Genetics for Probability -- or vice versa

The following links provide a very basic introduction to genetics, and to associated probability computations. These notes were written for use in the undergraduate Probability sequence MATH/STAT 394-5-6 in 1998-9. They are not intended for graduate students in Statistical Genetics, but may be useful for those with no genetics background, or no probability background.

Genetics is almost unique among the sciences, in that its fundamental laws were stated as probability laws. Thus the probabilities we compute have a reality as long-run frequencies, and are not just subjective. For example, the probability a parent of blood-type O has a child of blood-type O is the proportion of times this event occurs among all children of all parents of blood type O. However, the probability President Clinton will resign cannot be given this interpretation, and is known as a subjective probability.

Other advantages of genetics are that the basic laws can be very simply and briefly stated, but that it also provides examples of a wide range of probability ideas encountered in MATH/STAT 394-5-6. A disadvantage is that there is some basic terminology and facts to learn. These will be kept to a minimum.

Anna Schneider, a UW senior, wrote the first version of Sections 1-5 of these notes, as part of an Undergraduate Summer Research Project, in Summer 1998. Note that Anna has not taken probability. Where she writes "what proportion", that just means "what is the probability". Where she writes "how many...", I have edited it to "on average, how many ..." ... that is just the number times the probability for each -- remember a probability is just a long-run frequency.

The examples (for example 2.3) are intended just to make sure you understand. The problems (for example 2.4) should be straightforward -- again these are just to make sure you are following ok. If you have difficulty with any of these problems/examples PLEASE LET ME KNOW.

1. Introduction to Genetics

  • 1.1 DNA and Chromosomes
  • 1.2 Alleles of a gene
  • 1.3 Genotypes and phenotypes

    2. Mendelian segregation

  • 2.1 Mendel's first law
  • 2.2 Examples 1
  • 2.3 Problems 1
  • 2.4 Mendel's experiments

    3. Population allele frequencies

  • 3.1 Population allele frequencies
  • 3.2 Examples 2
  • 3.3 Problems 2

    4. X-linked Traits

  • 4.1 X-linked traits
  • 4.2 Examples 3
  • 4.3 Problems 3

    5. Joint inheritance of traits

  • 5.1 Two indep inherited traits
  • 5.2 Genetic linkage
  • 5.3 Problems 4

    6. Recombination as a Poisson process

  • 6.1 Haldane's recombination model
  • 6.2 Problems 5
  • 6.3 Problems 6

    7. Binomial and multinomial counts

  • 7.1 Offspring types, probabilities, and counts
  • 7.2 Problems 7

    8. Normal approximations and normally distributed genetic traits

  • 8.1 Mendel's experiments revisited: are his results too good?
  • 8.2 Problems 8: Normal approximations to binomial counts
  • 8.3 Standardized height, and correlations among relatives
  • 8.4 Problems 9: some bits and pieces on continuous dsns

    9. The process of meiosis

  • 9.1 Meiosis