Optimal Foraging Theory Model: N e = number prey encountered per unit time C s = cost to search for prey H = handling time E = energy gained by consuming prey Can calculate energy intake per unit time: E/T E/T = (N e1 E 1 -C s )/(1 + N e1 H 1 ) 1 refers to prey species 1 E: Energy gain minus Cost Time: reflects handling prey
What if 2 prey? E/T = (N e1 E 1 -C s ) + (N e2 E 2 -C s ) 1 + N e1 H 1 + N e2 H 2 Optimal Foraging Theory N e = number prey encountered per unit time C s = cost to search for prey H = handling time E = energy gained by consuming prey
What if 2 prey? E/T = (N e1 E 1 -C s ) + (N e2 E 2 -C s ) 1 + N e1 H 1 + N e2 H 2 If optimal foraging: prey choice maximizes E/T –Ex: if 2 prey, prey #2 eaten if E/T for both prey > E/T for prey #1 only Optimal Foraging Theory
Does it work? Ex, bluegill sunfish Optimal Foraging Theory
Values calculated for prey in lab Daphnia (water fleas), damselfly larvae, midge larvae Optimal Foraging Theory midge damselfly water flea
Prey abundance documented (top) Equation predicts optimal prey size (mid) Fish stomachs examined (bottom) Does it work? Yup... Optimal Foraging Theory
Allocation to leaves, stems & roots Principle of Allocation: Energy allocated to obtain resource in shortest supply –Do plants allocate to resource in shortest supply? –Where we see this before?
Optimal Foraging By Plants? Allocation to leaves, stems & roots Principle of Allocation: Energy allocated to resource in shortest supply –Do plants allocate to resource in shortest supply? Where we see this before?
Optimal Foraging By Plants Ex, N in soil Fig. 7.26
Evolution by Natural Selection Adaptation: Genetically determined trait with survival/reproductive advantages (improves “fitness”) –Genotype: Alleles for trait –Phenotype: Expression of trait. May be affected by environment. Phenotypic plasticity: ability phenotype to change based on environment
Evolution by Natural Selection Adaptation: Genetically determined trait with survival and/or reproductive advantages (improves “fitness”) Depends on heritability (h 2 ) trait (how “well” transmitted) h 2 = V G / V P V G : Variability due to genetic effect V P : Total variability phenotype
Evolution by Natural Selection Heritability: h 2 = V G / V P V G : Variability due to genetic effect V P : Total variability phenotype Phenotype influenced by both genes and environment Or, V P = V G + V E
Evolution by Natural Selection Modified equation: h 2 = V G / (V G + V E ) h 2 ranges 0-1 If V G small, little heritability If V E large (lots phenotypic plasticity), little heritability How measure?
Measuring heritability Linear Regression: Fits line to points –Equation line: Y = m X + b –m = slope (regression coefficient) –b = Y intercept –Regression coefficient: measures h 2
Variation Within Species Many species’ populations differ How much variation due V G vs. V E ? –Clausen, Keck, Hiesey (CA plants) How test V G vs. V E ?
Variation Within Species Common garden experiment: Grow same location.
Variation Within Species –Differences remain: genetic variation (V G ) –Differences disappear: phenotypic plasticity (V E ) Result?
Variation Within Species Found differences. Populations form ecotypes: locally adapted to environment –Same species (can interbreed)
Variation Within Species Do animal populations vary locally? Chuckwalla (Sauromalus obesus) –Herbivorous lizard (desert SW).
Variation Within Species Found at different elevations Rainfall amount & variation changes Lizards bigger where more rain Due to better environment (V E ) or genetic (V G )? How test?
Variation Within Species Chuckwalla “Common garden” expt. Genetic differences!
Variation Within Species Genetic differences suggest adaptations Experiments: can show natural selection in populations? Experiments: who am I?
Adaptive Change in Lizards Genus Anolis (anoles) Hundreds species New World Length hind leg reflects use vegetation Perch diameter Anolis carolinensis
Adaptive Change in Lizards Experiment: lizards from 1 island (Staniel Cay) put on islands with different vegetation Do they evolve (limb size changes)? Staniel Cay
Adaptive Change in Lizards Positive correlation (after 10-14 yr) between vegetation and change morphology Is this natural selection in action?
Adaptive Change in Lizards Positive correlation (after 10-14 yr) between vegetation and change morphology Is this natural selection in action? Probably. But genetic change not shown
Adaptation by Soapberry Bugs Soapberry Bug (Jadera haematoloma) feeds on seeds Beak pierces fruit walls
Soapberry Bugs Feeds on native or introduced plants (fruit size varies) Feed on bigger fruits: longer beaks How test if differences genetic?
Soapberry Bugs Raise bugs on common foods--beak length differences persisted Bugs adapted to different hosts: natural selection