1. Gause’s and Park’s competition experiments
Lotka-Volterra Competition equations
dNi /dt = ri Ni ({Ki – Ni – S aij Nj }/Ki )
Summation is over j from 1 to n, excluding i
Ni* = Ki – S aij Nj [Diffuse competition]
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, set dN/dt = 0
resultant vector analyses
Four cases, depending on K/a’s compared to K’s
Sp. 1 wins, sp. 2 wins, either/or, or coexistence
Lecture # 23
21 November 2017

2. Four Possible Cases of Competition. Under the Lotka–Volterra
Four Possible Cases of Competition Under the Lotka–Volterra Competition Equations _____________________________________________________________________ Species 1 can contain Species 1 cannot contain Species 2 (K2/a21 < K 1) Species 2 (K2/a21 > K 1) ______________________________________________________________________ Species 2 can contain Case 3: Either species Case 2: Species 2 Species 1 (K1/a12 < K2) can win always wins ______________________________________________________________________ Species 2 cannot contain Case 1: Species Case 4: Neither species Species 1 (K1/a12 > K2) always wins can contain the other; stable coexistence ______________________________________________________________________
Vito Volterra
Alfred Lotka

3. Galápagos Finches
Peter R. Grant
David Lack
“Darwin’s
Finches”

4. Character Displacement in Hydrobia mud snails
in Denmark (Thomas Fenchel)
Snail shell length, mm

5. Homage to Santa Rosalia, or why are there so
many kinds of animals? American Naturalist
Corixid Water Boatman
G. E. Hutchinson

6. Hutchinsonian Ratios

7. Hutchinsonian Ratios
Henry S. Horn
Bob May

8. Hutchinsonian Ratios
Henry S. Horn
Bob May
Recorders

9. Wind Instruments

11. Kitchen
Knives

12. Kitchen Pots

13. Tricycles

14. Bikes

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

17. Hutchinsonian ratios among Australian Varanus lizards

18. 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
Euclidean distances in n- space (Greek mathematician, 300 BC)
Fundamental versus Realized Niches

19. Resource matrices of utilization coefficients
Niche dynamics
Complementarity of niche dimensions
Niche Breadth:
Specialization versus generalization.
Similar resources favor specialists,
Different resources favor generalists
Niche dimensionality and diffuse competition
Periodic table of lizard niches (50+ dimensions)
Thermoregulatory axis: thermoconformers —> thermoregulators

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

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

23. Distance between two points along a line:
One Dimension:
Distance between two points along a line:
simply subtract smaller value from larger one
x2 - x1 = d
Two Dimensions:
Score position of each point on the first
and second dimensions. Subtract smaller
from larger on both dimensions. d1 = x2 - x1
d2 = y2 - y1
Square these differences, sum them and take
the square root. This is the distance between
the points in 2D: sqrt (d12 + d22) = d
Three Dimensions —> n-dimensions: follow
this same protocol summing over all
dimensions i = 1, n: sqrt Sdi2 = d
Euclid

24. Euclidean distance between two species in n-space
n-dimensional hypervolume
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 = 1 to n .
n is the number of resource dimensions n n
Euclid
i = 1

25. Multivariate statistics – correlated data
Change co-ordinate systems – reduce dimensionality
First Principal Component
Second Principal Component

28. 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)/Ki dNi/dt = 0 when Ni = Ki -ij Nj * ~ *

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

31. 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

32. 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

33. 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

34. 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

35. Within-phenotype versus between-phenotype components
of niche width

36. Compression Hypothesis: habitats contract, diets do not

37. Complementarity of Niche Dimensions, page 276
Anolis
Thomas W. Schoener

39. Periodic table of niches
Pianka 1974
Evolutionary Ecology

42. 134 Lizard Species
51 Niche Dimensions
46.35%
+15.28
=61.63%

43. 134 Lizard Species
51 Niche Dimensions
46.35%
+15.28
=61.63%

44. 134 Lizard Species
51 Niche Dimensions
46.35%
+15.28
=61.63%

45. Anolis landestoyi Hispaniola (2016)

46. Plots of PCA axes 1 versus 3, and 3 versus 2, showing that nocturnal
species (enclosed in ovals) lie behind the PC1 versus PC2 plane shown
in previous Figure. Even though a few diurnal species appear to cluster
with nocturnal species in the left-hand panel, they are separated on
PC1 (right-hand panel). Notice the two Australian nocturnal skinks in
the genus Liopholis (purple dots enclosed in orange ellipses).

47. Scatter Plots of PCA axes 1 versus 3, and 3 versus 2
Scatter Plots of PCA axes 1 versus 3, and 3 versus 2. Nocturnal members of the clade
Gekkota are enclosed in an orange ellipse. Two nocturnal Australian skinks are shown
(purple dots). Plot rotation reveals the clear separation between diurnal and nocturnal
lizards within the 3D ellipsoid. Crepuscular lizards and species with extended activity
occupy positions near the border of the ellipsoid.

49. 134 Lizard Species, 51 Niche Dimensions:
Convergent Species Pairs:
Foraging Mode:

50. Black = Africa
Orange = Australia
Blue = North America
Green = South America
Niche Convergences
Niche Conservatism
Niche Conservatism

51. Black = Africa
Orange = Australia
Blue = North America
Green = South America

52. Black = Africa
Orange = Australia
Blue = North America
Green = South America

53. Chapter 14. Experimental Ecology. Controls. Manipulation. Replicates
Chapter 14. Experimental Ecology Controls Manipulation Replicates Pseudoreplication Rocky Intertidal Space Limited System Paine’s Pisaster removal experiment Connell: Balanus and Chthamalus Menge’s Leptasterias and Pisaster experiment Dunham’s Big Bend saxicolous lizards Brown’s Seed Predation experiments Simberloff-Wilson’s defaunation experiment

54. R. T. Paine
(1966)

55. Joseph Connell
(1961)

57. Bruce Menge
(1972)

58. Size difference between Pisaster and Leptsterias
Menge 1972
Bruce Menge

59. Grapevine Hills, Big Bend National Park
Sceloporus merriami and Urosaurus ornatus
Six rocky outcrops: 2 controls, 2 Sceloporus removal
plots and 2 Urosaurus removal areas.
========================================================
4 year study: 2 wet and 2 dry: insect abundances
Monitored density, feeding success, growth rates, body weights,
survival, lipid levels
Urosaurus removal did not effect Sceloporus density
No effects during wet years (insect food plentiful)
Insects scarce during dry years: Urosaurus growth and survival
was higher on Sceloporus removal plots
Arthur Dunham

60. Pogonomyrmex harvester ants
James Brown
Pogonomyrmex harvester ants
Dipodomys kangaroo rats

61. Experimental Design of Seed Predation in the Chihuahuan Desert ___________________________________________________ Plots Treatments ___________________________________________________ ,14 Controls 6,13 Seed addition, large seeds, constant rate 2,22 Seed addition, small seeds, constant rate 9,20 Seed addition, mixed seeds, constant rate 1,18 Seed addition, mixed seeds, temporal pulse 5,24 Rodent removal, Dipodomys spectabilis (largest kangaroo rat) 15,21 Rodent removal, all Dipodomys species (kangaroo rats) 7,16 Rodent removal, all seed-eating rodents 8,12 Pogonomyrmex harvester ants 4,17 All seed-eating ants 3,19 All Dipodomys plus Pogonomyrmex ants 10,23 All seed-eating rodents plus all seed-eating ants ___________________________________________________________ Munger, J. C. and J. H. Brown Competition in desert rodents: an experiment with semipermeable enclosures. Science 211:

62. open circles =
rodents removed
solid circles =
controls

64. Defaunation Experiments in the Florida Keys
Islands of mangrove trees were
surveyed and numbers of
arthropod species recorded
Islands then covered in plastic tents
and fumigated with methyl bromide
Islands then resurveyed at intervals
to document recolonization
Simberloff and Wilson 1970

65. Simberloff and Wilson 1970

66. Evidence for Stability of Trophic Structure
Evidence for Stability of Trophic Structure? First number is the number of species before defaunation, second in parentheses is the number after _______________________________________________________________________________________ Trophic Classes ______________________________________________________________________________ Island H S D W A C P ? Total _______________________________________________________________________________________ E (7) 1 (0) 3 (2) 0 (0) 3 (0) 2 (1) 2 (1) 0 (0) 20 (11) E2 11 (15) 2 (2) 2 (1) 2 (2) 7 (4) 9 (4) 3 (0) 0 (1) 36 (29) E3 7 (10) 1 (2) 3 (2) 2 (0) 5 (6) 3 (4) 2 (2) 0 (0) 23 (26) ST (6) 1 (1) 2 (1) 1 (0) 6 (5) 5 (4) 2 (1) 1 (0) 25 (18) E7 9 (10) 1 (0) 2 (1) 1 (2) 5 (3) 4 (8) 1 (2) 0 (1) 23 (27) E (7) 1 (0) 1 (1) 2 (2) 6 (5) (10) 2 (3) 0 (1) 37 (29) Totals 55 (55) 7 (5) (8) 8 (6) (23) (31) (9) (3) (140) _______________________________________________________________________________________ H = herbivore S = scavenger D = detritus feeder W = wood borer A = ant C = carnivorous predator P = parasite ? = undetermined

67. Wilson 1969

69. Predation and Parasitism

70. Predator-Prey Experiments
Georgii F. Gause

71. Predator-Prey Experiments
Georgii F. Gause

72. Predator-Prey Experiments
Georgii F. Gause

73. Lotka-Volterra. Predation Equations
Lotka-Volterra Predation Equations coefficients of predation, p1 and p dN1 /dt = r1 N1 – p1 N1 N dN2 /dt = p2 N1 N2 – d2 N2 No self damping (no density dependence) dN1 /dt = 0 when r1 = p1 N2 or N2 = r1 / p1 dN2 /dt = 0 when p2 N1 = d2 or N1 = d2 / p2
Alfred J. Lotka
Vito Volterra

74. Neutral Stability
(Vectors spiral
in closed loops)

75. Vectors spiral
inwards
(Damped
Oscillations)

76. Damped
Oscillations