Essential resources

consumption vectors are parallel(essential)

R1

R2 Ci1

Ci2C1

Substitutable resources

consumption vectors are not parallel(substitutable)

R1

R2 Ci1

Ci2Ci

Switching resources

consumption vectors are perpendicularto isocline(switching)

R1

R2

C1

Renewal for 2 resources

supply vector: points at supplypoint S1,S2

R1

R2

S1,S2

U

Equilibrium: 1 sp. 2 resources

consumption vector equal &opposite supplyvector

R1

R2

Ci

Ci

Ci

U

S1,S2

UU

Equilibrium

• Equilibrium (R1,R2) falls on isocline• therefore, dN / N dt =0• U and C vectors equal in magnitude,

opposite direction• therefore dR1 / dt = 0 and dR2 / dt = 0

Competition for 2 resources

R1

R2

sp. 1

S1,S2

S1,S2

S1,S2

sp. 2

sp. 1 alwaysexcludes sp. 2

sp. 2 cannotsurvive

neither spp.can survive

Competition for 2 resources

R1

R2

S1,S2

S1,S2

S1,S2 neither spp.

can survive

sp. 2 cannotsurvive

sp. 1 alwaysexcludes sp. 2

S1,S2

coexistence

sp. 1

sp. 2

sp. 2

sp. 1

Equilibrium• sp. 1

– needs less R1 (limited by R2)– consumes more R2

• sp. 2– needs less R2 (limited by R1)– consumes more R1

• consumes more of the resource limiting to itself

Equilibrium is stable

R1

R2

sp. 1

sp. 2

sp. 2

sp. 1

Print starting here

Competition for 2 resources

R1

R2

S1,S2S1,S2

S1,S2 neither spp.

can survive sp. 2 cannotsurvive

sp. 1 alwaysexcludes sp. 2

S1,S2

one species eliminated

sp. 1

sp. 2sp. 2

sp. 1

Equilibrium• sp. 1

– needs less R1 (limited by R2)– consumes more R1

• sp. 2– needs less R2 (limited by R1)– consumes more R2

• consumes more of the resource limiting to its competitor

Equlibrium is unstable

R1

R2

sp. 1

sp. 2sp. 2

sp. 1

Substitutable resources (Tilman)

R1

R2

sp. 1

sp. 2

1 wins

R1

R2sp. 1

sp. 2

2 wins

R1

R2 sp. 1

sp. 2

stable

sp. 2

sp. 1

R1

R2 sp. 1

sp. 2

unstable

sp. 2

sp. 1

Displacement from

equilibrium

R1

R2 sp. 1

sp. 2

unstable

sp. 2

sp. 1

R1

R2 sp. 1

sp. 2

stable

sp. 2

sp. 1

Stable: each speciesconsumes more ofthe resource that most limits it

A digression: Conflicting diagrams

• Compare Fig. 27 C. of Tilman with Fig. 2.8 of Chase & Leibold

• Disagreement about what produces stable coexistence for substitutable resources

• Grover (1997) gives similar isoclines/consumption vectors to Tilman

Stable coexistence

R1

R2 sp. 1

sp. 2

Chase & Leibold

sp. 2

sp. 1

R1

R2 sp. 1

sp. 2

Tilman;Grover

sp. 2

sp. 1

Stable: each speciesconsumes more ofthe resource that most limits it

Chase & Leibold, p. 47Mathematical appendix to ch. 2

• For the equilibrium to be locally stable: “Verbally, the species with the shallowest slope to its ZNGI must have the steepest impact vector;…”

R1

R2 sp. 1

sp. 2

Chase & Leibold

sp. 2

sp. 1

The problem: what does it mean to be “most limited” by a resource?

R1

R2

sp. 1

sp. 2sp. 2

sp. 1

R1

R2 sp. 1

sp. 2sp. 2

sp. 1

Most limited at equilibrium

Most limited by a resource: For a unit increase of a resource, the most limiting resource produces the greatest increase in dN/dt.

most limited by R2 (R*2 < R*

1)

dN/dt=0 dN/dt>0

R2

R1

I

dN1/dt=0

dN2/dt=0

R2

R1

I1

I2

Grover and Tilmanboth agree with the statement: “…the species with the shallowest slope to its ZNGI must have the steepest impact vector;…”

isoclines given by Grover

Stable coexistence

R1

R2 sp. 1

sp. 2

Tilman;Grover

sp. 2

sp. 1

Species 1 is most limited by R1 because a given increase in R1

yields a greater increase in dN1/dt compared to the same increase in R2; Species 2 is most limited by resource 2 by similar logic.

These are the correct isoclines for stable coexistence

Displacement from

equilibrium

R1

R2 sp. 1

sp. 2

unstable

sp. 2

sp. 1

R1

R2 sp. 1

sp. 2

stable

sp. 2

sp. 1

Stable: each speciesconsumes more ofthe resource that most limits it

Kinds of resources

• General predictions do not depend on kind of resource (mostly)

• Suggests competition between autotrophs or between heterotrophs should lead to similar community structure– actually may not be true

• Combinations of resources can yield multiple equilibria

Competition for 2 resources

sp. 1 excludes sp. 2

coexistence sp. 2 excludes sp. 1

R1

R2

S1,S2

S1,S2

S1,S2

sp. 1

sp. 2

S1,S2

S1,S2

sp. 2

sp. 2

sp. 1

sp. 1

Some relevant references

• Grover, J.P. 1997. Resource competition. Chapman & Hall NY

• Leon, J. A. & Tumpson, D. B. 1975. Competition between two species for two complementary or substitutable resources. J. Theoretical Biology 50:185-201

Common pattern predicted

• Coexistence among competitors– requires specific intermediate ratio of two

resources– extreme ratios lead to elimination of one or

the other competitor– resource ratio hypothesis: competitive

coexistence or exclusion are products of specific environmental resource ratios

Assumptions

• Simplifying environmental– environment is homogeneous and constant

except for resources• Simplifying biological

– individuals identical, constant through time• Explanatory

– competition is expressed only through depression of resources

Laboratory environment:a chemostat

nutrient input (S1,S2)

outflow (m)

Real Chemostat

• Reaction vessel• Inflow• Outflow

Experiments: Tilman (1982) • Diatoms Asterionella &

Cyclotella• Resources PO4 & SiO2

• Determine R*’s & C vectors for each alone

• Predicts stable coexistence possible R1

R2

sp. 1

sp. 2sp. 2

sp. 1

Experiments: Tilman (1982) • Results

– 5/5 supply points predict Asterionella correctly

– 4/4 supply points predict stable coexistence correctly

– 2/4 supply points predict Cyclotella correctly• 2/4 yield coexistence

See fig. 4.1 in Chase & Leibold

More experiments • Tilman (1982) summarizes many more

studies with phytoplankton• Grover (1997) summarizes recent work

with– phytoplankton– bacteria– terrestrial plants– zooplankton

• R* rule, resource ratio hypothesis, and specific predictions largely supported

Resource competition theory

• more precise statement of competitive exclusion principle

• R* rule• resource ratio hypothesis• ground work for models of multiple

interacting species

Testing the resource ratio hypothesis• Competitive coexistence or exclusion

are products of specific environmental resource ratios

• Miller et al. 2005– Predictions of the resource-ratio

hypothesis supported 75% of the time– Prediction that dominance changes with

resource ratio supported 13/16 tests– Many purported tests deemed inadequate

• Replication; Controls; Time scale

Miller et al.

Competition in nature

• Miller et al.: Resource ratio hypothesis rarely tested in nature

• Is resource competition common?• Does R* rule predict outcome?• Does resource ratio affect coexistence?• What other mechanisms of coexistence

are observed?

Competition in ecological time

• Observe: coexistence in nature• Hypotheses:

– competition is not occurring– coexistence based on resource ratios or

limitation by different resources – heterogeneity of environments creates

refuges from competition

Demonstrating that competition occurs

• Observations– exclusive or abutting

distributions gradient– responses to unintentional

introductions, displacement of native species

Any natural pattern could be explained in

several ways

Distributions of barnacles• Rocky intertidal

zone• adult barnacles

immobile on rocks• larvae settle on

rocks from plankton• Joseph Connell

(1961)Ecology 42:710-723

• see Fig. 8.7

Distributions of Balanus & Chthamalus

lowest low tide

highest high tide Balanus

Adults Larvae

Balanus

Chthamalus

Chthamalus

Adults LarvaeROCK

Chthamalus & Balanus

• Hypothesis: Balanus excludes Chthamalus in competition

• Hypothesis: Chthamalus cannot tolerate submergence in low intertidal

• Hypothesis: Balanus cannot tolerate desiccation in high intertidal

• Hypothesis: Different predators in high vs. low intertidal

Testing interspecific competition in nature

• Reynoldson & Bellamy 1971• 5 criteria

– Comparative distribution / abundance of species suggest competition

– Species share some resource (or interfere)

– Evidence for interspecific competition• performance of species + related to resources

• Observational criteria

Reynoldson & Bellamy 1971• 5 criteria (continued)

– Manipulation of the resource and each population yield effects consistent with intraspecific competition

resource

perf

orm

ance

sp. 1 density

sp. 1

per

f.sp. 1 density

sp. 2

per

f.

– Manipulations of species abundances yield effects on the other species consistent with interspecific competition

Experimental criteria Controls, replication

Performance

• Surivival• Growth• Feeding success• Fecundity• Assumed to be correlates of population

rate of increase

Experimental studies• Evidence is cumulative• Density manipulations are now the

standard• Not always feasible

– spatial scale– ethics

• Reviews of experiments– Connell 1983– Schoener 1983– Gurevitch et al. 1992