Assignments Falconer & Mackay, chapters 1 and 2

AssignmentsFalconer & Mackay, chapters 1 and 2 (1.5, 1.6, 2.5, and 2.6) Sanja Franic VU University Amsterdam 2011

1.4 As an exercise in algebra, work out the gene frequency of a recessive mutant in a random-breeding population that would result in one-third of normal individuals being carriers.

1.4 As an exercise in algebra, work out the gene frequency of a recessive mutant in a random-breeding population that would result in one-third of normal individuals being carriers. • (q-x)2=q2 – 2xq + x2 • 2x=1 • x=.5 • (q-.5)2=q2 – q + .52

1.5 Three allelic variants, A, B, and C, of red cell acid phosphatase enzyme were found in a sample of 178 English people. All genotypes were distinguishable by electrophoresis, and the frequencies in the sample were What are the gene frequencies in the sample? Why were no CC individuals found?

1.5

1.5 (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc

1.5 (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc AA BB CC AB AC BC

1.5 (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc (but this is assuming Hardy-Weinberg eq.) AA BB CC AB AC BC

1.5 Without assuming anything, we can count: a=.096+.5(.483+.028)=.3515 b=.343+.5(.483+.05)=.6095 c=0+.5(.028+.05)=.039 (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc (but this is assuming Hardy-Weinberg eq.) AA BB CC AB AC BC

1.5 Without assuming anything, we can count: a=.096+.5(.483+.028)=.3515 b=.343+.5(.483+.05)=.6095 c=0+.5(.028+.05)=.039 Now, back to Hardy-Weinberg expectations: c2=.0392=.001521 .001521*178=.27, so less than 1 individual (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc (but this is assuming Hardy-Weinberg eq.) AA BB CC AB AC BC

1.5 Without assuming anything, we can count: a=.096+.5(.483+.028)=.3515 b=.343+.5(.483+.05)=.6095 c=0+.5(.028+.05)=.039 Now, back to Hardy-Weinberg expectations: c2=.0392=.001521 .001521*178=.27, so less than 1 individualBtw: is the system in Hardy-Weinberg eq.? a2=.124 2ab=.428 b2=.371 2ac=.027 c2=.0015 2bc=.048 (a+b+c)2= a2 + b2 + c2 + 2ab + 2ac + 2bc (but this is assuming Hardy-Weinberg eq.) AA BB CC AB AC BC

1.6 About 7% of men are colour-blind in consequence of a sex-linked recessive gene. Assuming Hardy-Weinberg equilibrium, what proportion of women are expected to be (1) carriers, (2) colour-blind? (3) In what proportion of marriages are both husband and wife expected to be colour-blind?

1.6 About 7% of men are colour-blind in consequence of a sex-linked recessive gene. Assuming Hardy-Weinberg equilibrium, what proportion of women are expected to be (1) carriers, (2) colour-blind? (3) In what proportion of marriages are both husband and wife expected to be colour-blind? XX XY

1.6 About 7% of men are colour-blind in consequence of a sex-linked recessive gene. Assuming Hardy-Weinberg equilibrium, what proportion of women are expected to be (1) carriers, (2) colour-blind? (3) In what proportion of marriages are both husband and wife expected to be colour-blind?

2.5 Medical treatment is, or will be, available for several serious autosomal recessive diseases. What would be the long-term consequences if treatment allowed sufferers from such a disease to have on average half the number of children that normal people have, whereas without treatment they would have no children? Assume that the present frequency is the mutation versus selection equilibrium, that in the long term a new equilibrium will be reached, and that no other circumstances change.

2.5 Medical treatment is, or will be, available for several serious autosomal recessive diseases. What would be the long-term consequences if treatment allowed sufferers from such a disease to have on average half the number of children that normal people have, whereas without treatment they would have no children? Assume that the present frequency is the mutation versus selection equilibrium, that in the long term a new equilibrium will be reached, and that no other circumstances change. Aa aa AA 1-s 1 fitness

2.5 Medical treatment is, or will be, available for several serious autosomal recessive diseases. What would be the long-term consequences if treatment allowed sufferers from such a disease to have on average half the number of children that normal people have, whereas without treatment they would have no children? Assume that the present frequency is the mutation versus selection equilibrium, that in the long term a new equilibrium will be reached, and that no other circumstances change. Aa 1-hs=1 aa AA 1-s=1-1=0 1 fitness Old s=1 New s=.5 h=0

2.5 Medical treatment is, or will be, available for several serious autosomal recessive diseases. What would be the long-term consequences if treatment allowed sufferers from such a disease to have on average half the number of children that normal people have, whereas without treatment they would have no children? Assume that the present frequency is the mutation versus selection equilibrium, that in the long term a new equilibrium will be reached, and that no other circumstances change. Aa 1-hs=1 aa AA 1-s=1-1=0 1 fitness Old s=1 New s=.5 h=0 Equilibrium: u=sq2 q2=u/s Old equilibrium: q2=u/s q2=u New equilibrium: q2=u/s q2=u/.5=2u So at the new equilibrium, the frequency of recessive homozygotes (aa) will double.

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births.

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004 If u1=2u0, Δq=?

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004 If u1=2u0, Δq=? u1=2*.0004=.0008

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004 If u1=2u0, Δq=? u1=2*.0004=.0008 change from mutation: Δq=p0u1+q0v Δq=p0u1 Δq=.98*.0008 Δq=.000784 change from selection: Δq=-sq02(1-q0) Δq=-.0004*.98 Δq=-.000392

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004 If u1=2u0, Δq=? u1=2*.0004=.0008 change from mutation: Δq=p0u1+q0v Δq=p0u1 Δq=.98*.0008 Δq=.000784 change from selection: Δq=-sq02(1-q0) Δq=-.0004*.98 Δq=-.000392 total change: Δq=.000784-.000392 Δq=.000392 q1=q0+ Δq q1=.020392 q12=.0004158

2.6 Cystic fibrosis is an autosomal recessive human disease with an incidence of about 1 in 2,500 live births among Caucasians. What would be the consequence in the immediately following generation if the mutation rate were doubled? Assume that the present frequency is the mutation versus selection equilibrium, that back-mutation is negligible, and that affected individuals have no children. Express your result as a percentage increase of incidence and as the number of additional cases per million births. So, q02=.0004, q12=.0004158. Difference = .0000158 .0000158/.0004=.0395 -> there are 3.95% more aa homozygotes .0000158*1,000,000=15.8 -> around 16 more births per million q0=.02 p0=.98 s=1 v=0 q02=u0/s u0=.0004 If u1=2u0, Δq=? u1=2*.0004=.0008 change from mutation: Δq=p0u1+q0v Δq=p0u1 Δq=.98*.0008 Δq=.000784 change from selection: Δq=-sq02(1-q0) Δq=-.0004*.98 Δq=-.000392 total change: Δq=.000784-.000392 Δq=.000392 q1=q0+ Δq q1=.020392 q12=.0004158

Assignments Falconer & Mackay, chapters 1 and 2