Transcript 15-Competition

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.
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
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
Complementarity of Niche Dimensions, page 276
Thomas Schoener
Prey size versus predator size
Prey size versus predator size
Ctenotus skinks
Hawks
Character Displacement, Galápagos finches
Peter R. Grant
David Lack
Character Displacement in Hydrobia mud snails in Denmark
Snail shell length, mm
Corixid Water Boatman
G. E. Hutchinson
Hutchinsonian Ratios
Hutchinsonian Ratios
Henry S. Horn
Bob May
Hutchinsonian Ratios
Limiting Similarity
Henry S. Horn
Bob May
Hutchinsonian Ratios
Limiting Similarity
Henry S. Horn
Bob May
Recorders
Wind Instruments
Kitchen
Knives
Kitchen Pots
Tricycles
Bikes
Hutchinsonian ratios among short wing Accipiter hawks
Thomas W. Schoener
Nicole hugs
A komodo monitor
Hutchinsonian ratios among Australian Varanus lizards
25
Expected
Observed (R)
Observed (L)
Frequency
20
15
10
5
0
0
1
2
3
4
5
Hutchinsonian Ratio
6
7
8
9
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)
Ecological Niche = sum total of adaptations of an organismic unit
How does the organism conform to its particular environment?
Resource Utilization Functions = RUFs
Within-phenotype versus between-phenotype components
of niche width
Within Phenotype
Individuals are generalists
Between Phenotype
More specialized individuals
n-Dimensional Hypervolume Model
Fitness density
Hutchinson’s Fundamental and Realized Niches
G. E. Hutchinson
Euclid
Euclidean distance
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
Robert H. MacArthur
Geographical Ecology
Range of Available Resources
Average Niche Breadth
Niche Overlap
MacArthur, R. H. 1970. Species packing and competitive
equilibrium for many species. Theoret. Population Biol. 1: 1-11.
Species Packing, one dimension
Resource Utilization Functions = RUFs
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
Niche Breadth
Jack of all trades is a master of none
Robert H. MacArthur
MacArthur & Levin’s
Theory of Limiting Similarity
Richard Levins
Specialists are favored when resources are very different
Niche Breadth
Jack of all trades is a master of none
Robert H. MacArthur
MacArthur & Levin’s
Theory of Limiting Similarity
Richard Levins
Generalists are favored when resources are more similar
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 -Saij Nj)
dNi/dt = 0 when Ni = Ki -Saij Nj
Niche Overlap Hypothesis