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Essential resources

R 2. C i1. C i2. C 1. R 1. Essential resources. consumption vectors are parallel (essential). R 2. C i1. C i2. C i. R 1. Substitutable resources. consumption vectors are not parallel (substitutable). R 2. C 1. R 1. Switching resources. consumption vectors are

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Essential resources

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  1. R2 Ci1 Ci2 C1 R1 Essential resources consumption vectors are parallel (essential)

  2. R2 Ci1 Ci2 Ci R1 Substitutable resources consumption vectors are not parallel (substitutable)

  3. R2 C1 R1 Switching resources consumption vectors are perpendicular to isocline (switching)

  4. S1,S2 R2 U R1 Renewal for 2 resources supply vector: points at supply point S1,S2

  5. S1,S2 R2 U U Ci Ci Ci U R1 Equilibrium: 1 sp. 2 resources consumption vector equal & opposite supply vector

  6. 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

  7. S1,S2 S1,S2 S1,S2 R2    sp. 2 sp. 1 R1 Competition for 2 resources  sp. 1 always excludes sp. 2  sp. 2 cannot survive  neither spp. can survive

  8. S1,S2 S1,S2 S1,S2 S1,S2 R2     sp. 2 sp. 2 sp. 1 sp. 1 R1 Competition for 2 resources  neither spp. can survive  sp. 2 cannot survive  sp. 1 always excludes sp. 2  coexistence

  9. 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

  10. Equilibrium is stable Print starting here R2 sp. 2 sp. 1 sp. 2 R1 sp. 1

  11. Competition for 2 resources S1,S2 S1,S2 S1,S2 S1,S2  R2    sp. 2 sp. 1 sp. 1 sp. 2 R1  neither spp. can survive  sp. 2 cannot survive  sp. 1 always excludes sp. 2  one species eliminated

  12. 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

  13. Equlibrium is unstable R2 sp. 2 sp. 1 sp. 1 R1 sp. 2

  14. Substitutable resources (Tilman) R2 R2 1 wins sp. 1 2 wins sp. 1 sp. 2 sp. 2 R1 R1 R2 R2 sp. 1 sp. 1 stable unstable sp. 2 sp. 1 sp. 2 sp. 2 sp. 1 sp. 2 R1 R1

  15. Displacement from equilibrium R2 sp. 1 stable sp. 1 sp. 2 sp. 2 R1 R2 sp. 1 unstable Stable: each species consumes more of the resource that most limits it sp. 2 sp. 2 sp. 1 R1

  16. 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

  17. Stable coexistence R2 sp. 1 Tilman; Grover sp. 1 sp. 2 sp. 2 R1 R2 Chase & Leibold sp. 1 Stable: each species consumes more of the resource that most limits it sp. 2 sp. 2 sp. 1 R1

  18. 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;…” R2 Chase & Leibold sp. 1 sp. 2 sp. 2 sp. 1 R1

  19. The problem: what does it mean to be “most limited” by a resource? R2 sp. 2 sp. 1 R2 sp. 1 sp. 2 sp. 1 R1 sp. 1 sp. 2 sp. 2 R1 Most limited at equilibrium

  20. R2 dN/dt>0 dN/dt=0 I R1 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)

  21. R2 dN2/dt=0 I2 I1 dN1/dt=0 R1 isoclines given by Grover Grover and Tilman both agree with the statement: “…the species with the shallowest slope to its ZNGI must have the steepest impact vector;…”

  22. Stable coexistence R2 sp. 1 Tilman; Grover sp. 1 sp. 2 sp. 2 R1 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

  23. Displacement from equilibrium R2 sp. 1 stable sp. 1 sp. 2 sp. 2 R1 R2 sp. 1 unstable Stable: each species consumes more of the resource that most limits it sp. 2 sp. 2 sp. 1 R1

  24. 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

  25. Competition for 2 resources S1,S2 S1,S2 S1,S2 S1,S2 S1,S2  R2     sp. 1 sp. 1 sp. 2 sp. 1 sp. 2 sp. 2 R1  sp. 1 excludes sp. 2  coexistence  sp. 2 excludes sp. 1

  26. 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

  27. 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

  28. 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

  29. Laboratory environment:a chemostat nutrient input (S1,S2) outflow (m)

  30. Real Chemostat Reaction vessel Inflow Outflow

  31. Experiments: Tilman (1982) Diatoms Asterionella & Cyclotella Resources PO4 & SiO2 Determine R*’s & C vectors for each alone Predicts stable coexistence possible R2 sp. 2 sp. 1 sp. 2 sp. 1 R1

  32. 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

  33. 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

  34. Resource competition theory more precise statement of competitive exclusion principle R*rule resource ratio hypothesis ground work for models of multiple interacting species

  35. 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

  36. Miller et al.

  37. 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?

  38. 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

  39. Demonstrating that competition occurs Observations exclusive or abutting distributions gradient • responses to unintentional • introductions, displacement • of native species

  40. Any natural pattern could be explained in several ways

  41. 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

  42. Distributions of Balanus & Chthamalus Chthamalus Balanus Adults Larvae Adults Larvae highest high tide Chthamalus Balanus ROCK lowest low tide

  43. 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

  44. 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

  45. Reynoldson & Bellamy 1971 5 criteria (continued)  Manipulation of the resource and each population yield effects consistent with intraspecific competition performance resource sp. 1 perf. sp. 1 density sp. 2 perf. sp. 1 density •  Manipulations of species abundances yield effects on the other species consistent with interspecific competition • Experimental criteria • Controls, replication

  46. Performance Surivival Growth Feeding success Fecundity Assumed to be correlates of population rate of increase

  47. 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

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