Lotka-Volterra Models of Interspecific Competition
• Use α12 to calculate affect of one species on another.
– K1 =1000
– N1 = 600
– N2 = 300
– α12 = 0.8; 0.8 * 300 = 240
– N1 = 600 + 240 equivalent competitors = 840
 K1 − N 1 − a12 N 2 
dN 1
= r1 N 1 

dt
K1


• Models change in population size of species 1,
accounting for impact of species 2.
• Similarly, affect of species 1 on species 2:
 K2 − N 2 − a21 N 1 
dN 2

= r2 N 2 
dt
K2


Zero isoclines
N1=K1=1 – stable, all resources used by species 1
N2=K1/α12 =1 - stable, all resources used by species 2 (equivalent
population)
Combine the
isoclines for both
species to produce
a graphical model
of competitive
interactions.
Possible outcomes:
-Stable coexistence
-Dominance by one
species
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Competitive Release and Ghost of Competition Past
• Competitive release - In the absence of a competitor, a
species niche expands. Realized niche expands, more
similar to fundamental niche.
• Ghost of competition past - Past competitive
interactions lead to change in a species such that the
fundamental niche is different, competitive release does
not occur.
Werner and Hall 1976
Character Displacement
• Single species
occupying variety of
niches
• Morphological variability
• Density dependent
competition
• Extreme morphotypes
most succesful in
slightly different niches
• Extreme morphotypes
selected for (reduced
competition increases
fitness)
• Different habitat
preference evolves after
morphology
Werner and Hall 1976
Distribution in Nature
Green sunfish
Most abundant prey
Bluegill
Pumpkinseed
Reduced in all 3
Increased in all 3
2
Werner and Hall 1976
Ghost of Competition Past
• Invoking Ghost of Competition Past - It’s tempting to
conclude two coexisting species do not compete because
past competitive interactions lead to niche differentiation
that reduced competitive pressure.
• Evolutionary and ecological explanation
• Phylogenetic explanation
Niche Conservatism
• Tendency for a species to retain the ecological niche of
its ancestors
A
A
F
F
H
H
Fitness
– Phylogenetic signal – niches are similar, show a
phylogenetic pattern, change gradually. Not under
strong selection.
Three competing species,
color represents two distinct
mouth morphologies. All are
endemic to an island
archipelago ~3 million years
old.
– Niche conservatism – niches are more similar than
expected. Stabilizing selection results in little change
from ancestral niche.
Niche Space (diet related to mouth
morphology, related to w)
Is the difference in mouth morphology due to past competition?
3
F
H
Phylogenetic Tree 1
Fitness
A
Three species in
sympatry
Niche Space (diet related to mouth
morphology, related to w)
A
B
C
D
E
G
H
Time
Time when trait changed
Need to prove these two species
competed in a similar ecological
setting (~1.5 mya).
3 mya
F or H alone
H (or F) alone, no
niche expansion…
ghost of competition
past possible ?
Fitness
F
Niche Space (diet related to mouth
morphology, related to w)
Phylogenetic Tree 2
A
B
Phylogenetic Tree 2
F
D
E
C
G
H
A
B
F
D
E
C
G
H
Time
Time
Time
when trait
changed
Time when trait changed
3 mya
3 mya
For species H, nothing changed in
this tree. Need to prove these two
species competed in a similar
ecological setting (~1.5 mya).
For species F, need to prove F
competed with A, B or common
ancestor of A and B in a similar
ecological setting (~0.5 mya).
Easiest ghost of comp past to
demonstrate is D and F – sister
taxa recently diverged, endemic to
a “new” habitat.
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