Mendelian Genetics

Mendelian GeneticsChapter 3

Mendelian (Transmission) Geneticsthe transfer of genetic information from genes to another generation (from parent to offspring)

Figure 3-1 Copyright 2006 Pearson Prentice Hall, Inc.

3Figure 3-1 A summary of the seven pairs of contrasting traits and the results of Mendels seven monohybrid crosses of the garden pea (Pisum sativum). In each case, pollen derived from plants exhibiting one trait was used to fertilize the ova of plants exhibiting the other trait. In the F1 generation, one of the two traits (dominant) was exhibited by all plants. The contrasting trait (recessive) then reappeared in approximately one-fourth of the F2 plants.

Mendels FindingsDetermined there are distinct units of inheritanceBehavior of units could be predicted during the formation of gametesLater researchers linked the behavior of chromosomes during meiosis to Mendels principles of inheritanceThe study of transfer of inheritance in this manner to offspring is called Mendelian (or transmission) genetics

Monohybrid Cross

P F1 F2

Monohybrid Cross

Reciprocal CrossesShows if traits are sex-dependent

Reciprocal Crosses

Mendels three postulates(1) Unit factors in pairs(2) Dominance/Recessiveness(3) SegregationRandom, gametes have equal chance

Modern TerminologyPhenotype is the physical expression of a traitMendels unit factors are now called genesAlternate forms of a gene are called allelesThe first letter of recessive trait is used to symbolize gene (d = dwarf, D = tall)

Modern TerminologyGenotype refers to the actual alleles presentTwo unit factors are present in diploid individualPossible combinations - DD, Dd, or dd

Monohybrid Cross

Figure 3-2 Copyright 2006 Pearson Prentice Hall, Inc.

13Figure 3-2 The monohybrid cross between tall and dwarf pea plants. The symbols D and d designate the tall and dwarf unit factors, respectively, in the genotypes of mature plants and gametes. All individuals are shown in rectangles, and gametes are shown in circles.

Punnett SquareA Punnet square is a method for visualizing combinations of gametes in a cross

Testcross

Dihybrid CrossA cross containing two pairs of contrasting traits

Dihybrid Cross

Dihybrid Cross

Dihybrid Cross

Mendels 4th PostulateResults of Mendels dihybrid crosses can be understood by considering the probabilities separatelyCOLOR: are yellow, are greenSHAPE: are round, are wrinkledUse the product law of probability the combined probability of the two outcomes is equal to the product of their individual probabilities

Probabilities

Mendels 4th Postulate(4)Independent AssortmentDuring gamete formation, segregating pairs of unit factors assort independently of each otherThis means that all possible combinations of gametes will be formed with equal frequencyFinal dihybrid ratio (assumes independent assortment and random fertilization) is 9:3:3:1

Testcrosses with two characters

Trihybrid CrossPunnett square has 64 boxesDemonstrates that Mendels principles apply to inheritance of multiple traits

Forked Line Method

Useful Rules

Examples:1. Aa [A, a] [AA, Aa, aa] [A or a]2. AaBb [AB, Ab, aB, ab] [AABB, AaBB, aaBB, AABb, AaBb, aaBb, aaBB, aaBb, aabb] [AB, Ab, aB, BB]

Correlation of Mendels Postulates with the Behavior of ChromosomesFormed the foundation of modern transmission genetics Unit factors, genesPairs, homologous chromosomes

Laws of ProbabilityGenetic ratios are expressed as probabilitiesPredict the outcome of each fertilization event0 = certain not to occur1.0 = certain to occurIn the Tall/dwarf monohybrid cross:3 out of 4 zygotes become tall (0.75)1 out of 4 zygotes are dwarf (0.25)

Laws of ProbabilityProduct LawDiscussed in relation to independent assortmentProbability of two or more outcomes occurring simultaneously is equal to the product of their individual probabilitiesExample: Coin toss (penny and nickel)Sum LawGeneralized outcomes can be predicted by adding probabilities (head/tails + tails/heads)

Laws of ProbabilitySum Law (cont.)Example: one heads, one tailsPH:NT = PT:NH = + = Sample Problem: In an F1 self-cross (Tall/dwarf parents), what is the probability that an F2 generation plant is true-breeding (homozygous) for the trait

Laws of ProbabilityConditional ProbabilityProbability of an outcome dependent on a specific condition of that outcomeExample: probability that any tall F2 plant from a Tall/dwarf monohybrid cross will be heterozygousCondition is to consider only tall plants (we already know that dwarfs are homozygous)pc = pa/pb (pa, probability of heterozygote, pb; probability of dominant phenotype, pc; probability of dominant phenotype being a carrier)Can be applied to genetic counselingChances if a normal person being a carrier

Binomial TheoremUsed to calculate probability of outcomes for any number of potential eventsBinomial theorem: (a+b)n = 1a and b are respective probabilities of the two alternate outcomesn = the number of trialsa2 + 2ab + b2 [n = 2]a3+ 3a2b + 3ab2 + b3 [n = 3]a4 + 4a3b + 6a2b2 + 4ab3 + b4 [n = 4]

Pascals TriangleExpand the binomialDetermines the numerical coefficients preceding each expression

More Binomial Theorem

Example: Probability of a family of four having two boys and two girlsExponent of a represents # of boysExponent of b represents # of girlsp = 6a2b2Formula for determining numerical coefficients for any set of exponentsn!/(s!t!) where n = total # of events, s = # of times a occurs and t = # of times b occurs! means factorial

Chi-Square AnalysisEvaluates the Influence of Chance on Genetic DataDegrees of freedomNumber of possible outcomes minus one (n - 1)

Chi-Square AnalysisNull Hypothesis assumes there is no real difference between the measured (experimental) and predicted valuesThe apparent difference can be attributed to chance (Null hypothesis proven)Null hypothesis fails if chance cannot reasonably explain deviation from expected

Chi-Square Calculations

Figure 3-12ab Copyright 2006 Pearson Prentice Hall, Inc.[difference may be real]

Random variation

38Figure 3-12ab (a) Graph for converting values to p values. (b) Table of values for selected values of df and p. values greater than those shown at justify failing to reject the null hypothesis, while values less than those at justify rejecting the null hypothesis. In our example, for 1 degree of freedom is converted to a p value between 0.20 and 0.50. The graph in (a) provides an estimated p value of 0.48 by interpolation. In this case, we fail to reject the null hypothesis.

Interpreting X2 and p value calculationsWhat do p values mean????

As 2 values increase, p values decrease

Dihybrid cross, p = 0.26Then 26% of the time the value obtained from an experiment would vary from the expected value by this much or more based solely upon chance

Interpreting X2 and p value calculationsTraditionally a p value of 0.05 is the accepted standard to accept the null hypothesis

More than 0.05 is considered confirmatory (chance variation is thus the likely explanation for any deviation from expected results)

Less than 0.05 means chance variation is an unlikely explanation (though still a possible one, probability depending upon the actual p value) Null Hypothesis fails

Pedigrees reveal patterns of inheritance in humansPedigreeFamily treeIndicates presence or absence of trait in question for each member

Pedigree ConventionsCircles for females, squares for malesParents connected by horizontal line, offspring by vertical lines connected to horizontal oneRelated parents (cousins) said to be consanguineous and connected by double lineSiblings written in birth order, left to rightGenerations indicated by Roman numeralsTwins indicated by forked line, identical twins by fork connected by horizontal lineFor single trait, shaded symbols indicate trait expressedShaded with dot indicates known carriersLine through symbol indicates deceased

Pedigree Conventions

Sample PedigreeConstructing a pedigree:

= male

= female

= unknown

= shape is shaded if phenotype under study is expressed

= known heterozygotes are shaded on the left half only

Parents horizontal line

Sibship lineFraternal twins

Identical twins

Pedigree symbols and notations

Autosomal Recessive

Autosomal Dominant

Familial HypercholesterolemiaDominant but note varied phenotype of homozygote vs. heterozygoteLDL receptor for cholesterol uptake by cellsHeterozygotes have about 2X LDL levels in blood, heart attacks by 40 yrs commonHomozygotes have no receptors, 10X LDL levels and may have heart attach by 5 yrs of age, rarely survive to age 20