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) A B
Competition - A B
Amensalism - A B
Antagonism
(Predation/Parasitism) + - - A B
Amensalism - A B
Neutralism
(No interaction) A B
Commensalism +
Influence of Species B A B
Antagonism
(Predation/Parasitism) - + A B
Commensalism + A B
Mutualism + +
Redrawn from Abrahamson (1989); Morin (1999, pg. 21)

3. between two sympatric competitors
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 ( )
& Vito Volterra ( )
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
Exponential growth was identified by Turchin (2001) as a general law in ecology.
Murdoch (1994) discussed varies means by which populations are regulated (which appears to occur frequently, but discerning the mechanisms remains a great challenge).
Exponential growth (including exponential decay) occurs when the growth rate of a mathematical function is proportional to the function's current value. Only unlimited resources would allow exponential growth.
Remember: the equations are relevant to model world, and are only as relevant to the real world as the assumptions that go into the models.
Time 4

5. (= carrying capacity, K)
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
Note that r is defined by density-independent (or max.) intrinsic rate of increase.
As an aside to this aside on population dynamics, negative Allee effects occur when per capita fitness decreases with decreases in pop. size.
Remember: the equations are relevant to model world, and are only as relevant to the real world as the assumptions that go into the models. d
Equilibrium
(= carrying capacity, K) N 5

6. Population Dynamics ∆N N Logistic growth = r • N • (1 – ) ∆t K N Time
K = carrying capacity ∆N ∆t
= 0 N ∆N ∆t
is maximized
Remember: the equations are relevant to model world, and are only as relevant to the real world as the assumptions that go into the models.
K represents carrying capacity, owing to the struggle for existence of T. Malthus that results from intraspecific competition.
Note that a population is regulated around a particular carrying capacity when it has a tendency to increase when rarer or to decline when commoner than the carrying capacity. ∆N ∆t
= 0
Time 6

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 & Volterra’s 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]
K results from intraspecific competition (i.e., we model intraspecific competition with K).
Then, when terms for the other species are added to the population models, imagine what would happen at K for a given species (the addition of the competitor would make the pop. growth rate go negative).

8. Competition Lotka-Volterra Competition Equations:
The function (f) could take on many forms, e.g.:
Species 1: dN1/dt = r1N1[(K1-N1-αN2)/K1]
Species 2: dN2/dt = r2N2[(K2-N2-βN1)/K2]
The competition coefficients α & β measure the per capita effect of one species on the population growth of the other, measured relative to the effect of intraspecific competition
Note: sometimes the first equation’s alpha is labeled “alpha subscript one-two” for the per capita effect on Species 1 of Species 2.
If α = 1, then per capita intraspecific effects = interspecific effects
If α < 1, then intraspecific effects are more deleterious
to Species 1 than interspecific effects
If α > 1, then interspecific effects are more deleterious

9. Individuals of Sp. 2 consume 4x resources consumed 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-αN2)/K1] … where α = 4.
Redrawn from Gotelli (2001)

10. Competition is occurring because both α & β > 0  α = 4 & β = ¼2 2 1 2 1 2 1 1 1 1 1 1 1
Competition is occurring because both α & β > 0  α = 4 & β = 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. Asymmetric competition2 2 1 2 1 2 1 1 1 1 1 1 1
Asymmetric competition
In this case:
α > β
α > 1
β < 1

12. Asymmetric competition1 2 2 1 2 2 1
Asymmetric competition
In this case:
α > β
β = 1
Asymmetric competition can occur throughout the spectrum of:
α  β, (α < = > 1, or β < = > 1)
What circumstances might the figure above represent?
Exclusively interspecific territoriality, intra-guild predation…

13. Symmetric competition1 2 2 1 2 2 1
Symmetric competition
In this case:
α = β = 1, i.e., the special case of competitive equivalence
Symmetric competition can occur throughout the spectrum of:
(α = β) < = > 1

14. Lotka-Volterra Phenomenological Competition Model
Find equilibrium solutions to the equations, i.e., set dN/dt = 0:
Species 1: N1 = K1 - αN2
Species 2: N2 = K2 - βN1 ^ ^
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 (α N2) ^
However, each species’ equilibrium depends on the equilibrium of the other species! So, by substitution…
Species 1: N1 = K1 - α(K2 - βN1)
Species 2: N2 = K2 - β(K1 - αN2)

15. Lotka-Volterra Phenomenological Competition Model
The equations for equilibrium solutions become:
Species 1: N1 = [K1 - αK2] / [1 - α β]
Species 2: N2 = [K2 - βK1] / [1 - α β] ^ ^
These provide some insights into the conditions required for coexistence under the assumptions of the model
E.g., the product αβ must be < 1 for N to be > 0 for both species (a necessary condition for coexistence)
Solve previous slide’s equations for N (use algebra).
But they do not provide much insight into the dynamics of competitive interactions, e.g., are the equilibrium points stable?

16. Mapping state-space trajectories onto single population trajectories
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. Mapping state-space trajectories onto single population trajectories
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. Lotka-Volterra Model
Remember that equilibrium solutions require dN/dt = 0
Species 1: N1 = K1 - αN2 ^
Therefore:
When N2 = 0, N1 = K1
K1 / α
When N1 = 0, N2 = K1/α
Isocline for Species 1
dN1/dt = 0 N2 K1 N1

19. Lotka-Volterra Model
Remember that equilibrium solutions require dN/dt = 0
Species 2: N2 = K2 - βN1 ^
Therefore:
When N1 = 0, N2 = K2 K2
When N2 = 0, N1 = K2/β
Isocline for Species 2
dN2/dt = 0 N2
K2 / β N1

20. Competitive exclusion of
Lotka-Volterra Model
Plot the isoclines for 2 species together to examine population trajectories
K1/α > K2
K1 > K2/β
For species 1:
K1 > K2α
(intrasp. > intersp.)
For species 2:
K1β > K2
(intersp. > intrasp.)
Competitive exclusion of
Species 2 by Species 1
K1 / α N2 K2
Solve the first 2 equations for K1 and K2, respectively, to give the inequality for Sp. 1 and Sp.2, respectively. Remember that K represents intraspecific competition.
= stable equilibrium
K2 / β K1 N1

21. Competitive exclusion of
Lotka-Volterra Model
Plot the isoclines for 2 species together to examine population trajectories
K2 > K1/α
K2/β > K1
For species 1:
K2α > K1
(intersp. > intrasp.)
For species 2:
K2 > K1β
(intrasp. > intersp.)
Competitive exclusion of
Species 1 by Species 2 K2 N2
K1/ α
= stable equilibrium K1
K2 / β N1

22. Competitive exclusion in an
Lotka-Volterra Model
Plot the isoclines for 2 species together to examine population trajectories
K2 > K1/α
K1 > K2/β
For species 1:
K2α > K1
(intersp. > intrasp.)
For species 2:
K1β > K2
Competitive exclusion in an
unstable equilibrium K2
K1/ α N2
Starting conditions determine the winner.
= stable equilibrium
K2 / β K1
= unstable equilibrium N1

23. Coexistence in a stable equilibrium
Lotka-Volterra Model
Plot the isoclines for 2 species together to examine population trajectories
K1/α > K2
K2/β > K1
For species 1:
K1 > K2α
(intrasp. > intersp.)
For species 2:
K2 > K1β
Coexistence in a stable equilibrium
K1 / α N2 K2
= stable equilibrium K1
K2 / β 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)
In MacArthur’s (1958) words: “Actually, to permit coexistence, it seems necessary that each species, when very abundant, should inhibit its own further increase more than it inhibits the other’s.”

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:
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)
Preemptive (comp. for space; a.k.a. founder control)
Overgrowth (cf. size-asymmetric competition of Weiner 1990)
Chemical (e.g., allelopathy)
Territorial
Encounter
One might ask “haven’t we advanced beyond MacArthur’s Niche Theory and strictly competitively-based community structure; Lotka-Volterra models; and Tilman’s R* modeling sufficiently that we don’t need to spend so much time in class on it?” Even though we understand more-and-more the limitations of some of these earlier ideas and even though we have made progress towards understanding the consequences for relaxing some of their assumptions, each provides us with gold nuggets of insight that have been carried forward and continue to help guide us towards better understanding Nature.
Exploitative / consumptive further divided by Byers (2000):
Resource suppression due to consumption rate
Resource-conversion efficiency

27. exists between two species
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. Tilman’s Resource-Based Competition Models
Per capita reproductive rate of Species 1
(dN/(N *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
Use Tilman (1977) as an example of resource-based competition (Si/P ratio important for algae). R *
Resource, R

29. Tilman’s 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

30. Tilman’s 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 < 0
dN/dt > 0 R1 * R1

31. Tilman’s 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 > 0 R2 *
dN/dt < 0 R1 * R1

32. Tilman’s Resource-Based Competition Models
Now consider the growth response of one species to two essential resources
The two R*s divide the region into portions favorable and unfavorable to population growth
Zero Net Growth Isocline (ZNGI) R2
Consumption vectors can be of any slope, but the slope predicted under optimal foraging would equal R2/R1 *
dN/dt > 0 R2 *
dN/dt < 0
Optimal foraging predicts consumption of resources in a such a way that both are simultaneously limiting.
If R*(subscript2)/R*(subscript1)=1, then the consumption vector would have a slope of 1.
See Dybzinski & Tilman, pg. 191, in “The Princeton Guide to Ecology,” S. A. Levin, ed. R1 *
If a population deviates from the equilibrium along the ZNGI, it will return to the equilibrium R1
Consumption
vector
Resource
supply point

33. Tilman’s 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 R2 1 2 3 R1

34. Tilman’s 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 R2 1 2 ? 6 R1
Consumption
vectors
Resource
supply points

35. Tilman’s 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 R2 1 2 ?
The point at which the ZNGIs cross is the equilibrium point. 6 R1

36. Tilman’s 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 R2 1 2 3 4 5
The point at which the ZNGIs cross is the equilibrium point. 6 R1

37. Tilman’s 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 R2 1 2 3 4 5
Each species will return to its species-specific equilibrium (i.e., where its own consumption vector crosses its own ZNGI) if the system is displaced along its own ZNGI away from the two-species equil. point towards its population specific equil. point, and in this case that means each species’ growth rate is positive when the other species is at its own species-specific equil. 6 R1
Each species will return to its equilibrium if displaced on its ZNGI
Consumption
vectors
Resource
supply point

38. Tilman’s 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 R2 1 2 3 4 5
The point at which the ZNGIs cross is the equilibrium point. 6 R1

39. Tilman’s 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 R2 1 2 3 4 5
Each species will return to its species-specific equilibrium (i.e., where its own consumption vector crosses its own ZNGI) if the system is displaced along its own ZNGI away from the two-species equil. point towards its population specific equil. point, and in this case that means each species’ growth rate is negative when the other species is at its own species-specific equil. 6 R1
Each species will return to its equilibrium if displaced on its ZNGI
Consumption
vectors
Resource
supply point

40. Competition
The Lotka-Volterra competition model and Tilman’s 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

41. 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”

42. 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

43. 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
Literature reviews…
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

44. 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])?

45. 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

46. 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?

47. Effect of territorial honeyeaters on homopteran abundance Loyn et al
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

48. 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

49. Lepidodactylus lugubris,
Competition between sexual and asexual species of gecko Petren 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
Here is an example of the “ecology of fear” (see other examples in Predation lecture).
Lepidodactylus lugubris,
asexual native on
south Pacific islands

50. 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
See Losos (2009, pg. 227) – “Despite uncertainties about the prevalence and importance of predation and parasitism, the data as a whole make a strong case that interspecific competition is a major, probably the predominant, force structuring anole communities, at least in the West Indies.”

51. 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
See Losos (2009, pg. 227) – “Despite uncertainties about the prevalence and importance of predation and parasitism, the data as a whole make a strong case that interspecific competition is a major, probably the predominant, force structuring anole communities, at least in the West Indies.”

52. 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
See Losos (2009, pg. 227) – “Despite uncertainties about the prevalence and importance of predation and parasitism, the data as a whole make a strong case that interspecific competition is a major, probably the predominant, force structuring anole communities, at least in the West Indies.”

53. 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
See Losos (2009, pg. 227) – “Despite uncertainties about the prevalence and importance of predation and parasitism, the data as a whole make a strong case that interspecific competition is a major, probably the predominant, force structuring anole communities, at least in the West Indies.”

54. 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
See Losos (2009, pg. 227) – “Despite uncertainties about the prevalence and importance of predation and parasitism, the data as a whole make a strong case that interspecific competition is a major, probably the predominant, force structuring anole communities, at least in the West Indies.”

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 Connell’s [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