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Competition in theory
• one individual uses a resource, reducing its availability to others
• negative-negative interaction– intraspecific competition – interspecific competition– interference competition– exploitative competition– diffuse competition– apparent competition
Exploitative and interference competition.
The competitive exclusion principle
• two species cannot coexist if they both depend on the same limiting resource
The competitive exclusion principle
• two species cannot coexist if they both depend on the same limiting resource
• disturbance and predation
• habitat heterogeneity• metapopulation
dynamics
Lotka-Voltera competition model
• adding a competing species j reduces the growth rate and the steady state equilibrium population of species i
j
iji
j
jjj
j
i
jij
i
iii
i
K
Na
K
NNr
dt
dN
K
Na
K
NNr
dt
dN
1
1
Lotka-Voltera competition model
• competition coefficients aij and aji express the effects of each competitor in terms of the other competitor’s resource use– competition coefficients
usually α and β– aij means “the effect of
each member of species j on species i”
j
iji
j
jjj
j
i
jij
i
iii
i
K
Na
K
NNr
dt
dN
K
Na
K
NNr
dt
dN
1
1
Lotka-Voltera competition model
• (a) per-capita growth rate for species i– zero growth isocline in the
(Ni, Nj) plane
• (b) ZGI for species i– Ni → Ki only when Nj → 0– Ki/aij is the equilibrium
population of species i expressed in “equivalent units” of species j
• (c) ZGI for species j
Lotka-Voltera competition model
• species i zero growth isocline crosses the Ni axis at Ki and the Nj axis at Ki/aij
• species j zero growth isocline crosses the Nj axis at Kj and the Ni axis at Kj/aji
Lotka-Voltera competition model
• species i zero growth isocline crosses the Ni axis at Ki and the Nj axis at Ki/aij
• species j zero growth isocline crosses the Nj axis at Kj and the Ni axis at Kj/aji
• the species with the outer ZGI wins (Ni)
Lotka-Voltera competition model
• coexistence can occur when the zero growth isoclines cross one another
• equilibrium with both populations > 0
• stable if intraspecific competition limits growth before interspecific competition
Lotka-Voltera competition model
• coexistence can occur when the zero growth isoclines cross one another
• equilibrium with both populations > 0
• unstable otherwise• outcome depends on
starting population sizes
Lotka-Voltera competition
Rhizopertha and Oryzaephilus Rhizopertha and Sitotraga
Resource competition model
• the Lotka-Voltera models do not express competitive interactions in terms of resource consumption
• zero growth isoclines for a single species with two limiting resources
Resource competition model
• the Lotka-Voltera models do not express competitive interactions in terms of resource consumption
• zero growth isoclines for a single species with two limiting resources
R2*
R1*Resource 1
Res
ourc
e 2
Resource competition model
R2*
R1*Resource 1
Res
ourc
e 2
iA
B
• zero growth isoclines for a single species with two limiting resources
• consumption vector reflects an optimal resource use ratio
• resource supply points and depletion vectors
• species i is excluded from the shaded area
Resource competition model
• trivial example of ZGI’s for two species competition
• Ni always wins
Resource competition model
• two species competition• outcome depends upon
initial resource supply point and joint depletion vectors
j
R2i*
R1i*
Resource 1
Res
ourc
e 2
R2j*
R1j*
i
j
i onl
y
j only
i exc
lude
s j
j excludes i
Both coex
ist
Resource competition model
• two species competition• outcome depends upon
initial resource supply point and joint depletion vectors
• ZGIs and consumption vectors for two diatom species