第二十五讲概率统计模型（1）——遗传模型

yunjiang · 发表于 2004-7-22 10:41:24

为了揭示生命的奥秘，现代人越来越重视遗传学的研究，特别是遗传特征的逐代传播，引起人们更多的重视.无论是人还是动植物都会将本身的特征遗传给下一代，这是因为后代继承了双亲的基因，形成了自己的基因对，而基因对则确定了后代所应具有的特征.以下仅就常染色体遗传方式建立遗传数学模型，来分析逐代总体的基因型分布趋势，为有目的的遗传控制提供依据。
　　问题分析 
　　所谓常染色体遗传，是指后代从每个亲体的基因中各继承一个基因从而形成自己的基因型.如果所考虑的遗传特征是由两个基因A和B控制的，那么就有三种可能的基因型：AA，AB和BB.例如，金鱼草是由两个遗传基因决定它开花的颜色，AA型开红花，AB型的开粉花，而BB型的开白花.这里的AA型和AB型表示了同一外部特征(红色)，则人们认为基因A支配基因B，也说成基因B对于A是隐性的.当一个亲体的基因型为AB，另一个亲体的基因型为BB，那么后代便可从BB型中得到基因B，从AB型中得到A或B，且是等可能性地得到。
　　问题：某植物园中一种植物的基因型为AA，AB和BB.现计划采用AA型植物与每种基因型植物相结合的方案培育植物后代，试预测，若干年后，这种植物的任一代的三种基因型分布情况。

yunjiang · 发表于 2004-7-22 10:41:36

模型假设
　　（1）按问题分析，后代从上一代亲体中继承基因A或B是等可能的,即有双亲体基因型的所有可能结合使其后代形成每种基因型的概率分布情况如表5－1。<

>
　　表5-1<TABLE medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt" cellSpacing=0 cellPadding=0 align=center border=1><TR align=middle><TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; 104: " vAlign=top rowSpan=2 ="139"><

>下一代基因型（n代）<

></TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; 324: ; mso-border-left-alt: solid windowtext .5pt" vAlign=top colSpan=6 ="432">上一代父-母基因型（n-1代）</TD></TR><TR><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">AA-AA</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">AA-AB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">AA-BB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">AB-AB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">AB-BB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">BB-BB</TD></TR><TR align=middle><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; 104: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="139">AA</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/2</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/4</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD></TR><TR align=middle><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; 104: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="139">AB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/2</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/2</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/2</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD></TR><TR align=middle><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; 104: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="139">BB</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">0</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/4</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1/2</TD><TD class=word style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; mso-border-left-alt: solid windowtext .5pt; 54: ; mso-border-top-alt: solid windowtext .5pt" vAlign=top ="72">1</TD></TR></TABLE>　　(2)以 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image002.gif"> 和 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image004.gif"> 分别表示第n代植物中基因型为AA，AB和BB的植物总数的百分率， <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image006.gif"> 表示第n代植物的基因型分布，即有
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image008.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image010.gif"> (5 .1)
　　特别当n=0时， <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image012.gif"> 表示植物基因型的初始分布(培育开始时所选取各种基因型分布)，显然有 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image014.gif">

yunjiang · 发表于 2004-7-22 10:41:50

<

>　　模型建立<

>
　　注意到原问题是采用AA型与每种基因型相结合，因此这里只考虑遗传分布表的前三列。
　　首先考虑第n代中的AA型，按上表所给数据，第n代AA型所占百分率为<

>
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image016.gif"> 
　　即第n-1代的AA与AA型结合全部进入第n代的AA型，第n-1代的AB型与AA型结合只有一半进入第n代AA型，第n-1代的BB型与AA型结合没有一个成为AA型而进入第n代AA型，故有
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image018.gif"> (5 .2)
　　同理，第n代的AB型和BB型所占有比率分别为
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image020.gif"> (5 .3)
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image022.gif"> (5 .4)
　　将(５ .2)、(５ .3)、(５ .4)式联立，并用矩阵形式表示，得到
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image024.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image026.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image028.gif"> (5 .5)
　　其中
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image030.gif"> 　　利用(5 .5)进行递推，便可获得第n代基因型分布的数学模型
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image032.gif"> (5 .6)
　　(5．6)式明确表示了历代基因型分布均可由初始分布 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image034.gif"> 与矩阵M确定。

yunjiang · 发表于 2004-7-22 10:42:02

<

>　　模型求解<

>
　　这里的关键是计算 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image036.gif"> .为计算简便，将M对角化，即求出可逆阵

，使 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image038.gif"> ，即有
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image040.gif"> 
　　从而可计算 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image042.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image044.gif"> 
　　其中 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image046.gif"> 为对角阵，其对角元素为M的特征值，P为M的特征值所对应的特征向量.分别为
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image048.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image050.gif"> <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image052.gif"> 
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image054.gif"> 
　　故有
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image056.gif"> 
　　即得
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image058.gif"> 
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image060.gif">

yunjiang · 发表于 2004-7-22 10:42:16

于是 <

>
　　 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image062.gif"> <

>
　　或写为<

>
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image064.gif"> 
　　由上式可见，当 <img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image066.gif"> 时，有
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image068.gif"> 
　　即当繁殖代数很大时，所培育出的植物基本上呈现的是AA型，AB型的极少，BB型不存在。

yunjiang · 发表于 2004-7-22 10:42:29

<

>　　模型分析<

>
　　1．完全类似地，可以选用AB型和BB型植物与每一个其它基因型植物相结合从而给出类似的结果.特别是将具有相同基因植物相结合，并利用前表的第1、4、6列数据使用类似模型及解法而得到以下结果：<

>
　　<img src="http://202.205.160.49:8080/media_file/rm/ip3/zhangxh/2004_03_01/sxjm_25/htm/sxjm25.files/image070.gif"> 
　　这就是说，如果用基因型相同的植物培育后代，在极限情形下，后代仅具有基因AA与BB，而AB消失了.2．本例巧妙地利用了矩阵来表示概率分布，从而充分利用特征值与特征向量，通过对角化方法解决了矩阵n次幂的计算问题，可算得上高等代数方法应用于解决实际的一个范例。

duanshumo · 发表于 2004-7-24 00:29:30

谢谢你的帖子

coeeoc · 发表于 2004-8-10 03:02:49

<

>谢谢

lf_storm · 发表于 2004-8-11 23:00:51

厉害啊，写了这么多

ywh_2163 · 发表于 2004-8-12 01:25:32

如果是随机交配呢？？[em06][em06]

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第二十五讲 概率统计模型（1）——遗传模型

第二十五讲概率统计模型（1）——遗传模型