1. ES100: Community Ecology 8/22/07

2. What Controls Population Size and Growth Rate (dN/dt)? Density-dependent factors: Intra-specific competition food Space contagious disease waste production Interspecific competition Other species interactions! Density-independent factors: disturbance, environmental conditions hurricane flood colder than normal winter

3. Types of Interactions  Competition  Predator-Prey  Mutualism  Commensalism

4. Competition Natural Selection minimizes competition!

5. Species Interactions How do we model them? Start with logistic growth = r * N (1 – ) = r * N (1 – ) NKNK dN dt = r * N ( - ) = r * N ( - ) NKNK dN dt K = r * N ( ) = r * N ( ) dN dt K-N K Use this equation for 2 different species

6. Species Interactions Population 1  N 1 Population 2  N 2 But the growth of one population should have an effect the size of the other population = r 1 * N 1 ( ) = r 1 * N 1 ( ) dN 1 dt K 1 -N 1 K 1 = r 2 * N 2 ( ) = r 2 * N 2 ( ) dN 2 dt K 2 -N 2 K 2

7. Species Interactions New term for interactions a 12  effect of population 2 on population 1 a 21  effect of population 1 on population 2 Multiply new term by population size the larger population 2 is, the larger its effect on population 1 (and vice versa) a 12 * N 2 a 21 * N 1

8. Competition: Lotka-Volterra Model  If two species are competing, the growth of one population should reduce the size of the other  Population 1  N 1  Population 2  N 2 = r 1 * N 1 = r 1 * N 1 dN 1 dt K 1 - N 1 - a 12 N 2 K 1 = r 2 * N 2 = r 2 * N 2 dN 2 dt K 2 - N 2 - a 21 N 1 K 2

9. Competition  If two species are competing, the growth of one population should reduce the size of the other  Population 1  N 1  Population 2  N 2 = r 1 * N 1 = r 1 * N 1 dN 1 dt K 1 - N 1 - a 12 N 2 K 1 = r 2 * N 2 = r 2 * N 2 dN 2 dt K 2 - N 2 - a 21 N 1 K 2 Because this is a negative term, K is reduced

10. Blue Area = Bluejay’s Carrying Capacity It takes 1squirrel to use the portion of the carrying capacity occupied by 4 bluejays. a BS = 4 Interspecific competition regulates bluejay population COMPETITION

11. Green Area = Squirrel’s Carrying Capacity It takes 4 bluejays to use the portion of the carrying capacity occupied by 1 squirrel. a SB =.25 Intraspecific competition regulates squirrel population COMPETITION

12. Outcomes of Competition Model  Many possible outcomes, depends on the balance of:  r 1 vs r 2  K 1 vs K 2  a 21 vs a 12  a 12 > 1Interspecific competition dominates population size of species 1  a 12 < 1Intraspecific competition dominates population size of species 1 a 12 is the per capita effect of species 2 on the the pop’n growth rate of species 1, measured relative to the effect of species 1.

13. Predator-prey

14. Predator-Prey Relationships Prey defenses: avoid conflict! coevolution as predator evolves, prey evolves to evade it warning coloration and mimicry Camouflage

15. Red = Fox’s Carrying Capacity It takes 10 rabbits to support 1 fox a FR =.10 Predator-Prey

16. Yellow = Rabbits Carrying Capacity It takes 10 rabbits to support 1 fox a RF = 10 Predator-Prey

17. Bottom-up vs. Top-Down control Predators can promote diversity by keeping competition in check Predator-Prey Relationships

18. Predatory-Prey  If it is a predator-prey relationship, then the two populations have opposite effects on one another  Prey (N 1 )  Predator (N 2 ) = r 1 * N 1 = r 1 * N 1 dN 1 dt K 1 - N 1 - a 12 N 2 K 1 = r 2 * N 2 = r 2 * N 2 dN 2 dt K 2 - N 2 + a 21 N 1 K 2 Because this is a negative term, K is reduced Because this is a positive term, K is increased

19. Mutualism  Both species benefit

20. Mutualism  If it is a mutually beneficial relationship, then the two populations increase each other’s size  Population 1  N 1  ti  Population 2  N 2 = r 1 * N 1 = r 1 * N 1 dN 1 dt K 1 - N 1 + a 12 N 2 K 1 = r 2 * N 2 = r 2 * N 2 dN 2 dt K 2 - N 2 + a 21 N 1 K 2 Because this is a positive term, K is increased

21. Commensalism  One species benefits, the other is unaffected

22. Commensalism  If the relationship is commensalistic, one species benefits (the commensal) and the other is unaffected  Population 1  N 1  Population 2  N 2 = r 1 * N 1 = r 1 * N 1 dN 1 dt K 1 - N 1 + a 12 N 2 K 1 = r 2 * N 2 = r 2 * N 2 dN 2 dt K 2 - N 2 K 2 Because this is a positive term, K is increased Because there is no a 21 term, K is unchanged

23. Assumptions of Lotka-Volterra Models  All assumptions of logistic growth model… plus:  Interaction coefficients, carrying capacities, and intrinsic growth rates are constant.

24. Summary of Interaction Equations: Competition: (-, -) Predator/Prey:(+, -) Mutualism:(+, +) Commensalism: (+, 0)

25. Test you knowledge! What type of relationship– what equation to use?  A coati eats tree fruit.  Your dog has a flea  You use a fast bicyclist to “draft” off of

26. Problems with Simple Logistic Growth 1. Births and deaths not separated -you might want to look at these processes separately -predation may have no effect on birth rate 2. Carrying capacity is an arbitrary, set value 3. No age structure

27. 1. Separate Births and Deaths = Births - Deaths Births = b*N Deaths = d*N dN dt Births and deaths may be density dependent

28. 1. Separate Births and Deaths = Births - Deaths Births = b*N Deaths = d*N dN dt Births rate may be density dependent Death rate may be dominated by predator effects Example: Births = b*N(1- N ) K Deaths = d b +a 21 N 2

29. 2. Refine Carrying Capacity If the population is a herbivore, K may depend on the population of plants = r H * N H (1 – ) = r H * N H (1 – ) dN H dt NHNPNHNP K herbivore = N plant

30. Remaining Problems  Age Structure  Space: animals rely on different parts of landscape for different parts of their life cycle  Individuality: Populations are collections of individuals, not lumped pools

31. General Notes on Using Models  How complex should model be? K.I.S.S.  Identify research needs:  Build model structure  Test model to see what it is most sensitive to  Do research to find values of unknown parameters  If build a model that accurately predicts dynamics, it can be used as a management tool.  Look critically at assumptions!

32. Community Dynamics Community: a group of populations (both plants and animals) that live together in a defined region.

33. Trophic Cascade Eagles Foxes Mice Plants1 st trophic level 2 nd trophic level 3 rd trophic level 4 th trophic level autotroph/ primary producer herbivore/ primary consumer predator/ secondary consumer predator/ tertiary consumer

34. How would we Model the Fox Population? Why not include the effect of the plant population? What if foxes had a competitor?

35. Trophic Cascade Eagles Foxes Mice Plants1 st trophic level 2 nd trophic level 3 rd trophic level 4 th trophic level if eagles go extinct, what could happen to… foxes? mice? plants?

36. Trophic Cascade Eagles Foxes Mice Plants1 st trophic level 2 nd trophic level 3 rd trophic level 4 th trophic level If a new predator on mice is introduced, what could happen to… mice? plants? foxes? eagles?

37. Trophic Cascade Eagles Foxes Mice Plants1 st trophic level 2 nd trophic level 3 rd trophic level 4 th trophic level If drought caused a dip in plant production, what would happen to… mice? foxes? eagles?

38. Simplified Temperate Forest Food Web What happens to when it’s a WEB instead of a CHAIN? Oak seedling Deer Wolf Fox Rabbit GrassesHerbs Caterpillars Shrews Eagle In long term, balance is restored

39. Food Web doesn’t account for Keystone Species Kelp provides otter habitat Sea urchins eat kelp Otters eat sea urchins

40. Summary  Modeling Species Interactions  Competition  Predator-prey  Mutualism  Commensalism  Community Dynamics  Food Webs  Keystone Species