Mendelian Genetics The laws of probability govern Mendelian

Mendelian Genetics

The laws of probability govern Mendelian inheritance • Mendel’s laws of segregation and independent assortment reflect the rules of probability • The multiplication rule states that the probability that two or more independent events will occur together is the product of their individual probabilities • Probability in a monohybrid cross can be determined using this rule

Rr Segregation of alleles into eggs Rr Segregation of alleles into sperm Sperm 1/ R 2 2 1/ 4 r 2 r R R Eggs 1/ r 2 R R 1/ 1/ 1/ 4 r r R r 1/ 4

Punnett Square

Monohybrid Cross

The rule of addition • States that the probability that any one of two or more exclusive events will occur is calculated by adding together their individual probabilities

Each box in this dihybrid cross has a 1/16 chance of occurring. Add them up for chances of any phenotype

Dihybrid cross - The traits are: long tail (s), short tail (S), brown hair (B) and white hair (b)

Solving Complex Genetics Problems with the Rules of Probability • We can apply the rules of probability to predict the outcome of crosses involving multiple characters • A dihybrid or other multicharacter cross is equivalent to two or more independent monohybrid crosses occurring simultaneously • In calculating the chances for various genotypes from such crosses each character first is considered separately and then the individual probabilities are multiplied together

Trihybrid Cross of Pp. Yy. Rr x Ppyyrr ppyy. Rr pp. Yyrr Ppyyrr PPyyrr ppyyrr (probability of pp) 1/2 (yy) 1/2 (Rr) 1/ 1/ 4 2 2 1/ 1/ 2 2 2 1/ 1/ 1/ 4 2 2 1/ 4 Chance of at least two recessive traits 1/16 2/16 1/16 6/16 or 3/8

Summary of Basic Mendelian Genetics • We cannot predict with certainty the genotype or phenotype of any particular seed from the F 2 generation of a dihybrid cross, but we can predict the probabilities that it will fit a specific genotype of phenotype. • Mendel’s experiments succeeded because he counted so many offspring and was able to discern this statistical feature of inheritance and had a keen sense of the rules of chance. • Mendel’s laws of independent assortment and segregation explain heritable variation in terms of alternative forms of genes that are passed along according to simple rules of probability.

Extending Mendelian Genetics • The inheritance of characters by a single gene may deviate from simple Mendelian patterns • Inheritance patterns are often more complex than predicted by simple Mendelian genetics • The relationship between genotype and phenotype is rarely simple • But we can extend Mendelian principles to patterns of inheritance more complex than Mendel described

The Spectrum of Dominance • Complete dominance occurs when the phenotypes of the heterozygote and dominant homozygote are identical • In incomplete dominance the phenotype of F 1 hybrids is somewhere between the phenotypes of the two parental varieties

Red and White Snapdragons

Incomplete Dominance P Generation White CW CW Red CRCR Gametes CR CW

Incomplete Dominance P Generation White CW CW Red CRCR Gametes CR CW F 1 Generation Gametes 1/2 CR Pink CRCW 1/ 2 CW

Incomplete Dominance P Generation White CW CW Red CRCR Gametes CR CW F 1 Generation Pink CRCW 1/ Gametes 1/2 CR 2 CW Sperm F 2 Generation 1/ 1/ 2 CR 1/ 2 CW Eggs 2 CR 1/ 2 CW CRCR CRCW CWCW

The Spectrum of Dominance • In codominance two dominant alleles affect the phenotype in separate, distinguishable ways • The human blood group MN is an example of codominance

MN Blood Groups

The Relation Between Dominance and Phenotype • Dominant and recessive alleles – Do not really “interact” – Lead to synthesis of different proteins that produce a phenotype

Tay-Sachs Disease • Humans with Tay-Sachs disease produce a non-functioning enzyme to metabolize gangliosides (a lipid) which then accumulate in the brain, harming brain cells, and ultimately leading to death. Tay-Sachs most common in Ashkenazic Jews (from Central Europe) • Children with two Tay-Sachs alleles have the disease. • Heterozygotes with one working allele and homozygotes with two working alleles are “normal” at the organismal level, but heterozygotes produce less functional enzymes. • However, both the Tay-Sachs and functional alleles produce equal numbers of enzyme molecules, codominant at the molecular level.

Tay-Sachs Disease

Frequency of Dominant Alleles • Dominant alleles are not necessarily more common in populations than recessive alleles • Polydactyly is a dominant trait – Antonio Alfonseca • 399 out of 400 people have 5 digits

Dominance/recessiveness relationships • Range from complete dominance through various degrees of incomplete dominance to codominance • Reflect the mechanisms by which specific alleles are expressed in the phenotype and do not involve the ability of one allele to subdue another at the level of DNA

Multiple Alleles (a) The three alleles for the ABO blood groups and their carbohydrates Allele Carbohydrate IA IB i none B A (b) Blood group genotypes and phenotypes Genotype IAIA or IAi IBIB or IBi IA IB ii A B AB O Red blood cell appearance Phenotype (blood group)

Pleiotropy – gene affects more than one phenotypic trait Sickle-cell Anemia

Pleiotropy - Phenotypic traits affected by sickle-cell anemia • • Sickled red-blood cells Anemia Heart failure Brain damage Spleen damage Rheumatism Kidney failure

Coat color in Labrador Retrievers

Bb. Ee Epistasis – a gene at one locus alters the phenotypic expression of a gene at another locus Eggs 1/ 4 BE 1/ 4 b. E 1/ 4 Be 1/ 4 be Sperm 1/ BE 4 1/ Bb. Ee 4 b. E 1/ 4 Be 1/ 4 be BBEE Bb. EE BBEe Bb. EE bb. EE Bb. Ee bb. Ee BBEe Bb. Ee BBee Bb. Ee bb. Ee Bbee bbee 9 : 3 : 4

Polygenic. Trait, Quantative Characters – Human height in 175 students at Connecticut Agricultural College

Polygenic. Trait, Quantative Characters – How human skin color might work Sperm 1/ 1/ 8 8 1/ 1/ Eggs Aa. Bb. Cc 8 1/ 1/ 8 8 1/ 8 1/ 8 Phenotypes: Number of dark-skin alleles: 1/ 64 0 6/ 64 1 15/ 64 2 20/ 64 3 15/ 64 4 6/ 64 5 1/ 64 6

Figure 14. UN 03 Relationship among alleles of a single gene Complete dominance of one allele Description Heterozygous phenotype same as that of homozygous dominant Incomplete dominance Heterozygous phenotype intermediate between of either allele the two homozygous phenotypes Codominance Both phenotypes expressed in heterozygotes Example PP Pp CRCR CRCW CWCW IAIB Multiple alleles In the whole population, some genes have more than two alleles Pleiotropy One gene is able to affect Sickle-cell disease multiple phenotypic characters ABO blood group alleles IA, IB, i

Figure 14. UN 04 Relationship among two or more genes Epistasis Description The phenotypic expression of one gene affects that of another Example Bb. Ee BE Bb. Ee b. E Be be BE b. E Be be 9 Polygenic inheritance A single phenotypic character is affected by two or more genes Aa. Bb. Cc : 3 : 4 Aa. Bb. Cc