Download Chapter 1: Mendel`s breakthrough: patterns, particles and principles

Chapter 1: Mendel’s breakthrough:
patterns, particles and principles of
heredity
please read pages 10 through 13
R. Ward: Spring 2001
Slide 1 of Chapter 1
•One of Mendel’s express aims was to understand how first generation traits (parents) would disappear in the
second generation (F1 or hybrid) and reappear in the third generation (F2)
•Gregor Mendel conducted experiments with peas between 1857 and 1863
lPresented results in 1865
lPoorly received/understood: Karl Wilhelm von
Nageli, a noted Swiss botanist. Nageli, whose
thinking sometimes veered from science to mysticism, dismissed Mendel's work
Note: Correns, one of three re-discoverers in 1900, was a nephew of Nageli!
1
Plant life
cycles
Endosperm is 3N
2 copies of egg
chromosomes, 1 of
sperm
Maternal tissue:
seed coat=ovule wall
Pod/fruit wall= ovary wall
From: Plant Life Cycles and
Angiosperm Development:
Susan R. Singer from
Embryology: Constructing the
Organism (S.F. Gilbert and A.
M. Raunio, eds.) 1997. Sinauer
Associates, Sunderland, MA.
Seed
First 2N cell=zygote
Sperm and eggs= gametes (N)
Slide 2 of Chapter 1
R. Ward: Spring 2001
•Review the life cycles of plants and be familiar with these terms:
lSporophytic
lGametes
or maternal tissue
(sperm and eggs)
lpollination
and Fertilization
lZygote
2
Mendel’s Experimental Organism
R. Ward: Spring 2001
Slide 3 of Chapter 1
•experimental organism was the garden pea: advantagesØnaturally self pollinated which generates “true breeding” plants (later we’ll call these homozygous
plants)
Øeasily cross fertilized or cross-pollinated
Øreadily available clear-cut alternative forms of traits
Øseed traits (color, shape) allowed for easy generation of large data sets
3
Mendel’s traits
Slide 4 of Chapter 1
R. Ward: Spring 2001
ltwo of Mendel’s traits exhibited Xenia
•XENIA: genetic differences among pollen grains can manifest as phenotypic differences in seed set on
female parent in P generation.
lXenia
genes expressed in embryo (including cotyledons) or endosperm.
But not seed coat or pod attributes
lgenotypes of both egg and pollen determine phenotype
lphenotype of F1 generation manifest in F1 seeds produced on true breeding
female parent.
•Phenotype could vary within a pod
•seed shape: round vs wrinkled – embryo/cotyledon trait
•seed color: yellow vs green
lMendel
referred to this as “albumen” color
lactually
is color of cotyledon, which is embyronic tissue
lfive of Mendel’s traits manifest in flowers, pods or stem morphology
•phenotype of F1 generation manifest in plants grown from seeds produced by cross pollination
•pod shape: inflated vs constricted
lNote: P generation pods contain F1 seed, and F1 pods contain F2 seeds, etc.!
lTherefore, parental generation pods have same genotype and phenotype
irrespective of pollen
genotype
•pod color: green vs yellow
•flower/pod position: axillary vs terminal
•stem length: standard vs dwarf
4
Fn seed vs. Fn plants
pollen
P
plant
P
plant
Male
(pollen source)
Female
(emasculated)
F1
F2 plants
F1 seed
P seed
R. Ward: Spring 2001
P seed
F2 seed
Slide 5 of Chapter 1
•P generation fruit tissue (ovary walls=pericarp, ovule walls=seed coat) is derived from cells that are direct
descendents of the parental mitotic divisions of the zygote/embryo in the seed from which the P generation
plant arose. All such tissue is therefore genetically identical on a single plant, even if the P generation plant
was pollinated/fertilized by a genetically different plant.
•Seeds on P generation plants used as females in a cross-fertilization carry F1 generation embryos.
•Seeds can have three distinct tissuesØembryo, including cotyledons (can be different from mother plant)
Øseed coat (derived from maternal tissue just like the fruit wall or pericarp is)
Øendosperm- derived from union of two clones of the egg and one clone of the sperm
•The embryo represents the progeny, so fruits and seeds are bi-generational.
•This is important when considering mendel’s experiments since some traits are expressed in embryonic
tissue which is enclosed within ovule walls (seed coats) and ovary walls (pericarp)
5
Xenia in Pea
P1 male
•purple
flower
•yellow
seeds
•yellow pod
P1 female
•white
flower
•green seeds
•green pod
true breeding
(all progeny from self pollination
identical to mother plant)
R. Ward: Spring 2001
F1 seed
•all seed on female in the cross will have yellow
seed (since seed color is an embryonic trait, and
yellow is dominant to green)
•but pods are maternal tissue and not affected
by the pollen genotype
F1 plant
•purple flower only
•Seeds: ¼ green, ¾ yellow
•green pod only
Slide 6 of Chapter 1
•segregation for xenia traits can be viewed among seeds within pods of F1 plants.
•segregation for non-xenia traits only manifest on plants derived from the seed on the F1 plants (i.e., F2
seed).
6
Gregor Mendel: context and tools
• Background: the historical puzzle of inheritance
Fig. 1.6 from Hartwell et al
•Genetics involves:
Øcareful observation of populations over generations
R. Ward: Spring 2001
Slide 7 of Chapter 1
Øanalysis of carefully acquired data on individuals
Ødevelopment and testing of theoretical frameworks
•Mendel was the first person to put these three elements together to form a theory of inheritance
Øa great deal of observation took place in the time before Mendel
-huge efforts at cataloging species was conducted (Linnaeus, Darwin)
-cross fertilization within and among species was induced and observed
•Artificial selection was the first applied genetic practice
Øplants and animals were domesticated through selection of individuals that exhibited favorable traits (e.g., nonaggressiveness in the progenitors of domesticated dogs, horses, cattle etc.; longer seed retention in cereals, etc.)
•The puzzle of passing on desirable traits
Øby Mendel’s birth (1822), plant and animal breeders were able to generate individuals with new and valued
combinations of traits by controlled matings
Øbut the value of these progeny as parents was unpredictable (i.e., the value of an individuals own progeny was
unpredictable)
•Sheep breeding was a particularly important activity in Moravia, and at a 1837 conference of the Moravian Sheep Breeders
Society, the Abbott Cyril Napp proposed that breeders needed to discover three things:
Øwhat is inherited
Øhow is it inherited, and
Øwhat is the role of chance in inheritance?
•before Mendel, blending, preformation (e.g., the idea of a homunculus) and other erroneous theories were proposed to explain
the contradiction between 1) the obvious reality that members of a species had progeny who were of the same species; and 2)
the equally obvious reality that variation of individual phenotype (appearance) exists within and among families
•Mendel’s work laid the foundation for our current view of heredity
•Key features of his approach include:
Øfocus on a single species, the naturally self-pollinated but easily cross-pollinated annual pea (Pisum sativum)
Øfocus on traits that had distinct, mutually exclusive (“antagoni
-furthermore- Mendel worked with only two forms of each of the seven traits he studied
Øselection and propagation of “pure-breeding lines” which upon self-pollination produce progeny that are collectively
identical in form to their parents and to each other. Pure-breeding lines in a self-pollinated crop can be maintained in a
pure state throughout multiple generations simply by isolating their progeny from other lines.
Øcareful control of matings between plants of different pure-lines, with attention to which parent was used as the
female.
Øgeneration of large datasets consisting of observations on individual progeny plants
-note that the word ‘plant’ here is inclusive of the embryo within a seed.
Øcomparison of such results with predictions based on hypothetical models
7
Creating a monohybrid
P1 male
•yellow
seeds
P1 female
•green seeds
F1 seed
•all seed on female in the cross will have yellow
seed (since seed color is an embryonic trait, and
yellow is dominant to green)
true breeding
(all progeny from self pollination
identical to mother plant)
R. Ward: Spring 2001
Slide 8 of Chapter 1
•Genetic Analysis According to Mendel
•The embryos (i.e., progeny plants) that develop within the seeds of a plant used as a female in a cross (or hybridization) are
deemed an “F1” generation if the parents differed in at least one trait.
•analyses of the progeny of plants grown from the F1 seed was the basis of Mendel’s work
•Mendel began his work by focusing on one trait at a time
Øanalysis of the frequencies of alternate forms of a single trait in the P, F1, subsequent generations of one cross is called
“Monohybrid analyses”
Øin reality, the parents used in Mendel’s monohybrid crosses must have differed for other traits.
Øthe key is that Mendel ignored the other traits and focused on only one at a time (at first)
8
P, F1, and F2 generations
R. Ward: Spring 2001
Slide 9 of Chapter 1
•Figure 1.9: Monohybrid analysis of seed color in pea (an embryonic trait)
•Mendel took pollen from a yellow seeded pure breeding line and placed it on stigmas of emasculated flowers of plants from a
green seeded pure breeding line
•The F1 seeds (which matured in the pods on the female parent), were all yellow
Øthe reciprocal cross was also made (using the yellow seeded pure breeding line as the male parent)
Øagain, all of the F1 seeds were yellow
•Mendel planted the F1 seeds and allowed them to self pollinate and develop mature seed.
•The F2 seeds (which matured on the F1 plants) included both yellow and green forms of the seed color trait, in a ratio of
approximately 3 yellow for every 1 green seed.
•These results refuted the concept of blending, since the green form of the trait in the P generation reappeared in the F2 generation
after disappearing in the F1 generation.
•Mendel observed that there are two kinds of behavior of yellow pea derived plants:
Øsome breed true (have only yellow seed progeny upon self pollination)
Øsome generate both yellow and green seed upon self pollination
•Mendel hypothesized that
Ø1) for each trait, each plant carries two discrete copies of a unit of inheritance (which we now call genes)
Ø2) these genes come in two forms, which we now call “alleles”
Ø3) one allele is dominant and the other is recessive
-the yellow allele of the seed color gene in pea is dominant to the green allele of the same gene.
•The P generation plants in Fig. 1.9 either carry two dominant alleles (the yellow parent), or two recessive alleles (the green parent)
•F1 generation seeds in Figure 1.9 carry one yellow and one green allele.
•end
•end
9
The Law of Segregation
R. Ward: Spring 2001
Slide 10 of Chapter 1
•Figure 1.10: The law of segregation is two part
Ø1) gametes (sperm and eggs) contain only one allele of a given gene;
-pure breeding yellow peas form gametes that all have the yellow allele, and
-pure breeding green peas form gametes that all have the green allele
-F1 generation plants form both kinds of gametes in equal quantities ( ½ with the yellow
allele, and ½ with the green allele).
-in other words, both alleles can reside in and pass through an F1 generation without any
change in their fundamental behavior
-so alleles are SEGREGATED from each other in gamete formation
Ø2) Individual progeny are created from the random union of one male gamete and one female
gamete.
10
Self pollination of the F1 Generation
R. Ward: Spring 2001
Slide 11 of Chapter 1
•gametes have only one allele (Y or y)
•the two alleles of an F1 appear in equal frequencies in that F1’s gametes
•since the frequency of ‘Y’ equals the frequency of ‘y’ in both eggs and pollen of an F1,
•the probability of a random male gamete carrying ‘Y’ = 0.5, which equals the probability of it carrying the
‘y’ allele
•gametic union in self fertilization is random, leading to four possible ways to form a zygote:
Ø (egg-derived written first): Yy, YY, yY, and yy
•each of those outcomes has a probability of ¼, by two lines of reasoning:
Ønone of the four is more likely than the other, so they are equally probable
Øthe “Law of the Product” states that the probability of two (or more) independent events occurring
simultaneously ( or sequentially) equals the product of the probabilities of the individual events.
11
The outcomes of two “events” are independent if they
satisfy two constraints:
v1)
the outcome of one event doesn’t influence the
outcome of the other event; and
v2) they can occur together (i.e., they are not
mutually exclusive)
vexamples:
Ø two consecutive coin tosses- one coin doesn’t
influence the other; and it’s possible to do
Ø a ‘Y’ egg combining with a ‘y’ sperm- the
probability of the egg being ‘Y’ is not affected
by the identity of the sperm; and zygotes always
derive from one sperm and one egg
R. Ward: Spring 2001
Slide 12 of Chapter 1
12
Law of the Sum
v if
an event can be achieved by two or more mutually
exclusive routes, the probability of the event equals
the sum of all possible routes.
v the Yy genotype in the F2 generation depicted in
both Figures 1.9 and 1.11 can occur in one of two
mutually exclusive routes:
Ø
Ø
v Since
the probability of both routes equals 0.5, and
they are mutually exclusive, we add the probabilities
to determine the probability of a heterozygous F2
plant.
R. Ward: Spring 2001
Slide 13 of Chapter 1
•“events” are in the eye of the beholder
•possible events in the context of genetics:
Øthe genotype of a gamete randomly selected from one plant
Øthe phenotype of a plant randomly selected from a population of plants
Øa zygote is formed by union of an egg carrying ‘Y’ and a sperm c
Øa zygote is formed by union of an egg carrying ‘Y’ and a sperm c
13
Laws of probability in Action
just one way to
form YY or yy
two mutually
exclusive ways
to achieve Yy
R. Ward: Spring 2001
Slide 14 of Chapter 1
14
Frequencies and ratios
vFrequencies
are used in genetics to represent the
proportion that one class of individuals represents
of a whole population.
vA list of the frequencies of all classes is a
“frequency distribution”. A complete frequency
distribution must sum to 1.0 .
vWe often speak of “ratios” in genetics.
Frequency distributions are converted to ratios by
using the numerator of the fractional frequencies
after application of a common denominator.
R. Ward: Spring 2001
Slide 15 of Chapter 1
15
Frequencies and corresponding ratios:
examples
vBelow
are examples of frequency distributions
and their corresponding ratios
Frequency distribution Ratio
0.75 yellow, 0.25 green
3 yellow : 1 green
0.25 YY, 0.5Yy, 0.25 yy
1 YY : 2 Yy : 1 yy
0.8 tall, 0.2 short
4 tall : 1 short
R. Ward: Spring 2001
Slide 16 of Chapter 1
16
Inter-converting frequencies and ratios
v Assume you have 25 blue, 50 green, and 25 black marbles for a
total of 100 marbles.
v The Frequency distribution of marble colors is 1/4 blue : 1/2 green
: 1/4 black .
v The ratio of marble colors is 1 : 2 : 1 (blue/green/black)
v To convert from fractional frequencies to ratios,
Ø apply a common denominator to each frequency, (in this case the
common denominator is 4, so the freq. dist. becomes 1/4 blue : 2/4
green : 1/4 black).
Ø Then use the numerators to represent the ratios: 1 blue : 2 green : 1
black.
v To
convert a ratio to frequencies,
Ø sum each of the values in the ratio expression (in this case 1, 2 and
1, which sums to 4) ;
Ø and use that as the denominator under each of the ratio values. So
a ratio of 1 : 2 :1 translates into a frequency distribution of 1/4 : 2/4
: 1/4.
R. Ward: Spring 2001
Slide 17 of Chapter 1
17
Ratios and Frequencies of a subset of classes
v Ratios
among classes remain constant even if one or more classes
is discarded
v If we discard all of the black marbles from the slide above, the
ratio of blue to green marbles is unchanged and remains:
Ø 1 blue : 2 green
v But the frequencies in an original population do not equate with
the correct frequencies in a subset of classes. We had 1/4 blue
and 1/2 green when we had the black marbles included, but that
cannot be a complete frequency distribution since it does not sum
to 1.0 .
v To derive the correct frequencies of a subset of classes, first write
down the ratios (1 : 2), and then convert that to a frequency
distribution. The sum of ratio values is 1+2=3, so using 3 as the
denominator, the ratio of 1 : 2 converts to a frequency distribution
of 1/3 and 2/3.
R. Ward: Spring 2001
Slide 18 of Chapter 1
18
Frequencies and Ratios: an application (1 of 2)
¼
¼
1/4 YY
¼
¼
1/4 yy
2/4 Yy
•Ratio of homozygous to heterozygous Yellow
F2 Progeny: 1 YY : 2 Yy;
•Which is equivalent to a frequency
distribution of 1/3 YY and 2/3 Yy
R. Ward: Spring 2001
Slide 19 of Chapter 1
From fig. 1.12, Hartwell
•When we look only at the yellow progeny we are
•If you know the ratio of the occurrences of two events (for instance 1 YY for every 2 Yy), you can convert
the ratio into frequency distribution (frequency of each type of event- 1/4, 1/2, etc.) by summing the values
in the ratio ( in this case 2+1) and using that sum as a denominator for each events ratio value.
19
Frequencies and Ratios: an application (2 of 2)
Yellow
F2’s
YY
Yy
1/3 YY
2/3 Yy
Self pollination
F3
1/3 * [1/1 YY]
=4/12 YY
2/3 * [1/4 YY 2/4 Yy 1/4 yy]
= 2/12 YY 4/12 Yy 2/12 yy
Ratio 6(=4+2) YY : 4 Yy :2 yy
Yellow
F3’s
Ratio 6 YY : 4 Yy
Frequencies 6/10 YY, 4/10 Yy; or 3/5 YY, 2/5 Yy
R. Ward: Spring 2001
Slide 20 of Chapter 1
•Why multiply the frequencies of genotypes derived from Yy by 2/3?
•Because two independent events are required for a given genotype to occur in the progeny of a Yy F2 plant.
Øfirst, the F2 had to be Yy. That probability is 2/3
Øsecond, the probability of, say, YY is 1/4 in the progeny of a Yy F2
•Since these two events are independent, we multiply the two probabilities: 2/3 * 1/4 = 2/12
20
Some Definitions
R. Ward: Spring 2001
Slide 21 of Chapter 1
•Phenotype- appearance
•Genotype- Alleles present in cells of a plant for one or more genes
•Homozygous- both alleles of a gene are identical
•Heterozygous- the two alleles are different
21
Further proof of the law of segregation and Ratios:
Progeny testing of F2 seed
¼
1/4 YY
¼
¼
¼
1/4 yy
2/4 Yy
•Ratio of homozygous to heterozygous Yellow
F2 Progeny: 1 YY : 2 Yy;
•Which is equivalent to a frequency
distribution of 1/3 YY and 2/3 Yy
R. Ward: Spring 2001
Slide 22 of Chapter 1
From fig. 1.12, Hartwell
•As shown earlier, self-pollination of an F1 plant generates F2 seed that has a segregation ratio of 3:1 yellow
to green seeds
22
Mendels experiments 1 of 2
pure-breeding
(plant, grow,
collect pollen)
P
plant
x
pure-breeding
(plant, grow,
grow, emasculate)
Harvest ->F2 seed: 3:1 ratio
of yellow to green seeds
(in pods of F1 plants)
1/3 Y
breed
true
2/3 Y
segregate
F2
plants
P
plant
F1
plant(s)
F2
plant
F2
plants
Harvest-> F1 seed:all yellow
(in pods of female plant)
Slide 23 of Chapter 1
R. Ward: Spring 2001
all green
F3
(pure
breeding)
•Mendel’s Monohybrid experiment with seed color (an embryo trait)
•F2 segregated in a 3:1 ratio of yellow to green (F2 seed is in F1 plant pods)
•Progeny tests of F2 seed were conducted
Øgrow F2 plants from F2 seed
Øharvest F3 seed from each plant separately, categorize F2 plants as having progeny that are:
-all green (pure breeding green- yy homozygotes)
-all yellow (pure breeding yellow- YY homozygotes)
- 3:1 yellow to green segregation- Yy heterozygotes
ØResults showed :
•that all green F2 seeds produced plants that on self pollination had only green seeds.
•1/3 of yellow F2 seeds produced plants that on self pollination had only yellow seeds, and
•2/3 of yellow F2 seeds produced plants that on self pollination had yellow and green seeds in
a 3:1 ratio
•Mendel also conducted test crosses of F2 plants yellow F2 seeds
Øcross yellow F2 plants with pure breeding green parent
Ø1/3 of yellow F2 plants pollinated with pollen from pure breeding green parent had only yellow
seed (Yy)
Ø2/3 of yellow F2 plants pollinated with pollen from pure breeding green parent had 1/2 green and
1/2 yellow seed
23
Mendels experiments 1 of 2
R. Ward: Spring 2001
Slide 24 of Chapter 1
24
Dihybrid crosses
R. Ward: Spring 2001
Slide 25 of Chapter 1
25
Dihybrid cross introduction
Monohybrid
F1
F2
3 Yellow: 1 Green
Di
hy
br
id
Cr
os
s
3 Round: 1 Wrinkled
Note: Round/Wrinkled trait is a
xenia trait like seed color
X
Dihybrid F1
R. Ward: Spring 2001
Slide 26 of Chapter 1
26
What progeny will appear in the dihybrid F2?
Dihybrid F1
SELF POLLINATION
?
•would only ‘parental’ phenotypes occur?
•i.e., yellow round and green wrinkled in
a 3:1 ratio?
•or could ‘recombinants’ occur, i.e.,
•yellow wrinkled or green round?
R. Ward: Spring 2001
Slide 27 of Chapter 1
27
Recombinants did occur in the dihybrid F2
Phenotypes seen in the Pods on dihybrid F1 plants
indicates
unknown
allele
R. Ward: Spring 2001
Slide 28 of Chapter 1
•both parental and recombinant phenotypes occurred in the F2 generation
Øseeds in pods on selfed F1 dihybrid plants
Øgreen round and yellow wrinkled seeds were not present in the parents and are new combinations of
the parental traits. We call these ‘recombinant’ phenotypes.
•without progeny testing, we don’t know if a yellow seed is homozygous dominant or heterozygous; the
same is true for round seeds
•to indicate this uncertainty, we represent a dominant phenotype with a the dominant allele symbol (‘Y’ or
‘R’), followed by a dash. The dash indicates that the second allele could be either the dominant or the
recessive form.
•for recessive phenotypes, we know the genotype (wrinkled is ‘rr’
yy’)
28
Dihybrid Data confirms monohybrid 3:1
416 : 140
3.18 : 1
R. Ward: Spring 2001
Slide 29 of Chapter 1
•Mendel observed the combined phenotype 556 F2 seeds
•in the parental classes there were:
Ø315 of the parental phenotype with both dominant traits (yellow, round)
Ø32 of the parental phenotype with both recessive traits (green, wrinkled)
•in the recombinant classes there were:
Ø108 of the green, round; and
Ø101 of the yellow, wrinkled
•grouping the yellows together (ignoring the seed shape trait), there were 416 round seeds
•grouping the green seeds together (ignoring the seed shape trait), there were 140 wrinkled seeds
Øthis gives a 416: 140 ratio, or a 3.18: 1 ratio, which is the expected ratio for a monohybrid
segregation with dominance.
29
Dihybrid Data confirms monohybrid 3:1 (2)
423 : 133
2.97 : 1
R. Ward: Spring 2001
Slide 30 of Chapter 1
•the ratio of round : wrinkled (ignoring the color trait) was also very close to 3 : 1
30
Independent assortment: Mendel’s second law
vthe
law of segregation applied for both traits
vin other words, the two traits segregated
independently of each other
Ø i.e., green occurred independent of wrinkled even
though they were together in the parents
vWe
say that alleles of these two genes “assort”
independently of each other
vit would be simpler, and still accurate to say that
these two genes “segregate independently” from
each other
R. Ward: Spring 2001
Slide 31 of Chapter 1
•“Law of independent assortment: during gamete formation, different pairs of alleles segregate independently
of each other” (Hartwell et al pg 22)
31
Dihybrids form four kinds of gametes
R. Ward: Spring 2001
Slide 32 of Chapter 1
•gametes receive one or the other, but not both types of alleles at a single heterozygous gene
•this is true for each gene, so gametes in a dihybrid (considering only the genes of interest), will receive one
allele from the color gene, and one from the shape gene.
•the law of independent assortment states that this joint distribution occurs such that the allele that a gamete
receives for one gene does not influence which allele it receives from a second gene.
•Since the probabilities of ‘Y’ and ‘y’ are equal (i.e., both = 0.5), and the same is true for ‘R’ vs. ‘r’, and the
segregation for Y/y is independent of R/r, each of the joint outcomes (YR, Yr, yR, yr) each equal 0.5 x 0.5 =
0.25 or ¼.
32
dihybrid punnett
R. Ward: Spring 2001
Slide 33 of Chapter 1
•the Punnet square illustrates that there are 16 ways to combine the four types of gametes together in
fertilization. Each of these ways has a probability of 1/16.
•But there are only 9 genotypes and 4 phenotypes possible
33
dihybrid punnett (2)
1
2
4
5
2
3
5
6
4
5
7
8
5
6
8
9
R. Ward: Spring 2001
ID
Geno.
cnt
1
2
3
4
5
6
7
8
9
YYRR
YYRr
YYrr
YyRR
YyRr
Yyrr
yyRR
yyRr
yyrr
1
2
1
2
4
2
1
2
1
Slide 34 of Chapter 1
•in this case, each cell in the punnett square has the same probability
Øbecause each gamete has an equal probability, and the product of the frequencies of the two
gametes combining to make a cell in the punnett square is the frequency of that cell. In this case, all
gametes have a probability of 1/4, and all cells in the punnett have a frequency of 1/16 (1/4* 1/4) by
the law of the product
•There are 4 gametes from a dihybrid. The general formula for the number of gametes is 2n, where n is the
number of heterozygous loci in the plant generating the gametes.
•There are 9 distinct genotypes (ignoring parental origin of alleles) in the progeny of a dihybrid. The general
formula is for the number of genotypes in the progeny of a selfed plant is 3n where n =the number of
heterozygous loci. The ratio of genotypes is based on the number of ways that a given F2 genotype can
occur. Each of the cells represents a way that a genotype can occur in the F2. If a genotype can occur 2
ways (YYRr, YyRR, Yyrr, yyRr), then its probability is 2 * 1/16 (i.e., 1/16 + 1/16), because of the law of the
sum.
•In this case we have only 4 phenotypes.
34
Phenotypic frequencies in a dihybrid F2
vY-
and R- each have a frequency of 3/4 in the F2.
vyy and rr each have a frequency of 1/4 in the F2
vcombinations that are possible (phenotypically) in
the F2 are:
Ø Y-R- prob= 3/4*3/4= 9/16
Ø Y-rr
prob=3/4*1/4=3/16
Ø yyR- prob=1/4*3/4=3/16
Ø yyrr prob=1/4*1/4=1/16
vF2
ratio is then: 9:3:3:1
R. Ward: Spring 2001
Slide 35 of Chapter 1
35
Independence of segregation proved by ratio of the four
phenotypes in a dihybrid F2
R. Ward: Spring 2001
Slide 36 of Chapter 1
•product law only works if two events are independent.
•If seed color and shape were controlled by a single gene (pleiotropy), then the frequency of Y-R- would
have been 3/4, not 9/16.
•So independent assortment proven by the presence of recombinants, and the predicted ratios or frequencies
based on the law of the product.
36
Mendel used test crosses to confirm genotypic ratios in dihybrid
F2s
R. Ward: Spring 2001
Slide 37 of Chapter 1
•crosses to a plant that is homozygous recessive at all loci (that you are studying) is called a test cross.
•This figure illustrates testcross outcomes for each of the 4 genotypes that produce the Yellow Round
phenotype in the F2. Each testcross has a unique outcome, thereby defining the genotype of the tested plant.
•Mendel found that the genotypic ratios matched that which was predicted by the law of independent
assortment.
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Summary: Mendel’s Contributions
v inferred
the existence of genes, units of inheritance
the reappearance of ‘hidden’ traits that
disappeared in an F1 generation
v disproved the theory of blended inheritance
v demonstrated that both the male and female parent
contribute equally to the next generation
v revealed the two basic principles of gene transmission:
v explained
Ø segregation of each gene’s alleles during gamete
formation
Ø the independent assortment of alleles of two or more
genes
R. Ward: Spring 2001
Slide 38 of Chapter 1
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