近亲繁殖群体的信息论模型研究
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摘要
群体遗传学是研究生物群体的遗传结构及其变化规律的遗传学分支学科。生物进化
从基因水平上看就是群体遗传结构的变化，群体遗传学的发展和生物进化理论密切相
关。群体的遗传变异受多种因子的影响，进化中许多重要问题是无法通过对自然群体或
实验群体的观察或实验来解决的，要研究群体遗传变异的程度，进行的速度，限制的条
件，进行数学处理是必不可少的。
数学模型是对有关系统的特性的高度概括，以往群体遗传学中的数学模型基本上是
统计学模型。群体遗传学所研究的世代传递过程本身也是一个信息传递的过程，因此信
息论模型也应该是研究该门学科的一种数学模型。1998 年以来，袁志发、郭满才等提出
用 Shannon信息熵作为度量群体遗传多样性的数量指标，为群体遗传学的发展提供了新
思路。本研究正是在他们工作的基础上，应用信息论模型进一步研究群体遗传学中近亲
繁殖群体的有关问题。
当信息论方法用于具体学科时，尽管信息的基本统计学性质本质是一样的，但在具
体学科中会有其特殊的具体内容。在本研究中中，始终坚持下面的两个原则：
１．当涉及到与频率分布有关的 Ｓｈａｎｎｏｎ 信息熵、互信息等概念及推理时，总是把
正反交分开，并且假定正反交频率相等。
２．一切应用到群体遗传学中的信息概念、公式以及约束条件等均不依赖取值，与
取值无关。
通过对近亲繁殖群体的信息论模型研究，得出以下主要结论：
1．基因型信息熵是关于基因型频率改变量或近交系数的单调递减的上凸函数。从
随机交配下的平衡群体开始，在近亲繁殖制度下，其基因型信息熵 S(G)逐代减少，且
满足S(G1) = S(G0 ) 2 ≤ S(G) ≤ S(G0)；经过足够多的世代后，基因型信息熵S(G)逐代减
少的趋势越来越慢，最终趋于固定值，群体达到近亲繁殖下的平衡；随着世代交替中基
因型信息熵S(G)的逐代减少，群体的遗传多样性程度也逐渐减小；基因型信息熵S(G)趋
于固定值的过程，也是群体趋向于近亲繁殖平衡的过程。
II 近亲繁殖群体的信息论模型研究
2．配子间互信息是关于基因型频率改变量或近交系数的单调递增的上凹函数。从
随机交配下的平衡群体开始，在近亲繁殖制度下，配子间互信息 I(X,Y)逐代增加，且
满足0≤ I(X,Y) ≤ S(X ) = S(Y) = S(A) = S(G1) = S(G0) 2；经过足够多的世代后，配子间
互信息 I(X,Y)逐代增加的趋势越来越慢，最终趋于固定值，群体达到近亲繁殖下的平
衡。
3．从随机交配下的平衡群体开始，在近亲繁殖制度下，配偶间的基因型联合信息
熵逐代减少。配偶间互信息I(GX (t),GY (t))并不一定是关于世代数t的单调函数，但满足
0 ≤ I(GX (t), GY(t)) ≤ S(G0)。
4．母子间基因型联合信息熵 S(G(t)G(t +1)) 是关于世代数 t的减函数。从随机交配
下的平衡群体开始施以自交比例为w的近亲繁殖，则在世代交替中，母子间的基因型联
合信息熵逐代减少；母子间的基因型联合信息熵满足m ≤ S(G(t)G(t +1)) ≤ M ，其中
m = lim S(G(t)G(t +1)) = S(G(∞)G(∞))， M = S(G( G( )，m 的意义是：近亲繁殖的平
0) 1)
t→∞
衡状态下母子间的基因型联合信息熵；随世代交替，母子间基因型联合信息熵的变化率
逐渐趋向于零，直到群体平衡。
5．定义并讨论了强相对基因型信息熵、弱相对基因型信息熵、强近交关联信息系
数、弱近交关联信息系数等指标，用以进一步刻画群体的遗传、变异。
Population genetics which study mainly on genetic structure of biological population and
its disciplinarian is the branch subject of genetics. From the aspect of gene standard,
biological evolution is the change of genetic structure of population. The development of
population genetics relates to the theory of biological evolution closely. Population genetic
variation is affected by many factors. It is difficult to solve many important problems only by
the observation or experiment to natural population or experimental population in evolution.
So mathematical method is absolutely necessary to research on the degree of genetic variation,
the evolutionary speed, and the limited condition.
Mathematical model is the high summary about some property of a certain studying
system. Beforehand mathematical model in population genetics is basically statistic model.
But in fact, hereditary process itself is the process of informational pass. So information
model should be also applied to the genetic science as another mathematical method. Since
1998, Prof. Yuan Zhi-fa and Prof. Guo Man-cai et al. argue that Shannon entropy can be used
as the metrical indexof genetic diversity, providing a new method for the development of
population genetics. The study will apply information model to further discuss some problems
on inbreeding population.
When information method is applied in the other subjects, although basic statistic
property of information is the same, it holds special content in different subjects. In this study,
the two principles following are observed from beginning to end:
1．We always suppose that reciprocal crosses are divided, and that the frequency of
reciprocal crosses is the same, when Shannon entropy and interentropy related to distribution
of frequency are involved.
2．All information concepts, formula and limited condition in population genetics have
nothing to do with the value of frequency.
According to studying on inbreeding populationwith the information model, the main
IV 近亲繁殖群体的信息论模型研究
results following are given:
1．Genotype entropy is monotonically decreasing and convex function by the genotype
frequency or inbreeding coefficient in inbreeding system. From the beginning of equilibrium
population of random mating system, in inbreeding system, its genotype entropy decreases by
generation number, meeting: S(G1) = S(G0 ) 2 ≤ S(G) ≤ S(G0); after enough generations, the
genotype entropy decreases by generation becomes slower and slower, finally tends to fixed
value, population reaches equilibrium of inbreeding; with the decrease of genotype entropy,
the genetic diversity degree of population also decreases; the process that genotype entropy
tends to fixed value also is the process that population tends to inbreeding equilibrium.
2．Interentropy among gametes is monotonically increasing concave function by
genotype frequency or inbreeding coefficient. From the beginning of equilibrium of random
matting system, in inbreeding system, interentropy among gametes increases by generation
number, meeting:0 ≤ I(X,Y) ≤ S(X ) = S(Y) = S(A) = S(G1) = S(G0) 2 ; after enough genera-
tion, the interentropy among gametes increases by generation becomes slower and slower,
finally tends to the fixed value, population reaches inbreeding equilibrium.
3．Associated genotype entropy between parents is monotonically decreasing function by
generation number. Inter-entropy between parents is not always monotonically function about
generation numbers, but meeting:0 ≤ I(GX (t),GY (t)) ≤ S(G0).
4．The associated entropy between a female genotypes and its descendant genotypes is
monotonic- ally decreasing function about generation number. From the beginning of
equilibrium of random mating system, inbreeding is given in mating proportion to w, in
alternate generation, the associated entropybetween a female genotypes and its descendant
genotypes will decrease by generation, and
从基因水平上看就是群体遗传结构的变化，群体遗传学的发展和生物进化理论密切相
关。群体的遗传变异受多种因子的影响，进化中许多重要问题是无法通过对自然群体或
实验群体的观察或实验来解决的，要研究群体遗传变异的程度，进行的速度，限制的条
件，进行数学处理是必不可少的。
数学模型是对有关系统的特性的高度概括，以往群体遗传学中的数学模型基本上是
统计学模型。群体遗传学所研究的世代传递过程本身也是一个信息传递的过程，因此信
息论模型也应该是研究该门学科的一种数学模型。1998 年以来，袁志发、郭满才等提出
用 Shannon信息熵作为度量群体遗传多样性的数量指标，为群体遗传学的发展提供了新
思路。本研究正是在他们工作的基础上，应用信息论模型进一步研究群体遗传学中近亲
繁殖群体的有关问题。
当信息论方法用于具体学科时，尽管信息的基本统计学性质本质是一样的，但在具
体学科中会有其特殊的具体内容。在本研究中中，始终坚持下面的两个原则：
１．当涉及到与频率分布有关的 Ｓｈａｎｎｏｎ 信息熵、互信息等概念及推理时，总是把
正反交分开，并且假定正反交频率相等。
２．一切应用到群体遗传学中的信息概念、公式以及约束条件等均不依赖取值，与
取值无关。
通过对近亲繁殖群体的信息论模型研究，得出以下主要结论：
1．基因型信息熵是关于基因型频率改变量或近交系数的单调递减的上凸函数。从
随机交配下的平衡群体开始，在近亲繁殖制度下，其基因型信息熵 S(G)逐代减少，且
满足S(G1) = S(G0 ) 2 ≤ S(G) ≤ S(G0)；经过足够多的世代后，基因型信息熵S(G)逐代减
少的趋势越来越慢，最终趋于固定值，群体达到近亲繁殖下的平衡；随着世代交替中基
因型信息熵S(G)的逐代减少，群体的遗传多样性程度也逐渐减小；基因型信息熵S(G)趋
于固定值的过程，也是群体趋向于近亲繁殖平衡的过程。
II 近亲繁殖群体的信息论模型研究
2．配子间互信息是关于基因型频率改变量或近交系数的单调递增的上凹函数。从
随机交配下的平衡群体开始，在近亲繁殖制度下，配子间互信息 I(X,Y)逐代增加，且
满足0≤ I(X,Y) ≤ S(X ) = S(Y) = S(A) = S(G1) = S(G0) 2；经过足够多的世代后，配子间
互信息 I(X,Y)逐代增加的趋势越来越慢，最终趋于固定值，群体达到近亲繁殖下的平
衡。
3．从随机交配下的平衡群体开始，在近亲繁殖制度下，配偶间的基因型联合信息
熵逐代减少。配偶间互信息I(GX (t),GY (t))并不一定是关于世代数t的单调函数，但满足
0 ≤ I(GX (t), GY(t)) ≤ S(G0)。
4．母子间基因型联合信息熵 S(G(t)G(t +1)) 是关于世代数 t的减函数。从随机交配
下的平衡群体开始施以自交比例为w的近亲繁殖，则在世代交替中，母子间的基因型联
合信息熵逐代减少；母子间的基因型联合信息熵满足m ≤ S(G(t)G(t +1)) ≤ M ，其中
m = lim S(G(t)G(t +1)) = S(G(∞)G(∞))， M = S(G( G( )，m 的意义是：近亲繁殖的平
0) 1)
t→∞
衡状态下母子间的基因型联合信息熵；随世代交替，母子间基因型联合信息熵的变化率
逐渐趋向于零，直到群体平衡。
5．定义并讨论了强相对基因型信息熵、弱相对基因型信息熵、强近交关联信息系
数、弱近交关联信息系数等指标，用以进一步刻画群体的遗传、变异。
Population genetics which study mainly on genetic structure of biological population and
its disciplinarian is the branch subject of genetics. From the aspect of gene standard,
biological evolution is the change of genetic structure of population. The development of
population genetics relates to the theory of biological evolution closely. Population genetic
variation is affected by many factors. It is difficult to solve many important problems only by
the observation or experiment to natural population or experimental population in evolution.
So mathematical method is absolutely necessary to research on the degree of genetic variation,
the evolutionary speed, and the limited condition.
Mathematical model is the high summary about some property of a certain studying
system. Beforehand mathematical model in population genetics is basically statistic model.
But in fact, hereditary process itself is the process of informational pass. So information
model should be also applied to the genetic science as another mathematical method. Since
1998, Prof. Yuan Zhi-fa and Prof. Guo Man-cai et al. argue that Shannon entropy can be used
as the metrical indexof genetic diversity, providing a new method for the development of
population genetics. The study will apply information model to further discuss some problems
on inbreeding population.
When information method is applied in the other subjects, although basic statistic
property of information is the same, it holds special content in different subjects. In this study,
the two principles following are observed from beginning to end:
1．We always suppose that reciprocal crosses are divided, and that the frequency of
reciprocal crosses is the same, when Shannon entropy and interentropy related to distribution
of frequency are involved.
2．All information concepts, formula and limited condition in population genetics have
nothing to do with the value of frequency.
According to studying on inbreeding populationwith the information model, the main
IV 近亲繁殖群体的信息论模型研究
results following are given:
1．Genotype entropy is monotonically decreasing and convex function by the genotype
frequency or inbreeding coefficient in inbreeding system. From the beginning of equilibrium
population of random mating system, in inbreeding system, its genotype entropy decreases by
generation number, meeting: S(G1) = S(G0 ) 2 ≤ S(G) ≤ S(G0); after enough generations, the
genotype entropy decreases by generation becomes slower and slower, finally tends to fixed
value, population reaches equilibrium of inbreeding; with the decrease of genotype entropy,
the genetic diversity degree of population also decreases; the process that genotype entropy
tends to fixed value also is the process that population tends to inbreeding equilibrium.
2．Interentropy among gametes is monotonically increasing concave function by
genotype frequency or inbreeding coefficient. From the beginning of equilibrium of random
matting system, in inbreeding system, interentropy among gametes increases by generation
number, meeting:0 ≤ I(X,Y) ≤ S(X ) = S(Y) = S(A) = S(G1) = S(G0) 2 ; after enough genera-
tion, the interentropy among gametes increases by generation becomes slower and slower,
finally tends to the fixed value, population reaches inbreeding equilibrium.
3．Associated genotype entropy between parents is monotonically decreasing function by
generation number. Inter-entropy between parents is not always monotonically function about
generation numbers, but meeting:0 ≤ I(GX (t),GY (t)) ≤ S(G0).
4．The associated entropy between a female genotypes and its descendant genotypes is
monotonic- ally decreasing function about generation number. From the beginning of
equilibrium of random mating system, inbreeding is given in mating proportion to w, in
alternate generation, the associated entropybetween a female genotypes and its descendant
genotypes will decrease by generation, and
引文
[1] 储明星. 数量遗传学[M]. 北京:中国农业出版社,2000.
[2] 戴君惕,王身立. 遗传分析方法[M]. 长沙:湖南科技出版社,1989.
[3] 傅祖芸. 信息论基础理论及应用[M]. 北京:电子工业出版社,2001.
[4] 郭满才,解小莉,刘建军,等. 复等位基因平衡群体熵的性质[J]. 西北农林科技大学学
报(自然科学版), 2002,30(4):119-122.
[5] 郭满才,宋世德,周静芋,等. 非平衡群体基因变异测量的 Shannon信息量方法[J]. 生
物数学学报,2001,16(3):341-347.
[6] 郭满才,袁志发,陈宏,等. 陕西四个黄牛群体遗传变异的 Shannon信息量分析[J]. 黄
牛杂志,2003,29(1):22-24.
[7] 郭满才,袁志发,陈宏,等. 遗传多样性指标体系研究[J].Animalbiotechnologybulletin,
2002, 8(1):359-364.
[8] 郭满才. 群体遗传变异的信息学模型研究(西北农林科技大学博士论文),2002,5.
[9] 郭平仲. 群体遗传学导论[M]. 北京:农业出版社,1993,5.
[10] 郭平仲. 数量遗传分析[M]. 北京:北京师范学院出版社,1987.
[11] 胡上序,陈德钊. 观测数据的分析与处理[M]. 杭州:浙江大学出版社,2002.
[12] 贾世搂. 信息理论基础[M]. 哈尔滨:哈尔滨工业大学出版社,2001.
[13] 解小莉,郭满才,张宏礼,等. 两对等位基因群体熵的性质[J]. 生物数学学报,2003,
18(4):482-486.
[14] 兰斌,等,译. 遗传分析导论[M]. 西安:陕西人民教育出版社,1990.
[15] 兰斌,袁志发译,马育华校. 数量遗传学的数学理论[M]. 北京:农业出版社,1991.
[16] 李宝健. 展望 21 世纪的生命科学[J]. 生命科学,2000,12(1):37-40.
[17] 李难. 进化论教程[M]. 北京:高等教育出版社,2001.
[18] 刘建军,郭满才,解小莉,等. 性连锁群体平衡的信息模型研究[J]. 西北农林科技大学
学报(自然科学版), 2002,30(5):114-116.
[19] 刘祖洞. 遗传学(上,下)[M]. 北京:高等教育出版社,2001,5.
[20] 鲁晨光. 广义信息论[M]. 合肥:中国科学技术大学出版社,1993.
[21] [美]C.C.L.著,吴仲贤译. 群体遗传学[M]. 北京:中国农业出版社,1981.
[22] [美]根井正利. 分子群体遗传学与进化论[M]. 北京:农业出版社,1983.
[23] 匿名. 进化论的进化. 参考消息[J],2001,08,19.
[24] 裴新澍. 生物进化控制论[M]. 北京:科学出版社,1998.
[25] [日]大羽 滋著,赵敏,孙勇如,李良材译. 群体遗传[M]. 北京:科学出版社,1983.
参 考 文 献75
[26] [日]向井辉美著,隋文彬,孙广芝译. 群体遗传学[M]. 吉林:科学技术出版社,1984.
[27] 盛志廉,陈瑶生. 数量遗传学[M]. 北京:科学出版,2001.
[28] 舒炜光,张之沧. 重建与优选[M]. 北京:人民出版社,1987.
[29] 孙之荣译,Minoru Kanehisa 著. 后基因组信息学[M]. 北京:清华大学出版社,2002.
[30] 童克中. 基因及其表达[M]. 北京:科学出版社,2002.
[31] 汪小龙,袁志发,郭满才,等. 最大信息熵原理与群体遗传平衡[J]. 遗传学报 2002,29
(6) :562-564.
[32] 王金良. 家畜近亲繁殖群体的遗传组成分析[J]. 畜牧兽医学报,1995,26(6):500-505.
[33] 王身立,许康. 系统科学的产生是历史的必然[J]. 自然辩证法研究,1990,6(2):42-46.
[34] 王身立. 基因研究 140 年大事年表[J]. 湖南师范大学自然科学学报,2001,24(1):69-77.
[35] 王身立. 控制论与信息论在遗传学中的应用Ⅲ: 群体融合对基因型熵变与表型熵变
的影响[J]. 湖南师范大学自然科学学报,1992,15(3):257-262.
[36] 王身立. 控制论与信息论在遗传学中的应用 I: 热力学第二定律的信息论表述方式
及其在群体遗传学中的应用[J]. 湖南师范学院学报(自然科学版),1983,6(2):55-60.
[37] 王身立. 控制论与信息论在遗传学中的应用 II: 连锁与交换中的信息论问题[J]. 湖
南师范学院学报,1984,7(1):81-84.
[38] 王身立. 生物物理遗传学[M]. 长沙:湖南科学技术出版社,1992.
[39] 王身立编. 耗散结构向何出去[M]. 北京:人民出版社,1989.
[40] 王身立著. 控制论与遗传进化问题[M]. 长沙:湖南科学技术出版社,1985.
[41] 王身立著. 生物物理遗传学[M]. 湖南:湖南科学技术出版社,1992.
[42] 王昕. 中国部分地方猪种 DNA指纹的群体遗传学研究(西北农林科技大学硕士论文),
2001,12.
[43] 王亚馥,戴灼华. 遗传学[M]. 北京:高等教育出版社,1999.
[44] 吴彦虎,路兴中. 群体遗传变异的测度方法[J]. 黄牛杂志,1993,19(1):79-81.
[45] 吴仲贤. 统计遗传学[M]. 北京:中国科学出版社,1977.
[46] 夏立容. 信息时代与信息科学[M]. 汉口:湖北教育出版社,1998.
[47] 徐云碧,王志华,愈志华译,朱军校,[美]Bruce S.Weir 著. 遗传学数据分析[M]. 北京:中
国农业出版社,1996.
[48] 杨纪珂. 数量遗传基础知识[M]. 北京:科学出版社,1979.
[49] 于晓秋,李欣,张宏礼. MATLAB 数学实验[M]. 辽宁:辽宁科学技术出版社,2004.
[50] 袁志发,郭满才,宋世德,等. 相对 Shannon信息量与基因变异的测量[J]. 西北农业大
学学报,1998,26(4):30-34.
[51] 袁志发,周静芋,郭满才,等. 基因多样度与Shannon信息熵[J].Animalbiotechnology
bulletin,2002,8(1):353-358.
[52] 袁志发,周静芋. 多元统计分析[M]. 北京:科学出版社,2002.
76 近亲繁殖群体的信息论模型研究
[53] 张宏礼,郭满才,杜俊莉,等. 复等位基因群体完全自交下母子间基因型联合分布的信
息熵性质[J]. 黑龙江八一农垦大学学报, 2003,15(2):31-35.
[54] 张宏礼,郭满才,解小莉,等. 近亲繁殖下一对等位基因群体的熵性质[J]. 西北农林科
技大学学报(自然科学版), 2003,31(1):148-150.
[55] 张宏礼,郭满才,解小莉,等. 近亲交配下母子间基因型联合分布的信息熵性质[J]. 西
北农林科技大学学报(自然科学版), 2003,31(3):193-197.
[56] 张宏礼,郭满才,刘建军,等. 遗传同型交配下母子间基因型联合分布的信息熵性质[J].
黄牛杂志,2003,29(2):13-15.
[57] 张宏礼,郭满才,吴晓华,等. 遗传同型交配下一对等位基因群体的 Shannon 信息熵[J].
西北农业学报, 2004,13(2):47-51.
[58] 张宏礼,刘海泉. 近亲繁殖下复等位基因群体的熵性质[J]. 黑龙江八一农垦大学学报,
2002,14(4):94-98.
[59] 张宏礼,张鸿雁. 遗传学的发展[J]. 陕西农业科学,2003(3):27-29.
[60] 张劳,李玉奎编著. 群体遗传学概论[M]. 北京:中国农业出版社,1999.
[61] 张宗炳. 遗传与进化[M]. 北京:人民教育出版社,1981.
[62] 钟义信. 信息科学原理[M]. 北京:北京邮电大学出版社,1996.
[63] 周厚高,朱军. 等位基因频率资料分支分类方法及模拟研究[M]. 北京:气象出版社,
2000.
[64] 朱军著. 遗传模型分析方法[M]. 北京:中国农业出版社,1997.
[65] 朱雪龙. 应用信息论基础[M. 北京:清华大学出版社,2001.
[66] Allen Shearn. Complementation analysis of late lethal mutants of drosophila melano-
gaster[J]. Genetics,1974,77:115-125.
[67] D.de Nettancourt. Incompatibility in angiosperms[J].Sexual Plant Reproduction,1997,
10(4): 185-199.
[68] David W.Mount. Bioinformatics: Sequence and Genome Analysis[M]. CSHL Press,
2001.
[69] E. A. Thompson, T. R. Meagher. Genetic linkage in the estimation of pairwise relation-
ship[J]. TAG theoretical andApplied Genetics,1998,97(5/6):857-864.
[70] Falconer D.S. Introduction to Quantitative Genetics[M]. London:LongmanPress, ,1981.
[71] Fisher R.A. The General Theory of Natural Selection[M]. Oxford: Clarendon Press, 1930
[72] Fisher, H.D. The Genetical Theroyof Natural Selection[M]. Oxford: Clarendon Press,
1930.
[73] Gale, J. S. Population Genetic[M]s. John Wiley, New York,1980.
[74] Guo Man-cai, Yuan Zhi-fa, Chen Hong, et al. Research of the Homological DNA Simila-
rity Index[A]. Animal Biotechnology Bulletin,2002, 8(1): 359-364.
参 考 文 献 77
[75] H. X. Lin, T. Yamamoto, T. Sasaki, et al. Characterization and detection of epistatic inter-
actions of 3 QTLs, Hd1, Hd2, and Hd3, controlling heading date in rice using nearly iso-
genic lines[J]. TAG theoretical andApplied Genetics,2000,100(7):1021-1028.
[76] J.Kumar,R.J.Nelson,R.S.Zeigler. Population structure and dynamics of magnaporthe
grisea in the indian himalayas[J].Genetics,1999,152:971-984.
[77] James F.Crow,Ray D.Owen. Kay Wilson and the NIH genetics study sectiongenetics[J].
Genetics,2000, 155:1-5.
[78] James F.Crow. Shannon's brief foray into genetics[J].Genetics,2001,159: 915-917.
[79] JT.C.Kaufman, M.P.Shannon,M.W.Shen,et al. A revision of the cytology and ontogeny
of several deficiencies in the 3a1–3c6 region of the xchromosome of drosophila melano-
gaster[J]. Genetics,1975,79:265-282.
[80] K. K. Shimizu. Special feature: review: Ecology meets molecular genetics in Arabidopsis
[J]. Population Ecology,2002,44(3):221-223.
[81] L.-z.Gao,S.G.De-y.Hong.Allozyme variation and population genetic structure of common
wild rice Oryza rufipogon Griff. in China[J]. TAG Theoretical andApplied Genetics,
2000, 101(3):494-502.
[82] Leonard G.Robbins. Developmental use of gene products in drosophila: the maternal-
zygotic transition[J]. Genetics,1984,108:361-375.
[83] M. A. Jobling, A. Pandya, C. Tyler-Smith. The Y chromosome in forensic analysis and
paternity testing[J]. International Journal of Legal Medicine,1997,110(3):118-124.
[84] M.P.Shannon,T.C.Kaufman,M.W.Shen,et al. Lethality patterns and morphology of
selected lethal and semi-lethal mutations in the zeste-white region of drosophila melano-
gaster[J]. Genetics,1972,72:615-638.
[85] M.V.Albeza, A.Picornell, N.Acreche, et al. Genetic variability at 14 STR loci in the Puna
population of north western Argentina[J]. Table of Contents,2002,116(3):126-132.
[86] Norbert Perrimon,Lee Engstrom,Anthony P. Mahowald. Developmental genetics of the
2e-f region of the drosophila xchromosome:a region rich in "developmentallyimportant"
genes[J]. Genetics,1984,108:559-572.
[87] Paul F.Slade. Conditional ancestral times and related properties of an extant mutant at a
locus A given the number of segregating sites observed at a linked locus B[J]. Journal of
Mathematical Biology,2002,44(5):427-449.
[88] R.Durbin,S.Eddy,A.Krogh,G.Mitchison. Biological Sequence Analysis[M]. 北京:清华大
学出版社,2002.
[89] Regina M.Vidaver,David M. Fortner, Liana S.Loos-Austin,et al. Multiplefunctionsof
saccharomyces cerevisiae splicing protein prp24 in u6 rna structural rearrangements[J].
78 近亲繁殖群体的信息论模型研究
Genetics,1999,153:1205-1218.
[90] S. Klinbunga, P. Ampayup, A. Tassanakajon, P. Jarayabhand, et al. Genetic diversity and
molecular markers of cupped oysters in Thailand revealed by aandomly amplified polym-
orphic DNAanalysis[J]. Mar. Biotechnol,2001,3:133-144.
[91] S. Uthicke, J. A. H. Benzie, E. Ballment. Population genetics of the fissiparous holothur-
ian Stichopus chloronotus (Aspidochirotida) on the Great Barrier Reef[J]. Coral Reefs,
1999,18(2): 123-132.
[92] Yuan Zhi-fa, Zhou Jing-yu, Guo Man-cai, et al. Gene Diversity and Shannon Information
Entropy. Animal[A]. Biotechnology Bulletin,2002,8(1):353-358.
[2] 戴君惕,王身立. 遗传分析方法[M]. 长沙:湖南科技出版社,1989.
[3] 傅祖芸. 信息论基础理论及应用[M]. 北京:电子工业出版社,2001.
[4] 郭满才,解小莉,刘建军,等. 复等位基因平衡群体熵的性质[J]. 西北农林科技大学学
报(自然科学版), 2002,30(4):119-122.
[5] 郭满才,宋世德,周静芋,等. 非平衡群体基因变异测量的 Shannon信息量方法[J]. 生
物数学学报,2001,16(3):341-347.
[6] 郭满才,袁志发,陈宏,等. 陕西四个黄牛群体遗传变异的 Shannon信息量分析[J]. 黄
牛杂志,2003,29(1):22-24.
[7] 郭满才,袁志发,陈宏,等. 遗传多样性指标体系研究[J].Animalbiotechnologybulletin,
2002, 8(1):359-364.
[8] 郭满才. 群体遗传变异的信息学模型研究(西北农林科技大学博士论文),2002,5.
[9] 郭平仲. 群体遗传学导论[M]. 北京:农业出版社,1993,5.
[10] 郭平仲. 数量遗传分析[M]. 北京:北京师范学院出版社,1987.
[11] 胡上序,陈德钊. 观测数据的分析与处理[M]. 杭州:浙江大学出版社,2002.
[12] 贾世搂. 信息理论基础[M]. 哈尔滨:哈尔滨工业大学出版社,2001.
[13] 解小莉,郭满才,张宏礼,等. 两对等位基因群体熵的性质[J]. 生物数学学报,2003,
18(4):482-486.
[14] 兰斌,等,译. 遗传分析导论[M]. 西安:陕西人民教育出版社,1990.
[15] 兰斌,袁志发译,马育华校. 数量遗传学的数学理论[M]. 北京:农业出版社,1991.
[16] 李宝健. 展望 21 世纪的生命科学[J]. 生命科学,2000,12(1):37-40.
[17] 李难. 进化论教程[M]. 北京:高等教育出版社,2001.
[18] 刘建军,郭满才,解小莉,等. 性连锁群体平衡的信息模型研究[J]. 西北农林科技大学
学报(自然科学版), 2002,30(5):114-116.
[19] 刘祖洞. 遗传学(上,下)[M]. 北京:高等教育出版社,2001,5.
[20] 鲁晨光. 广义信息论[M]. 合肥:中国科学技术大学出版社,1993.
[21] [美]C.C.L.著,吴仲贤译. 群体遗传学[M]. 北京:中国农业出版社,1981.
[22] [美]根井正利. 分子群体遗传学与进化论[M]. 北京:农业出版社,1983.
[23] 匿名. 进化论的进化. 参考消息[J],2001,08,19.
[24] 裴新澍. 生物进化控制论[M]. 北京:科学出版社,1998.
[25] [日]大羽 滋著,赵敏,孙勇如,李良材译. 群体遗传[M]. 北京:科学出版社,1983.
参 考 文 献75
[26] [日]向井辉美著,隋文彬,孙广芝译. 群体遗传学[M]. 吉林:科学技术出版社,1984.
[27] 盛志廉,陈瑶生. 数量遗传学[M]. 北京:科学出版,2001.
[28] 舒炜光,张之沧. 重建与优选[M]. 北京:人民出版社,1987.
[29] 孙之荣译,Minoru Kanehisa 著. 后基因组信息学[M]. 北京:清华大学出版社,2002.
[30] 童克中. 基因及其表达[M]. 北京:科学出版社,2002.
[31] 汪小龙,袁志发,郭满才,等. 最大信息熵原理与群体遗传平衡[J]. 遗传学报 2002,29
(6) :562-564.
[32] 王金良. 家畜近亲繁殖群体的遗传组成分析[J]. 畜牧兽医学报,1995,26(6):500-505.
[33] 王身立,许康. 系统科学的产生是历史的必然[J]. 自然辩证法研究,1990,6(2):42-46.
[34] 王身立. 基因研究 140 年大事年表[J]. 湖南师范大学自然科学学报,2001,24(1):69-77.
[35] 王身立. 控制论与信息论在遗传学中的应用Ⅲ: 群体融合对基因型熵变与表型熵变
的影响[J]. 湖南师范大学自然科学学报,1992,15(3):257-262.
[36] 王身立. 控制论与信息论在遗传学中的应用 I: 热力学第二定律的信息论表述方式
及其在群体遗传学中的应用[J]. 湖南师范学院学报(自然科学版),1983,6(2):55-60.
[37] 王身立. 控制论与信息论在遗传学中的应用 II: 连锁与交换中的信息论问题[J]. 湖
南师范学院学报,1984,7(1):81-84.
[38] 王身立. 生物物理遗传学[M]. 长沙:湖南科学技术出版社,1992.
[39] 王身立编. 耗散结构向何出去[M]. 北京:人民出版社,1989.
[40] 王身立著. 控制论与遗传进化问题[M]. 长沙:湖南科学技术出版社,1985.
[41] 王身立著. 生物物理遗传学[M]. 湖南:湖南科学技术出版社,1992.
[42] 王昕. 中国部分地方猪种 DNA指纹的群体遗传学研究(西北农林科技大学硕士论文),
2001,12.
[43] 王亚馥,戴灼华. 遗传学[M]. 北京:高等教育出版社,1999.
[44] 吴彦虎,路兴中. 群体遗传变异的测度方法[J]. 黄牛杂志,1993,19(1):79-81.
[45] 吴仲贤. 统计遗传学[M]. 北京:中国科学出版社,1977.
[46] 夏立容. 信息时代与信息科学[M]. 汉口:湖北教育出版社,1998.
[47] 徐云碧,王志华,愈志华译,朱军校,[美]Bruce S.Weir 著. 遗传学数据分析[M]. 北京:中
国农业出版社,1996.
[48] 杨纪珂. 数量遗传基础知识[M]. 北京:科学出版社,1979.
[49] 于晓秋,李欣,张宏礼. MATLAB 数学实验[M]. 辽宁:辽宁科学技术出版社,2004.
[50] 袁志发,郭满才,宋世德,等. 相对 Shannon信息量与基因变异的测量[J]. 西北农业大
学学报,1998,26(4):30-34.
[51] 袁志发,周静芋,郭满才,等. 基因多样度与Shannon信息熵[J].Animalbiotechnology
bulletin,2002,8(1):353-358.
[52] 袁志发,周静芋. 多元统计分析[M]. 北京:科学出版社,2002.
76 近亲繁殖群体的信息论模型研究
[53] 张宏礼,郭满才,杜俊莉,等. 复等位基因群体完全自交下母子间基因型联合分布的信
息熵性质[J]. 黑龙江八一农垦大学学报, 2003,15(2):31-35.
[54] 张宏礼,郭满才,解小莉,等. 近亲繁殖下一对等位基因群体的熵性质[J]. 西北农林科
技大学学报(自然科学版), 2003,31(1):148-150.
[55] 张宏礼,郭满才,解小莉,等. 近亲交配下母子间基因型联合分布的信息熵性质[J]. 西
北农林科技大学学报(自然科学版), 2003,31(3):193-197.
[56] 张宏礼,郭满才,刘建军,等. 遗传同型交配下母子间基因型联合分布的信息熵性质[J].
黄牛杂志,2003,29(2):13-15.
[57] 张宏礼,郭满才,吴晓华,等. 遗传同型交配下一对等位基因群体的 Shannon 信息熵[J].
西北农业学报, 2004,13(2):47-51.
[58] 张宏礼,刘海泉. 近亲繁殖下复等位基因群体的熵性质[J]. 黑龙江八一农垦大学学报,
2002,14(4):94-98.
[59] 张宏礼,张鸿雁. 遗传学的发展[J]. 陕西农业科学,2003(3):27-29.
[60] 张劳,李玉奎编著. 群体遗传学概论[M]. 北京:中国农业出版社,1999.
[61] 张宗炳. 遗传与进化[M]. 北京:人民教育出版社,1981.
[62] 钟义信. 信息科学原理[M]. 北京:北京邮电大学出版社,1996.
[63] 周厚高,朱军. 等位基因频率资料分支分类方法及模拟研究[M]. 北京:气象出版社,
2000.
[64] 朱军著. 遗传模型分析方法[M]. 北京:中国农业出版社,1997.
[65] 朱雪龙. 应用信息论基础[M. 北京:清华大学出版社,2001.
[66] Allen Shearn. Complementation analysis of late lethal mutants of drosophila melano-
gaster[J]. Genetics,1974,77:115-125.
[67] D.de Nettancourt. Incompatibility in angiosperms[J].Sexual Plant Reproduction,1997,
10(4): 185-199.
[68] David W.Mount. Bioinformatics: Sequence and Genome Analysis[M]. CSHL Press,
2001.
[69] E. A. Thompson, T. R. Meagher. Genetic linkage in the estimation of pairwise relation-
ship[J]. TAG theoretical andApplied Genetics,1998,97(5/6):857-864.
[70] Falconer D.S. Introduction to Quantitative Genetics[M]. London:LongmanPress, ,1981.
[71] Fisher R.A. The General Theory of Natural Selection[M]. Oxford: Clarendon Press, 1930
[72] Fisher, H.D. The Genetical Theroyof Natural Selection[M]. Oxford: Clarendon Press,
1930.
[73] Gale, J. S. Population Genetic[M]s. John Wiley, New York,1980.
[74] Guo Man-cai, Yuan Zhi-fa, Chen Hong, et al. Research of the Homological DNA Simila-
rity Index[A]. Animal Biotechnology Bulletin,2002, 8(1): 359-364.
参 考 文 献 77
[75] H. X. Lin, T. Yamamoto, T. Sasaki, et al. Characterization and detection of epistatic inter-
actions of 3 QTLs, Hd1, Hd2, and Hd3, controlling heading date in rice using nearly iso-
genic lines[J]. TAG theoretical andApplied Genetics,2000,100(7):1021-1028.
[76] J.Kumar,R.J.Nelson,R.S.Zeigler. Population structure and dynamics of magnaporthe
grisea in the indian himalayas[J].Genetics,1999,152:971-984.
[77] James F.Crow,Ray D.Owen. Kay Wilson and the NIH genetics study sectiongenetics[J].
Genetics,2000, 155:1-5.
[78] James F.Crow. Shannon's brief foray into genetics[J].Genetics,2001,159: 915-917.
[79] JT.C.Kaufman, M.P.Shannon,M.W.Shen,et al. A revision of the cytology and ontogeny
of several deficiencies in the 3a1–3c6 region of the xchromosome of drosophila melano-
gaster[J]. Genetics,1975,79:265-282.
[80] K. K. Shimizu. Special feature: review: Ecology meets molecular genetics in Arabidopsis
[J]. Population Ecology,2002,44(3):221-223.
[81] L.-z.Gao,S.G.De-y.Hong.Allozyme variation and population genetic structure of common
wild rice Oryza rufipogon Griff. in China[J]. TAG Theoretical andApplied Genetics,
2000, 101(3):494-502.
[82] Leonard G.Robbins. Developmental use of gene products in drosophila: the maternal-
zygotic transition[J]. Genetics,1984,108:361-375.
[83] M. A. Jobling, A. Pandya, C. Tyler-Smith. The Y chromosome in forensic analysis and
paternity testing[J]. International Journal of Legal Medicine,1997,110(3):118-124.
[84] M.P.Shannon,T.C.Kaufman,M.W.Shen,et al. Lethality patterns and morphology of
selected lethal and semi-lethal mutations in the zeste-white region of drosophila melano-
gaster[J]. Genetics,1972,72:615-638.
[85] M.V.Albeza, A.Picornell, N.Acreche, et al. Genetic variability at 14 STR loci in the Puna
population of north western Argentina[J]. Table of Contents,2002,116(3):126-132.
[86] Norbert Perrimon,Lee Engstrom,Anthony P. Mahowald. Developmental genetics of the
2e-f region of the drosophila xchromosome:a region rich in "developmentallyimportant"
genes[J]. Genetics,1984,108:559-572.
[87] Paul F.Slade. Conditional ancestral times and related properties of an extant mutant at a
locus A given the number of segregating sites observed at a linked locus B[J]. Journal of
Mathematical Biology,2002,44(5):427-449.
[88] R.Durbin,S.Eddy,A.Krogh,G.Mitchison. Biological Sequence Analysis[M]. 北京:清华大
学出版社,2002.
[89] Regina M.Vidaver,David M. Fortner, Liana S.Loos-Austin,et al. Multiplefunctionsof
saccharomyces cerevisiae splicing protein prp24 in u6 rna structural rearrangements[J].
78 近亲繁殖群体的信息论模型研究
Genetics,1999,153:1205-1218.
[90] S. Klinbunga, P. Ampayup, A. Tassanakajon, P. Jarayabhand, et al. Genetic diversity and
molecular markers of cupped oysters in Thailand revealed by aandomly amplified polym-
orphic DNAanalysis[J]. Mar. Biotechnol,2001,3:133-144.
[91] S. Uthicke, J. A. H. Benzie, E. Ballment. Population genetics of the fissiparous holothur-
ian Stichopus chloronotus (Aspidochirotida) on the Great Barrier Reef[J]. Coral Reefs,
1999,18(2): 123-132.
[92] Yuan Zhi-fa, Zhou Jing-yu, Guo Man-cai, et al. Gene Diversity and Shannon Information
Entropy. Animal[A]. Biotechnology Bulletin,2002,8(1):353-358.