Download - Essential resources
![Page 1: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/1.jpg)
Essential resources
consumption vectors are parallel(essential)
R1
R2 Ci1
Ci2C1
![Page 2: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/2.jpg)
Substitutable resources
consumption vectors are not parallel(substitutable)
R1
R2 Ci1
Ci2Ci
![Page 3: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/3.jpg)
Switching resources
consumption vectors are perpendicularto isocline(switching)
R1
R2
C1
![Page 4: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/4.jpg)
Renewal for 2 resources
supply vector: points at supplypoint S1,S2
R1
R2
S1,S2
U
![Page 5: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/5.jpg)
Equilibrium: 1 sp. 2 resources
consumption vector equal &opposite supplyvector
R1
R2
Ci
Ci
Ci
U
S1,S2
UU
![Page 6: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/6.jpg)
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
![Page 7: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/7.jpg)
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
![Page 8: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/8.jpg)
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
![Page 9: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/9.jpg)
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
![Page 10: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/10.jpg)
Equilibrium is stable
R1
R2
sp. 1
sp. 2
sp. 2
sp. 1
Print starting here
![Page 11: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/11.jpg)
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
![Page 12: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/12.jpg)
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
![Page 13: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/13.jpg)
Equlibrium is unstable
R1
R2
sp. 1
sp. 2sp. 2
sp. 1
![Page 14: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/14.jpg)
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
![Page 15: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/15.jpg)
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
![Page 16: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/16.jpg)
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
![Page 17: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/17.jpg)
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
![Page 18: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/18.jpg)
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
![Page 19: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/19.jpg)
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
![Page 20: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/20.jpg)
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
![Page 21: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/21.jpg)
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
![Page 22: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/22.jpg)
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
![Page 23: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/23.jpg)
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
![Page 24: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/24.jpg)
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
![Page 25: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/25.jpg)
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
![Page 26: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/26.jpg)
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
![Page 27: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/27.jpg)
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
![Page 28: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/28.jpg)
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
![Page 29: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/29.jpg)
Laboratory environment:a chemostat
nutrient input (S1,S2)
outflow (m)
![Page 30: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/30.jpg)
Real Chemostat
• Reaction vessel• Inflow• Outflow
![Page 31: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/31.jpg)
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
![Page 32: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/32.jpg)
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
![Page 33: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/33.jpg)
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
![Page 34: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/34.jpg)
Resource competition theory
• more precise statement of competitive exclusion principle
• R* rule• resource ratio hypothesis• ground work for models of multiple
interacting species
![Page 35: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/35.jpg)
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
![Page 36: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/36.jpg)
Miller et al.
![Page 37: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/37.jpg)
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?
![Page 38: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/38.jpg)
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
![Page 39: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/39.jpg)
Demonstrating that competition occurs
• Observations– exclusive or abutting
distributions gradient– responses to unintentional
introductions, displacement of native species
![Page 40: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/40.jpg)
Any natural pattern could be explained in
several ways
![Page 41: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/41.jpg)
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
![Page 42: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/42.jpg)
Distributions of Balanus & Chthamalus
lowest low tide
highest high tide Balanus
Adults Larvae
Balanus
Chthamalus
Chthamalus
Adults LarvaeROCK
![Page 43: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/43.jpg)
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
![Page 44: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/44.jpg)
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
![Page 45: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/45.jpg)
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
![Page 46: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/46.jpg)
Performance
• Surivival• Growth• Feeding success• Fecundity• Assumed to be correlates of population
rate of increase
![Page 47: Essential resources](https://reader036.vdocuments.site/reader036/viewer/2022081513/56816823550346895dddb42a/html5/thumbnails/47.jpg)
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