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Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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Page 1: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific
Page 2: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 3: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

Exploitative and interference competition.

Page 4: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

The competitive exclusion principle

• two species cannot coexist if they both depend on the same limiting resource

Page 5: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

The competitive exclusion principle

• two species cannot coexist if they both depend on the same limiting resource

• disturbance and predation

• habitat heterogeneity• metapopulation

dynamics

Page 6: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 7: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 8: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 9: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 10: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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)

Page 11: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 12: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 13: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

Lotka-Voltera competition

Rhizopertha and Oryzaephilus Rhizopertha and Sitotraga

Page 14: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 15: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 16: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 17: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

Resource competition model

• trivial example of ZGI’s for two species competition

• Ni always wins

Page 18: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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

Page 19: Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific

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