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--- chapter_20 [2024/09/14 20:03] – [First cousin marriages] mike
+++ chapter_20 [2024/09/15 09:31] (current) – mike
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 <- chapter_19|Chapter 19^table_of_contents|Table of Contents^chapter_21|Chapter 21 ->
-<typo fs:x-large>Chapter 19. Effects of inbreeding</typo>
+<typo fs:x-large>Chapter 20. Effects of inbreeding</typo>
 In this chapter we will examine how inbreeding between close relatives (also known as consanguineous matings) influences the appearance of autosomal recessive traits. Inbreeding will not make a difference for dominant traits because they need only be inherited from one parent or for X-linked traits in males since they are inherited from the mother.
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 $$p(\text{homozygous by descent})=F_\text{cousins}=\frac{1}{64}+\frac{1}{64}+\frac{1}{64}+\frac{1}{64}=\frac{1}{16}$$
-Clearly, $F_\text{siblings}$ is significantly greater than $F_\text{cousins}$. Now, let's imagine that there is a rare recessive disease allele $a$, where the allele frequency $f(a)=q=10^{-4}$. If we assume that this allele exists in a large population and mating is random, the frequency of homozygotes due to random mating is $f_\text{random}(a/a)=q^2=10^{-8}$. In the United States, first cousin marriages happen at around 1 in 1000 marriages, or 10<sup>-3</sup>. Therefore, the frequency of $a/a$ honozygosity from first cousin marriages $f_\text{cousins}(a/a)=\frac{1}{16}\times 10^{-8)\times 10^{-3}=6.3\times 10^{-9}$, The ratio of $\frac{f_\text{cousins}}{f_\text{random}}=\frac{6.3 \times 10^{-9}}{10^{-8}}=0.63. in other words, two-thirds of all affected individuals will come from a first cousin marriage.
+Clearly, $F_\text{siblings}$ is significantly greater than $F_\text{cousins}$. Now, let's imagine that there is a rare recessive disease allele $a$, where the allele frequency $f(a)=q=10^{-4}$. If we assume that this allele exists in a large population and mating is random, the frequency of homozygotes due to random mating is $f_\text{random}(a/a)=q^2=10^{-8}$. In the United States, first cousin marriages happen at around 1 in 1000 marriages, or 10<sup>-3</sup>. Therefore, the frequency of $a/a$ honozygosity from first cousin marriages $f_\text{cousins}(a/a)=\frac{1}{16}\times 10^{-8}\times 10^{-3}=6.3\times 10^{-9}$, The ratio of $\frac{f_\text{cousins}}{f_\text{random}}=\frac{6.3 \times 10^{-9}}{10^{-8}}=0.63$. in other words, two-thirds of all affected individuals will come from a first cousin marriage.
 Note that the proportion we calculated above depends on our assumption of allele frequency ($q=10^{-4}$). If allele frequency is very rare, affected individuals will more often be a result of consanguineous marriages. For rare diseases, it is often difficult to tell whether or not they are of genetic
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 ===== Recessive lethal alleles =====
+For much of our discussion up to this point, we have used 10<sup>-4</sup> as an estimate for the frequency of recessive loss of function alleles in the human population. This may seem like a comfortably small number but given that the total number of human genes is about 2x10<sup>4</sup>, each of us must be carrying many recessive loss of function alleles. If we start with a guess that about 50% of genes are essential, this means that each person should carry on average $(2\times 2\times 10^4)(0.5\times 2\times 10^{-4})= 4$ recessive lethal mutations!
+We can determine whether this is a good estimate or not by measuring the genetic load. We define genetic load as the number of lethal mutation equivalents per genome. Usually the genetic load is not a problem since it is very unlikely that both parents will happen to have lethal mutations in the same genes. However, that chance is considerably increased for parents that are first cousins. As we have already calculated, the probability that an allele from a grandparent will become homozygous is 1/64 for 1st cousins. Thus, each recessive lethal allele for which one of the grandparents is a carrier will
+contribute an increased probability of 0.016 (one-sixteenth) that the grandchild will be homozygous and
+therefore be afflicted by a lethal inherited defect.
+We will use the frequency of stillbirth or neonatal death from first cousin marriages to estimate this. We must be careful to subtract the background frequency of stillbirths and neonatal deaths that are not due to genetic factors. These frequencies can be obtained from the cases where parents are not related.
+<table Tab1>
+<columns 100% *100%*>
+^    ^  unrelated parents  ^  first cousins  ^  difference  ^
+|  Observed frequency of still- \\ birth or neonatal death  |  0.04  |  0.11  |  0.07  |
+</columns>
+<caption>
+placeholder
+</caption>
+</table>
+If the adjusted frequency of stillbirths and neonatal deaths from first cousin marriages is $f_\text{cousins}=0.07$, and this frequency is adjusted at a rate of 0.016 above the general population, this means that the average frequency for recessive lethal alleles in both grandparents is $\frac{0.07}{0.016}=4.4$. Each grandparent (and therefore a typical person in the population) has an average of $\frac{4.4}{2}=2.2$ recessive lethal alleles in their genome. Our estimate of the recessive loss of function mutation rate (10<sup>-4</sup>), as well as our guess of the percentage of essential genes (50%), were reasonably close.