Use a Punnett square showing the two possible gene versions (alleles) from one parent across the top, and the two possible alleles from the other parent down the left side.

P-1 cross A A a Aa Aa a Aa Aa	Hybrid cross H h H HH Hh h Hh hh
Test or Back cross    t    t T Tt Tt t tt tt	(Failed cross) F f F FF Ff F FF Ff

Note that a homozygous dominant parent (AA) has only these possibilities in its gametes: A or A. 
A homozygous recessive parent has these possibilities: a or a.
A heterozygous parent has these possibilities: A or a.

Notice that as long as we're using alternative alleles for only one type of gene (like spotted or not-spotted), we use one kind of letter, like S and s (but not S and N). That keeps us from getting confused when problems become more complex, like needing to figure out how many will be spotted and maybe also curly or not-curly (c and C) and also 5-fingers or more-than-five (b and B). These combination problems come later (below); so you should start out with good habits of doing one trait (B & b?) at a time with a Punnett square for only one trait, four boxes in the square. The ones in the book with 16 or 64 boxes per square are fine for illustration and examples of what happens, but they are not good for making calculations.   Biology majors, especially, should be advised that when they will not solve problems with the huge Punnett square method when they take Biology 402.   So stop doing it, no matter what your high school teacher said.

• Review the four possible types of crosses above:
  • A. P-1 or homozygous cross (AA x aa) (Freeman text fig. 10.4 with RR x rr)
  • H. Hybrid cross (Hh x Hh) (text fig.10.7)
  • T. Test cross (Tt x tt)  
  • F. (Failed test cross) (Ff x FF)

   

• Make sure you can draw Punnett Squares for the four types, using any letters (like D, E, G, and M).
  
• Match these offspring phenotype ratios to the crosses above

  1. half the offspring with the phenotype of the dominant allele + half the phenotype of the recessive allele
  2. three-fourths the offspring with the phenotype of the dominant allele + a fourth the phenotype of the recessive allele
  3. all offspring with the phenotype of the dominant allele (two matches)
     

• All possible problem types are based on two basic questions:
  1. Given these parents, what is the probability that an offspring will have __ genotype or ___ phenotype?
  2. Given this ratio of offspring, what are the most likely parental genotypes or phenotypes?

   

• Variations of these problem types
  • actual numbers instead of ratios so that you must estimate ratios.
  • Pedigrees (textbook fig. 17.5 p.  341)       for later 17.4 
  • Predicted phenotypes from crosses involving hypothetical genotypes (example: Is the gene for cystic fibrosis recessive?)

   

• SOME recessive traits in humans (don't memorize the traits; but remember that recessive means that only homozygous recessive genotypes have the trait)
  • Cystic fibrosis (textbook page 85)
  • Tay-Sachs disease (textbook p. 110)
  • Albinism
  • Galactosemia (lactose intolerance in babies)
  • Sickle-cell anemia (textbook p. 51, 244- 245)
  • Alkaptonuria  
  • PKU (phenylketonuria:  see the label on a diet drink)
    
• SOME dominant traits in humans
  • Huntingdon's disease (textbook pp. 331-2, 339-345)
  • Achondroplasia (a type of dwarfism)
  • Polydactyly (extra digits)
  • PTC "taster"
  • Left-hand-on-top
  • Some types of deafness

   

• EXAMPLES of PROBLEMS
  1. Two people with cystic fibrosis are thinking about marrying.  They ask you whether their children are likely to have cystic fibrosis, too.
  2. Two people who have been screened (genes tested) know that they are carriers for cystic fibrosis.  What's the probability that their first child will have the disease?
  3. Huntingdon's disease is fairly rare, but dominant; people with the disease are almost always heterozygous.  Two people with Huntingdon's disease marry.  What's the probability that their first child will have this disease?

• answers

  1. yes.  100%, barring new reverse mutations; it's like dd x dd; 0 chance of the normal allele.
  2. 1/4.  (It's the Hh problem above)
  3. 3/4  (it's a variation of the Hh problem again)

 

All complex genetics problems are simply combinations of easier problems, hardly ever worse than the problems below.

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.

• 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  

DOWNLOAD the real set of problems for the take-home quiz due Friday.

Having trouble?  Make sure you have the basic ideas right; try these links:

• intro movie http://www.brainpop.com/health/growthanddevelopment/genes/index.asp
• basic intro http://gslc.genetics.utah.edu/basic/index.html
• http://vector.cshl.org/dnaftb/1/concept/   choose#1—Mendel's experiments
• pea traits, phenotypes, generations http://vector.cshl.org/dnaftb/2/animation/fs.html
• no blending http://vector.cshl.org/dnaftb/3/animation/fs.html
• dominance, alleles, genotypes, homozygous http://vector.cshl.org/dnaftb/4/animation/fs.html
• Punnett, law of segregation http://vector.cshl.org/dnaftb/4/animation/fs.html
• genetic disorders (easy): http://gslc.genetics.utah.edu/disorders/definition/index.html
• Human genetic disorders (easy-to-understand textbook chapter; look for "single gene disorders") http://gened.emc.maricopa.edu/bio/bio181/BIOBK/BioBookhumgen.html
•  
• For more depth and detail see 
  • Technical summaries of all known human genes and genetic disorders.
  • more links

Genetics Home Page                                                      Biology 103 Home Page                                                            Queens College