Genetic Exchange in Hardy-Weinberg Equilibrium Dynamics

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

2. Gene flow dispersal = movement of individuals between popns (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

3. 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

4. neutral alleles, two populations m let qA = f(A2) in popn A and qB = f(A2) in popn B if qA == qB ?? m m = fraction of immigrants 1-m = fraction of natives Single generation recursion: qA’ = (1-m)qA + mqB = qA - mqA + mqB = qA - m(qA – qB)

5. qA’ = qA-m(qA – qB) DqA = qA’ - qA = qA - m(qA – qB) - qA = -m(qA – qB) at equilibrium, DqA = 0 0 = -m(qA – qB) qA = qB gene flow homogenizes allele frequencies rate of convergence determined by m

6. neutral alleles, many populations qi = f(A2) in popn i, q = f(A2) in all other popns qi’ = (1-m)qi + mq = qi - m(qi –q) Dqi = qi’ - qi = qi - m(qi –q) - qi = -m(qi –q) at equilibrium, qi = q i m = fraction immigrants 1-m = fraction natives v

7. 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

8. m = 0.001 m = 0.005 m = 0.01 m = 0.05 m = 0.1 for all, m = 10-4 d = 10 N = 25 * Average frequency of allele Number of demes where an allele is found

10. gene flow and selection deme i A1A1 A1A2 A2A2 wij 1 1-s 1-2s if selection is weak, Dq ~ ~ -sqi(1-qi) i -sqi(1-qi) w if deme i is now connected to a set of populations where A2 is not deleterious, what happens?? selection will decrease f(A2), but gene flow will increase f(A2)

11. qi decreases via selection qi increases via gene flow -sqi(1 - qi) m(qi – q) Dq = -sqi(1 - qi) + m(qi – q) at equilibrium Dq = 0, qi = & (m+s) + [(m+s)2 – 4smq] 2s v

12. three biological outcomes: m>>s gene flow replaces A2 faster than selection removes it qi~ q m<<s selection eliminates A2 faster than gene flow replaces it qi~ 0 m~s gene flow maintains A2 at a frequency higher than under selection alone, but its frequency in deme i does not converge on the other demes qi~ q(m/s) v v & v (m+s) + [(m+s)2 – 4smq] 2s v qi = Dq = -sqi(1 - qi) + m(qi – q)

13. 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

15. trade-off: strong advantage on contaminated soil, but overgrown on clean soil w = Agrostis 0.16 - 0.32 Anthoxanthum 0.001 - 0.03 Plantago 0.03 - 0.28 Rumex 0.23 - 0.27 Xyield tolerant Xyield susceptible wij tolerant susceptible contaminated 1 0.01 – 0.05 soil metal-free 0.6 – 0.7 1 soil

16. 1 wtol 0 gene flow via wind pollination tolerant favored susceptible favored susceptible favored mine

17. adults seeds

18. 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