Hardy-Weinberg Equilibrium No Selection  No Mutation  No Exchange of Genes (today) Infinite (very large) Population Size (Monday) Random Mating (after midterm)

Gene flow dispersal = movement of individuals between pop ns (necessary but not sufficient for gene flow) gene flow individuals leave their natal population reach new suitable habitat successfully reproduce infer dispersal from studies of movement infer gene flow from allele frequency patterns model this as genetic exchange among demes deme = subpopulation that is genetically connected to other subpopulations

effects of gene flow: 1) introduce new alleles into a population 2) eliminate genetic differences among populations (reduce among-population genetic variance) 3) reduce the probability of fixation of neutral alleles by genetic drift 4) may retard adaptation to local conditions via natural selection

neutral alleles, two populations let q A = f(A 2 ) in pop n A andq B = f(A 2 ) in pop n B if q A == q B ?? Single generation recursion: q A ’= (1-m)q A + mq B = q A - mq A + mq B = q A - m(q A – q B ) m m m = fraction of immigrants 1-m = fraction of natives

q A ’ = q A -m(q A – q B )  q A = q A ’ - q A = q A - m(q A – q B ) - q A = -m(q A – q B ) at equilibrium,  q A = 0 0= -m(q A – q B ) q A = q B gene flow homogenizes allele frequencies rate of convergence determined by m

neutral alleles, many populations q i = f(A 2 ) in pop n i, q = f(A 2 ) in all other pop ns q i ’ = (1-m)q i + mq = q i - m(q i –q)  q i = q i ’ - q i = q i - m(q i –q) - q i = -m(q i –q) at equilibrium, q i = q i m = fraction immigrants 1-m = fraction natives v

measuring gene flow in natural populations models: gene flow equalizes frequency of neutral alleles among populations, independent of their frequency alleles that are moderately common should be present in all demes at ~same frequency only rare alleles should be restricted to one or a few demes conditional average frequency -- mean frequency of an allele (when it is present) as a function of its distribution

m = m = m = 0.01 m = 0.05 m = 0.1 for all,  = d = 10 N = 25 * Number of demes where an allele is found Average frequency of allele

gene flow and selection deme iA 1 A 1 A 1 A 2 A 2 A 2 w ij 1 1-s 1-2s if selection is weak,  q ~ ~ -sq i (1-q i ) i -sq i (1-q i ) w if deme i is now connected to a set of populations where A 2 is not deleterious, what happens?? selection will decrease f(A 2 ), but gene flow will increase f(A 2 )

q i decreases via selection q i increases via gene flow -sq i (1 - q i ) m(q i – q)  q = -sq i (1 - q i ) + m(q i – q) at equilibrium  q = 0, q i = (m+s) + [(m+s) 2 – 4smq] 2s & v

three biological outcomes: m>>sgene flow replaces A 2 faster than selection removes it q i ~ q m<<sselection eliminates A 2 faster than gene flow replaces it q i ~ 0 m~sgene flow maintains A 2 at a frequency higher than under selection alone, but its frequency in deme i does not converge on the other demes q i ~ q(m/s) v v v (m+s) + [(m+s) 2 – 4smq] 2s & v q i =  q = -sq i (1 - q i ) + m(q i – q)

interaction of selection and gene flow -- evolution of metal tolerance in plants soil near mines contaminated by tailings or seepage copper, lead, zinc low in nitrogen, phosphorus, potassium adaptations -- metal not taken up metal taken up but sequestered metal required degree of adaptation measured by a tolerance index (TI) TI = root growth in metal root growth in control

trade-off: strong advantage on contaminated soil, but overgrown on clean soil w = X yield tolerant X yield susceptible Agrostis Anthoxanthum Plantago Rumex w ij tolerant susceptible contaminated – 0.05 soil metal-free0.6 – soil

w tol 0 1 tolerant favored susceptible favored susceptible favored mine gene flow via wind pollination

seeds adults

dispersal is necessary, but not sufficient, for gene flow gene flow reduces among population genetic variance gene flow can maintain a deleterious allele (prevent adaptation to local conditions the degree of gene flow can be inferred from the distribution of neutral alleles across a set of populations