©2000 Timothy G. Standish 2 Kings 6:17 17And Elisha prayed, "O LORD, open his eyes so he may see."...

©2000 Timothy G. Standish

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.


Mendelian GeneticsMendelian Genetics

Timothy G. Standish, Ph. D.


Biography - Gregor MendelBiography - 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 Austro-Hungarian 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


Biography - Gregor Mendel:Biography - Gregor Mendel:EducationEducation

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


Biography - Gregor Mendel:Biography - Gregor Mendel:ResearchResearch

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."


Biography - Gregor Mendel:Biography - Gregor Mendel:Publication and DeathPublication and Death

1865 first reported results of his workPublished 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


Biography - Gregor Mendel:Biography - Gregor Mendel:RediscoveryRediscovery

Mendel’s work was rediscovered in 1900 by three botanists:– Carl Correns (Germany)

– Erich von Tschermak (Austria)

– Hugo de Vries (Holland)


Why Peas?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


Why Peas?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


Why Peas?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

StigmaPea flower

Anthers


Why Peas?Why Peas? By removing the anthers of one flower and

artificially pollinating using a brush, crosses can be easily controlled in peas.




. .... .

...

...




.... ....


Mendel’s ResultsMendel’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


Interpreting Mendel’s ResultsInterpreting Mendel’s Results Because the F1 generation did not produce light- purple

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


Interpreting Mendel’s ResultsInterpreting Mendel’s Results

CC

Cc

Cc

cc

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 were white

C c

C

c

F2 GenerationF2 Generation

Cc

Cc

Cc

Cc

C C

c

c

F1 GenerationF1 GenerationGametes from the P generation

Heterozygous parents make gametes either one or the other allele

The F1 Generation is all heterozygous

Homozygous parents can only make gametes with one type of allele


Mendel’s ResultsMendel’s ResultsTraitSeeds

round/wrinkledyellow/greenfull/constricted

Podsgreen/yellowaxial/terminal

Flowersviolet/white

StemTall/dwarf

TraitSeeds

round/wrinkledyellow/greenfull/constricted

Podsgreen/yellowaxial/terminal

Flowersviolet/white

StemTall/dwarf

F1 Results All RoundAll YellowAll Full

All GreenAll Axial

All Violet

All Tall

F1 Results All RoundAll YellowAll Full

All GreenAll Axial

All Violet

All Tall

F2 Results 5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted

428 Green 152 yellow651 Axial 207 terminal

705 Violet 224 white

787 Tall 277 dwarf

F2 Results 5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted

428 Green 152 yellow651 Axial 207 terminal

705 Violet 224 white

787 Tall 277 dwarf

Dominent traits mask recessive traits

Masked recessive traits reappear


Mendel’s ResultsMendel’s ResultsF2 Results Seeds5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted

Pods428 Green 152 yellow651 Axial 207 terminal

Flowers705 Violet 224 white

Stem787 Tall 277 dwarf

F2 Results Seeds5,474 Round 1,850 wrinkled6,022 Yellow 2,001 green 882 Full 299 constricted

Pods428 Green 152 yellow651 Axial 207 terminal

Flowers705 Violet 224 white

Stem787 Tall 277 dwarf

F2 Ratios Seeds2.96:1 Round:wrinkled3.01:1 Yellow:green2.95:1 Full:constricted

Pods2.82:1 Green:yellow3.14:1 Axial:terminal

Flowers3.15:1 Violet:white

Stem2.84:1 Tall:dwarf

F2 Ratios Seeds2.96:1 Round:wrinkled3.01:1 Yellow:green2.95:1 Full:constricted

Pods2.82:1 Green:yellow3.14:1 Axial:terminal

Flowers3.15:1 Violet:white

Stem2.84:1 Tall:dwarf

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


Chi SquareChi 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 “” or “X”

d2

e (Obs. Ex.)2

ExChi Square:


Chi Square:Chi Square:On Mendel’s Seed Texture DataOn Mendel’s Seed Texture Data

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

d2

e (Obs. Ex.)2

ExChi Square:

192/1,831 = 0.20

-192/5,493 = 0.066

(1,850+5,474) x 1/4 = 1,831

(1,850+5,474) x 3/4 = 5,493

1,850

5,474

0.266X2 =

(O-E)2/EEx.Obs.

wrinkled

Round

O - E

1,850 - 1,831 = 19

5,474 - 5,493 =-19


Chi Square:Chi Square:On Mendel’s Flower Color DataOn Mendel’s Flower Color Data

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

d2

e (Obs. Ex.)2

ExChi Square:

-82/232 = 0.276

82/697 = 0.092

(705+224) x 1/4 = 232

(705+224) x 3/4 = 697

224

705

0.368X2 =

(O-E)2/EEx.Obs.

white

Violet

O - E

224 - 232 =-8

705 - 697 = 8


Mendel’s ConclusionsMendel’s Conclusions1 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?


Mendel’s Experiment:Mendel’s Experiment:A Case Study In Good ScienceA 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


Mendel’s Dihybrid CrossMendel’s Dihybrid Cross

In other dihybrid crosses a 9:3:3:1 ratio was also found

Mendel chose to see if the round and yellow seed genes segregated independently

Ratio9/16

3/16

3/16

1/16

P GenerationRound green

RRyyX

wrinkled YellowrrYY

F1

All Round YellowRrYy

F2

315 Round YellowRrYy RRYy or RrYY

101 wrinkled YellowrrYy or rrYY

108 Round greenRRyy or Rryy

32 wrinkled greenrryy


3 Reasons Mendel’s Work 3 Reasons Mendel’s Work Was IgnoredWas Ignored

Mendel was not on the ballBiologists were idiots (at

least when it came to math)Lack of independent

supporting discoveries


Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:

1) Mendel was not on the ball1) 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.


Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:2) Biologists were idiots2) Biologists were idiots

Biologists didn’t understand mathBiologists 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).


Reasons Mendel’s Reasons Mendel’s Work Was Ignored:Work Was Ignored:

3) Lack of independent supporting 3) Lack of independent supporting discoveries: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.


Chromosomes:Chromosomes:The Physical Basis of InheritanceThe Physical Basis of Inheritance

1866 Mendel published his work1875 Mitosis was first described1890s Meiosis was described1900 Mendel's work was rediscovered1902 Walter Sutton, Theodore Boveri and

others noted parallels between behavior of chromosomes and alleles.


Chromosomal Theory Chromosomal Theory of Inheritanceof Inheritance

Genes have specific loci on chromosomes.

Chromosomes undergo segregation (meiosis) and independent assortment,

Thus alleles of genes are independently assorted.


E

n

e

N

Chromosomal Theory Chromosomal Theory of Inheritanceof Inheritance

e

N

E

n

Father

Mother

N

eE

n

N

E

n

e e

n

E

N

e

n

E

N

e

n

E

N

e

N

E

n

Telophase II

Replication

Telophase IProphase I

Crossing Over


En

eN

en

EN

Sperm e ne NE nE N

EggsIndependent AssortmentIndependent Assortment

n

E

e

N

e

n

N

E

n

Ee

n

e

NN

E

EeNnEeNNEENnEENN

EennEeNnEEnnEENn

eeNneeNNEeNnEeNN

eenneeNnEennEeNn

As long as genes are on different chromosomes, they will assort independently


E

A a

e

Two Genes On One Two Genes On One ChromosomeChromosome

Telophase II

Father

Mother

e

a

E

A

Telophase I

A

eE

A

E

a

e

a

E

A A

e E

a a

e

Replication

e

a

E

A

Prophase I

E

AA a

e

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


Laws Of ProbabilityLaws 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


Determination of Gamete and Determination of Gamete and Zygote Variability Zygote Variability

248

16

1234

248

16

39

2781

Number of Different

Phenotypes2n

Number of Heterozygous

Pairsn

Number of Different Gametes

2n

Number of Different

Genotypes3n


Laws Of Probability:Laws Of Probability:1 Product Law1 Product Law

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


Laws Of Probability:Laws Of Probability:2 Sum Law2 Sum Law

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


Laws Of Probability:Laws Of Probability:3 Conditional Probability3 Conditional Probability

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


Laws Of Probability:Laws Of Probability:4 Binomial Expansion4 Binomial Expansion

The probability of a set of events arranged in no specified order:

= 0.121

asbt

s!t!n!p =

0.58 x 0.54

8!4!12!= = 495 x 0.00024

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

asbt

s!t!n!p =

a = probability of outcome a

b = probability of outcome b

p = probabilityn = number of eventss = number of outcome at = number of outcome b

Number of possible

ways

Probability of any one way

Number of ways to have 8 boys and 4 girls

Probability of any specific order of 8 boys and 4 girls

©2000 Timothy G. Standish 2 Kings 6:17 17And Elisha prayed, "O LORD, open his eyes so he may see."...

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Transcript of ©2000 Timothy G. Standish 2 Kings 6:17 17And Elisha prayed, "O LORD, open his eyes so he may see."...