Mendel’s Four Postulates

1
Mendels Four Postulates

• Unit factors in pairs
• genetic characteristics are controlled by unit
  factors which exist in pairs
• genes on homologous chromosomes diploid
  individuals

2
Mendels Four Postulates ...

• Dominance/recessiveness
• When two unlike unit factors are present in a
  single individual, one is usually dominant to the
  other, which is recessive
• One allele may be dominant to a second
  heterozygotes express phenotype of dominant allele

3
Mendels Four Postulates ...

• Random segregation
• During the formation of gametes, the paired unit
  factors separate (segregate) randomly so that
  each gamete receives one or the other
• Homologous chromosomes segregate into different
  gametes

4
Mendels Four Postulates ...

• Independent assortment
• During the formation of gametes, segregating
  pairs of factors assort independently of each
  other
• Genes on non-homologous chromosomes will assort
  into gametes independently of one another
  (Remember meiosis)
• Aa Bb --gt AB Ab aB ab

5
Monohybrid cross(one trait)
Purple X White
parentals or P generation
first filial or F1 generation
Purple
6
Monohybid cross ...
Purple F1 X Purple F1
Purple White
1/4
3/4
7
Monohybrid cross ...
Purple X White
PP
pp
Purple
Pp
8
Monohybrid cross ...
Purple F1 X Purple F1
Pp
Pp
F2
PP
Pp
Pp
pp
9
Monohybrid cross ...

• Mendel found same ratios no matter what trait he
  used
• Data provide the basis for his first three
  postulates

10
Review of monohybrid cross and Mendels first
three postulates

• Heredity is controlled by unit factors in pairs
• trait which was hidden in the F1 reappears
• no blending, discrete units
• 31 ratio explained by paired units
• Modern translation genes are carried on each of
  two homologous chromosomes

11
Review ...

• One unit factor may be dominant to another
• F1 generation all have the same phenotype as one
  of the parents
• The purple allele masks the white allele
• Heterozygotes express phenotype of dominant allele

12
Review ...

• Random segregation each gamete receives one or
  the other unit factor
• 31 ratio in F2 indicate each factor equally
  likely to be passed on
• Heterozygotes produce 2 types of gametes 1/2 w/
  one allele, 1/2 w/ other

13
Rules for labeling genes and alleles

• Use same letter for each allele of a gene
• Generally use the first letter of one allele
• Choose letter for which upper and lower case are
  easily distinguishable

14
Rules for labeling ...

• Use upper case for the dominant allele lower
  case for the recessive
• Example
• Free vs. attached earlobes
• Free F attached f

15
Rules for labeling ...

• Sometimes, one allele is said to be the wild type
• this is simply the most common allele in the
  population
• may be dominant or recessive
• in Drosophila, the flies normally have red eyes
  this is wild type

16
Rules for labeling

• Wild type is sometimes symbolized with a
• eye color in fruit flies
• red white w
• and w red
• w w white

17
Brief review

• Gene vs. allele vs. locus
• gene - segment of DNA coding for a trait
• allele - specific form of the gene
• locus - location on the chromosome of the gene
• Gene flower color
• Alleles purple and white

18
Brief review ...

• Genotype
• The genetic make-up of the individual what
  alleles it has
• heterozygous
• homozygous recessive
• homozygous dominant

19
Brief review ...

• Phenotype
• The outwardly detectable trait what the
  individual looks like, etc.

AA and Aa give phenotype A
aa gives phenotype a
20
Dihybrid Cross

• Looking at two traits at the same time
• two genes
• two alleles each
• Here we will see evidence for Mendels 4th
  Postulate Independent Assortment

21
Dihybrid Cross
smooth, yellow X wrinkled, green
SS YY
ss yy
smooth, yellow
F1
Ss Yy
22
Dihybrid Cross ...
Ss Yy X Ss Yy
Remember We are now dealing with two
independent genes! Each individual will pass
on one allele of each gene.
23
Punnett Squares

• Step 1 what kinds of gametes will each produce?
• gametes are haploid -- carry one copy of each
  gene
• Heterozygotes produce 1/2 gametes with one
  allele, 1/2 with the other (random segregation)
• There can be ANY combination of alleles of
  independent genes. INDEPENDENT ASSORTMENT

24
Punnett Squares ...

• Helpful hint
• The number of different types of gametes an
  individual will produce is equal to 2n where
  n the number of heterozygous loci

25
Punnett Squares ...
s
S
Y
y

• Back to our example
• Ss Yy X Ss Yy
• 22 gametes for each (parents identical)
• four types of gametes each
• SY Sy sY sy
• Review meiosis to prove this!

26
Punnett Squares ...

• Assign gametes from one parent to rows
• Assign gametes from second parent to columns

SS YY
27
Punnett Squares ...

• Ratios obtained through a Punnett square tell you
  the expected frequencies of those phenotypes in
  the offspring
• 3/16 of the offspring should be smooth, green
• Another way of looking at it any given
  offspring has a 3/16 chance of being smooth,
  green
• You can work backwards ratios are clues to
  genotypes of parents

28
Test Crosses

• cross between an individual of unknown genotype
  and a homozygous recessive individual
• allows us to deduce the genotype of the unknown
  parent

29
Test Crosses ...
DR
DD RR X dd rr
dr
30
Test Crosses ...
DD Rr X dd rr
31
Test Crosses ...
Dd RR X dd rr
32
Test Crosses ...
Dd Rr X dd rr
33
In mice, agouti fur color is dominant to white.
Spotting is recessive to no spots. A solid,
agouti mouse is mated to a spotted, white mouse
producing 3 solid, agouti mice and 4 solid,
white mice. What are the genotypes of the
parents?
Offsprings genotypes Ss Aa and Ss
aa
Parents genotypes SS Aa and ss
aa
34
In mice, agouti fur color is dominant to white.
Spotting is recessive to no spots. A spotted,
agouti mouse is mated to a solid white mouse
producing 3 spotted, agouti mice and 2 spotted
white mice. What are the genotypes of the
parents?
Offsprings genotypes
Parents genotypes
35
Review of phenotypic ratiosin offspring

• Monohybrid
• homozygote X homozygote --gt heterozygote
• heterozygote X heterozygote --gt 31
• heterozygote X homozygous recessive --gt 11
  

36
Review of phenotypic ratiosin offspring

• Dihybrid
• homozygote X homozygote --gt heterozygote
• heterozygote X heterozygote --gt 9331
• heterozygote X homozygous recessive --gt
  1111

37
Reciprocal crosses

• Does it matter which sex has which trait?
• i.e., male red-eyed fly X brown female or
  male brown-eyed X red female?
• NO!

RR X rr --gt Rr
rr X RR --gt Rr

• For autosomal traits (traits located on non-sex
  chromosomes)reciprocal crosses will give
  identical results.

38
Trihybrid crosses and beyond!

• Trihybrid crosses deal with three independent
  traits at once
• i.e., flower color, plant height, and seed color
• each gene is independent!
• each gene has two alleles

39
Trihybrid crosses ...

• The basic concepts are the same as with mono- or
  dihybrid crosses
• Just remember
• each gamete must have ONE COPY OF EACH GENE
• random segregation and independent assortment
  still apply

40
Trihybrid crosses ...
tall, pinched pod, axial X dwarf, inflated,
terminal
tt PP aa
TT pp AA
tall, inflated, axial
F1
Tt Pp Aa
F1 X F1 --gt ?
41
Trihybrid crosses ...

• Step one Figure out the gametes produced by
  each parent (use 2n)
• Parents Tt Pp Aa 23 8
• eight possible gametes from each parent
• TPA TPa TpA tPATpa tPa tpA tpa

42
Forked-line Method

• Breaks down multi-hybrid crosses into a series of
  monohybrid crosses
• Combine the individual ratios (multiply) to get
  the final ratio

43
Forked-line Method ...
Tt Pp Aa X Tt Pp Aa
Break into Tt X Tt Pp X Pp Aa X Aa
Tt X Tt --gt 3/4 T 1/4 t
Pp X Pp --gt 3/4 P 1/4 p
Aa X Aa --gt 3/4 A 1/4 a
44
Forked-line ...
F2 offspring
lt
3/4 A
--gt 27/64 TPA
3/4 P
1/4 a
--gt 9 /64 TPa
lt
3/4 T
lt
3/4 A
--gt 9 /64 TpA
1/4 p
1/4 a
--gt 3 /64 Tpa
lt
3/4 A
--gt 9 /64 tPA
3/4 P
lt
1/4 a
--gt 3 /64 tPa
1/4 t
lt
3/4 A
--gt 3 /64 tpA
1/4 p
1/4 a
--gt 1 /64 tpa
45
Forked-line ...

• Can find genotypic ratios
• substitute 1/4 TT 1/2 Tt 1/4 tt, etc.
• Can go straight to one phenotype or genotype
• ignore all branches except those leading to the
  desired phenotype or genotype

46
Forked-line ...
What proportion of the offspring of the cross Ss
Nn Vv X Ss nn VV will be genotype Ss Nn Vv?
47
Forked-line ...
What proportion of the offspring of the cross Ss
Nn Vv X Ss nn VV will be phenotype SNV?
48
Forked-line ...
What proportion of the offspring of the cross Cc
Dd Ee Rr X cc Dd ee Rr will be phenotype cder?
49
Aa Bb cc DD Ee Ff gg x Aa Bb Cc Dd ee ff Gg
1. What proportion of offspring phenotype
AbcDEFg?
2. What proportion of offspring genotype
AAbbCcDdEeFfGg?
50
Ratios -- one more time!

• Monohybrid
• Aa X Aa --gt 31
• Aa X aa --gt 11
• Dihybrid
• Aa Bb X Aa Bb --gt 9331
• Aa Bb X aa bb --gt 1111
• Trihybrid
• AaBbCc X AaBbCc --gt 279993331
• AaBbCc X aabbcc --gt 11111111