Probabilities in Genetics

6 Key excerpts on "Probabilities in Genetics"

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  Stochastic Processes In Genetics And Evolution: Computer Experiments In The Quantification Of Mutation And Selection

  Computer Experiments in the Quantification of Mutation and Selection

  • Charles J Mode, Candace K Sleeman(Authors)
  • 2012(Publication Date)
  • World Scientific

    (Publisher)

  Chapter 1 An Introduction to Mathematical Probability with Applications in Mendelian Genetics 1.1 Introduction Genetics is a major and basic field of biology with a vast literature. Indeed this literature is so vast that it is doubtful if any person has a complete grasp of the available material on genetics in numerous books and on the world wide web. A current and excellent introduction to genetics is contained in the text book, Principles of Genetics, by Snustad and Simmons (2006), and it is suggested that if a reader encounters a term that is not familiar, either this book, a similar book or the world wide web be consulted. In this chapter, however, it will be assumed that a reader has a grasp of such terms from Mendelian genetics as gene, genotype, chromosomes and phenotype, and in subsequent chapters other terms will be introduced as attempts are made to deal with problems in genetics that arise at the molecular level. Genetics deals with biological processes that are not deterministic. That is, the present state of a process does not fully determine the next state. For example, suppose a couple marries and intends to have children, but, given this state of matrimony, it is impossible to predict with certainty how many children they may have or the distribution of boys and girls in their family. There are also many examples in medicine that are characterized by uncertainty. A doctor may, for example, administer the same treatment to patients with a disease of the same phenotype, but the patients will react differently to the same treatment. Processes that are characterized by uncertainty or randomness are called stochastic, a term that is derived from the Greek word which means to aim at or characterized by randomness. From the mathematical point of view, stochastic processes are rooted in concepts and procedures of probability theory, a field of mathematics that deals with the concept of uncertainty. 1

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  Evidence in Science

  A Simple Account of the Principles of Science for Students of Medicine and Biology

  • Kenneth Stone(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The predictions it makes are about the class of lives to which you belong—healthy men, or women, of a given age. If the parents think: 'Well, at least it is probable that the next child will be healthy', they are unconsciously leaving 'mathematical probability' for 'credibility'. They are validly inferring from your information: 'The next child will be healthy has some degree of credibility.' One great use of probability theory in biology is in the science of genetics. The simple basic concepts are its foundation, for genetic hypotheses and their consequences involve random behaviour. Let us look again at one of Mendel's experiments. He crossed a pure-breeding round-seeded garden pea plant with a wrinkled-seeded plant, and the following year grew the hybrids. Denoting the dominant factor for roundness of seed by ' ', and the recessive factor for the wrinkled character by 'a', the pair of factors in the F x hybrid is 'Aa'. When these hybrids make their egg cells and pollen cells, the factors separate: two kinds of eggs ( A ) and ( a ) are formed in equal numbers; * That a Mendelian ratio will be found in a small family is a common mistake, which, with others, appears in the well-known limerick:— There was a young woman called Starkie, Who had an affair with a darkie. The result of her sins Was quadruplets, not twins— One black, and one white, and two khaki.

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  Introduction to Genetics

  11th Hour

  • Sandra Pennington(Author)
  • 2009(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  11'\ TilE CI.II'\IC Probabilities and statistics are used extensively in genetic counseling. Counselors use family histories, laboratory tests, or both to determine the likelihood that a person has an affected genotype or is a carrier (heterozygous) for a recessive disorder. Approximately 4% of newborns have a significam abnormality (about half of these are genetic) that is present at binh or recognized within the first year of life. Parents of such babits, ur l.:ouplts who suspect they might have genetic disorders in their families, seek genetic counseling to determine the likelihood of having additional affected children, or a first child with the disorder. Counselors are trained in genetics, medicine, and counseling and they provide individuals and families with support services as well as information on the diseases, treatments, and options. Chapter Test True/False I. Probability is the likelihood something will happen in the future. 2. The sum rule requires that the probabilities for getting an outcome are mutually exclusive. 3. The product rule is the best way to determine the probability of drawing a full house in poker (three of onc vaJue of card and two of another value of card) in the first five cards dealt from a full deck. 4. Binomial probabilities do not account for all possible orders of events. 5. Chi-square testing will indicate samples that are too small. 6. Observed measurements that are different from the expected values may not be significantly different and this hypothesis can be tested. 7. Smaller numbers are inherently more accurate. 8. As the number of classes increases, the total deviation will increase. 34 Chapter 2 Probability and Statistics Multiple Choice 9. In the cross of a female with genotype AahhCcDdEe to a male of genotype AaBhccDdEE, what proportion of progeny will have exactly the same phenotype as the male parent? a.

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  Python Programming for Biology

  Bioinformatics and Beyond

  • Tim J. Stevens, Wayne Boucher(Authors)
  • 2015(Publication Date)
  • Cambridge University Press

    (Publisher)

  21 Probability Contents The basics of probability theory Sample space Probability values Restriction enzyme example Combining probabilities Conditional probabilities Bayesian analysis Random variables Binomial distribution Poisson distribution Geometric distribution Markov chains Markov processes Hidden Markov models Using Python for hidden Markov models The Viterbi algorithm The forward-backward algorithm Implementing a protein sequence HMM The basics of probability theory The theory of probability was based on the observation of random physical events, most notably for games of chance. And naturally, calculating accurate probabilities became espe- cially important for people when money was wagered on the outcome. Probability is a way of ascribing numerical values to the possible outcomes to help us understand a random process more fully. This enables us to ask questions like how much more often one event occurs compared to another, but because of the random nature of what we are studying we can never say what the outcome will definitely be. Rather we tend to think of the process in terms of what the long-term proportions of different outcomes are, if the random experiment were repeated a very large number of times, or perhaps if money is involved what a wager on a particular outcome is worth. Turning to biological systems, some things in living organisms occur as a result of random processes, like the segregation of a parent’ s chromosomes among their children or base-pair changes in DNA (such as a result of replication errors or ionising radiation), though, under most circumstances we don’t get to see the actual random event. For the most part we just view the outcomes, sometimes billions of years later in the case of DNA sequence changes. Of course a DNA sequence isn’t actually random, given that it exists to contain biologically meaningful information representing genes and gene control elements etc.

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  Origin Of Individuals, The

  • Jean-jacques Kupiec(Author)
  • 2009(Publication Date)
  • World Scientific

    (Publisher)

  It varies depending on the conditions in which the chromosomes find themselves. The probability 18 The Origin of Individuals of a phenomenon always depends on the physical and chemical con-ditions for it to occur, and in this sense, one cannot speak of indeter-minism here. Probability does not deny the causality of phenomena: it just opens up to plurality the relationship between the cause and effect, which is one-to-one in the context of determinism. 2.2.2 Probability is not incompatible with reproducibility Another very widespread error which must be avoided in a discus-sion dealing with the mechanisms of embryogenesis consists in believing that a probabilistic phenomenon is not reproducible because it involves chance. On the contrary, the concept of proba-bility expresses the existence of order and reproducibility where there was thought to be none, before it was conceived. 7 When chance is rationally mastered by mathematics, predictions can be made with a very great degree of accuracy by calculating probabil-ity. This is commonly done nowadays in modelling numerous natu-ral or economic processes. We have already seen that the probability of an event is seen in the frequency of its occurrence being stable when it is repeated a very great number of times. To be precise, the definition of the probability of an event X occurring is its frequency as the number of experiments performed approaches infinity. In practice, if we repeat an experiment involving random events a very great number of times, each time we perform it the events occur with constant frequency, ignoring minute negligible deviations. For example, if I play heads or tails, the frequency of each of these events will always be 50%. Probability thus expresses a stable structure of the world which is not manifested by individual events but by populations of events which are repeated a great many times. Unlike common sense, probability expresses reproducibility where it is not immedi-ately obvious.

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  Basic Biostatistics for Geneticists and Epidemiologists

  A Practical Approach

  • Robert C. Elston, William Johnson(Authors)
  • 2008(Publication Date)
  • Wiley

    (Publisher)

  Her physician checks published tables and finds that the probability of a 25-year-old woman having a Down syndrome child is about 1 in 400. If she is counseled that the probability of her second child having Down syndrome is only about 1 in 400, she will have been quoted a valid probability; only 1 in 400 such women coming for counseling will bear a child with Down syndrome. But this probability will not be relevant if the first child has Down syndrome because of a translocation in the mother, that is, because the mother has a long arm of chromosome 21 attached to another of her chromosomes. If this is the case, the risk to the unborn child is about 1 in 6. A physician who failed to recommend the additional testing required to arrive at such a relevant probability for a spe-cific patient could face embarrassment, perhaps even a malpractice suit, though the quoted probability, on the basis of all the information available, was perfectly valid. The mathematical (axiomatic) definition of probability avoids the disadvant-ages of the two other definitions and is the definition used by mathematicians. A simplified version of this definition, which, although incomplete, retains its main features, is as follows. A set of probabilities is any set of numbers for which: each number is greater than or equal to zero; and the sum of the numbers is unity (one). This definition, unlike the other two, gives no feeling for the practical meaning 82 BASIC BIOSTATISTICS FOR GENETICISTS AND EPIDEMIOLOGISTS of probability. It does, however, describe the essential characteristics of probability: there is a set of possible outcomes, each associated with a positive probability of occurring, and at least one of these outcomes must occur. We now turn to some fundamental laws of probability, which do not depend on which definition is taken.

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