2. Competition in theory one individual uses a resource, reducing its availability to others negative-negative interaction –intraspecific competition –interspecific competition –interference competition –exploitative competition –diffuse competition –apparent competition

3. Exploitative and interference competition.

4. The competitive exclusion principle two species cannot coexist if they both depend on the same limiting resource

5. The competitive exclusion principle two species cannot coexist if they both depend on the same limiting resource disturbance and predation habitat heterogeneity metapopulation dynamics

6. Lotka-Voltera competition model adding a competing species j reduces the growth rate and the steady state equilibrium population of species i

7. Lotka-Voltera competition model competition coefficients a ij and a ji express the effects of each competitor in terms of the other competitor’s resource use –competition coefficients usually α and β –a ij means “the effect of each member of species j on species i”

8. Lotka-Voltera competition model (a) per-capita growth rate for species i –zero growth isocline in the (N i, N j ) plane (b) ZGI for species i –N i → K i only when N j → 0 –K i /a ij is the equilibrium population of species i expressed in “equivalent units” of species j (c) ZGI for species j

9. Lotka-Voltera competition model species i zero growth isocline crosses the N i axis at K i and the N j axis at K i /a ij species j zero growth isocline crosses the N j axis at K j and the N i axis at K j /a ji

10. Lotka-Voltera competition model species i zero growth isocline crosses the N i axis at K i and the N j axis at K i /a ij species j zero growth isocline crosses the N j axis at K j and the N i axis at K j /a ji the species with the outer ZGI wins (N i )

11. Lotka-Voltera competition model coexistence can occur when the zero growth isoclines cross one another equilibrium with both populations > 0 stable if intraspecific competition limits growth before interspecific competition

12. Lotka-Voltera competition model coexistence can occur when the zero growth isoclines cross one another equilibrium with both populations > 0 unstable otherwise outcome depends on starting population sizes

13. Lotka-Voltera competition Rhizopertha and OryzaephilusRhizopertha and Sitotraga

14. Resource competition model the Lotka-Voltera models do not express competitive interactions in terms of resource consumption zero growth isoclines for a single species with two limiting resources

15. Resource competition model the Lotka-Voltera models do not express competitive interactions in terms of resource consumption zero growth isoclines for a single species with two limiting resources

16. Resource competition model zero growth isoclines for a single species with two limiting resources consumption vector reflects an optimal resource use ratio resource supply points and depletion vectors species i is excluded from the shaded area

17. Resource competition model trivial example of ZGI’s for two species competition N i always wins

18. Resource competition model two species competition outcome depends upon initial resource supply point and joint depletion vectors

19. Resource competition model two species competition outcome depends upon initial resource supply point and joint depletion vectors ZGIs and consumption vectors for two diatom species