Effects of Selection on HardyWeinberg

1
Effects of Selection on Hardy-Weinberg Consider
a population with 2 alleles, A1 and A2, such
that A1 p 0.4 A2 (1-p) 0.6 So, p2
2p(1-p) (1-p)2 .42 2 (.4)(.6) .62 .16
A1A1 .48 A1A2 .36 A2A2 ? 1.0
2
Effects of Selection on Hardy-Weinberg Select
against the recessive, A2A2, HW p2 2p(1-p)
(1-p)2 .42 2 (.4)(.6) .62 .16 A1A1 .48
A1A2 .36 A2A2 Select against the recessive,
A2A2,
3

• Effects of Selection on Hardy-Weinberg
• Select against the recessive, A2A2,
• HW p2 2p(1-p) (1-p)2
• .42 2 (.4)(.6) .62
• .16 A1A1 .48 A1A2 .36 A2A2
• First recalculate allelic frequencies
• (.16 A1A1 .48 A1A2) 0.64
• Freq. of A1 .08 .08 (.5)(.48) / .64
  0.625 p
• Freq. of A2 by calculation or subtraction
  0.375 (1-p)
• Second recalculate HW
• .6252 2(.625)(.375) .3752
• .390625 A1A1 .46875 A1A2 .140625 A2A2

4

• Effects of Selection on Hardy-Weinberg
• Select against the recessive, A2A2,
• HW p2 2p(1-p) (1-p)2
• .42 2 (.4)(.6) .62
• .16 A1A1 .48 A1A2 .36 A2A2
• .390625 A1A1 .46875 A1A2 .140625 A2A2
• Is this population in HW Equal.?

5

• Effects of Selection on Hardy-Weinberg
• Select against the recessive, A2A2,
• HW p2 2p(1-p) (1-p)2
• .42 2 (.4)(.6) .62
• .16 A1A1 .48 A1A2 .36 A2A2
• .390625 A1A1 .46875 A1A2 .140625 A2A2
• Is this population in HW Equal.?
• Determine by recalculating HW frequencies!
• p.390625 (.5)(.46875) 0.625 A1 previous
  generation
• Therefore this generation is in HWE AND we had
  decreased the proportion of A2A2 from 0.36 to
  0.14

6
Effects of Selection on Hardy-Weinberg Selection
After Pollination In the previous example, we
made selections before pollination, i.e. we
removed some plants and allowed the remainder to
intermate without restriction (population
size??) What happens to HW if we cant see A2A2
until after pollination? Well, lets start with
the same population .16 A1A1 .48 A1A2 .36
A2A2 Essentially, our selections are going to be
maternal selections i.e., the pollen can and
will come from any plant in the nursery but we
will attempt to select on A1A1 and A1A2 females
7

• Effects of Selection on Hardy-Weinberg
• Selection After Pollination
• Therefore
• let pf and (1-pf) the freq. of A1 and A2 for
  the female gametes
• and pm and (1-pm) the freq. of A1 and A2 for
  the male gametes
• Such that for the female gametes
• .16 A1A1 .48 A1A2 .36 A2A2 (same original
  population)
• First recalculate allelic frequencies
• (.16 A1A1 .48 A1A2) 0.64
• Freq. of A1 .08 .08 (.5)(.48) / .64
  0.625 pf
• Freq. of A2 by calculation or subtraction
  0.375 (1-pf)

8
Effects of Selection on Hardy-Weinberg Selection
After Pollination Therefore let pf and (1-pf)
the freq. of A1 and A2 for the female gametes and
pm and (1-pm) the freq. of A1 and A2 for the
male gametes Since we do not select male
gametes they will have the same allelic
frequencies as the original population, i.e pm
.4 A1m 1-pm .6 A2m Such that HW
becomes pmpf pm(1-pf) pf(1-pm)
(1-pm)(1-pf)
9
Effects of Selection on Hardy-Weinberg Selection
After Pollination Therefore If pm .4 AND 1-pm
.6 AND pf .625 AND 1-pf .375 (SEE NEXT
DUPLICATE SLIDE) Then HW becomes pmpf
pm(1-pf) pf(1-pm) (1-pm)(1-pf) (.4)(.625)
A1A1 .4(.375) .625(.6) A1A2 (.6)(.375)
A2A2 .25 A1A1 .525 A1A2 .225 A2A2 ? 1.0
10

• Effects of Selection on Hardy-Weinberg
• Select against the recessive, A2A2,
• HW p2 2p(1-p) (1-p)2
• .42 2 (.4)(.6) .62
• .16 A1A1 .48 A1A2 .36 A2A2
• First recalculate allelic frequencies
• (.16 A1A1 .48 A1A2) 0.64
• Freq. of A1 .08 .08 (.5)(.48) / .64
  0.625 p
• Freq. of A2 by calculation or subtraction
  0.375 (1-p)
• Second recalculate HW
• .6252 2(.625)(.375) .3752
• .390625 A1A1 .46875 A1A2 .140625 A2A2

11
Effects of Selection on Hardy-Weinberg Selection
After Pollination .25 A1A1 .525 A1A2 .225
A2A2 ? 1.0 Is this population in HWE? First
recalculate p and (1-p) p .25 (.5)(.525)
.5125 1-p .4875 Therefore (.5125)2
2(.5125)(.4875) (.4875)2 .262656 A1A1
.499688 A1A2 .237656 A2A2 ? 1.0
12
Effects of Selection on Hardy-Weinberg Selection
After Pollination .25 A1A1 .525 A1A2 .225
A2A2 ? 1.0 Is this population in HWE? First
recalculate p and (1-p) p .25 (.5)(.525)
.5125 1-p .4875 Therefore (.5125)2
2(.5125)(.4875) (.4875)2 .262656 A1A1
.499688 A1A2 .237656 A2A2 ? 1.0
NO WHY NOT?
13

• Quantitative Genetics Plant Breeding
• HWE states that genotypic and allelic freq. will
  not change in a cross pollinating species under
  the following assumptions
• random mating
• no selection is practiced (naturally or
  otherwise)
• no differential migration
• mutation rates are equal, i.e. A?a a?A
• species in question is diploid
• usually considering 1 gene and 2 alleles or 1
  allele of an allelic series against all other
  alleles in the series

14

• Effects of Selection on Hardy-Weinberg
• Original cross pollinating population in HWE
• .16 A1A1 .48 A1A2 .36 A2A2
• Selection against A2A2 before pollination
• .390625 A1A1 .46875 A1A2 .140625 A2A2
• Selection against A2A2 after pollination
• .25 A1A1 .525 A1A2 .225 A2A2
• So selection before pollination (i.e. control
  both male and female gametic selection) is about
  twice as effective as after pollination!

15
Effects of Selection on Hardy-Weinberg What if
this had been a self pollinating population? What
would have been our progress with 1 generation of
selection against A2A2? Original genotypic
frequencies .16 A1A1 .48 A1A2 .36
A2A2 Therefore the new genotypic frequencies
are .16/(.16 .48) .25 A1A1 .48/(.16 .48)
.75 A1A2
16
Effects of Selection on Hardy-Weinberg What if
this had been a self pollinating population? What
would have been our progress with 1 generation of
selection against A2A2? Original genotypic
frequencies .16 A1A1 .48 A1A2 .36
A2A2 Therefore the new genotypic frequencies
are .16/(.16 .48) .25 A1A1 .48/(.16 .48)
.75 A1A2
.25(.75) A1A1 .5(.75) A1A2 .25(.75) A2A2
.1875 A1A1 .375 A1A2 .1875 A2A2
17
Effects of Selection on Hardy-Weinberg What if
this had been a self pollinating population? What
would have been our progress with 1 generation of
selection against A2A2? Original genotypic
frequencies .16 A1A1 .48 A1A2 .36
A2A2 Therefore the new genotypic frequencies
are .16/(.16 .48) .25 A1A1 .48/(.16 .48)
.75 A1A2
.25(.75) A1A1 .5(.75) A1A2 .25(.75) A2A2
.1875 A1A1 .375 A1A2 .1875 A2A2
.25 .1875 A1A1 .375 A1A2 .1875 A2A2 ..4375
A1A1 .375 A1A2 .1875 A2A2 ? 1.0
18

• Effects of Selection on Hardy-Weinberg Versus
  Selfing
• Original cross pollinating population in HWE
• .16 A1A1 .48 A1A2 .36 A2A2
• Selection against A2A2 before pollination
• .390625 A1A1 .46875 A1A2 .140625 A2A2
• Selection against A2A2 after pollination
• .25 A1A1 .525 A1A2 .225 A2A2
• Selection in the same population through natural
  or forced selfing
• ..4375 A1A1 .375 A1A2 .1875 A2A2