1Variation and probability

• Gamete production is source of variation and genetic diversity, an advantage of sex.– As a result of segregation and independent

assortment, lots of combinations possible.– 2n possibilities exist for diploids where n = haploid

number of chromosomes• In humans, this is 8 million different gametes

– Crossing over during meiosis creates even more combinations of genetic information

– This diversity important in evolution, survival.

2Trihybrid cross

• Mendel also crossed peas and looked at inheritance of 3 traits simultaneously.– These showed independent assortment also.

• A Punnett square to determine the phenotypic ratios would be unwieldy– It would require an 8 x 8 matrix: 64 squares

• Because independent events are involved, one can use the product law– Multiply each probability. – Simplest way: forked-line method = branch diagram

3Product law

• Product law used to calculate odds of an outcome from independent events – Flip a coin: heads or tails, 50:50 chance (1/2)– Flip a coin 3 times, get 3 heads; the next flip,

there’s still a 50:50 chance of getting a head.– The chance of getting 4 heads in a row:

• ½ x ½ x ½ x ½ = 1/16 the product law.– Odds of round, yellow seeds in a cross of Ww GG x

Ww gg: ¾ x 4/4 = 3/4

4Sum Law

• The sum law: outcomes of events are independent, but can be accomplished in more than one way.

Flip a penny and a nickel: odds of 1 heads and 1 tails?

There are 4 possible outcomes from this flip.

1 head, 1 tail can be from the penny being heads (odds 1/4), but also from the nickel (1/4): ¼ + ¼ = ½

5Branch diagram for figuring trihybrid cross

Crossing 2 individuals heterozygous for all 3 traits:Ww Gg Pp x Ww Gg Pp

What proportion of the offspring are expected to have round, green peas and purple flowers, where W is round, w is wrinkled; G is yellow, g is green; and P is purple and p is white?

W_ gg P_ ¾ x ¼ x ¾ = 9/64

6Alterations to Mendel

• Incomplete or partial dominance

• Codominance

• Multiple alleles

• Lethal alleles

• Gene interactions

• Sex-linked, sex-limited, & sex-influenced

• Effect of environment

• Extranuclear inheritance

7Incomplete or partial dominance

www.people.virginia.edu/ ~rjh9u/snapdragon.html

One allele only partially masks the other.

Half as much enzyme makes half as much pigment.

Phenotypic ratio is the same as genotypic: 1:2:1

8Partial dominance-2

• Partial dominance is not a common visual phenotype– A molecular phenotype showing partial dominance

is more common– One allele instead of 2 is producing enzyme, so on

a gel, a protein band is half as intense.

9Codominance

• M and N blood groups: LM LN – Glycoprotein on blood cell

surface– If one of each allele, both

expressed.– Phenotype indicates

genotype.– Heterozygote cross: shows

1:2:1 ratio

http://boneslab.chembio.ntnu.no/Tore/Bilder/BlodMN.jpg

10Multiple alleles

• In peas, Mendel following the inheritance of two contrasting traits, e.g. purple vs. white flowers

• Often, more than two alleles for a trait exist.

• Study of multiple alleles requires a population!– In diploid organisms, an individual can only have a

maximum of two alleles. (2 different alleles)– In populations, many different alleles may be

present.– Classic example: the ABO blood group system

11ABO Blood groups

http://science.uwe.ac.uk/StaffPages/na/abo_ho2.gif

Series of sugars added to cell lipid creates trait.Genotypes include:AA, AO = type ABB, BO = type BOO = type OAB = type AB where A and B are co-dominant,O is recessive.In AB and O, the genotype is known from the phenotype.

12Lethal alleles

• In genetic crosses, information is obtained by examining the phenotype of the offspring.– In some instances, the genotype is lethal– Lethality may present itself late in life

(Huntington Disease) or may result in no offspring.

– Example:

Fur color in mice:Agouti on left, yellow on right.

http://www.cumc.columbia.edu/news/in-vivo/Vol1_Iss21_dec18_02/img/obesity-mice.jpg

13Lethal alleles-2

– If certain genotypes are lethal, results of a cross may be quite confusing.• Agouti x agouti = all agouti• Yellow x yellow = 2/3 yellow, 1/3 agouti• Agouti x yellow = ½ yellow, ½ agouti

– 2:1 ratio is tip-off that something odd happens– Homozygous for yellow is lethal, so that genotype is

NOT represented. – For lethality, yellow allele acts as recessive.– For coat color, yellow allele acts as dominant

• A = agouti, Ay = yellow. Heterozygote is yellow.

14Complex inheritance and dihybrid crosses

• Example: inheritance of simple trait and multiple allele trait: albinism and ABO– Crossing of heterozygotes

• Mm (albinism) and AB (blood type)– Assume independent assortment– Simple trait shows 3:1 ratio, co-dominant trait

shows 1:2:1 ratio– Phenotypic classes in offspring no longer 9:3:3:1

• Actually come out 3:6:3:1:2:1

• Complex inheritance produces odd ratios.

15Really good practice problems

• http://www.biology.arizona.edu/mendelian_genetics/mendelian_genetics.html

• Do all the problems from the links “Monohybrid cross” and from “Dihybrid cross”.