LS1b08_1_Hartl Probability

LS1b08_1_Hartl Probability - Probability in Genetic...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Probability in Genetic Analysis Daniel L. Hartl Harvard University M ENDEL’S LAWS of genetic transmission are fundamentally laws of chance (proba- bility). He surpassed any of his contemporaries in understanding that his principles of inheritance accounted for the different types of progeny he observed, as well as for the ratios in which they were found. No discoveries in genetics made since Mendel’s time have undermined the fundamental role of chance in heredity that he was the first to recog- nize. To understand Mendelian genetics, we therefore need to understand the elementary principles of probability. Every problem in probability begins with an experiment, which may be real or imaginary. In genetics, the experiment is typically a cross. Associated with the experiment is a set of possible outcomes of the experiment. In genetics the pos- sible outcomes are typically genotypes or phenotypes. The possible outcomes are called elementary outcomes. They are elementary outcomes in the sense that none of them can be reduced to combinations of the others. In our applications of probability, the number of elementary outcomes is often relatively small, or in any case can be enumerated. The principles of probability can also deal with conceptual experiments in which there are an infinite number of elementary outcomes, but this requires some technicalities that are not essential for present purposes. Each elementary outcome is assigned a probability that is proportional to its likeli- hood of occurrence. Probabilities always conform to two fundamental rules. First, the probability of each elementary outcome must be a nonnegative number between 0 and 1, and may actually equal 0 or 1. An elementary outcome with a probability of 0 cannot occur, and one with a probability of 1 must occur. The second rule is that the sum of the probabilities of all the elementary outcomes must equal 1. This rule means that some one of the elementary outcome must occur. These two rules also handle an annoying question often asked in regard to a coin toss: What happens if it lands on its edge? The answer is that this elementary outcome is assigned a probability of 0, so we need not bother with it. Here it will be helpful to consider a specific example. Consider a conceptual experi- ment whose outcomes consist of all possible combinations of girls (G) and boys (B) among four offspring produced by a mating between a normal female and a normal male. These are shown in Figure 1A, where the offspring are listed in order of birth from left to right. Each of the elementary outcomes is equally likely, and so the probability of each ele- mentary outcome is assigned a value of 1/16. Note that there are six types of sibships consisting of exactly two girls and exactly two boys. This is because there are six possible orders for the births, namely BBGG, BGBG, GBBG, BGGB, GBGB, and GGBB.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern