1. Exploitation vs. interference competition
Lotka-Volterra Competition equations
Assumptions: linear response to crowding both within and between
species, no lag in response to change in density, r, K, a constant
Competition coefficients aij, i is species affected and j is the species
having the effect
Solving for zero isoclines, resultant vector analyses
Point attractors, saddle points, stable and unstable equilibria
Four cases, depending on K/a’s compared to K’s
Sp. 1 wins, sp. 2 wins, either/or, or coexistence
Gause’s and Park’s competition experiments
Mutualism equations, conditions for stability:
Intraspecific self damping must be stronger than
interspecific positive mutualistic effects.

2. Diffuse competition: Ni* = Ki – S aij Nj
Alpha matrices, N and K vectors
Matrix Algebra Notation: N = K – AN
Partial derivatives, ∂Ni/∂Nj sensitivity of species i to changes in j
Jacobian matrix (community matrices), Lyapunov stability
Evidence for competition in nature
Resource partitioning among sympatric congeneric pairs
Resource Matrices, food, place, time niche dimensions
Complementarity of niche dimensions
Galapagos finches, beak depth, seed size
Character displacement
Hydrobia mud snails
Hutchinsonian ratios
Corixids, musical instruments, knives, pots, trikes, bikes
Accipter hawks, monitor lizards

3. Evidence of Competition in Nature. often circumstantial. 1
Evidence of Competition in Nature often circumstantial 1. Resource partitioning among closely-related sympatric congeneric species (food, place, and time niches) Complementarity of niche dimensions 2. Character displacement 3. Incomplete biotas: niche shifts 4. Taxonomic composition of communities

4. Complementarity of Niche Dimensions, page 276
Thomas Schoener

5. Prey size versus predator size

6. Prey size versus predator size
Ctenotus skinks Hawks

7. Character Displacement, Galápagos finches
Peter R. Grant
David Lack

8. Character Displacement in Hydrobia mud snails in Denmark
Snail shell length, mm

9. Corixid Water Boatman
G. E. Hutchinson

10. Hutchinsonian Ratios

11. Hutchinsonian Ratios
Henry S. Horn
Bob May

12. Hutchinsonian Ratios
Limiting Similarity
Henry S. Horn
Bob May

13. Hutchinsonian Ratios Limiting Similarity Recorders Henry S. Horn
Bob May
Recorders

14. Wind Instruments

16. Kitchen
Knives

17. Kitchen Pots

18. Tricycles

19. Bikes

20. Hutchinsonian ratios among short wing Accipiter hawks
Thomas W. Schoener

26. Nicole hugs
A komodo monitor

30. Hutchinsonian ratios among Australian Varanus lizards

31. The ecological niche, function of a species in the community
Resource utilization functions (RUFs)
Competitive communities in equilibrium with their resources
Hutchinson’s n-dimensional hypervolume concept
Fundamental and Realized Niches
Resource matrices
Niche Breadth (vector)
Niche Overlap (matrix)

32. Resource Utilization Functions = RUFs
Ecological Niche = sum total of adaptations of an organismic unit How does the organism conform to its particular environment?
Resource Utilization Functions = RUFs

33. Within-phenotype versus between-phenotype components
of niche width
Within Phenotype Between Phenotype
Individuals are generalists More specialized individuals

34. Fitness density Hutchinson’s Fundamental and Realized Niches
n-Dimensional Hypervolume Model
Fitness density Hutchinson’s Fundamental and Realized Niches
G. E. Hutchinson

36. Euclidean distance Euclid djk = sqrt [S (pij - pik)2]
where j and k represent species j and species k, the pij and pik’s represent the proportional utilization or electivities of resource state i used by species j and species k, respectively
and the summation is from i to n.
n is the number of resource dimensions

39. Robert H. MacArthur Geographical Ecology Range of Available Resources
Average Niche Breadth
Niche Overlap

40. Resource Utilization Functions = RUFs
MacArthur, R. H Species packing and competitive
equilibrium for many species. Theoret. Population Biol. 1: 1-11.
Species Packing, one dimension
Rate of Resource
Resource Utilization Functions = RUFs

41. Species Packing , one dimension, two neighbors in niche space
Three generalized abundant
species with broad niche breadths
Nine specialized less abundant
species with with narrow niche
breadths

42. Specialists are favored when resources are very different
Niche Breadth Jack of all trades is a master of none MacArthur & Levin’s Theory of Limiting Similarity
Robert H. MacArthur
Richard Levins
Specialists are favored when resources are very different

43. Niche Breadth Jack of all trades is a master of none
MacArthur & Levin’s
Theory of Limiting Similarity
Robert H. MacArthur
Richard Levins
Generalists are favored when resources are more similar

44. Niche Dimensionality. 1 D = ~ 2 Neighbors. 2 D = ~ 6 Neighbors
Niche Dimensionality 1 D = ~ 2 Neighbors 2 D = ~ 6 Neighbors 3 D = ~ 12 Neighbors 4 D = ~ 20 Neighbors NN = D + D2 Diffuse Competition dNi/dt = riNi(Ki -Ni -ij Nj) dNi/dt = 0 when Ni = Ki -ij Nj

45. Niche Overlap Hypothesis