32.2
哈代 - 温伯格原理
The Hardy–Weinberg Principle states that in a large, randomly mating population, allele frequencies stay the same over time if the population is not evolving.
When a gene has two alleles at one locus, such as red and brown coat alleles in squirrels, their frequencies—represented by p and q—add up to one.
We can calculate the frequency of each genotype. The frequency of homozygous red and homozygous brown individuals is the square of the allele frequency—p² and q²—which gives the probability of inheriting the same allele from both parents.
Heterozygous individuals with red-brown coats can form in two ways: the egg can carry the red allele and the sperm the brown allele, or the egg can carry the brown allele and the sperm the red allele. So, the frequency of heterozygous individuals equals two times the product of the allele frequencies, or 2pq.
Together, these genotype frequencies sum to one. This principle is true only under specific, non-evolving conditions.
There must be no natural selection, and mating must be random with no preference for particular genotypes. There must be no gene flow from outside the population and no mutations within the population.
Finally, the population must be very large because random events can strongly change allele frequencies in small populations.
Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
二倍体生物在其体细胞中具有每个基因的两个等位基因，每个基因一个来自父母。因此，每个个体为群体的基因库贡献两个等位基因。群体的基因库是该群体中所有基因的每个等位基因的总和，并且具有一定程度的变异。遗传变异通常表示为相对频率，其是具有给定等位基因，基因型或表型的总群体的百分比。
在20世纪初，科学家们想知道，为什么在随机交配的每一代种群中，一些很少观察到的显性性状的频率没有增加。例如，为什么在许多动物物种中，显性多指性状 (E，额外的手指和/或脚趾) 不比通常的手指数 ( e )更常见？1908年，德国医生威廉·温伯格（Wilhelm Weinberg）和英国数学家哈迪（G. H. Hardy）独立证明了这种世代遗传变异不变的现象。这一原理后来被称为 哈迪-温伯格平衡。
哈-温等式（Hardy-Weinberg Equation）
哈-温等式 (p2 + 2pq + q2 = 1)将等位基因频率与基因型频率优雅地联系起来。例如，在有多指症的人群中，基因库中分别含有 E 和 e等位基因，其相对频率分别为 p 和 q。由于等位基因的相对频率是总人口的一部分，p 和 q 加起来等于1( p + q = 1)。
这个群体中个体的基因型要么是EE， Ee要么是 ee。因此，具有EE基因型的个体比例为p×p，或 p2，而具有 ee 基因型的个体比例为 q × q，或 q2。杂合子 ( Ee )的比例为 2pq ( p× q 和 q × p)，因为有两个可能的杂交产生杂合子基因型（即显性等位基因可能来自父母双方）。与等位基因频率相似，基因型频率加起来也为1；因此，p2 + 2pq + q2 = 1，这就是哈-温方程。
哈-温条件
哈-温平衡指出，在某些条件下，一个群体中的等位基因频率将随时间保持不变。这样的群体满足五个条件：无限的群体规模，个体的随机交配，没有基因突变，自然选择和基因流动。由于进化可以简单地定义为基因库中等位基因频率的变化，因此符合哈-温标准的种群不会进化。大多数自然种群至少违背了其中一个假设，因此很少处于平衡状态。然而，哈-温原理是研究进化的一个有用的起点或零模型，也可以应用于群体遗传学研究，以确定遗传关联和检测基因分型错误。
The Hardy–Weinberg Principle states that in a large, randomly mating population, allele frequencies stay the same over time if the population is not evolving.
When a gene has two alleles at one locus, such as red and brown coat alleles in squirrels, their frequencies—represented by p and q—add up to one.
We can calculate the frequency of each genotype. The frequency of homozygous red and homozygous brown individuals is the square of the allele frequency—p² and q²—which gives the probability of inheriting the same allele from both parents.
Heterozygous individuals with red-brown coats can form in two ways: the egg can carry the red allele and the sperm the brown allele, or the egg can carry the brown allele and the sperm the red allele. So, the frequency of heterozygous individuals equals two times the product of the allele frequencies, or 2pq.
Together, these genotype frequencies sum to one. This principle is true only under specific, non-evolving conditions.
There must be no natural selection, and mating must be random with no preference for particular genotypes. There must be no gene flow from outside the population and no mutations within the population.
Finally, the population must be very large because random events can strongly change allele frequencies in small populations.
Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
From Chapter 32:
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