Genetics IN BRIEF

Assume: large population, random mating

Let: proportion of allele A = p

proportion of allele a = q

p + q = 1

Eg g s

Sperm

AA

p2

Aa

pq

Aa

pq

aa

q2

Aa x Aa

p2 + 2pq + q2

Hardy-Weinberg equilibrium p2 + 2pq + q2

MM Mn nn Total

Num. 1787 3037 1305 6129

M 3574 3037 0 6611

n 0 3037 2610 5647

M+n 3574 6074 2610 12258

p = 6611/12258 = .53932

q = 5647/12258 = .46068

Expect. p2=.2909 2pq=.4969 q2=.2122

Expect. # 1782.7 3045.6 1300.7

Χ2 = (1787-1782.7)2/1782.7 + (3037-3045.6)2/3045.6 + (1305-1300.7)2/1300.7

= 0.04887

Probability associated with this value and 1 d.f. = 0.90

Factors that cause populations to go out of HWE

Drift

Mutation

Immigration

Selection

Inbreeding/asexual reproduction

Founder effects

Bottlenecks

Inbreeding

Inbreeding coefficient (I)

Freq in population

Genotype With inbreeding With I=0 random mating

With I=1 complete

inbreeding

Not inbred Inbred

AA p2(1-I) pI p2 P

Aa 2pq(1-I) 2pq 0

aa q2(1-I) qI q2 q

Fst = fixation index or amount of genetic differentiation among subpopulations

Allele Freq. Subpop 1

Subpop 2

Hs Sp1

Hs

Sp2_

pi

Ht Fst

A1 P1 .011 .150 .0218 .255 .0805 .1480 .0652

A2 P2 .169 .769 .2809 .3553 .469 .4981 .3614

A3 P3 .801 .081 .3188 .1489 .441 .4930 .5257

A4 P4 .019 0 .0373 0 .0095 .0188 .0096

Fst .3878

Hs = 2pi(1-pi)

Ht=2pi(1-pi)

Fst=(Ht-Hs)/Ht

Fst=∑pi(1-pi)Fst/ ∑pi(1-pi)

.05-.15 = moderate differentiation

.15-.25 = great differentiation

Other genetic terms and calculations:

Average Heterozygosity

Genetic Diversity

Genetic Distance

Relatedness

           

Class N Ho He t- test F

One-leaf 37 0.211 0.346 7.313* 0.390

(0.047) (0.045)

Three-leaf NF 115 0.238 0.390

10.484* 0.390

(0.031) (0.032)

Flowering 110 0.256 0.402 2.584* 0.363

(0.061) (0.031)

Entire pop. 262 0.242 0.389 9.231* 0.381

(0.043) (0.031)

Example: Trillium maculatum