
+
Example: one species eats
the other (predation):
Species 2
Species 1
One population has a negative effect on the
other, but the other benefits from the first.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
EXPLOITATION (+,-)
+
Example: grazing:
Species 2
Species 1
One population has a negative effect on the
other, but the other benefits from the first.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
EXPLOITATION (+,-)
+
Species 2
Species 1
Example: parasitism:
One population has a negative effect on the
other, but the other benefits from the first.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
COMMENSALISM (+,0)
+
Example: where one species
creates another’s habitat
Species 2
Species 1
0
One population has a positive effect on the
other, but the other has no effect on the first.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2dt   0
dN1
AMENSALISM (-,0)
Species 2
Species 1
0
One population has a negative effect on the
other, but the other has no effect on the first.
d (ln N1 )
d (ln N 2 )
0
0
dN 2
dN1
Example: competition between
very unequal competitors.
NEUTRALISM (0,0)
0
Species 2
Species 1
0
Neither population affects the other’s growth
rate.
d (ln N1 )
d (ln N 2 )
0
0
dN 2
dN1
Example: two species without
any direct or indirect ecological
relationship.
What’s the interaction?
Task for the next few weeks:
1) How do two populations grow when they affect each other’s
growth rates?
2) What factors determine the population sizes of species
engaged in an interaction?
3) When do interacting populations coexist? When does one
population wipe out the other? When do populations wipe out
each other?
COMPETITION (-,-)
-
Example: two or more
annual plants compete for
soil resources in spring:
Species 2
Species 1
Each population has a negative effect on the other.
 dN1 

d 
 N1dt   0
dN 2
 dN 2 

d 
 N 2 dt   0
dN1
Paramecium caudatum
Testing the
consequences of
species interactions:
Georgii Frantsevich
Gause (b. 1910)
Paramecium aurelia
Gause’s competitive exclusion principle:
Two species competing for the same resources cannot stably coexist
if other ecological factors are constant. One of the two competitors
will always overcome the other, leading to the extinction of this
competitor: Complete competitors cannot coexist.
Overcoming Gause’s exclusion principle:
If two species utilize sufficiently separate niches, the competitive
effects of one species on another decline enough to allow stable
coexistence.