Lecture 4. Heritability. Heritability: An Intuitive Approach First Definition

Transcription

1 Lecture Hertablty Hertablty: n Intutve pproac Frst enton Broa Sense: Proporton o te penotypc varaton ue to genetc causes H G Y Narro Sense: Proporton o te penotypc varaton ue to atve genetc eects Y Useul to etermne to at extent genetcs vs envronment mpact a trat Useul to etermne to at extent rectonal selecton can mprove a trat lternatvely, s te proporton o te total varaton attrbutable to erences n breeng values.

2 Perectly ertable trat Osprng Hegt Y R Precte Superorty o Osprng ll o te superorty o parent s passe to te osprng Pop Mean Y P Superorty o parents Parents Hegt Pop Mean Y P Y S 3 Estmaton o Hertablty: Full sbs x x x O O O O O O O k O k O k

3 From Lecture 3 Covarance Full sbs Number o IB 0 IB alleles IB alleles IB alleles Probablty o Sarng /6 8/6 /6 Contrbuton to varances 0 + Cov ( G, G O ) O Total covarancesum Probablty x contrbuton 8 ( )( ) + ( )( + ) Parttonng Varances nto Sources o Varaton NOV Least Squares Meto o Moments Lnear Moel μ + + j j Trat Value Penotype o te jt osprng rom te t amly + 3 Famly 6 3

4 Genetc Varance Equvalence Te penotypc covarance beteen members o te same group equals te varance among groups Note te subscrpt s te same Cov( tn _ amly) ( [( μ + + )(, μ + + )] (, ) + (, ) + (, ) + (, ) j k j j, k k ) j k 7 Wtn amly observaton correlate vs. uncorrelate Trat Value Correlate Trat Value Uncorrelate 3 Famly 3 Famly Correlate observatons tn a amly ncates tat, gven te amly mean, you kno sometng about te perormance o te nvual. Uncorrelate observatons tn amly: knolege o te amly mean tells you notng about perormance o te nvual. Tus amly means vary, ten nvuals tn amles are correlate. 8

5 Relatonsp o Estmate Varance Component t Causal Unerlyng Varance Components Covarance tn FamlyVarance mong Famles + Estmate te Varance mong Famles by NOV 9 NOV Computatonal Formulas 0 5

6 Meto o Moments Set Expecte mean squares equal to estmate mean squares an solve ˆ MS ˆ MS P MS n ˆ ˆ + ˆ + Varances Famly 3kg kg kg Beteen Famly Wtn Famly Famly kg 3kg 5kg + 6

7 Turkey Example Source ss ms E(ms) mong Famly Wtn Famly ˆ (.5 ) (.67) ˆ s.e.ormulas gven n notes Typcally very large 3 Neste Full-sb an Hal Sb μ + s + + jk j jk + + s 7

8 8 5 NOV Table 6 Components o Varance Covarance among members o a group equals te varance beteen groups Total varance can be parttone nto tat tn an among ull sb amles Ec + + From Lecture 3 Total Varance parttone by NOV HS s HS Wtn among + + s

9 Total Varance n terms o lnear moel an n terms o genetc components + + s Lnear Moel + + Genetc Eects E s + + Ec Es 7 Estmatng Genetc Components s ˆ s ( MS MS ) Mn s + + Ec ˆ ( MS MS ) n Es ˆ MS 8 9

10 Example: Table. 0 sres; 3 ams/sre; 0 osprng/am Source ms E(MS) sres s ams/(sres) tn ams s ( 0 ) P Estmatng parent osprng regresson p p pn + e o β 0 + βo p p o E o ( β ) o p on ( o, p ) ( ) p o μ + βo p ( p u) e + + ( e, e ) p o Wen s te envronmental covarance beteen parent osprng not ero? βo p 0 0

11 Regresson on One Parent: Example Butterat (kg) Parent am (X) Osprng augter (Y) X, 369 Y, 79 X 90, 7 X 76, 7 Y 76,7 90,7 (,369)(,79) 0 (,369) 0.96 Sex Lmte Trats must be multple by Because only one o te parents as measure Estmatng m parent osprng regresson m o E E ( β ) o mp ( β ) o mp mn on ( o, mp ) ( ) n [ (, ) + (, )] mp p o ( + ) o p p m + o μ + βo mp μ + e m + o, m + p [ (, ) + (, )] m o ( + ) ( o, p ) p o m P

12 Example cal egt a ay 08 Sre Parents am Parental verage (X) Osprng (Y) Computaton o X 3,69. 5 Y 3, 97 X,8,9. 7 X,0, 68 Y,0,68,8,9.7 ( 3,69.5)( 3,97) 0 ( 3,69.5) 0.797

13 Estmaton as Response to Selecton (Reale Hertablty) Example: Brolers 000 Brs egte at 7 eeks o age t an average egt o kg Te best 00 brs ere save or breeng an egte.kg Tese brs ere ranomly mate en mature an use to prouce te next generaton,500 progeny ere prouce an egte an average o.kg Wat as te reale ertablty? 5 Computaton o Reale Hertablty R R R Y Y R S Y Y P P

14 Examples o ertabltes Back Fat Tckness Pgs aly Gan Ltter se generally range. to.6, n breeng programs.35 s consere g,. s consere lo General tren: trats more closely relate to tness ave loer ertabltes Wy Hnt : at trat(s) oes natural selecton act on? Wat o te allele requences? Hnt : trats more closely relate to tness generally so eteross an H > 7 Problem set. Contnung rom te prevous problem set, Falconer (98) reporte a partally omnant gene n te mouse calle pg pygmy. t sx eeks o age, tey prouce te ollong average egt penotypes n grams (te actual egt o te eteroygote as, but t as reuce to 0 or ts example): + / + :, + / pg : 0, pg / pg : 6 I te populaton o mce s ranomly matng t p+ 0.3, q pg 0.7 ssumng no Envronmental Eects, at are te narro an broa sense ertabltes or ts trat? 8

15 Problems ) I or a gven trat te broa sense an narro sense ertabltes are as ollos, n eac c oul be more eectve at mprovng te trat, a breeng program, mprovng management, neter or bot? H.9,. H.,. H.9,.9 9 5