2 Kings 6:17
17 And Elisha prayed, "O LORD,
open his eyes so he may see."
Then the LORD opened the
servant's eyes, and he looked
and saw the hills full of horses
and chariots of fire all around
Elisha.
©2000 Timothy G. Standish
Mendelian Genetics
Timothy G. Standish, Ph. D.
©2000 Timothy G. Standish
Biography - Gregor Mendel
Father of classical genetics.
Born 1822 to peasant family in the Czech
village of Heinzendorf (now called Hyncice),
northern Moravia, part of the AustroHungarian empire at the time
1843 - Admitted to the St. Thomas
Augustinian Monastery in Brunn (Brno),
southern Moravia, now in the Czech Republic
Studied mathematics in Olmutz college
©2000 Timothy G. Standish
Biography - Gregor Mendel:
Education
Attended University of Vienna 1851 1853. Influenced by:
– Franz Unger, a plant physiologist who
believed new species could come about via
hybridization.
– Christian Doppler, physicist who
discovered the Doppler effect. Sharpened
his math skills.
1854 Returned to Brunn
©2000 Timothy G. Standish
Biography - Gregor Mendel:
Research
Studied peas which he grew in a garden
outside of the Abbey where he lived
starting 1856 (3 years prior to
publication of Origin of Species).
Showed that the traits he studied
behaved in a precise mathematical way
and disproved the theory of "blended
inheritance."
©2000 Timothy G. Standish
Biography - Gregor Mendel:
Publication and Death
1865 first reported results of his work
Published rules of transmission of
genes in 1866 (handwritten in German,
not Latin!). Work was totally ignored.
1868 - Elected Abbot of the monastery
and ceased investigation of inheritance
1884 - Died of kidney failure
©2000 Timothy G. Standish
Biography - Gregor Mendel:
Rediscovery
Mendel’s work was rediscovered in
1900 by three botanists:
– Carl Correns (Germany)
– Erich von Tschermak (Austria)
– Hugo de Vries (Holland)
©2000 Timothy G. Standish
Why Peas?
Mendel used peas to study inheritance because:
True breeding commercial strains were available
Peas are easy to grow
Peas have many easy to observe traits including:
–
–
–
–
–
–
–
Seed color - Green or yellow
Seed shape - Round or wrinkled
Pod color - Green or yellow
Pod shape - Smooth or constricted
Flower color - White or purple
Flower position - Axial or terminal
Plant size - Tall or dwarf
©2000 Timothy G. Standish
Why Peas?
Pea flowers are constructed in such a way
that they typically self fertilize
Because of this, it is relatively easy to
control crosses in peas
Pea flower
©2000 Timothy G. Standish
Why Peas?
Pea flowers are constructed in such a way
that they typically self fertilize
Because of this, it is relatively easy to
control crosses in peas
Anthers
Pea flower
Stigma
©2000 Timothy G. Standish
Why Peas?
By removing the anthers of one flower and
artificially pollinating using a brush, crosses
can be easily controlled in peas.
©2000 Timothy G. Standish
Why Peas?
By removing the anthers of one flower and
artificially pollinating using a brush, crosses
can be easily controlled in peas.
©2000 Timothy G. Standish
Why Peas?
By removing the anthers of one flower and
artificially pollinating using a brush, crosses
can be easily controlled in peas.
..
.........
©2000 Timothy G. Standish
Why Peas?
By removing the anthers of one flower and
artificially pollinating using a brush, crosses
can be easily controlled in peas.
..
.........
©2000 Timothy G. Standish
Why Peas?
By removing the anthers of one flower and
artificially pollinating using a brush, crosses
can be easily controlled in peas.
........
©2000 Timothy G. Standish
Mendel’s Results
When crossing purple-flowered peas with
white-flowered peas, Mendel got the
following results:
In the first filial (F1) generation all offspring
produced purple flowers
In the second generation (second filial or F2):
– 705 purple
– 224 white
Approximately a 3:1 ratio of purple to white
©2000 Timothy G. Standish
Interpreting Mendel’s Results
Because the F1 generation did not produce lightpurple flowers and because white flowers
showed up in the F2 generation, Mendel
disproved blended inheritance.
Mendel said that the parents had two sets of
genes, thus two copies of the flower color gene
Each gene has two varieties called alleles
In the case of the flower color gene the two
alleles are white and purple
©2000 Timothy G. Standish
Interpreting Mendel’s Results
In the F1 generation, the white allele was
hidden by the purple “dominant” allele
In the F2 generation, 1/4 of the offspring wound
up with two copies of the white allele thus they
Heterozygous parents
were white
Homozygous
make gametes either
Gametes F1 Generation
from the P
generation
C C
c Cc Cc
c Cc Cc
parents can only one or the other allele
make gametes Fwith
2 Generation
one type of allele
The F1 Generation
is all heterozygous
C
C
c
CC Cc
c Cc cc
©2000 Timothy G. Standish
Mendel’s Results
Trait
F1 Results F2 Results
Dominent traits
round/wrinkled All Round
5,474
Round
1,850 wrinkled
mask
recessive
yellow/green All Yellow
6,022 Yellow 2,001 green
traits
full/constricted All Full
882 Full
299 constricted
Masked recessive
Pods
traits reappear
Seeds
green/yellow
axial/terminal
All Green
All Axial
428 Green
651 Axial
152 yellow
207 terminal
violet/white
All Violet
705 Violet
224 white
Tall/dwarf
All Tall
787 Tall
277 dwarf
Flowers
Stem
©2000 Timothy G. Standish
Mendel’s Results
F2 Results
F2 Ratios
Seeds
Seeds
5,474 Round 1,850 wrinkled 2.96:1 Round:wrinkled
6,022 Yellow 2,001 green
3.01:1 Yellow :green
882 Full
299 constricted 2.95:1 Full:constricted
Pods
428 Green
651 Axial
152 yellow
207 terminal
2.82:1 Green:yellow
3.14:1 Axial:terminal
Flowers
224 white
Stem
787 Tall
l
Pods
Flowers
705 Violet
l
3.15:1 Violet:white
Stem
277 dwarf
2.84:1 Tall:dwarf
l
Ratios are not
exactly 3:1
How do we
decide if the
ratios are
close enough
to 3:1 to
support and
not reject our
theory?
The chi
square
statistical test
provides the
tool used for
this purpose
©2000 Timothy G. Standish
Chi Square
Statistics fall into two categories:
1 Descriptive - Summarize characteristics of a data
set
– Mean, standard deviation . . .
2 Decision making - Assist in deciding whether a
set of data is consistent or inconsistent with a
hypothesis called the null hypothesis
– T test, f test, chi square . . .
Called chi square after the Greek letter “c” or “X”
2
Chi Square:
d =
=
2


C
e
2
(Obs. Ex.)
Ex
©2000 Timothy G. Standish
Chi Square:
On Mendel’s Seed Texture Data
2
Chi Square:
d =
=
2


C
e
2
(Obs. Ex.)
Ex
Obs.
Ex.
O-E
(O-E)2/E
Round 5,474 (1,850+5,474) x 3/4 = 5,493 5,474 - 5,493 =-19 -192/5,493 = 0.066
wrinkled 1,850 (1,850+5,474) x 1/4 = 1,831 1,850 - 1,831 = 19 192/1,831 = 0.20
X2 =
0.266
Degrees of freedom = N - 1 = 2 - 1 = 1
0.90 > p > 0.50 that this amount of deviation is
due to chance
In this case we retain the hypothesis that this data
represents a 3:1 ratio
©2000 Timothy G. Standish
Chi Square:
On Mendel’s Flower Color Data
2
Chi Square:
d =
=
2


C
e
2
(Obs. Ex.)
Ex
Obs.
Ex.
O-E
(O-E)2/E
Violet 705 (705+224) x 3/4 = 697 705 - 697 = 8 82/697 = 0.092
white 224 (705+224) x 1/4 = 232 224 - 232 =-8 -82/232 = 0.276
X2 =
0.368
Degrees of freedom = N - 1 = 2 - 1 = 1
0.90 > p > 0.50 that this amount of deviation is
due to chance
In this case we retain the hypothesis that this data
represents a 3:1 ratio
©2000 Timothy G. Standish
Mendel’s Conclusions
1 Phenotypic traits are controlled by pairs of
genes which act as individual units of
inheritance
2 In genes that have multiple alleles (variations)
the presence of some traits, called dominant
traits, masks the presence of recessive traits
3 Gene pairs segregate randomly during gamete
formation with either member of a pair
equally likely to end up in a given gamete
But do multiple genes assort independently?
©2000 Timothy G. Standish
Mendel’s Experiment:
A Case Study In Good Science
Gregor Mendel’s investigation of principles
of inheritance is a case study in how science
should be done:
He asked a good question
Chose an appropriate organism to work with
Practiced reductionism
Made good use of his data and allowed it
(not prevailing theory) to drive his
conclusions
©2000 Timothy G. Standish
Mendel’s Dihybrid Cross
Mendel chose to see if the round and yellow seed
genes segregated independently
P Generation
F1
F2
Ratio
Round green
RRyy
X
wrinkled Yellow
rrYY
All Round Yellow 315 Round Yellow
9/16
RrYy
RrYy RRYy or RrYY
101 wrinkled Yellow 3/16
rrYy or rrYY
108 Round green
3/16
RRyy or Rryy
32 wrinkled green
1/16
rryy
In other dihybrid crosses a 9:3:3:1 ratio was also
found
©2000 Timothy G. Standish
3 Reasons Mendel’s Work
Was Ignored
Mendel was not on the ball
Biologists were idiots (at
least when it came to math)
Lack of independent
supporting discoveries
©2000 Timothy G. Standish
Reasons Mendel’s
Work Was Ignored:
1) Mendel was not on the ball
Wrote in an obscure journal
(Proceedings of the Natural History
Society of Brunn).
Wrote in German, not Latin.
Mendel was not well known and did not
persevere in his attempt to push his
ideas.
©2000 Timothy G. Standish
Reasons Mendel’s
Work Was Ignored:
2) Biologists were idiots
Biologists didn’t understand math
Biologists were interested in the
explaining the transmission of continuous
traits like height, esp. after publication of
Origin of Species in 1859. Mendel
suggested that inherited characteristics
were discrete units (discontinuous).
©2000 Timothy G. Standish
Reasons Mendel’s
Work Was Ignored:
3) Lack of independent supporting
discoveries:
There was no physical element in which
Mendel’s inherited particles could be
identified.
By the turn of the century, chromosomes
had been discovered (physical particles)
and biologists were better at math.
©2000 Timothy G. Standish
Chromosomes:
The Physical Basis of Inheritance
1866 Mendel published his work
1875 Mitosis was first described
1890s Meiosis was described
1900 Mendel's work was rediscovered
1902 Walter Sutton, Theodore Boveri
and others noted parallels between
behavior of chromosomes and alleles.
©2000 Timothy G. Standish
Chromosomal Theory
of Inheritance
Genes have specific loci on
chromosomes.
Chromosomes undergo segregation
(meiosis) and independent
assortment,
Thus alleles of genes are
independently assorted.
©2000 Timothy G. Standish
Chromosomal Theory
of Inheritance Telophase I
E
Prophase I
Crossing Over
e
Replication
E
n
E e
n N
E
e
n
N
e
n
N
e
E
e
n
N
N
n
e
N
E
N
E
e
E
n
Telophase II
N
n
©2000 Timothy G. Standish
Independent Assortment
Eggs
As long as genes are on
different chromosomes,
they will assort
independently
Sperm
EN En
eN
en
EN
EENN
EENn
EeNN
EeNn
En
EENn
EEnn
EeNn
Eenn
eN
EeNN
EeNn
eeNN
eeNn
en
EeNn
Eenn
eeNn
eenn
©2000 Timothy G. Standish
Two Genes On One
Chromosome Telophase I
Prophase I
Replication
E
E
e
e
e
E
e
A
A
E
a
A
a
a
A
E e
A A
a a
Telophase II
a
As long as genes on the same
chromosome are located a long
distance apart, they will assort
independently due to crossing
over during Prophase I of
meiosis
E e
E
e
E
e
A
A
a
a
©2000 Timothy G. Standish
Laws Of Probability
Because alleles are usually distributed randomly,
the laws of probability can describe their behavior:
1 Product Law - Describes the probability of two or
more independent events occurring in a defined
sequence or way
2 Sum Law - Describes the probability of two or
more individual mutually exclusive events
3 Conditional Probability - Probability of events in
which both events share some dependent condition
4 Binomial Expansion - The probability of a set of
events arranged in no specified order
©2000 Timothy G. Standish
Determination of Gamete and
Zygote Variability
Number of
Heterozygous
Pairs
n
1
2
3
4
Number of
Different
Gametes
2n
2
4
8
16
Number of
Different
Genotypes
3n
3
9
27
81
Number of
Different
Phenotypes
2n
2
4
8
16
©2000 Timothy G. Standish
Laws Of Probability:
1 Product Law
l
l
l
l
l
l
The “and” law
Describes the probability of two or more
independent events occurring in a defined
sequence or way.
Example - What is the probability of flipping a
coin and getting heads and then tails?
Probability of getting heads on the first flip = 0.5
Probability of heads on the second flip = 0.5
Total probability = 0.5 x 0.5 = 0.25
©2000 Timothy G. Standish
Laws Of Probability:
2 Sum Law
l
l
l
l
l
l
The “or” law
Describes the probability of two or more
individual mutually exclusive events
Example - What is the probability of flipping a
coin and getting heads or tails?
Probability of getting heads = 0.5
Probability of tails on the same flip = 0.5
Total probability = 0.5 + 0.5 = 1.0
©2000 Timothy G. Standish
Laws Of Probability:
3 Conditional Probability
l
l
l
l
Probability of events in which both events share
some dependent condition
Example - If one card in a deck of 52 is the queen
of hearts, and hearts make up 1/4 of the deck, if
you have a card with hearts on it, what are the
odds that it is the queen of hearts?
Probability queen of hearts/probability of hearts =
(1/52)/(1/4) = 4/52 = 1/13
©2000 Timothy G. Standish
Laws Of Probability:
4 Binomial Expansion
The probability of a set of events arranged in no
of any one way
specified order: pProbability
= probability
a = probability of
Number of
n = number of events
outcome a
n!
s
t
a b s = number of outcome a b = probability of
possible p =
s!t!
ways
t = number of outcome b
outcome b
l
l
l
Example - If James and Bertha have 12 children,
what is the chance they will have 8 boys and 4 girls?
n = 12, a = prob of boy = 0.5, b = prob of girl = 0.5,
s = no. boys = 8, t = no. girls Number of ways to have
8 boys and 4 girls
p = n! asbt = 12! 0.58 x 0.54 = 495 x 0.00024 = 0.121
s!t!
8!4! Probability of any specific
order of 8 boys and 4 girls
©2000 Timothy G. Standish
©2000 Timothy G. Standish