ケント・E・ホルジンガーがウェブ上で公表している集団遺伝学テキストから抜粋。
特に13章が印象的で、6つの仮説検定をカイ2乗分布で行い自然選択の有無を判定する
Chapter 9
Two-locus population genetics
省略する
Part II
The genetics of natural selection
Chapter 10
The Genetics of Natural Selection
The only assumption we’ve violated so far is Assumption #2, the random-mating assumption. We’re going to spend the next several lectures talking about what happens when you violate
Assumptions #3, #6, and #8. When any one of those assumptions is violated we have some form of natural selection going on
We’ll use the following notation throughout our discussion:
Symbol Definition
N number of individuals in the population
x11 frequency of ST/ST genotype
x12 frequency of ST/CH genotype
x22 frequency of CH/CH genotype
w11 fitness of ST/ST genotype, probability of surviving from egg to adult
w12 fitness of ST/CH genotype
w22 fitness of CH/CH genotype
We’ll be using the convention that genotype frequencies in eggs (or newly-formed zygotes) are the genotype frequencies before selection and that genotype frequencies in adults are the
genotype frequencies after selection.
This illustrates the following general principle:
The consequences of natural selection (in an infinite population) depend only on the relative magnitude of fitnesses, not on their absolute magnitude.
That means, for example, that in order to predict the outcome of viability selection, we don’t have to know the probability that each genotype will survive, their absolute viabilities.
We only need to know the probability that each genotype will survive relative to the probability that other genotypes will survive, their relative viabilities.
Fisher’s Fundamental Theorem of Natural Selection.
For now all you need to know is that viability selection causes the mean fitness of the progeny generation to be greater than or equal to the mean fitness of the parental generation, with equality only at equilibrium, i.e., ¯ w' ≥ w .
Figure 10.1: With directional selection (in this case w11 > w12 > w22) viability selection leads to an ever increasing frequency of the favored allele.
Ultimately, the population will be monomorphic for the homozygous genotype with the highest fitness.
Two-locus population genetics
省略する
Part II
The genetics of natural selection
Chapter 10
The Genetics of Natural Selection
The only assumption we’ve violated so far is Assumption #2, the random-mating assumption. We’re going to spend the next several lectures talking about what happens when you violate
Assumptions #3, #6, and #8. When any one of those assumptions is violated we have some form of natural selection going on
We’ll use the following notation throughout our discussion:
Symbol Definition
N number of individuals in the population
x11 frequency of ST/ST genotype
x12 frequency of ST/CH genotype
x22 frequency of CH/CH genotype
w11 fitness of ST/ST genotype, probability of surviving from egg to adult
w12 fitness of ST/CH genotype
w22 fitness of CH/CH genotype
We’ll be using the convention that genotype frequencies in eggs (or newly-formed zygotes) are the genotype frequencies before selection and that genotype frequencies in adults are the
genotype frequencies after selection.
This illustrates the following general principle:
The consequences of natural selection (in an infinite population) depend only on the relative magnitude of fitnesses, not on their absolute magnitude.
That means, for example, that in order to predict the outcome of viability selection, we don’t have to know the probability that each genotype will survive, their absolute viabilities.
We only need to know the probability that each genotype will survive relative to the probability that other genotypes will survive, their relative viabilities.
Fisher’s Fundamental Theorem of Natural Selection.
For now all you need to know is that viability selection causes the mean fitness of the progeny generation to be greater than or equal to the mean fitness of the parental generation, with equality only at equilibrium, i.e., ¯ w' ≥ w .
Figure 10.1: With directional selection (in this case w11 > w12 > w22) viability selection leads to an ever increasing frequency of the favored allele.
Ultimately, the population will be monomorphic for the homozygous genotype with the highest fitness.
Figure 10.2: With disruptive selection (w11 > w12 < w22) viability selection may lead either to an increasing frequency of the A allele or to a decreasing frequency. Ultimately, the population will be monomorphic for one of the homozygous genotypes. Which homozygous genotype comes to predominate, however, depends on the initial allele frequencies in the population.
Fisher’s Fundamental Theorem tells us which of these equilibria matter. I’ve already mentioned that depending on which side of the bowl you start, you’ll either lose the A1 allele or
the A2 allele. But suppose you happen to start exactly at the bottom of the bowl. That corresponds to the equilibrium with ˆ p = s2/(s1 + s2). What happens then? Well, if you start exactly there, you’ll stay there forever (in an infinite population). But if you start ever so slightly off the equilibrium, you’ll move farther and farther away. It’s what mathematicians call an unstable equilibrium. Any departure from that equilibrium gets larger and larger. For evolutionary purposes,
we don’t have to worry about a population getting to an unstable equilibrium. It never will. Unstable equilibria are ones that populations evolve away from.
Fisher’s Fundamental Theorem tells us which of these equilibria matter. I’ve already mentioned that depending on which side of the bowl you start, you’ll either lose the A1 allele or
the A2 allele. But suppose you happen to start exactly at the bottom of the bowl. That corresponds to the equilibrium with ˆ p = s2/(s1 + s2). What happens then? Well, if you start exactly there, you’ll stay there forever (in an infinite population). But if you start ever so slightly off the equilibrium, you’ll move farther and farther away. It’s what mathematicians call an unstable equilibrium. Any departure from that equilibrium gets larger and larger. For evolutionary purposes,
we don’t have to worry about a population getting to an unstable equilibrium. It never will. Unstable equilibria are ones that populations evolve away from.
Figure 10.3: With stabilizing selection (w11 < w12 > w22; also called balancing selection or heterozygote advantage) viability selection will lead to a stable polymorphism.
All three genotypes will be present at equilibrium.
Unlike directional selection or disruptive selection, in which natural selection tends to eliminate one allele or the other, stabilizing selection tends to keep both alleles in the
population.
Chapter 11
Estimating viability
Consider that our data looks like this:
All three genotypes will be present at equilibrium.
Unlike directional selection or disruptive selection, in which natural selection tends to eliminate one allele or the other, stabilizing selection tends to keep both alleles in the
population.
Chapter 11
Estimating viability
Consider that our data looks like this:
Since Wij is a probability and the outcome is binary (survive or die),
you should be able to guess what kind of likelihood relates the observed data to the unseen parameter, namely, a binomial likelihood.
P93の画像
So it looks as if we have balancing selection, i.e., the fitness of the heterozygote exceeds that of either homozygote.
確かに、MAOA遺伝子の反復パターンでも2R/2Rは少なく2R/3Rと2R/4Rである
Chapter 12
Selection at one locus with many alleles, fertility selection, and sexual selection
Selection at one locus with multiple alleles
sickle-cell anemia とは、黒人に多い鎌形赤血球による貧血のことだ
glutamic acid =グルタミン酸
valine＝たんぱく質を構成する必須アミノ酸の1つ
lysine＝必須アミノ酸の1つ。ほとんどのたんぱく質中に存在
An example
The way we always teach about sickle-cell anemia isn’t entirely accurate. We talk as if there is a wild-type allele and the sickle-cell allele. In fact, there are at least three
alleles at this locus in many populations where there is a high frequency of sickle-cell allele. In the wild-type, A, allele there is a glutamic acid at position six of the β chain
of hemoglobin. In the most common sickle-cell allele, S, there is a valine in this position. In a rarer sickle-cell allele, C, there is a lysine in this position.
The fitness matrix looks like this:
A S C
A 0.976 1.138 1.103
S 0.192 0.407
C
0.550
There is a stable, complete polymorphism with these allele frequencies:
Pa= 0.83 Ps = 0.07 Pc = 0.10 .
If allele C were absent, A and S would remain in a stable polymorphism:
Pa = 0.85 Ps = 0.15
If allele A were absent, however, the population would fix on allele C.
The existence of a stable, complete polymorphism does not imply that all subsets of alleles could exist in stable polymorphisms. Loss of one allele as a result of random chance
could result in a cascading loss of diversity
If the fitness of AS were 1.6 rather than 1.103, C would be lost from the population, although the A−S polymorphism would remain.
Fertility selectionは、省略
Sexual selectionは、省略
Chapter 13
Selection Components Analysis
H1: Half of the offspring from heterozygous mothers are also heterozygous.
H2: The frequency of transmitted male gametes is independent of the mother’s genotype.
H3: The frequency of the transmitted male gametes is equal to the allele frequency in adult males.
H4: The genotype frequencies of reproductive females are the same as those of “sterile” females.
H5: The genotype frequencies of adult females and adult males are equal.
H6: The genotype frequencies in the adult population are equal to those of the zygote population.
以上の6つの仮説を一度立て、カイ2乗分布で判定する。
Well, there’s a very nice approach known as selection components analysis that generalizes the approach to estimating relative viabilities that we’ve already seen
エステラーゼ（Esterase）は、エステルを水との化学反応で酸とアルコールに分解する加水分解酵素である。
確かに、MAOA遺伝子の反復パターンでも2R/2Rは少なく2R/3Rと2R/4Rである
Chapter 12
Selection at one locus with many alleles, fertility selection, and sexual selection
Selection at one locus with multiple alleles
sickle-cell anemia とは、黒人に多い鎌形赤血球による貧血のことだ
glutamic acid =グルタミン酸
valine＝たんぱく質を構成する必須アミノ酸の1つ
lysine＝必須アミノ酸の1つ。ほとんどのたんぱく質中に存在
An example
The way we always teach about sickle-cell anemia isn’t entirely accurate. We talk as if there is a wild-type allele and the sickle-cell allele. In fact, there are at least three
alleles at this locus in many populations where there is a high frequency of sickle-cell allele. In the wild-type, A, allele there is a glutamic acid at position six of the β chain
of hemoglobin. In the most common sickle-cell allele, S, there is a valine in this position. In a rarer sickle-cell allele, C, there is a lysine in this position.
The fitness matrix looks like this:
A S C
A 0.976 1.138 1.103
S 0.192 0.407
C
0.550
There is a stable, complete polymorphism with these allele frequencies:
Pa= 0.83 Ps = 0.07 Pc = 0.10 .
If allele C were absent, A and S would remain in a stable polymorphism:
Pa = 0.85 Ps = 0.15
If allele A were absent, however, the population would fix on allele C.
The existence of a stable, complete polymorphism does not imply that all subsets of alleles could exist in stable polymorphisms. Loss of one allele as a result of random chance
could result in a cascading loss of diversity
If the fitness of AS were 1.6 rather than 1.103, C would be lost from the population, although the A−S polymorphism would remain.
Fertility selectionは、省略
Sexual selectionは、省略
Chapter 13
Selection Components Analysis
H1: Half of the offspring from heterozygous mothers are also heterozygous.
H2: The frequency of transmitted male gametes is independent of the mother’s genotype.
H3: The frequency of the transmitted male gametes is equal to the allele frequency in adult males.
H4: The genotype frequencies of reproductive females are the same as those of “sterile” females.
H5: The genotype frequencies of adult females and adult males are equal.
H6: The genotype frequencies in the adult population are equal to those of the zygote population.
以上の6つの仮説を一度立て、カイ2乗分布で判定する。
Well, there’s a very nice approach known as selection components analysis that generalizes the approach to estimating relative viabilities that we’ve already seen
エステラーゼ（Esterase）は、エステルを水との化学反応で酸とアルコールに分解する加水分解酵素である。
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