All complex genetics problems are simply combinations of easier problems, hardly ever worse than the problems below.  The product principle of probability (= the "both-and" rule described in the text book on p. 200) is the way to combine easy problems to solve the trickier problems.

The trick to solving the hard problems is to separate the problem into a series of easy problems, solve each of them, and then multiply the results of all the easy problems.   This works because the law of independent assortment tells us that the inheritance of one trait (eye color, for example) occurs without affecting the inheritance of traits on other chromosomes (nose size, for example).  You can have lovely brown eyes and a small nose while your sister has lovely brown eyes but your father's big nose and your brother has blue eyes and a small nose.  Since the two traits are inherited independently, you can calculate their probabilities separately just like the problems in the previous problem sets.  But now, once you've calculated the probability for brown eyes and the probability for big nose, you multiply the two together to calculate the probability for both happening.  If you also wanted to include another trait, like freckles, you'd just figure it separately and then multiply all three problems together.   You could easily include a fourth trait or even more unless you ignored our advice with the first problem set and you still do giant Punnett squares, in which case all you get from us is pity.

• To work some problems in this set you need to understand how meiosis causes independent assortment.  If you already learned all the stages of meiosis, that's not so important as knowing this:

• Meiosis produces gametes (ova and sperm), each with only one allele from each gene pair.
• Gametes are haploid, with half the genes of other human cells.
• Each gamete is highly unlikely to be genetically identical to any other gamete.  (This explains your superiority over any siblings.)
• In the problems you work involving more than one pair of alleles, you should assume that loci for different traits are on different chromosomes; so independent assortment applies.

• Another variation which trips up some students (but not you maybe) is the concept that each conception is also an independent event.  
  • The probability of a second child having a particular genotype is the same as the probability of the first child having that genotype
  • but the probability of both children having that genotype is calculated by multiplying the two independent probabilities.
    
• SAMPLE PROBLEMS
  1. What is the probability that your first child will be a boy?   
  2. What is the probability that your first three children will be boys?
  3. What if you already have three sons, what's the probability that the next kid will be a boy?
  4. You and your gamete-donor are both heterozygous for sickle-cell anemia.  What's the probability that your first child will have sickle-cell anemia?
  5. What is the probability that your first child will be a boy and have sickle-cell anemia? 
  6. If both parents are carriers for both sickle-cell anemia and cystic fibrosis, what's the probability that their first child will have both diseases?

• answers
  1. 1/2
  2. 1/2 * 1/2 * 1/2  = 1/8
  3. 1/2   (his conception is independent of all earlier conceptions)
  4. 1/4   (it's the Hh problem)
  5. 1/2  *  1/4   =  1/8
  6. 1/4 *  1/4  =   1/16  

• Checklist of Terms:  reciprocal cross, testcross, 3:1, 1:2:1, 9:3:3:1, 1:1:1:1, principle of segregation, principle of independent assortment, probability, both-and rule, chromosome theory of inheritance, hybrids, phenotype, trait, genotype, dominant, recessive, gene, allele, homozygous, heterozygous, parental generation (P1), F1 generation, F2 generation, progeny (offspring), 
• Preview of Test2 questions:
  • From textbook web site or textbook and CD
    • Activity 10.1 Mendel's Experiments PostQuiz #1, 2, 4, 5
    • summary review #7-9
    • genetics problems # 10, 13, 14, 15
  • questions above (in the box) and these:
    • How does meiosis explain independent assortment?
    • Why are segregation and independent assortment often called Mendel's laws?  Why not call them hypotheses or theories?
  • The take-home quiz for Problem set 2 is due after lab or by 5 pm Thursday.  You may hand it in during your lab period or email it by 5 pm Thursday to jannr@queens.edu .
• Want to know more?  
  • check out  http://www.biology.arizona.edu/mendelian_genetics/problem_sets/dihybrid_cross/dihybrid_cross.html
  • More?

• Text pp. 205-207, fig. 17.4 (pp. 339-340)
• The new trick in this set is the inheritance of traits found on the X-chromosome but not on the Y-chromosome.  These are called sex-linked traits.
• More help, including sample problems

• Text pp. 207b-209
• LINKAGE in general applies to somatic chromosomes in addition to the sex chromosome.  This term refers to the fact that with at least 30,000 genes and only 23 pairs of human chromosomes, many genes are inherited together, not independently 
• No problems will be assigned, but there are three main points worth noting:
  • When two genes have their loci on the same chromosome, they are "linked" and will be inherited together most of the time.  Independent Assortment no longer applies, and the Product Principle of Probability no longer works (since the inheritance of the two traits are linked, and not independent events).
  • The farther apart the loci of different genes are, the more often they get recombined (or separated onto different chromatids) during meiosis Prophase I.  This fact is the basis of a classical procedure called "mapping," and mapping provided the first data used in the genome projects, which we'll study in Chapter 16.
  • Sometimes in trying to diagnose a genetic disease, we don't know yet how to find its gene on a chromosome, but we can identify its probable presence by a known marker gene which is nearby on the same chromosome.
• More information:  mapping & recombination http://vector.cshl.org/dnaftb/11/animation/fs.html

• Text p. 210, especially. fig 10.17
• INCOMPLETE DOMINANCE, CODOMINANCE, or BLENDING all occur when both alleles of a gene pair are expressed, like the flowers on fig. 10.17.  Many human traits work this way.  You solve the problems just like the problems in set I, except that you must remember that heterozygotes have an intermediate phenotype so that there are three types of genotypes and three types of phenotypes.

• SAMPLE PROBLEMS.  Incomplete dominance problems are easier to understand if you use notation with superscripts like D^R for the red allele, and D^W for the white allele.

  1. A red snapdragon crossed with a white snapdragon flower produces seeds which grow into many snapdragons plants, all with pink flowers.  If the pink snapdragons are interbred, will their offspring be pink, too?
  2. In the previous problem, which flowers are the F-1 generation? 
  3. Two palomino horses (with a golden color) are stabled together; after about a decade they have produced four palomino colts, but two extremely light-colored (Cremello) colts and two darker sorrel colts-- eight colts but only four palomino colts?  What's with palominos?

  answers

  1. only 1/2 will be pink; 1/4 will be red and 1/4 will be white.
  2. the pink ones with the red parent and white parent.
  3. they're hybrids with incomplete dominance.
   (like P^sP^c if sorrels are  P^sP^s 
  and cremellos are P^cP^c 

• Textbook pp. 210-211
• More help on blood types.  

• textbook p. 211
• essay on p. 214

• textbook pp. 211--212a

• Epistasis is a special case explaining albinism and some other tricky inheritance problems.  Only "A" students are successful at working problems involving epistatic genes usually.  The odds of getting an epistasis problem on Test 2 or the final exam are much lower than the odds of getting any other kind of problem.  We won't spend much time on this type, even though they're really interesting and challenging.  You could beg for bonus problems.

• Textbook pp. 212--213
• POLYGENIC INHERITANCE of quantitative traits is when the phenotype is affected by more than one pair of genes, like eye color, wheat kernel color (fig. 10.20),   and height, fig. 10.19.  Many more human traits are polygenic, like skin color, shoe size, and the genetic contribution to intelligence.  When only two pairs of genes are involved, you can solve the problems with Punnett squares.  With three or four or more pairs of genes, the phenotype distribution begins to resemble a bell-shaped curve,  then it's easier to estimate or "eye-ball" predictions.  This technique will be demonstrated in class.  A normal distribution is another name for what looks like a bell-shaped curve once it's graphed.  

  Try not to   confuse polygenic traits and multiple alleles.  For multiple alleles one pair of loci on homologous chromosomes can have more possibilities than "A" and "a," but polygenic traits involve at least several different pairs of chromosomes and loci.

  A note about intelligence inheritance from www.theatlantic.com/genetic: "In Japan the Buraku are a caste of people discriminated against in education, housing, and employment. Their children typically score ten to fifteen points below other Japanese children on IQ tests—about the average black-white difference in the United States. Yet when the Buraku emigrate to the United States, the IQ gap between them and other Japanese vanishes."  What does this observation have to do with environmental effects above?

• Checklist of Terms:  linkage, sex-linked inheritance pattern, wild type, mutant, recombinants, linkage map (genetic map), incomplete dominance, codominant, recessive, multiple alleles, locus, diploid, haploid, homozygous, heterozygous, autosomes, autosomal inheritance, sex-linked chromosomes, quantitative traits, epistasis, normal distribution, ABO blood types, phenylketonuria (PKU)
• Preview of Test 2 questions:
  • Textbook problems #5, 7,  9, 11, 16, 17, 18, 19 (challenging) and all figure review problems
  • questions embedded in the explanations above
  • The take-home quiz for Problem set 4 is due at the beginning of class Monday, 29 Sept.  
• Want to know more?  
  • More?