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

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 1 Case 4: Neither species Species 1 (K1/a12 > K2) always wins can contain the other; stable coexistence ______________________________________________________________________ Vito Volterra Alfred Lotka

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

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

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

Hutchinsonian Ratios

Hutchinsonian Ratios Henry S. Horn Bob May

Hutchinsonian Ratios Henry S. Horn Bob May Recorders

Wind Instruments

Kitchen Knives

Kitchen Pots

Tricycles

Bikes

Hutchinsonian ratios among short wing Accipiter hawks Thomas W. Schoener

Hutchinsonian ratios among Australian Varanus lizards

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

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

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

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

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

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

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

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 * ~ *

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

Resource Utilization Functions = RUFs MacArthur, R. H. 1970. 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

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

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

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

Within-phenotype versus between-phenotype components of niche width

Compression Hypothesis: habitats contract, diets do not

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

Periodic table of niches Pianka 1974 Evolutionary Ecology

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

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

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

Anolis landestoyi Hispaniola (2016)

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).

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.

134 Lizard Species, 51 Niche Dimensions: http://www.zo.utexas.edu/faculty/pianka/ModelsMK/ http://www.zo.utexas.edu/faculty/pianka/ModelsMK/Model1.html Convergent Species Pairs: http://www.zo.utexas.edu/faculty/pianka/ModelsMK/convergent.html Foraging Mode: http://www.zo.utexas.edu/faculty/pianka/ModelsMK/sw_wf.html

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

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

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

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

R. T. Paine (1966)

Joseph Connell (1961)

Bruce Menge (1972)

Size difference between Pisaster and Leptsterias Menge 1972 Bruce Menge

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

Pogonomyrmex harvester ants James Brown Pogonomyrmex harvester ants Dipodomys kangaroo rats

Experimental Design of Seed Predation in the Chihuahuan Desert ___________________________________________________ Plots Treatments ___________________________________________________ 11,14 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. 1981. Competition in desert rodents: an experiment with semipermeable enclosures. Science 211: 510-512.

open circles = rodents removed solid circles = controls

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

Simberloff and Wilson 1970

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 _______________________________________________________________________________________ E1 9 (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) ST2 7 (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) E9 12 (7) 1 (0) 1 (1) 2 (2) 6 (5) 13 (10) 2 (3) 0 (1) 37 (29) Totals 55 (55) 7 (5) 13 (8) 8 (6) 32 (23) 36 (31) 12 (9) 1 (3) 164 (140) _______________________________________________________________________________________ H = herbivore S = scavenger D = detritus feeder W = wood borer A = ant C = carnivorous predator P = parasite ? = undetermined

Wilson 1969

Predation and Parasitism

Predator-Prey Experiments Georgii F. Gause

Predator-Prey Experiments Georgii F. Gause

Predator-Prey Experiments Georgii F. Gause

Lotka-Volterra. Predation Equations Lotka-Volterra Predation Equations coefficients of predation, p1 and p2 dN1 /dt = r1 N1 – p1 N1 N2 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

Neutral Stability (Vectors spiral in closed loops)

Vectors spiral inwards (Damped Oscillations)

Damped Oscillations