Gause ’ s and Park ’ s competition experiments Lotka-Volterra Competition equations

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Mutualism Equations (pp. 234-235, Chapter 11)

dN1 /dt = r1 N1 ({X1 – N1 + 12 N2 }/X1)

dN2 /dt = r2 N2 ({X2 – N2 + 21 N1 }/X2)

(X1 – N1 + 12 N2 )/X1 = 0 when N1 = X1 + 12 N2

(X2 – N2 + 21 N1 )/X2 = 0 when N2 = X2 + 21 N1

If X1 and X2 are positive and 12 and 21 are chosen so that isoclines cross,

a stable joint equilibrium exists.

Intraspecific self damping must be stronger than interspecific positive mutualistic

effects.

The ecological niche, function of a species in the community

Resource utilization functions (RUFs)

Niche breadth and overlap

Competitive communities in equilibrium with their resources

Hutchinson’s n-dimensional hypervolume concept

Niche dimensionality and diffuse competition

Euclidean distances in n- space (Greek mathematician, 300 BC)

Fundamental versus Realized Niches

Niche dynamics

Resource matrices of utilization coefficients

Niche dynamics

Niche dimensionality and diffuse competition

Complementarity of niche dimensions

Niche Breadth: Specialization versus generalization.Similar resources favor specialists, different resources favor generalists

Periodic table of lizard niches (many dimensions)Thermoregulatory axis: thermoconformers —> thermoregulators

Experimental EcologyControls

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

Defaunation Experiments in the Florida Keys

Islands of mangrove trees weresurveyed and numbers ofarthropod species recorded

Islands then covered in plastic tentsand fumigated with methyl bromide

Islands then resurveyed at intervalsto document recolonization

Simberloff and Wilson 1970

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 = herbivoreS = scavengerD = detritus feederW = wood borerA = antC = carnivorous predatorP = parasite? = undetermined

Wilson 1969

Predation and Parasitism

Predator-Prey Experiments

Georgii F. Gause

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 spiralin closed loops)

Vectors spiral inwards (Damped Oscillations)

DampedOscillations

Vectors spiral inwards (Damped Oscillations)

Prey self damping

Mike Rosenzweig Robert MacArthur

Moderately efficient predatorNeutral stability — Vectors form a closed ellipse. Amplitude of oscillations remains constant.

<—Mike Rosenzweig Robert MacArthur —>

Unstable — extremely efficient predatorVectors spiral outwards until a Limit Cycle is reached

Robert MacArthur —><—Mike Rosenzweig

Damped Oscillations — inefficient predatorVectors spiral inwards to stable equilibrium point

Robert MacArthur —><—Mike Rosenzweig

Functional response = rate at which Individual predators capture and eat more prey per unit time as prey density increases C. S. Holling

Numerical response = increased prey density raises the predator’spopulation size and a greater number of predators consume An increased number of prey

Gause’s Didinium ExperimentsLotka-Volterra Predation Equations: N1 N2 = Contacts

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

Neutral StabilityPrey RefugesFunctional and Numerical Responses

Adding Prey self-damping stabilizes

Prey-Predator isocline analyses

Predator efficiency, Prey escape ability

Prey refuges, coevolutionary race

Predators usually destabilizing

Prey Isocline Hump

Efficient Predator —> unstable

Inefficient Predator —> stable

Predator Switching, frequency dependence, stabilizes

“Prudent” Predation and Optimal Yield

Feeding territories

Consequence of senescence

Prey Isocline Hump

Inefficient Predator —> stable

Damped Oscillations

Efficient Predator —> unstable

Increasing Oscillations —> Limit Cycle

Limit Cycle

Prey Population Density

Predator Escape TacticsAspect Diversity

Cryptic coloration (countershading)

Disruptive coloration

Flash coloration

Eyespots, head mimicry

Warning (aposematic) coloration

Alarm signals

Hawk alarm calls

Selfish callers

Plant secondary chemicals

Aspect Diversity in Tide Pools

Cottid Fish <—

Shrimp —>

Secondary Chemical Defenses of Plants

Head Mimicry Papilio caterpillar Pit Viper caterpillar DeVries Snake head

Monarch(Model)

Viceroy(Mimic)

Batesian Mimicry

Mullerian Mimicry

Batesian Mimicry

Parasitism > Commensalism > Mutualism

(+, –) < (+, 0) < (+, +)

Host-Altered Behavior

Evolution of Virulence

Biological Control

Gause ’ s and Park ’ s competition experiments Lotka-Volterra Competition equations

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