Tilman's Model of Competition For Two Resources
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Coexistence is not possible. Species A would drive species B to extinction since it can reduce both resources below species B's zero net growth isocline.
Tilman's Model of Competition For Two Resources
- 1. Tilman’s Model of Competition For ResourcesMark McGinleyAssociate ProfessorHonors College and Department of Biological SciencesTexas Tech University
- 2. R* model- single speciesAt equilibriumB = DC = SB < DC < SB > DC > SR*Resource Level
- 3. R* model- 2 speciesAt equilibriumBa = DaBb <DbC = SBa > DaBb >DbC > SBa > DaBb < DbC > SBa < DaBb < DbC < SR*bR*aResource LevelSpecies A wins because it has the lower R*
- 4. Tilman’sModel- competition for 2 limiting resourcesZero Net Growth Isocline (ZNGI)Islocline is a line made up of all combination of points that share the same valueZNGIs are the line made up of all combinations of the level of R1 and R2 at which the population growth rate of a species is = 0ZNGIs are characteristics of species and have to be determined empirically
- 5. Tilman’s model- ZNGIsR2R2R1R1Completely substitutable resourcese.g., big macs and whoppersNon- substitutable resourcese.g., light and nitrogen
- 6. Tilman’s Model- Consumption VectorsConsumption vectors show the change in resource availability caused by consumptionThe total amount of consumption depends onConsumption of an individualNumber of individualsConsumption vectors are characteristics of species and have to be measured
- 7. Consumption vectorsConsumption of R1Consumption or R2Total consumptionR2R1
- 8. Interpreting Consumption VectorsThis species consumes moreR1 than R2R2R1
- 9. Tilman’s Model- Supply VectorsThe supply vectors measure the rate of supply of resources in the environmentThe supply vectors depend uponThe current resource levelsThe Resource Supply Point (S)
- 10. Resource Supply Point (S)The resource supply point measures the total amount of resources in an environmentResources can either be foundIn the environmentIn living organismsThe resource supply point is a characteristic of an environment and can be measured
- 11. Supply VectorsSR2R1Supply vectors point from the current resource levelTo the resource supply point
- 12. Tilman’s Model- 2 resources, 1 speciesNeed to determineZNGI
- 13. S
- 15. 2 resources, 1 speciesSR2R1If we add some individuals into an environment where the resource level equals the resource supply point then we expect the resource level to decrease over time. The resource level should reach equilibrium somewhere along the ZNGI,But where??
- 16. 2 resources, 1 speciesEThe equilibrium resource level(E) occurs where the Consumption vectors and the supply vectors are equal and opposite.R2R1When the resource level is at E then B = D and C = S. This is a stable equilibrium.
- 17. 2 resources, 2 speciesZNGIsR2Sp BSp AR1Species B is more limited by R1 than Species ASpecies B is more limited by R2 than Species A
- 18. 2 resources, 2 speciesConsumption VectorsAR2BR1Species A consumes more R1 than it does R2Species B consumes more R2 than it does R1
- 19. 2 resources, 2 specieswhat is outcome of competition?Depends on S.R2Sp BSp ASR1S below both isoclines, therefore neither species can survive
- 20. 2 resources, 2 specieswhat is outcome of competition?R2Sp BSp AR1Species B can not survive and Species A can survive
- 21. 2 resources, 2 speciesWhat is the outcome of competition?SR2Sp BSp AR1 Coexistence is only potentially possible if S falls in this region.Because species A can reduce the levels of both R1 and R2 below theZNGI for species B, species A will drive species B to extinction and thus be the winner of competition.What will the equilibrial resource level be?
- 22. R2Sp BSp ASpecies A winsESR1
- 23. Practice ProblemWhat is the outcome of competition and the equilibrial resource level if the position of the two species’ ZNGIs are reversed?
- 24. 2 resources, 2 speciesWhat is required for coexistence?In order for both species to coexist there needs to be a resource level in the environment at which the growth rate of both species is equal to zero.This can only happen if the ZNGIs intersect
- 25. 2 resources, 2 speciesintersecting ZNGIsR2Sp BSp AR1Species A is more limited by R1 than species BSpecies B is more limited by R2 than Species A
- 26. 2 resources, 2 speciesintersecting ZNGIsThe ultimate outcome of competition between two species when their ZNGIs intersect depends uponConsumption vectorsResource Supply Point
- 27. Add consumption vectorsR2Sp BASp ABR1Species A consumes more R1 than R2Species B consumes more R2 than R1
- 28. Importance of the location of S3241R25Sp B6ASp ABR1Extending the consumption curves allow us to divide the graph into 6 regions. The outcome of competition depends upon in whichregion the resource supply point falls.
- 29. S falls in region 13241R25Sp B6ASp ABR1Neither species A or B can survive
- 30. S falls in region 23241R25Sp B6ASp ABR1Only species B can survive
- 31. S falls in region 63241R25Sp B6ASp ABR1Only species A can survive
- 32. When is coexistence even imaginable?Both species must be able to grow to have any chance of co-existenceThus, coexistence is only potentially possible if S falls in regions 3, 4, or 5
- 33. S in region 33241R25Sp B6ASp ABR1If S is in region 3, eventually consumption of resources will moveThe current resource level into region 2. When that happens speciesA is unable to survive so species B wins.
- 34. S in region 53241R25Sp B6ASp ABR1If S is in region 5, eventually consumption of resources will moveThe current resource level into region 6. When that happens speciesB is unable to survive so species A wins.
- 35. Coexistence is only possible if S is in region 43241R25Sp B6ASp ABR1If S is in region 4 the level of resources will be reducedTo the point where the two ZNGIs cross. At that pointConsumption = supply and the growth rate of both speciesIs equal to zero.
- 36. If S is in region 4, then coexistence is possibleBut is this a stable or unstable equilibrium?If the equilibrium is unstable then we expect that any slight changes in population sizes or resource level that moves the system away from the equilibrium will move the system to another pointIf the equilibrium is stable, then we expect to see that situation continuing in natureWhether the equilibrium is stable or unstable depends on the consumption vectorsThis is a difficult math proof, so let’s just believe it and see what we can learn
- 37. Stable Equilibrium if S is in region 43241R25Sp B6ASp ABR1Species A consumes more R1 than R2Species B consumes more R2 than R1
- 38. Unstable Equilibrium if S is in Region 43241R25Sp BB6Sp AAR1Species A consumes more R2 than R1Species B consumes more R1 than R2
- 39. CoexistenceCoexistence is possible when species compete more strongly with themselves than with their competitorThat occurs when species A consumes more of the resources that most limits its growth and species B consumes more of the resource that most limits its growth
- 40. Test YourselfWhat is the outcome of competition whenSpecies A is more limited by R1 than species BSpecies B is more limited by R2 than species AAndSpecies A consumes more R2 than R1Species B consumes more R1 than R2