A man and a woman are each heterozygous carriers of an autosomal recessive mutation of a disorder that is fatal in infancy. They both want to have multiple children, they are concerned about the risk of the disorder appearing in one or more of their children. In separate calculations, determine the probabilities of the couple having five children with 0, 1, 2, 3, 4, and all 5 children being affected by the disorder.

0.2373, 0.0794, 0.0263, 0.0087, 0.0029, 0.0010

Explanation:

Let Aa be the heterozygous genotype for the autosomal recessive character.

Since both parents are heterozygous (Aa) the possibility genotype of one child is AA Aa Aa aa

Since the disease is a recessive disorder, the probability of giving birth to an affected child is 1/4 and the probability of giving birth to unaffected child is 3/4.

If the couple are having 5 children:

1. The probability of 0 Affected

Since 0 is affected it means 5 are unaffected.

(3/4)^5 = 243/1024 = 0.2373

2. The probability of 1 affected children

Since 1 is affected it means 4 are unaffected

1/4 * (3/4)^4 = 1/4 * 81/256 = 81/1024 = 0.0794

3. The probability of 2 affected children

Since 2 are affected it means 3 are unaffected

(1/4)^2 * (3/4)^3 = 1/16 * 27/64 = 27/1024 = 0.0263

4. The probability of 3 affected children

Since 3 are affected it means 2 are unaffected

(1/4)^3 * (3/4)^2 = 1/64 * 9/16 = 9/1024 = 0.0087

5. The probability of 4 affected children

Since 4 are affected it means 1 is unaffected

(1/4)^4 * (3/4)= 1/256 * 3/4 = 3/1024 = 0.0029

6. The probability of all five children affected

(1/4)^5 = 1/1024 = 0.0010

the african cheetah.

this species has a relatively low level of genetic

variation because the population was reduced to a small size approxi-

mately 10,000 to 12,000 years ago.

chapter   outline

24.1

genes in populations and the hardy-

weinberg equation

24.2

factors that change allele and genotype

frequencies in populations

24.3     sources of new genetic variation

population   genetics

24

until   now,   we   have   primarily   focused   our   attention   on   genes  

within   individuals   and   their   related   family   members.   in   this  

chapter   and   chapters   25   and   26   ,   we   turn   to   the   study   of   genes   in  

a   population   or   species.   the   field   of

population   genetics

  is   con-

cerned   with   changes   in   genetic   variation   within   a   group   of   indi-

viduals   over   time.   population   geneticists   want   to   know   the   extent  

of   genetic   variation   within   populations,   why   it   exists,   and   how   it  

changes   over   the   course   of   many   generations.   the   field   of   popu-

lation   genetics   emerged   as   a   branch   of   genetics   in   the   1920s   and  

1930s.   its   mathematical   foundations   were   developed   by   theoreti-

cians   who   extended   the   principles   of   gregor   mendel   and   charles  

darwin   by   deriving   formulas   to   explain   the   occurrence   of   geno-

types   within   populations.   these   foundations   can   be   largely   attrib-

uted to three scientists: sir ronald fisher, sewall wright, and j. b. s.

haldane.   as   we   will   see,   support   for   their   mathematical   theories  

was provided by several researchers who analyzed the genetic com-

position   of   natural   and   experimental   populations.   more   recently,  

population   geneticists   have   used   techniques   to   probe   genetic  

variation   at   the   molecular   level.   in   addition,   staggering   advances  

in   computer   technology   have   aided   population   geneticists   in   the  

analysis   of   their   genetic   theories   and   data.   in   this   chapter,   we   will  

explore   the   genetic   variation   that   occurs   in   populations   and   con-

sider   the   reasons   why   the   genetic   composition   of   populations   may  

change over the course of several generations