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Two populations interacting:
Species 1Species 2
Effect of species 1 density on species 2 per cap. growth rate
Effect of species 2 density on species 1 per cap. growth rate
Effect of species 1 density on its own per
cap. growth rate
Effect of species 2 on its own per cap.
growth rate(intraspecific interactions)
interspecific interactions
N
Intraspecific interactions are characterized by the form of density-dependence:
0
dNNdtdN
ddNNdt
Density-indendence
N
0
dNNdtdN
dNegative density-indendence
or competition
N
0
dNNdtdN
dPositive density-indendence
or cooperation
Similarly, one species can have a positive, a negative or no effect on another species.
Species 1Species 2
+,- or 0
+,- or 0
N2
Intraspecific interactions are characterized by the form of density-dependence:
02
1
1
dN
dtNdN
ddN1
N1dt
Density-indendence
N2
Negative density-indendenceor competition
N2
Positive density-indendenceor cooperation
02
1
1
dN
dtNdN
d
02
1
1
dN
dtNdN
d
Effect of
spc 1 on 2
Effect of
spc 2 on 1
Mutualism
Competition
Exploitation
+
-
-
+
-
+
Amensalism
Commensalism
Neutralism
-
+
0
0
0
0
Two-species interactions table:
Species 1Species 2
+
+
Each population has a positive effect on the other.
Example: hummingbird and a hummingbird pollinated plant:
MUTUALISM (+,+)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
Species 1Species 2
-
-
Each population has a negative effect on the other.
Example: two or more annual plants compete for soil resources in spring:
COMPETITION (-,-)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
Species 1Species 2
+
-
One population has a negative effect on the other, but the other benefits from the first.
Example: one species eats the other (predation):
EXPLOITATION (+,-)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
Species 1Species 2
+
-
One population has a negative effect on the other, but the other benefits from the first.
Example: grazing:
EXPLOITATION (+,-)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
Species 1Species 2
+
-
One population has a negative effect on the other, but the other benefits from the first.
Example: parasitism:
EXPLOITATION (+,-)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
COMMENSALISM (+,0)
Example: where one species creates another’s habitat
Species 1Species 2
+
0
One population has a positive effect on the other, but the other has no effect on the first.
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
AMENSALISM (-,0)
Species 1Species 2
-
0
One population has a negative effect on the other, but the other has no effect on the first.
0)n(l
0)n(l
1
2
2
1 dN
Nd
dN
Nd
Example: competition between very unequal competitors.
NEUTRALISM (0,0)
Species 1Species 2
0
0
Neither population affects the other’s growth rate.
0)n(l
0)n(l
1
2
2
1 dN
Nd
dN
Nd
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?
Species 1Species 2
-
-
Each population has a negative effect on the other.
Example: two or more annual plants compete for soil resources in spring:
COMPETITION (-,-)
001
2
2
2
1
1
dN
dtNdN
d
dN
dtNdN
d
Testing the consequences of
species interactions: Georgii Frantsevich
Gause (b. 1910)
Paramecium caudatum
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.
If two species utilize sufficiently separate niches, the competitive effects of one species on another decline enough to allow stable
coexistence.
Overcoming Gause’s exclusion principle:
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