22. Inbreeding. related measures: = coefficient of kinship, a measure of relatedness of individuals of a population; panmictic index, P = 1 F;

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1 . Inbreeding Inbreeding: maing beween relaives. has predicable consequences for gene and genoype frequencies; increases he frequency of homozygous genoypes a he expense of heerozygous genoypes; hus decreases heerozygosiy, geneic variance; similar in effec o: geneic drif; populaion subdivision (Wahlund effec; oher facors ha decrease he effecive populaion size, and hus increase he effec of geneic drif; variaion in populaion size over ime; skewed sex raios; non-random variaion in progeny/individual; in infinie populaions: can only arise by preferenial maing wih relaives (= nonrandom inbreeding; in finie populaions: have occasional maing beween relaives by chance, even wih random maing; = random inbreeding. Coefficien of inbreeding, : = probabiliy ha an individual receives wo alleles a a locus ha are idenical by descen (Maléco; equivalen concep: correlaion beween uniing gamees (Wrigh, ei. relaed measures: = coefficien of kinship, a measure of relaedness of individuals of a populaion; panmicic index, P = ; condiions: auozygous = alleles idenical by descen allozygous = alleles of independen origin = P(alleles idenical by descen = P(auozygous 0 = P(allozygous P(auozygous + P(allozygous = + ( =

2 . Inbreeding I. onrandom inbreeding ( Simples example: selfing (repeaed self-ferilizaion, as in many plans assume infinie populaion size; allele frequencies p and q remain consan, bu genoype frequencies change; proporion of heerozygoes decreased by half each generaion; requencies Generaion A A A A A A 0 D R D+ R D+ + 4 R D+ ( = p 0 R+ ( = q expeced heerozygosiy in generaion, under selfing: = ( 0 noe ha p, q remain consan even hough he genoype frequencies are changing. he magniude of he inbreeding effec ( is consan. Probabiliies of homozygosiy due o nonrandom inbreeding: assume iniial ardy-weinberg-casle frequencies; assume infinie populaion size, bu preferenial maing wih relaives (measured by ; Equilibrium genoype frequencies: req 0 P(allozygous + P(auozygous = req A A : p p (- + (p + pq ( = p = p ( + p A A : pq pq (- + 0 = pq ( A A : q q (- + (q + pq ( = q = q ( + q WC proporions Inbreeding Wahlund A A : p p + pq p + σ b A A : pq pq pq pq σ b A A : q q + pq q + σ b

3 . Inbreeding 3 or selfing plans: complee inbreeding, = ; equilibrium genoype frequencies: P = p + pq = p P = pq pq = 0 P = q + pq = q Incomplee inbreeding, 0 < < equilibrium heerozygosiy: 0 < P < pq Expeced heerozygoe freq p = 0.5 q = 0.5 Expeced heerozygoe freq p = 0.9 q = Inbreeding coefficien, Inbreeding coefficien, Populaion subdivision (he Wahlund effec represens a kind of nonrandom inbreeding in infinie populaions; gives rise o predicable deviaions from WC frequencies: genoype frequencies change, wih a reducion in heerozygosiy (geneic variance compared o he expeced WC proporions; bu here is no expeced change in allele frequencies due o inbreeding: P = P + P = ( p + pq + (pq pq = + + p pq pq pq = p + = p pq

4 . Inbreeding 4 II. Random inbreeding ( R Inbreeding due o chance in a finie populaion. Analogous o geneic drif, and he consequences are he same: changes in allele frequencies; no deviaions from WC genoype proporions. Probabiliies han an individual is auozygous: Generaion : R, = Generaion : R, = + R, Generaion 3: R,3 = + R, In general: R, = + R, R, = Random inbreeding: = ( R, Geneic drif: ( = pq σ (analogous o he drif model Thus random inbreeding and drif can be expressed in erms of one anoher: σ R, = pq σ = pq R,

5 . Inbreeding 5 Random inbreeding coefficien e Generaions 500 III. Toal inbreeding ( T Toal inbreeding is he accumulaion of boh nonrandom and random effecs, due, for example, o he presence of mae choice (e.g., assoraive maing in finie populaions. measured via he probabiliies of being allozygous: ( = ( ( T R Toal inbreeding of an individual can also be esimaed from a pedigree. The pedigree shows he acual hisory of maing, which migh be by design (non-random, by acciden (random, or by some combinaion of he wo. Esimaing oal inbreeding from a pedigree: idenify any ancesors in he pedigree ha are common o he moher and faher of he individual; race all circuis (pahs on he pedigree from he individual o he ancesor (via he faher and back again (via he moher; coun he number of ancesors in each circui (excluding he individual of ineres; he conribuion of each circui o he inbreeding coefficien is n ( ( = + A where n is he number of ancesors in he circui and A is he inbreeding coefficien of he common ancesor; he oal inbreeding coefficien of he individual is he sum of he s for all circuis. T pahs n ( ( A = +

6 . Inbreeding 6 Sample pedigrees

7 . Inbreeding 7 Summary of nonrandom and random inbreeding effecs: Effec ardy-weinberg proporions expeced? Allele-frequency changes expeced? Expec permanen consequences if sop inbreeding? o o onrandom inbreeding (infinie populaion o, WC proporions resored in single generaion Random inbreeding (finie populaion Yes, wihin subpopulaions o, across subpopulaions Yes, wihin subpopulaions o, across subpopulaions Yes, wihin subpopulaions (inbreeding boleneck o, across subpopulaions onrandom inbreeding (infinie, srucured populaions: P : p + pq = p ( + p P : pq pq = pq( P : q + pq = q ( + q = pq( = pq Random inbreeding (finie, unsrucured populaions: ( R, = ( σ = pq R, σ = pq σ = pq R, By analogy wih drif: = pq σ q, = pq pq = pq ( R, = ( R, 0 R, ( = 0 = 0

8 . Inbreeding 8 Measuremen of inbreeding coefficiens: Assume a populaion of consan (mean size across generaions, wih no selecion, muaion, or gene flow. The populaion need no be in ardy-weinberg proporions a any ime. In generaion, he genoype frequencies are: A A A A A A D R onrandom inbreeding ( is measured by he deviaion from ardy-weinberg proporions, based on he observed deficiency of heerozygoes in generaion. I is assumed o remain consan over ime. p = D + q = + R = pq ( = pq Random inbreeding ( R is assumed o increase over ime. I can be esimaed in hree differen ways (wo of which involve hisorical daa, eiher or q 0 : ( Measured by deviaions of p q from p 0 q 0 : pq = pq ( R R pq pq = = pq pq This is he mos precise esimae of random inbreeding because i explicily considers he iniial and final allele frequencies; however, he iniial allele frequencies are usually no known. The produc pq, of he weighed mean allele frequencies among loci (or populaions, is an esimae of p 0 q 0 [why?]. ( Based on he relaionship beween random inbreeding and geneic drif, R can be esimaed from σ pq, where σ is he variance in allele frequencies among loci (or replicae populaions in q q generaion and pq, he weighed mean allele frequencies among loci (or populaions, is an esimae of p 0 q 0.

9 . Inbreeding 9 (3 Esimaed from and : = R ( This is he leas precise esimae because i doesn ake ino accoun even he observed allele frequencies in generaion. Also, i requires knowledge of (or an esimae of. 3 Toal inbreeding ( T is: ( Measured by he deviaion of from p 0 q 0 : e = pq ( = pq ( ( = pq ( R T (a Given a se of replicae subpopulaions (or replicae loci assumed o have diverged from a common ancesral populaion: = pq ( ( T = pq T = = pq pq where, p, and q are he weighed means among replicaes. T (b Given R and : = pq ( ( = ( ( T R = ( ( T R T ( Calculaed direcly from pedigrees. T is he mean over all individuals in generaion.

10 Expeced Decreases in eerozygosiy Due o Populaion-Geneic Effecs Effec Populaion model Time componen across generaions Expeced proporion of heerozygoes Populaion Infinie Consan = pq σ b subdivision Geneic drif inie Cumulaive = pq σ q, Expeced decrease in heerozygosiy (addiive Expeced decrease in heerozygosiy (muliplicaive σ b q, σ onrandom Infinie Consan = pq ( pq ( pq ( inbreeding Random inbreeding inie Cumulaive = pq ( pq R, ( pq R, ( R,