George Williams described Mother Nature as a

1
Competition

• George Williams described Mother Nature as a
• Wicked Old Witch
• This seems especially appropriate for negative
  interactions

2
Pair-wise species interactions (owing to
acquisition or assimilation of resources, etc.)
Influence of species A
- (negative)
0 (neutral/null)
(positive)
-
Influence of Species B
0

Redrawn from Abrahamson (1989) Morin (1999, pg.
21)
3
Competition
Competition (generally an intra-trophic level
phenomenon) occurs when each species negatively
influences the population growth rate (or size)
of the other
This phenomenological definition is used in the
modeling framework proposed by Alfred Lotka
(1880-1949) Vito Volterra (1860-1940)
Their goal was to determine the conditions under
which competitive exclusion vs. coexistence would
occur between two sympatric competitors
4
Population Dynamics
?N
Exponential growth
r N
?t
Occurs when growth rate is proportional to
population size Requires unlimited resources
N
Time
5
Population Dynamics
Density-dependent per capita birth (b)
death (d) rates
Notice that per capita fitness increases with
decreases in population size from K
b
b
r
or d
d
Equilibrium ( carrying capacity, K)
N
6
Population Dynamics
?N
N
Logistic growth
r N (1 )
?t
K
K carrying capacity
0
N
is maximized
0
Time
7
Competition
Lotka-Volterra Competition Equations
In the logistic population growth model, the
growth rate is reduced by intraspecific
competition Species 1 dN1/dt
r1N1(K1-N1)/K1 Species 2 dN2/dt
r2N2(K2-N2)/K2
Lotka Volterras equations include functions to
further reduce growth rates as a consequence of
interspecific competition Species 1 dN1/dt
r1N1(K1-N1-f(N2))/K1 Species 2 dN2/dt
r2N2(K2-N2-f(N1))/K2
8
Competition
Lotka-Volterra Competition Equations
The function (f) could take on many forms,
e.g. Species 1 dN1/dt r1N1(K1-N1-aN2)/K1
Species 2 dN2/dt r2N2(K2-N2-ßN1)/K2
The competition coefficients a ß measure the
per capita effect of one species on the
population growth of the other, measured relative
to the effect of intraspecific competition
If a 1, then per capita intraspecific effects
interspecific effects
If a lt 1, then intraspecific effects are more
deleterious to Species 1 than interspecific
effects
If a gt 1, then interspecific effects are more
deleterious
9
2
2
1
2
1
2
1
1
1
1
1
1
1
Area within the frame represents carrying
capacity (K) of either species
The size of each square is proportional to the
resources an individual consumes and makes
unavailable to others (Sp. 1 purple, Sp. 2
green)
Individuals of Sp. 2 consume 4x resources
consumed by individuals of Sp. 1 For Species
1 dN1/dt r1N1(K1-N1-aN2)/K1 where a
4.
Redrawn from Gotelli (2001)
10
2
2
1
2
1
2
1
1
1
1
1
1
1
Competition is occurring because both a ß gt 0
? a 4 ß ¼
In this case, adding an individual of Species 2
is more deleterious to Species 1 than is adding
an individual of Species 1
but, adding an individual of Species 1 is less
deleterious to Species 2 than is adding an
individual of Species 2
Redrawn from Gotelli (2001)
11
2
2
1
2
1
2
1
1
1
1
1
1
1
Asymmetric competition
In this case a gt ß a gt 1 ß lt 1
12
1
2
2
1
2
2
1
Asymmetric competition
In this case a gt ß ß 1
Asymmetric competition can occur throughout the
spectrum of a ? ß, (a lt gt 1, or ß lt gt 1)
What circumstances might the figure above
represent?
Exclusively interspecific territoriality,
intra-guild predation
13
1
2
2
1
2
2
1
Symmetric competition
In this case a ß 1, i.e., the special case
of competitive equivalence
Symmetric competition can occur throughout the
spectrum of (a ß) lt gt 1
14
Predictions from the Lotka-Volterra Model
Find equilibrium solutions to the equations,
i.e., set dN/dt 0 Species 1 N1 K1 -
aN2 Species 2 N2 K2 - ßN1


This makes intuitive sense The equilibrium for
N1 is the carrying capacity for Species 1 (K1)
reduced by some amount owing to the presence of
Species 2 (a N2)
15
Predictions from the Lotka-Volterra Model
The equations for equilibrium solutions
become Species 1 N1 K1 - aK2 / 1 - a
ß Species 2 N2 K2 - ßK1 / 1 - a ß


These provide some insights into the conditions
required for coexistence under the assumptions of
the model
E.g., the product aß must be lt 1 for N to be gt 0
for both species (a necessary condition for
coexistence)
But they do not provide much insight into the
dynamics of competitive interactions, e.g., are
the equilibrium points stable?
16
4 time steps
State-space graphs help to track population
trajectories (and assess stability) predicted by
models
Mapping state-space trajectories onto single
population trajectories
From Gotelli (2001)
17
4 time steps
State-space graphs help to track population
trajectories (and assess stability) predicted by
models
4 time steps
Mapping state-space trajectories onto single
population trajectories
From Gotelli (2001)
18
Remember that equilibrium solutions require dN/dt
0 Species 1 N1 K1 - aN2

Therefore When N2 0, N1 K1
K1 / a
Isocline for Species 1 dN1/dt 0
When N1 0, N2 K1/a
N2
K1
N1
19
Remember that equilibrium solutions require dN/dt
0 Species 2 N2 K2 - ßN1

Therefore When N1 0, N2 K2
K2
Isocline for Species 2 dN2/dt 0
When N2 0, N1 K2/ß
N2
K2 / ß
N1
20
Plot the isoclines for 2 species together to
examine population trajectories K1/a gt K2 K1 gt
K2/ß For species 1 K1 gt K2a (intrasp.
gt intersp.) For species 2 K1ß gt K2
(intersp. gt intrasp.)
Competitive exclusion of Species 2 by Species 1
K1 / a
N2
K2
stable equilibrium
K2 / ß
K1
N1
21
Plot the isoclines for 2 species together to
examine population trajectories K2 gt K1/a K2/ß gt
K1 For species 1 K2a gt K1 (intersp. gt
intrasp.) For species 2 K2 gt K1ß
(intrasp. gt intersp.)
Competitive exclusion of Species 1 by Species 2
K2
N2
K1/ a
stable equilibrium
K2 / ß
K1
N1
22
Plot the isoclines for 2 species together to
examine population trajectories K2 gt K1/a K1 gt
K2/ß For species 1 K2a gt K1 (intersp.
gt intrasp.) For species 2 K1ß gt K2
(intersp. gt intrasp.)
Competitive exclusion in an unstable equilibrium
K2
K1/ a
N2
stable equilibrium
K1
K2 / ß
unstable equilibrium
N1
23
Plot the isoclines for 2 species together to
examine population trajectories K1/a gt K2 K2/ß gt
K1 For species 1 K1 gt K2a (intrasp. gt
intersp.) For species 2 K2 gt K1ß
(intrasp. gt intersp.)
Coexistence in a stable equilibrium
K1 / a
N2
K2
stable equilibrium
K1
K2 / ß
N1
24
Competition
Major prediction of the Lotka-Volterra
competition model Two species can only coexist
if intraspecific competition is stronger than
interspecific competition for both species
Earliest experiments within the Lotka-Volterra
framework Gause (1932) protozoans exploiting
cultures of bacteria
The Lotka-Volterra models, coupled with the
results of simple experiments suggested a general
principle in ecology The Lotka-Volterra-Gause
Competitive Exclusion Principle Complete
competitors cannot coexist (Hardin 1960)
25
Competition
The Lotka-Volterra equations have been used
extensively to model and better understand
competition, but they are phenomenological and
completely ignore the mechanisms of
competition In other words, they ignore the
question Why does a particular interaction
between species mutually reduce their population
growth rates and depress population sizes?
26
Competition
A commonly used, binary classification of
mechanisms of competition Exploitative /
scramble (mutual depletion of shared
resources) Interference / contest (direct
interactions between competitors)
More detailed classification of mechanisms (from
Schoener 1983) Consumptive (comp. for
resources clearly a subset of
exploitative) Preemptive (comp. for space,
which can be reused closer to exploitative
than interference a.k.a. founder
control) Overgrowth (usually considered
interference cf. size- asymmetric competition
of Weiner 1990) Chemical (clearly a subset of
interference e.g., allelopathy) Territorial
(usually considered interference) Encounter
(clearly a subset of interference)
Exploitative or consumptive competition was
further divided by Byers (2000) into Resource
suppression due to consumption rate Resource-conv
ersion efficiency
27
Competition
Case Gilpin (1975) and Roughgarden (1983)
claimed that interference competition should not
evolve unless exploitative competition exists
between two species Why?
Interference competition is costly, and is
unlikely to evolve under conditions in which
there is no payoff. If the two species do not
potentially compete for limiting resources (i.e.,
there is no opportunity for exploitative
competition), then there would be no reward for
engaging in interference competition.
28
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
29
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
Per capita reproductive rate of Species 1 (dN/dt)
is a function of resource availability, R
Species A
Mortality rate, mA, is assumed to remain constant
with changing R
mA
dN/ N dt (per capita)
R equilibrium resource availability at which
reproduction and mortality are balanced, and the
level to which species A can reduce R in the
environment

R
Resource, R
30
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
When two species compete for one limiting
resource, the species with the lower R
deterministically outcompetes the other
Species A
mA
Species B wins in this case
Species B
dN/ N dt (per capita)
mB


RB
RA
Resource, R
31
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
Now consider the growth response of one species
to two essential resources R divides the region
into portions favorable and unfavorable to
population growth
dN/dt gt 0
dN/dt lt 0
R1
32
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
Now consider the growth response of one species
to two essential resources R divides the region
into portions favorable and unfavorable to
population growth
R2
dN/dt gt 0
dN/dt lt 0
R1
33
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
Now consider the growth response of one species
to two essential resources The two Rs divide
the region into portions favorable and
unfavorable to population growth
Zero Net Growth Isocline (ZNGI)
R2
dN/dt gt 0
dN/dt lt 0
If a population deviates from the equilibrium
along the ZNGI, it will return to the equilibrium
R1
Resource supply point
Consumption vector
34
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
Now consider two species potentially competing
for two essential resources
In this case, species A outcompetes species B in
habitats 2 3, and neither species can persist
in habitat 1
A
B
1
2
3
R2
R1
35
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
In this case, species A wins in habitat 2,
species B wins in habitat 6, and neither species
can persist in habitat 1
A
B
1
2
R2
?
6
R1
Resource supply points
Consumption vectors
36
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
There is also an equilibrium point at which both
species can coexist The extent to which that
equilibrium is stable depends on the relative
consumption rates of the two species consuming
the two resources
A
B
1
2
R2
?
6
R1
37
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
The extent to which that equilibrium is stable
depends on the relative consumption rates of the
two species consuming the two resources In this
case, it is stable
Slope of consumption vectors for A
A
B
Slope of consumption vectors for B
1
2
3
R2
4
5
6
R1
38
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
The extent to which that equilibrium is stable
depends on the relative consumption rates of the
two species consuming the two resources In this
case, it is stable Species A can only reduce R2
to a level that limits species A, but not species
B, whereas species B can only reduce R1 to a
level that limits species B, but not species A
Slope of consumption vectors for A
A
B
Slope of consumption vectors for B
1
2
3
R2
4
5
6
R1
Each species will return to its equilibrium if
displaced on its ZNGI
Resource supply point
Consumption vectors
39
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
The extent to which that equilibrium is stable
depends on the relative consumption rates of the
two species consuming the two resources In this
case, it is unstable
Slope of consumption vectors for B
A
B
Slope of consumption vectors for A
1
2
3
R2
4
5
6
R1
40
Competition
Tilmans mechanistic approach Resource-Based
Competition Models
The extent to which that equilibrium is stable
depends on the relative consumption rates of the
two species consuming the two resources In this
case, it is unstable Species A can reduce R1 to
a level that limits species A and excludes
species B, whereas species B can reduce R2 to a
level that limits species B and excludes species
A
Slope of consumption vectors for B
A
B
Slope of consumption vectors for A
1
2
3
R2
4
5
6
R1
Each species will return to its equilibrium if
displaced on its ZNGI
Resource supply point
Consumption vectors
41
Competition
The Lotka-Volterra competition model and Tilmans
R model are both examples of mean-field,
analytical models (a.k.a. general strategic
models)
How relevant is the mean-field assumption to real
organisms?
In sessile organisms such as plants, competition
for resources occurs primarily between closely
neighboring individuals Antonovics Levin (1980)
Neighborhood models describe how individual
organisms respond to variation in abundance or
identity of neighbors
42
Competition
Spatially Explicit, Neighborhood Models of Plant
Competition
There are many ways to formulate these models,
and most require computer-intensive simulations
Cellular automata Start with a grid of cells
Spatially explicit individual-based models
Keep track of the demographic fate and spatial
location of every individual in the
population Sometimes these are empirical,
field-calibrated models
43
Competition
Spatially Explicit, Neighborhood Models of Plant
Competition
A key conclusion of these models At highest
dispersal rates, i.e., bath dispersal, the
predictions of the mean-field approximations are
often matched by the predictions of the more
complicated, spatially-explicit models
Low dispersal rates, however, lead to
intraspecific clumping, which tends to relax
(broaden) the conditions under which two-species
coexistence occurs this is similar to increasing
the likelihood of intraspecific competition
relative to interspecific competition
44
Literature reviews of the prevalence of
competition Connell (1983) Reviewed 54
studies 45/54 (83) were consistent with
competition Of 54 studies, 33 (61)
suggested asymmetric competition Schoener
(1983) Reviewed 164 studies 148/164
(90) were consistent with competition Of
61 studies, 51 (85) suggested asymmetric
competition
Kelly, Tripler Pacala (ms. 1993) But
apparently never published! Only 1/4 of
plot-based studies were consistent with
competition, whereas 2/3 of plant-centered
studies were consistent with competition
45
A classic competition study MacArthur
(1958) Five sympatric warbler species with
similar bill sizes and shapes broadly overlap in
arthropod diet, but they forage in different
zones within spruce crowns
Is this an example of the ghost of competition
past (sensu Connell 1980)?
46
Light and nutrient competition among rain forest
tree seedlings (Lewis and Tanner 2000)
Above-ground competition for light is considered
to be critical to seedling growth and
survival Fewer studies exist of in situ
below-ground competition
Design Transplanted seedlings of two species
(Aspidospermum - shade tolerant Dinizia - light
demanding) into understory sites (1 light) and
small gaps (6 light) in nutrient-poor Amazonian
forest
Reduced below-ground competition by trenching
(digging a 50-cm deep trench around each focal
plant and lining it with plastic) this
stops neighboring trees from accessing nutrients
and water
47
Results and Conclusion Trenching had as big an
impact as increased light did on seedling
growth Seedlings are apparently simultaneously
limited by (and compete for) nutrients and light
Could allelopathy also be involved?
48
Effect of territorial honeyeaters on homopteran
abundanceLoyn et al. (1983)
Flocks of Australian Bell Miners defend communal
territories in eucalypt forest, excluding other
(sometimes much larger) species of birds Up to
90 of miners diet is nymphs, secretions and
lerps (shields) of Homopterans (Psyllidae)
Experiment Counted birds, counted lerps,
removed miners
Results conclusion Invasion by a guild of 11
species of insectivorous birds (competitive
release), plus 3x increase in lerp removal rate,
reduction in lerp density, and 15 increase in
foliage biomass
49
Competition between seed-eating rodents and ants
in the Chihuahuan Desert Brown Davidson (1977)
Strong resource limitation seeds are the
primary food of many taxa (rodents, birds,
ants) Almost complete overlap in the sizes of
seeds consumed by ants and rodents demonstrates
the potential for strong competition
Design Long-term exclosure experiments fences
to exclude rodents, and insecticide to remove
ants re-censuses of ant and rodent populations
through time
Results and Conclusion Excluded rodents and the
number of ant colonies increased 70 Excluded
ants and rodent biomass increased
24 Competition can apparently occur between
distantly related taxa
50
Competition between sexual and asexual species of
geckoPetren et al. (1993)
Humans have aided the dispersal of a sexual
species of gecko (Hemidactylus frenatus) to
several south Pacific islands and it is
apparently displacing asexual species
Experiment Added H. frenatus and L. lugubris
alone and together to aircraft hanger walls
Results and Conclusion L. lugubris avoids H.
frenatus at high concentrations of insects on
lighted walls Sometimes obvious hypothesized
reasons for competitive dominance are incorrect
Lepidodactylus lugubris, asexual native on south
Pacific islands
51
Competition among Anolis lizards
(Pacala Roughgarden 1982)
What is the relationship between the strength of
interspecific competition and degree of
interspecific resource partitioning? 2 pairs of
abundant insectivorous diurnal Anolis lizards on
2 Caribbean islands St. Maarten A. gingivinus
A. wattsi pogus St. Eustatius A. bimaculatus
A. wattsi schwartzi
52
Competition among Anolis lizards
(Pacala Roughgarden 1982)
Body size (strongly correlated with prey size)
St. Maarten anoles large overlap in body
size St. Eustatius anoles small overlap
in body size Foraging location St.
Maarten anoles large overlap in perch ht.
St. Eustatius anoles no overlap in perch ht.
Experiment Replicated enclosures on both
islands, stocked with one (not A. wattsi) or both
species
53
Competition among Anolis lizards
(Pacala Roughgarden 1982)
Results and Conclusions St. Maarten (similar
resource use) Growth rate of A. gingivinus
was halved in the presence of A.
wattsi St. Eustatius (dissimilar resource use)
No effect of A. wattsi on growth or
perch height of A. bimaculatis Strength of
present-day competition in these species pairs is
inversely related to resource partitioning
54
Competition among Anolis lizards
(Pacala Roughgarden 1982)
Why do these pairs of anoles on nearby islands
(30 km) differ in degree of resource
partitioning? Hypothesis Character
displacement occurred on St. Eustatius during
long co-evolutionary history (i.e., the ghost of
competition past), whereas colonization of St.
Maarten occurred much more recently, and in both
cases colonization was by similarly sized Anolis
species Character displacement Evolutionary
divergence of traits in response to competition,
resulting in a reduction in the intensity of
competition
55
Character Displacement
Schluter McPhail (1992) surveyed the literature
on character displacement and listed criteria
necessary to exclude other potential
explanations for species that share similar
traits in allopatry, but differ in sympatry
(similar to Connells 1980 requirements to
demonstrate the ghost of competition past)
1. Chance should be ruled out as an explanation
for the pattern (appropriate statistical
tests, often involving null models)
2. Phenotypic differences should have a genetic
basis
3. Enhanced differences between sympatric species
should be the outcome of evolutionary
shifts, not simply the inability of
similar-sized species to coexist
4. Morphological differences should reflect
differences in resource use
5. Sites of sympatry and allopatry should be
similar in terms of physical characteristics
6. Independent evidence should be obtained that
similar phenotypes actually compete for
food
56
Competition among Anolis lizards
(Pacala Roughgarden 1985)
Pacala Roughgarden (1985) presented evidence to
suggest that both species pairs have a long
history of co-occurrence on their respective
islands and that different colonization histories
resulted in the observed patterns of resource
partitioning Both islands may have been
colonized by Anolis species differing in size,
yet on St. Maarten the larger Anolis colonized
later and has subsequently converged in body size
on the smaller resident