第5講-近交系數(shù)與親緣系數(shù)-群體與數(shù)量遺傳學(xué)-教課件

群體數(shù)量遺傳學(xué)第5講近交系數(shù)與親緣系數(shù)內(nèi)容一、個(gè)體的近交系數(shù)二、親緣系數(shù)三、群體近交系數(shù)的估計(jì)四、近交的遺傳效應(yīng)一、個(gè)體的近交系數(shù)近交：有親緣關(guān)系（有共同祖先）的個(gè)體進(jìn)行交配。有限群體中總是存在近交。有親緣關(guān)系（有共同祖先）的個(gè)體可能都攜帶共同祖先某一基因的復(fù)制品。近交產(chǎn)生的后代在某一位點(diǎn)上的2個(gè)等位基因可能是上一代中一個(gè)相同基因的復(fù)制品。124816..

N=(2)tt=20N=1048576一、個(gè)體的近交系數(shù)個(gè)體的近交系數(shù)FX是組成該個(gè)體的兩個(gè)配子之間的相關(guān)系數(shù)(FX=rg’1g1)。配子g’1到配子g1（配子世代）的通徑系數(shù)=1/2xg1g2FXaag’1g’2FAbbA個(gè)體的近交系數(shù)xg1g2FXaag’1g’2FAbbA個(gè)體的近交系數(shù)

n1=X的一個(gè)親本到共同祖先A的世代數(shù)；

n2=X的另外一個(gè)親本到共同祖先A的世代數(shù)；N=n1+n2+1:X的雙親通過共同祖先A的整個(gè)通徑鏈上所有的個(gè)體數(shù)（包括雙親）xDAS個(gè)體的近交系數(shù)如果X的雙親還有其他共同祖先,則rg’1g1就等于通過每一個(gè)共同祖先的全部通徑鏈的系數(shù)的總和。舉例著名短角品種近交公牛RoanGauntlet的系譜圖有兩個(gè)共同祖先A1和A2S-G-A2-DN=4S-M-A2-DN=4S-G-Da-A1-C1-Ca-DN=7S-M-M’-A1-C1-Ca-DN=7xA1SA2C1M’DaGMCaDRoanGauntletS-G-A2-DN=4S-M-A2-DN=4S-G-Da-A1-C1-Ca-DN=7S-M-M’-A1-C1-Ca-DN=7xA1SA2C1M’DaGMCaDRoanGauntlet二、親緣系數(shù)任何兩個(gè)個(gè)體的親緣系數(shù)即它們間的遺傳相關(guān)（親緣相關(guān)）。合子X’到合子X(合子世代)的通徑系數(shù)ba:xg1FaaX’g’1g’2F’a’a’b二、親緣系數(shù)xg1FaA’g‘1F’AnFnba’anFn-1bn-1an-1二、親緣系數(shù)SFSa1ADa2FDFA當(dāng)A為S的n1代祖先；同時(shí)為D的n2代祖先。二、親緣系數(shù)當(dāng)S和D有多個(gè)共同祖先時(shí)，rSD等于通過每一個(gè)共同祖先的全部通徑鏈的系數(shù)的和。在隨機(jī)交配的群體中，F(xiàn)S＝FD＝FA親緣系數(shù)與近交系數(shù)的關(guān)系SFXADXRSD作業(yè)1用通徑分析法計(jì)算下列系譜中個(gè)體8的近交系數(shù)以及個(gè)體6和7之間的親緣系數(shù)。87654321三、群體近交系數(shù)的估計(jì)1、按系譜逐個(gè)計(jì)算2、親緣協(xié)方差表法(Emiketal.,1949)Si,Sj:分別是個(gè)體i和個(gè)體j的父親Di,Dj:分別是個(gè)體i和個(gè)體j的母親一個(gè)已知個(gè)體和一個(gè)未知個(gè)體的親緣協(xié)方差為0。舉例一系譜圖如下：

ABEGFCH1234567父親11446母親235個(gè)體1234567♀♂♂♀♀♂父親S11446母親D235個(gè)體i12345671.G10.50.500.250.250.252.F10.2500.50.1250.31253.E100.1250.50.31254.H10.50.50.55.E10.31250.656256.B10.656257.A1.15625個(gè)體i12345671.G00.50.500.250.250.21622.F00.2500.50.1250.27033.E000.1250.50.27034.H00.50.50.43245.E00.31250.56766.B00.56767.A0.15625作業(yè)2利用親緣協(xié)方差表法計(jì)算下列公牛系譜中所有個(gè)體的近親系數(shù)和兩兩之間的親緣系數(shù)。(建議用Matlab編程)xA1SA2C1M’DaGMCaDRoanGauntletIDSDIDSDA100100A200200DaA10310M'A10410C1A10510GA2Da623MA2M'724CaC10850DA2Ca928SGM1067XSD11109p=[1 0 0;2 0 03 1 04 1 05 1 06 2 37 2 48 5 09 2 810 6 711 10 9];cov=zeros(11);fori=1:11;forj=i:11if(i==j&p(i,2)*p(i,3)=0)cov(i,i)=1;endif(i==j&p(i,2)*p(i,3)>0)cov(i,i)=1+cov(p(i,2),p(i,3))/2;endifj>i&p(j,2)=0&p(j,3)=0cov(i,j)=0;endifj>i&p(j,2)>0&p(j,3)=0cov(i,j)=cov(i,p(j,2))/2;endifj>i&p(j,2)=0&p(j,3)>0cov(i,j)=cov(i,p(j,3))/2;endifj>i&p(j,2)*p(j,3)>0cov(i,j)=(cov(i,p(j,2))+cov(i,p(j,3)))/2;end

cov(j,i)=cov(i,j);end;endpedigree=zeros(11);fori=1:11;forj=i:11

if(i==j)pedigree(i,i)=cov(i,i)-1;end

if(j>i)pedigree(i,j)=cov(i,j)/sqrt(cov(i,i)*cov(j,j));end

pedigree(j,i)=pedigree(i,j);end;end親緣方差協(xié)方差矩陣123456789101111.000000.50000.50000.50000.25000.25000.25000.12500.25000.1875201.00000000.50000.500000.50000.50000.500030.500001.00000.25000.25000.50000.12500.12500.06250.31250.187540.500000.25001.00000.25000.12500.50000.12500.06250.31250.187550.500000.25000.25001.00000.12500.12500.50000.25000.12500.187560.25000.50000.50000.12500.12501.00000.31250.06250.28130.65630.468870.25000.50000.12500.50000.12500.31251.00000.06250.28130.65630.468880.250000.12500.12500.50000.06250.06251.00000.50000.06250.281390.12500.50000.06250.06250.25000.28130.28130.50001.00000.28130.6406100.25000.50000.31250.31250.12500.65630.65630.06250.28131.15630.7188110.18750.50000.18750.18750.18750.46880.46880.28130.64060.71881.1406近交系數(shù)與親緣系數(shù)12345678910111000.50000.50000.50000.25000.25000.25000.12500.2325050000.500000.50000.46500.468230.5000000.25000.25000.50000.12500.12500.06250.29060.175640.500000.250000.25000.12500.50000.12500.06250.29060.175650.500000.25000.250000.12500.12500.50000.25000.11620.175660.25000.50000.50000.12500.125000.31250.06250.28130.61030.438970.25000.50000.12500.50000.12500.312500.06250.28130.61030.438980.250000.12500.12500.50000.06250.062500.50000.05810.263390.12500.50000.06250.06250.25000.28130.28130.500000.26160.5998100.23250.46500.29060.29060.11620.61030.61030.05810.26160.15630.6259110.17560.46820.17560.17560.17560.43890.43890.26330.59980.62590.1406三、群體近交系數(shù)的估計(jì)2、閉鎖小群體近交系數(shù)的估計(jì)假設(shè)：基礎(chǔ)群(無近交個(gè)體)由N個(gè)個(gè)體(雌雄個(gè)體數(shù)相等)組成。N個(gè)個(gè)體產(chǎn)生2N種不同的基因。配子結(jié)合產(chǎn)生合子時(shí)，每一種基因都有1/(2N)概率和同一基因的復(fù)制品配對形成（同一基因的）純合子。每一世代(同一基因)純合子的增加概率=近交系數(shù)增量(ΔF)舉例：雌雄同體的海洋生物A1A2A3A4A1A2A3A4A1A2A3A4基礎(chǔ)群配子1世代A1A1A1A1A2A2A3A4A1A2A3A4A2A1A2A2A3A1A2A3A3A3A3A4A4A1A2A4A3A4A4A4N＝2A1A2A3A4XY舉例：雌雄同體的海洋生物A1A4A3A1A1A4A3A1A1A4A3A1配子1世代A1A1A1A1A4A4A3A1A1A4A3A1A2A1A4A4A3A1A4A3A3A3A3A1A1A1A4A1A3A1A1A1N＝2A1A4A3A12世代舉例：雌雄同體的海洋生物A1A2A3A4A1A2A3A4A1A2A3A4基礎(chǔ)群配子1世代A1A1A1A1A2A2A3A4A1A2A3A4A2A1A2A2A3A1A2A3A3A3A3A4A4A1A2A4A3A4A4A4N＝2A1A2A3A4XY舉例：雌雄同體的海洋生物A1A1A2A1A1A1A2A1A1A1A2A1配子1世代A1A1A1A1A1A1A2A1A1A1A2A1A1A1A1A1A2A1A1A2A2A2A2A1A1A1A1A1A2A1A1A1N＝2A1A1A2A12世代每一世代同一基因純合子的增加概率=近交系數(shù)增量(ΔF)t世代群體的近交系數(shù)Ft=同一基因純合子的概率。t-1世代配子g1,g2,…,gi,…,gj,…g2N形成gigi合子(i=1→2N):概率=(1/2N)2×2N=1/2N=ΔF形成gigj合子(i,j=1→2N;i≠j):概率=1-1/2Ngigj合子為同一基因純合子的概率=gi和gj

為同一基因的概率=t-1世代同一基因純合子的概率=Ft-1Ft=1/2N+(1-1/2N)×Ft-1

t世代群體的近交系數(shù)Ft每一世代群體規(guī)模保持不變

t世代群體的近交系數(shù)Ft如果連續(xù)世代中規(guī)模不等,怎么辦？應(yīng)對每一世代的規(guī)模進(jìn)行調(diào)和平均。三、群體近交系數(shù)的估計(jì)當(dāng)群體中雌雄個(gè)體數(shù)不相等時(shí)，怎么辦？應(yīng)進(jìn)行調(diào)和平均。Nf=母畜數(shù)量；Nm=公畜數(shù)量Ne:群體有效規(guī)模在實(shí)際群體中，當(dāng)Nf

>>Nm舉例一畜群,基礎(chǔ)群近交系數(shù)為0,連續(xù)9個(gè)世代保持閉瑣繁育,而且公畜數(shù)始終保持2頭。估計(jì)當(dāng)前這個(gè)群體的近交系數(shù)。作業(yè)3一個(gè)閉鎖群體，每代隨機(jī)留10母3公，經(jīng)過5代，估計(jì)平均近交系數(shù)，經(jīng)過50代又達(dá)多少？一個(gè)閉鎖群體，每代隨機(jī)留10母3公，經(jīng)過5代，估計(jì)平均近交系數(shù)，經(jīng)過50代又達(dá)多少？三、群體近交系數(shù)的估計(jì)3、連續(xù)規(guī)則近交下的群體近交系數(shù)(1)連續(xù)全同胞交配(2)連續(xù)半同胞交配(3)連續(xù)與同一個(gè)體回交回顧：近交系數(shù)與親緣系數(shù)的關(guān)系三、群體近交系數(shù)的估計(jì)3、連續(xù)規(guī)則近交下的群體近交系數(shù)(1)連續(xù)全同胞交配N代N-1代N-2代r(n-1)r(n-2)P1P2三、群體近交系數(shù)的估計(jì)N代N-1代N-2代r(n-1)r(n-2)P1P23、連續(xù)規(guī)則近交下的群體近交系數(shù)(1)連續(xù)全同胞交配三、群體近交系數(shù)的估計(jì)3、連續(xù)規(guī)則近交下的群體近交系數(shù)(2)連續(xù)半同胞交配N代N-1代N-2代r(n-1)r(n-2)P1P2三、群體近交系數(shù)的估計(jì)3、連續(xù)規(guī)則近交下的群體近交系數(shù)(3)連續(xù)與同一個(gè)體回交A是N-1世代及N世代個(gè)體的父親N代N-2代N-1代rA(n-2)P1a2a1P2AA與n-1世代個(gè)體的親緣系數(shù)N代N-2代N-1代rA(n-2)P1a2a1P2AN代N-2代N-1代rA(n-2)P1a2a1P2A小結(jié)

連續(xù)規(guī)則近交下的群體近交系數(shù)(1)連續(xù)全同胞交配(2)連續(xù)半同胞交配(3)連續(xù)與同一個(gè)體A回交連續(xù)規(guī)則近交下各世代近交系數(shù)世代全同胞交配半同胞交配連續(xù)回交(FA=0)000010.250.1250.2520.3750.218750.37530.50.3046880.437540.593750.3808590.4687550.6718750.448730.48437560.7343750.5091550.49218870.7851560.5629580.49609480.8261720.6108630.49804790.8593750.6535170.499023100.886230.6914950.499512四、近交的遺傳效應(yīng)世代AAAa

aa0P0H0Q01P0+(1/4)H0(1/2)H0Q0+(1/4)H02P0+(1/4)H0+(1/8)H0(1/4)H0Q0+(1/4)H0+(1/8)H03P0+(1/4)H0+(1/8)H0+(1/16)H0(1/8)H0Q0+(1/4)H0+(1/8)H0+(1/16)H0

NP0+(1/2)[1-(1/2)n]H0(1/2)nH0Q0+(1/2)[1-(1/2)n]H0舉例世代AAAa

aa001010.25000.50000.250020.37500.2500.375030.43750.12500.437540.46880.06250.4688p

q0.50.50.50.50.50.50.50.50.50.5四、近交的遺傳效應(yīng)雜合率（H）：Hn＝H0（1-Fn）Hn:n世代的雜合子頻率H0:起始代的雜合子頻率Fn

：n世代的群體近交系數(shù)四、近交的遺傳效應(yīng)1、有限群體中每一世代雜合率的變化四、近交的遺傳效應(yīng)1、有限群體中每一世代雜合率的變化不同規(guī)模、起始雜合率時(shí)

各世代雜合率的變化四、近交的遺傳效應(yīng)2、連續(xù)規(guī)則近交下的群體雜合率變化(1)連續(xù)全同胞交配N代N-1代N-2代r(n-1)r(n-2)P1P2四、近交的遺傳效應(yīng)2、連續(xù)規(guī)則近交下的群體雜合率變化(2)連續(xù)半同胞交配N代N-1代N-2代r(n-1)r(n-2)P1P2四、近交的遺傳效應(yīng)2、連續(xù)規(guī)則近交下的群體雜合率(3)連續(xù)與同一個(gè)體回交N代N-2代N-1代rA(n-