Upload
freya-crosby
View
44
Download
0
Tags:
Embed Size (px)
DESCRIPTION
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 - PowerPoint PPT Presentation
Citation preview
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, constant
Competition coefficients ij, 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/’s compared to K’sSp. 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 – ij Nj
Alpha matrices, N and K vectors
Matrix Algebra Notation: N = K – ANPartial 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 pairsResource Matrices, food, place, time niche dimensionsComplementarity of niche dimensionsGalapagos finches, beak depth, seed sizeCharacter displacementHydrobia mud snailsHutchinsonian ratiosCorixids, musical instruments, knives, pots, trikes, bikesAccipter hawks, monitor lizards
Evidence of Competition in Natureoften 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
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 componentsof niche width
Within Phenotype Between Phenotype
Individuals are generalists More specialized individuals
Fitness density
Hutchinson’s Fundamental and Realized Niches
n-Dimensional Hypervolume Model
G. E. Hutchinson
Euclidean distance
djk = sqrt [ (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
Euclid
Robert H. MacArthur
Geographical Ecology
Range of Available Resources
Average Niche Breadth
Niche Overlap
Resource Utilization Functions = RUFs
Rat
e of
Res
ourc
eMacArthur, R. H. 1970. Species packing and competitive
equilibrium for many species. Theoret. Population Biol. 1: 1-11.
Species Packing, one dimension
Three generalized abundant
species with broad niche breadths
Nine specialized less abundant
species with with narrow niche
breadths
Species Packing , one dimension, two neighbors in niche space
Niche Breadth Jack of all trades is a master of none
MacArthur & Levin’s Theory of Limiting Similarity
Specialists are favored when resources are very different
Robert H. MacArthur Richard Levins
Generalists are favored when resources are more similar
MacArthur & Levin’s Theory of Limiting Similarity Robert H. MacArthur Richard Levins
Niche Breadth Jack of all trades is a master of none
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