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

Segregation of alleles into eggs Segregation of alleles into sperm Sperm Eggs 1/21/2 1/21/2 1/21/2 1/21/2 1/41/4 1/41/4 1/41/4 1/41/4 Rr R R R R R R r r r r r  r

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 PpYyRr x Ppyyrr Chance of at least two recessive traits ppyyRr ppYyrr Ppyyrr PPyyrr ppyyrr 1 / 4 (probability of pp)  1 / 2 (yy)  1 / 2 (Rr) 1/4  1/2  1/21/4  1/2  1/2 1/2  1/2  1/21/2  1/2  1/2 1/4  1/2  1/21/4  1/2  1/2 1/4  1/2  1/21/4  1/2  1/2  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 F2 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 Red White Gametes CWCWCWCW CRCRCRCR CRCR CWCW

Incomplete Dominance P Generation F 1 Generation 1/21/2 1/21/2 Red White Gametes Pink Gametes CWCWCWCW CRCRCRCR CRCR CWCW CRCWCRCW CRCR CWCW

Incomplete Dominance P Generation F 1 Generation F 2 Generation 1/21/2 1/21/2 1/21/2 1/21/2 1/21/2 1/21/2 Red White Gametes Pink Gametes Sperm Eggs CWCWCWCW CRCRCRCR CRCR CWCW CRCWCRCW CRCR CWCW CWCW CRCR CRCR CWCW CRCRCRCR CRCWCRCW CRCWCRCW CWCWCWCW

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

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

Sperm Eggs 9 : 3 : 4 1/41/4 1/41/4 1/41/4 1/41/4 1/41/4 1/41/4 1/41/4 1/41/4 BbEe BE bE Be be BBEE BbEE BBEeBbEe BbEE bbEEBbEe bbEe BBEe BbEe BBeeBbee BbEebbEe Bbee bbee Epistasis – a gene at one locus alters the phenotypic expression of a gene at another locus

PolygenicTrait, Quantative Characters – Human height in 175 students at Connecticut Agricultural College

Eggs Sperm Phenotypes: Number of dark-skin alleles: /81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1/81/8 1 / 64 6 / / / / 64 6 / 64 1 / 64 AaBbCc PolygenicTrait, Quantative Characters – How human skin color might work

Figure 14.UN03 Complete dominance of one allele Relationship among alleles of a single gene Description Example Incomplete dominance of either allele Codominance Multiple alleles Pleiotropy Heterozygous phenotype same as that of homo- zygous dominant Heterozygous phenotype intermediate between the two homozygous phenotypes Both phenotypes expressed in heterozygotes In the whole population, some genes have more than two alleles One gene is able to affect multiple phenotypic characters ABO blood group alleles Sickle-cell disease PP Pp CRCRCRCR CRCWCRCW CWCWCWCW IAIBIAIB I A, I B, i

Figure 14.UN04 Epistasis Polygenic inheritance Relationship among two or more genes Description Example The phenotypic expression of one gene affects that of another A single phenotypic character is affected by two or more genes 9 : 3 : 4 BbEe BE bE Be be AaBbCc