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bayesian_statistics [2019/10/03 02:58]
floyd |
bayesian_statistics [2019/10/03 03:10]
floyd |
| Here is an example of Bayesian statistics from genetics. Probabilities and frequencies have been rounded and some genetic details of the system are simplified for convenience; however, this should serve as a reasonable first pass approximation. The mouse //t//-haplotype is an example of meiotic drive (meiotic drive is a fascinating example of potentially powerful positive selection that does not necessarily result in Darwinian adaptation of the organism and in fact often lowers fitness). Heterozygote ($t$/+) males that have one copy of each allele, a $t$ allele and a wildtype "+" allele do not have an equal (1/2, 1/2) Mendelian probability of passing on each allele to their offspring. Rather there is a 90% chance of passing on the $t$ allele and a 10% chance of the "+" allele. Incidentally $t$/$t$ homozygotes are immediately lethal and do not exist in the population. The //t//-haplotype has an easily observable dominant phenotype. Heterozygous mice have much shorter tails than normal. In wild populations 5% of mice carry the $t$ allele (i.e., are $t$/+ heterozygotes). | Here is an example of Bayesian statistics from genetics. Probabilities and frequencies have been rounded and some genetic details of the system are simplified for convenience; however, this should serve as a reasonable first pass approximation. The mouse //t//-haplotype is an example of meiotic drive (meiotic drive is a fascinating example of potentially powerful positive selection that does not necessarily result in Darwinian adaptation of the organism and in fact often lowers fitness). Heterozygote ($t$/+) males that have one copy of each allele, a $t$ allele and a wildtype "+" allele do not have an equal (1/2, 1/2) Mendelian probability of passing on each allele to their offspring. Rather there is a 90% chance of passing on the $t$ allele and a 10% chance of the "+" allele. |
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| | {{thaplotypecross1.png?300}} |
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| | Incidentally $t$/$t$ homozygotes are immediately lethal and do not exist in the population. |
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| | {{thaplotypecross2.png?300}} |
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| | The //t//-haplotype has an easily observable dominant phenotype. Heterozygous mice have much shorter tails than normal. In wild populations 5% of mice carry the $t$ allele (i.e., are $t$/+ heterozygotes). |
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| You are doing a project on quantifying the reproductive success of male mice with the //t//-haplotype in the wild. However, you can only directly observe the offspring of individual (normal tailed, +/+) females without knowing the identity of the male parents. (Here assume each batch of offspring has only one male parent and belongs to the female it is found with in the nest.) You want to calculate the probability that the male parent was a $t$/+ heterozygote given the observation of the number of +/+ offspring. First off, before observing any more data, we can use the information of the 5% frequency of heterozygotes in the population from earlier studies. Our "prior" probability of a heterozygous father is $P(M_1) = 0.05$. Here were are using $P()$ to represent probability and $M_1$ to represent one of our models. A model is a hypothesis and our first hypothesis in this example is that the father is heterozygous. Our second model is that the father is a wildtype homozygote. | You are doing a project on quantifying the reproductive success of male mice with the //t//-haplotype in the wild. However, you can only directly observe the offspring of individual (normal tailed, +/+) females without knowing the identity of the male parents. (Here assume each batch of offspring has only one male parent and belongs to the female it is found with in the nest.) You want to calculate the probability that the male parent was a $t$/+ heterozygote given the observation of the number of +/+ offspring. First off, before observing any more data, we can use the information of the 5% frequency of heterozygotes in the population from earlier studies. Our "prior" probability of a heterozygous father is $P(M_1) = 0.05$. Here were are using $P()$ to represent probability and $M_1$ to represent one of our models. A model is a hypothesis and our first hypothesis in this example is that the father is heterozygous. Our second model is that the father is a wildtype homozygote. |
