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Allele frequency

Terms in the field of biology

The allele frequency is Population genetics A term used to show the diversity of genes in a population, or gene The richness of.

Chinese name: Allele frequency
Foreign name: Allele frequency
Category: Terminology of population genetics

Features: A specific Locus ，
Correlation calculation: n1/N+n2/2N
key word: Genetic balance gene frequency

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Allele frequency is defined as follows:

Allele frequency

If (1) a specific chromosome exists Locus , (2) there is a gene on the locus, (3) somatic cell There are n specific loci (e.g diploid There are two specific gene loci in the cells of organisms), (4) the gene has alleles or variants; that Allele The frequency is ------ allele in this population, all alleles in a specific Locus In percentage 。

For example, if an allele in a population gene frequency 20%, then in all members of the population, 1/5 of the chromosomes have that allele, while other 4/5 of the chromosomes have other corresponding variants of the allele - can be one or many.

As people know MN blood group , which is composed of a pair of Codominant allele Determined by M and N, three kinds of genotype M/M, M/N and N/N, while the corresponding phenotypes are M, MN and N, and the proportions are 1/4M, 1/2MN and 1/4N. This principle can be extended to General group within Marriage For example, the relative frequency can be obtained by dividing the specific number of samples of MN phenotype (genotype) in the population by the total number of observed samples.

Concept comparison

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gene frequency It is the proportion of a gene in a population. Genotype frequency It's a certain genotype The proportion of the individuals in the whole group. The former is the proportion of the number of individuals of a gene in the total number of genes, and the latter is the proportion of the number of individuals of a genotype in the total number of populations.

Correlation calculation

(1) Design diploid One of the individual organisms Locus There are two on Allele A and a, assuming that there are N individuals in the population, and AA , Aa, aa genotype The number of individuals is n1, n2, and n3 respectively, so the frequency of A gene and AA genotype in the population are:

① Frequency of A gene=total number of A genes/(total number of A genes+total number of a genes)=(2n1+n2)/2N or n1/N+n2/2N

② Frequency of AA genotype=number of individuals of AA genotype/this diploid Total population=n1/N.

⑵ gene frequency And Genotype frequency From the above ① ②, it can be inferred that the frequency of A gene=n1/N+1/2 · n2/N=the frequency of AA genotype+1/2Aa genotype.

Types of gene frequency calculation and its formula derivation

abstract

Biological evolution The essence of gene gene frequency In the environment Selection function Change of orientation under. application Mathematical method Calculating population gene frequency is conducive to understanding population evolution. This paper discusses the calculation type and Calculation formula The derivation process of.

key word ：

Genetic balance gene frequency

Gene frequency refers to that a gene accounts for all genes in a population gene pool Allele The proportion of the number. One of the species Gene locus The sum of different gene frequencies and various Genotype frequency The sum is equal to 1. For a population, Ideal state The gene frequency of the lower population remains stable in generations, however natural condition But it is affected by gene mutation Gene recombination , natural selection, migration and Genetic drift The gene frequency of the population is constantly changing, which makes the organism continuously develop and evolve. Therefore, by calculating the gene frequency It is helpful to understand the evolution of the population. In order to further deepen the understanding of this part Understanding of knowledge And master, the types and formulas of gene frequency calculation are summarized as follows:

Ideal state

The ideal population is Genetic balance The population under the condition of "Hardy Weinberg Law of equilibrium ”。 Genetic balance means that in a large random free mating population Mutagenesis Without natural selection and migration gene frequency and Genotype frequency Be stable and balanced from generation to generation.

One with Aa genotype Of Large groups (Zero generation or a generation in genetic balance), the frequency of A gene P (A)=p, the frequency of a gene P (a)=q, Dominant gene A gene frequency and Recessive gene The sum of gene frequencies of a is p+q=1, and its male and female individuals transmit gene type A to their offspring gamete The frequency is p, and the frequency corresponding to the transmission of recessive gene type a gametes is q, then the combination type of various gametes, the genotype of offspring and their occurrence probability can be expressed in Table 1 below:

Table 1

Table 1
Male gamete Female gamete	A（p）	a（q）
A（p）	AA（p）	Aa（pq）
a（q）	Aa（pq）	aa（q）

It can be seen from the table above that there are three kinds of genotype AA、Aa、aa， The frequency of three genotypes was P (AA)=p × p=p ^ 2=D; P（Aa）=2p×q=2pq=H； P（aa）= q×q = q^2=R。 And the sum of their frequencies is p ^ 2+2pq+q ^ 2=(p+q)=1. his gene frequency Is the frequency of A gene P (A)=D+1/2H=p ^ 2+pq=p (p+q)=p; The frequency of a gene P (a)=R+1/2H=q ^ 2+pq=q (p+q)=q. The relationship between gene frequency of visible offspring and Parental generation The gene frequency is the same. Therefore, in all future generations, if there is no interference from mutation, migration, selection and other factors, the genetic component of this population will always be p ^ 2+2pq+q ^ 2 Equilibrium state 。 Sex linked gene And many Allele Genetic balance The calculation of is still in accordance with the above rule. Using this rule, we know that Genotype frequency Calculable gene frequency ； On the contrary, genotype frequency can be calculated when gene frequency is known.

Example: Known Phenylketonuria Is located in Autosome On Recessive hereditary disease 。 According to the survey, the incidence of the disease is about 1/10000, and the phenylketonuria is recessive in the population Pathogenic gene (a) Gene frequency and carrying this Recessive gene Of carrier (Aa) Genotype frequency Respectively ()

A. 1% and 0.99% B.1% and 1.98% C.1% and 3.96% D.1% and 0.198%

Analysis: phenylketonuria is a kind of Autosomal recessive disease 。 Because of this disease genotype Is aa, that is, aa=0.0001, a=0．01，A= 1-a=1-0．01=0．99， The frequency of carrier genotype Aa=2 × 0.01 × 0.99=0.0198.

Answer: B

Variant 1. On an island, 500 men suffer from Red green colour blindness , then how many female carriers are there per 10000 people on the island? (Assuming that the ratio of men to women is 1:1) (B)

A. 1000 people B.900 people C.800 people D.700 people

Variant 2: Human ABO blood group Determined by 3 Allele I、I、i。 Through sampling survey, we found that the frequency of blood type: type A=0.45, type B=0.13, type AB=0.06, type O=0.36. Try to calculate the frequency of I, I and i alleles.

Answer: I frequency is 0.3, I frequency is 0.1, and I frequency is 0.6.

natural state

For the population living in the nature, the ideal condition is that the population cannot exist at the same time gene frequency It is impossible to maintain balance, but in constant change and development. This kind of non Balanced population The data obtained by sampling survey are often used to calculate the gene frequency, which can be divided into two types according to the location of genes.

2.1 About Autosomal inheritance Calculation of gene frequency According to the definition, the frequency of a gene=the number of a gene/the Allele Total number × 100%. If diploid Biological Autosome One of Gene locus There is one allele A and a on the, and their gene frequencies are p and q respectively, which can form three types genotype AA、Aa、aa， Genotype frequency D, H, R, the total number of individuals is N, the number of AA individuals is n1, the number of Aa individuals is n2, the number of aa individuals is n3, n1+n2+n3=N. Then:

The frequency of genotype AA=D=n1/N, n1=ND;

The frequency of genotype Aa=H=n2/N. n2=NH

The frequency of genotype aa=R=n3/N, n3=NR;

The frequency of gene A P (A)=(2n1+n2)/2N=(2ND+NH)/2N=D+1/2H=p

The frequency of gene a P (a)=(2n3+n2)/2N=(2NR+NH)/2N=R+1/2H=q

Because p+q=1, D+1/2H+R+1/2H=D+R+H=1

From the above derivation,

① Autosome gene frequency Basic calculation formula of:

The frequency of a gene=(2 × the gene Homozygote Number+1 × Heterozygote Number)/2 × Population survey Total number of individuals

② The derivation formula of autosomal gene frequency:

A gene frequency=homozygote frequency of a gene+1/2 heterozygote frequency

Example: 100 individuals randomly selected from a population genotype The number of individuals with AA, Aa and aa was 30, 60 and 10 respectively. Please, this pair Allele Of gene frequency 。

Solution 1:

First, find out the total number of alleles and the number of A or a. There are 200 genes in 100 individuals; Among them, A gene has 2 × 30+60=120, and a gene has 2 × 10+60=80. Then by Autosome The basic formula of gene frequency is calculated as follows:

The frequency of A gene: 120 ÷ 200=60%

The frequency of a gene: 80 ÷ 200=40%

Solution 2:

According to the meaning of the title, AA, Aa and aa Genotype frequency 30%, 60% and 10% respectively, calculated from the formula of autosomal gene frequency:

The frequency of A gene: 30%+1/2 × 60%=60%

The frequency of a gene: 10%+1/2 × 60%=40%

Variant 1: Known that brown (A) of human eyes is dominant to blue (a) Autosome Genetically controlled inheritance. In a crowd of 30000 people, 3600 people have blue eyes and 26400 people have brown eyes, of which Homozygote There are 12000 people in this population gene frequency Respectively (A)

A. 64% and 36% B.36% and 64% C.50% and 50% D.82% and 18%

Variant 2: A certain number of individuals are randomly selected from a population, where, genotype The individuals with BB account for 40%, the individuals with genotype Bb account for 50%, and the individuals with genotype bb account for 10%, so the frequencies of gene B and b are (B) respectively

A． 90%，10% B． 65%，35% C． 50%，50% D． 35%，65%

2.2 About X or Y chromosome inheritance gene frequency Calculation of

about Sex linked inheritance For X, Y Cognate segment The gene frequency calculation of Autosome The calculation is the same; The genes located in the non homologous regions of X and Y X chromosome Heredity Y chromosome The gene and its Allele 。 Similarly, there is no equivalent gene on the X chromosome for Y chromosome inheritance. Therefore, when calculating the total number of genes, only the total number of genes on the X chromosome (or Y chromosome) should be considered. If diploid There is an allele B and b on a gene site of the X chromosome of the organism, and their gene frequencies are p and q respectively, which can form five kinds genotype 20. XX, XX, XY and XY, Genotype frequency They are E, F, G, H and I, respectively. The total number of individuals is N, the number of XX individuals is n1, the number of XX individuals is n2, the number of XX individuals is n3, the number of XY individuals is n4, and the number of XY individuals is n5. And n1+n2+n3=n4+n5, then:

E=n1 /N、 F=n2 /N、G=n3 /N、H=n4 /N、 I=n5 /N；

p(X)=(2n1 +n2 +n4)/[2（n1+n2+n3）+（n4+n5）]=(2n1 +n2 +n4)/1．5N=2/3(2E+F+H)

q(X)=(2n3 +n2 +n5)/ [2（n1+n2+n3）+（n4+n5）]=(2n3 +n2 +n5)/ 1．5N=2/3(2G+F+I)

From the above derivation,

① X chromosome gene frequency Basic calculation formula of:

The frequency of a gene=(2 × female of the gene Homozygote Number+number of female heterozygotes+number of male containing the gene)/(2 × total number of female individuals+number of male individuals)

② Derivation formula of X chromosome gene frequency:

Gene frequency of a gene=2/3 (2 × female of a gene Homozygote Frequency+female Heterozygote Frequency+male Genotype frequency ）(When the number of female and male individuals is equal)

Example: 100 individuals randomly selected from a population genotype The individuals of XX, XX, XX and XY, XY are 44, 5, 1 and 43, 7 respectively. Find the gene frequency of X and X.

Solution 1:

This is it Allele For example, each female individual contains two genes, and each male individual contains one gene（ Y chromosome There is no allele on. So, there are 150 genes in the 100 individuals, including 2 × (44+5+1)=100 genes in female individuals and 43+7=50 genes in male individuals. X gene has 44 × 2+5+43=136, and X gene has 5+1 × 2+7=14. Therefore, according to X chromosome gene frequency The basic formula of

The gene frequency of X is: 136 ÷ 150 ≈ 90.7%

The gene frequency of X is: 14 ÷ 150 ≈ 9.3%

Solution 2:

According to the meaning of the title, XX, XX, XX and XY, XY Genotype frequency 44%, 5%, 1% and 43%, 7% respectively, because the genotype frequency of female and male individuals accounts for 50% respectively, so it can be calculated from the derivation formula of X chromosome gene frequency:

Gene frequency of X gene=2/3 × (2 × 44%+5%+43%) ≈ 90.7%

Gene frequency of X gene=2/3 × (2 × 1%+5%+7%) ≈ 9.3%

Variant 1: A factory has 200 male and 200 female employees, and the survey found that women Color blindness There were 15 gene carriers, 5 patients and 11 male patients. Then the frequency of color blindness gene in this population is (B)

A． 4．5% B． 6% C． 9% D． 7．8%

Variant 2: A genetic survey of students in a European school found that, hemophilia The patients accounted for 0.7% (male: female=2:1); Hemophilia carriers account for 5%, so the X frequency of this population is (C)

A．2．97%　B．0．7%　C．3．96%　D．3．2%

Resolution:

Method 1: First of all, we should make clear that 2:1 is the proportion of men and women in patients Male female ratio It is 1:1. The total number of people is assumed to be 3000. The male patient is 3000 × 0.7% × 2/3=14, and the female patient is 3000 × 0.7% × 1/3=7. The carrier is 3000 × 5%=150. Then the frequency of X=(14+7 × 2+150)/(1500 × 2+1500)=3.96%.

Method 2: The ratio of men and women in the population is 1:1, according to X chromosome gene frequency The derivation formula of is calculated as follows:

The frequency of X=2/3 (0.7% × 1/3 × 2+0.7% × 2/3+5%)=3.96%.

Answer: Choose C.

In conclusion, although the calculation types of gene frequency are complex and diverse Thinking method They are quite different, but we can accurately calculate the correct answer as long as we grasp the conditions and methods of gene frequency calculation, understand the reason and flexibly apply them.

Main References

1. Li Nan. Course of Evolution. Beijing: Higher Education Press ，1990．9：244—276．

2． Zhu Zhengwei ， Zhao Zhanliang Biology Compulsory Course 2 Genetics and Evolution, Experimental Textbook of Curriculum Standard for Ordinary High School. Beijing: People's Education Press ，2007：115

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Also known as "law", British mathematician in 1908 Godfrey Harold Hardy （ Godfrey Harold Hardy ）First discovered and proved this law; In 1909, German doctor William Weinberg（ Wilhelm Weinberg ）Also Independent certification This law is named after Hardy -Weinberg's Law.

Mainly used to describe the group Allele Frequency and Genotype frequency Relationship between. The content is:

① One Infinity In an ideal situation Random mating , can still be maintained after several generations gene frequency Stable with genotype frequency Equilibrium state [1]。

② In a pair Allele In the case of（ dominance ）The relationship with gene frequency of gene q (invisible) is:

（p+q）^ two =1

Binomial expansion: p^ two +2pq+q^ two =1

Visible, where "p^ two ”For dominant homozygote 2pq is Heterozygote Scale of, "q^ two ”For Invisible homozygote Scale of.

Hardy Weinberg's Law polyploid It can also be applied in more complicated cases.

Example 1 In a population, AA individuals account for 30%, Aa individuals account for 60%, and aa individuals account for 10%. Calculate the frequency of A and a genes.

The frequency of dissecting A gene is 30%+1/2 × 60%=60%

The frequency of a gene is 10%+1/2 × 60%=40%

Answer 60% 40%

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Example 2 (2006 Hebei College Entrance Examination) guinea pig Medium, black to white dominance 。 If 90% of the gene pool is Dominant gene B. 10% Yes Recessive gene b， Then the frequency of genes BB, Bb and bb in the population is ()

A81% 18% 1%

B45% 40% 15%

C18% 81% 1%

D45% 45% 10%

Problem solving idea BB frequency is (90%) ^ 2=81%, bb frequency is (10%) ^ 2=1%, and Bb frequency is 2 × 90% × 10%=18%, so select A

Answer A

Original on an island Drosophila melanogaster 20000, of which genotype Drosophila melanogaster accounted for 15%, 55% and 30% of VV, Vv and vv respectively. If 2000 Drosophila melanogaster with VV genotype invaded from the island at this time, and all Drosophila melanogaster Random mating , then V in F1 gene frequency About what?

V gene frequency=(20000 * 15% * 2+20000 * 55%+2000 * 2)/44000=47.7%

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It is worth noting that diploid The gene contains the Allele The maximum number of individuals may be 2/5. If allele random distribution Then you can use binomial theorem To calculate: 32% of individuals in the population are heterozygotes of the allele (with one allele and another variant), and 4% of individuals are heterozygotes of the allele Homozygote (with two of these alleles). So in total, 36% of individuals have this allele. However, the random distribution of alleles is established on the premise that selection does not participate and other conditions. When these premises are true, the state of a population is called Hardy Weinberg equilibrium (en: Hardy Weinberg principle ）。

The frequency of all alleles in a gene can be mapped as allele distribution Histogram 。 Population genetics The contents of the study include the impact Allele The factor of frequency - in other words, evolution. In addition to natural and artificial selection, these factors also include Genetic drift , mutation and migration.

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