Mendelian Genetics: Patterns of Inheritance A Bit on Gregor Mendel Born to a poor farming family in what is now part of Czech Republic Attended Augustinian monastery (1843) Became an excellent teacher Further study at University of Vienna (1851-53) Strong background mathematics, physics & botany. Strong foundation in scientific method Went back to teaching & began work with pea plants (1856-63) Discovered basic theories of inheritance Presented & Published (1866) Went unnoticed until 1900 (after his death) the first quantitative evidence of how variation was maintained & passed from generation to generation Rediscovered independently by 3 botanists studying heredity Interpreted their results in terms of Mendel s work Mendel s Experimental Approach The Garden Pea Plant Mendel used Seven True Breading Traits in his Experiments True Breeding: Adopted an experimental approach, formulated hypotheses and kept strict record of numbers of progeny.
Mendel s crosses Self fertilization The pea plant has both male & female gametes Cross fertilization: Transfer pollen (sperm) from one plants to the stigma of another Let s Talk Genes & Alleles A pair of homologous chromosomes, each in the unduplicated state (most often, one from a male parent and its partner from a female parent) A gene locus (plural, loci), the location for a specific gene on a specific type of chromosome A pair of alleles (each being a certain molecular form of a gene) at corresponding loci on a pair of homologous chromosomes Three pairs of genes (at three loci on this pair of homologous chromosomes); same thing as three pairs of alleles Some Necessary Terminology Genes units of genetic information (e.g. eye color) Alleles different forms of the same gene (R = red; r = white) Homozygous having two identical alleles (RR or rr) Heterozygous having two different alleles (Rr) Dominant the allele which is expressed in the heterozygote (R) - usually in uppercase Recessive the allele that is not expressed in the heterozygote (r) usually in lowercase Genotype the actual alleles (Rr) Phenotype how those alleles are expressed (red)
Mendel s Theory of Segregation Mendel s Question: When peas with that differ in a single trait are crossed, what phenotype will they display? Monohybrid Cross: Parents differ in a single characteristic Generations P = parental true breeding F1 = first filial all Smooth F2 = second filial wrinkled reappears The Monohybrid Cross in Detail Notational Conventions P - Dominant allele (purple) PP - p - Recessive allele (white) Pp - pp Parental Generation Cross True breeding cross (RR x rr) Gametes? Progeny are 100% Rr (the F1 generation) The F1 Cross to produce an F2 generation Self Fertilization Gametes? Progeny (the F2 generation) Genotypic Ratio? Phenotypic Ratio? The F2 Cross to produce an F3 generation. Self fertilization Heterozygous parents produce all 3 phenotypes Homozygous plants produce only homozygotes
Conclusions Drawn form the Monohybrid Cross The Principle of Segregation: Each individual diploid organism possesses two alleles (factors) for a given characteristic. During meiosis the two alleles for a given trait segregate (separate) into different gametes in equal proportions. The Concept of Simple Dominance: When two different alleles are present in a genotype, only one of them (the dominant allele) is observed in the phenotype. Segregation & Meiosis Chromosomal theory of Heredity: genes are located on chromosomes (Sutton). Homologous pair composed of one maternal & one paternal chromosome
Predicting the Outcome of Crosses Punnett Squares: shorthand method for predicting genotypic and phenotypic ratios. Parental cross Determine possible gametes F1 progeny? F1 cross What gametes? Determine possible F2 progeny Probabilities: the likelihood of a particular event occurring. Multiplication rule: the probability of two or more independent events occurring together Addition Rule:the probability of any one of two mutually exclusive events Applying probabilities to genetic crosses Can be used in place of a Punnett square Consider Pp x Pp What is the probability of obtaining a PP individual? What about pp? What about Pp?
Introducing Binomial Expansion: Consider Tt parents (where T (tall) is dominant) Probability of having 3 tt offspring? What about 3 offspring 1 short (p = ¼ ) & 2 tall (p = ¾ ) Short AND then Tall AND then Tall ( ¼ x ¾ x ¾ ) OR The greater the number of offspring, the more difficult this becomes Binomial Expansion makes it MUCH easier. Using Binomial Expansion to predict outcomes: (a + b) n a = probability of Tall (Tt or Tt) b = probability of short (tt) n = number of offspring For a family of 5 (n=5) (a + b) 5 = a 5 + 5a 4 b + 10a 3 b 2 + 10a 2 b 3 + 5ab 4 + b 5 Using Pascal s Triangle In a family of 5 what is the probability of obtaining 3 tall and 2 short? 10a 3 b 2 = 10 ( ¾ ) 3 ( ¼ ) 2 = 0.26 (26%) What is the probability of obtaining at least 3 tall? Means 3tall/2short OR 4tall/1short OR 5tall/0short a 5 + 5a 4 b + 10a 3 b 2 = 10( ¾ ) 3 ( ¼ ) 2 + 5( ¾ ) 4 ( ¼ ) + ( ¾ ) 5
Introducing to the factorial method Will yield the same results as the binomial expansion, but is sometimes easier to use. P = n! s! t! a s b t n = number of offspring a = probability of tall (Tt or Tt) = ¾ b = probability of short (tt) = ¼ s = the number of tall offspring t = the number of short offspring Using the factorial method for predicting outcomes Let s consider the same problem: In a family of 5 what is the probability of obtaining 3 tall and 2 short? n = number of offspring = 5 a = probability of tall (TT or Tt) = ¾ b = probability of short (tt) = ¼ s = the number of tall offspring = 3 t = the number of short offspring = 2 P = n! s! t! a s b t
The Test Cross To find out the genotype of an individual expressing a dominant trait (e.g. purple flower color; P--) If 100% Purple then If 50% Purple & 50% white, then Incomplete Dominance One allele in a pair is not completely dominant over another E.g. Snapdragons Not blending, Why?
Mendel s Theory of Independent Assortment Dihybrid Crosses: Parental Generation cross F1 generation cross Determine your gametes Calculate the progeny using a Punnett Square F2 generation Phenotypic ratio?
Using the Probability & Branch Diagram Method: Can split a dihybrid cross into two monohybrid crosses & then using the multiplication rule. If parents heterozygous at both loci are crossed, what is the probability of obtaining Round Yellow progeny?
What about a Trihybrid cross? Split it into 3 monohybrid crosses & apply the multiplication rule. If a true-breeding dominant & a true-breeding recessive parent are crossed, what is the probability of obtaining Round, Green & White progeny? Mendel s theory of independent assortment came from his work with dihybrid crosses: Also explained by meiosis
Comparing Mendel s Theories Segregation: Homologous chromosomes separate during meiosis (gamete formation) Alleles for the same character (same locus) separate Independent Assortment: alleles for different characters (different loci) move into gametes independently of each other. The paternal/ maternal alleles are shuffled in gamete formation. Other Notation in Genetics There may be one, two or three letter codes for an allele. hl = heart-shaped leaves in cucumbers Wild-type: Symbolized by 1-3 letters (based on the mutant phenotype) & a plus sign Red eyes in fruit flies are the wild-type condition; white is the mutant form & is recessive. Red eyes = w+ ; White eyes = w Gene Expression is Influenced by Environment & Other Genes Penetrance:. Hemophilia Expressivity:. Himalayan Rabbit & Siamese Cat environment influences degree of expression Less melanin in warm body regions.
Purple P h 346 Expected White 400 Comparing 746 Observed Results with Expected Ratios In a cross between pp & Pp we would expect a 1:1 ratio of Purple flowers & white flowers. What if you obtained 346 Purple flowers & 400 white flowers? Is this still a 1:1 ratio? Or, is it more likely that something else going on? We need to perform a statistical test to determine how well the observed values fit the expected values. The Chi-square test is used to determine whether the numbers differ by chance, or whether they are indeed different from the expected values. Chi-square test: Determine expected values Calculate chi-square 2 χ = (observed expected) expected 2
Determine degrees of freedom (df = n -1, where n= # of different classes) Look up critical value for chi-square (p=0.05; 95% confident that the # s are truly different.; 5% chance they are not) Compare calculated chi-square with critical chi-square If X 2 calculated is greater X 2 critical then there is a significant difference between the observed & expected numbers.