MENDEL GENETICS

This Bayes net is for the famous experiments of Mendel, in which he developed the foundations of hereditary genetics. The experiments involved breeding red and white flowered pea plants.

There is a gene for the color of the flower, and there are two possible kinds of alleles (genetic values) for it: red ones and white ones. Each plant has two alleles: one inherited from each parent. If both its alleles are for white, then its flowers will be white, but if either or both its alleles are for red, then its flowers will be red, since red is the dominant allele.

The red allele is represented as R, and the white one as r. So a plant that is Rr has one red and one white allele, and therefore red flowers. If a plant which is Rr is mated with a plant which is rr, then the offspring will be Rr or rr, since it always gets an r from one parent, and may get an R or r from the other. If the parents are RR and rr, then all offspring will be Rr.

Node Color_P1 represents the color of parent 1, and P1 represents its genetics. The relation table of Color_P1 is derived strictly from the dominance information, and the relation tables of Color_P2 and Color_C are the same. The relation table of P1 assumes R and r occur in equal proportion, and the relation table of P2 is the same. The relation table of C indicates that during mating there is an equal chance for the inheritance of either allele.

To use the network, first compile it. Then you can enter observed colors for any of the two parents and the child, and observe how the probabilities for the other ones change.

The really interesting thing is when you have a more complex family tree, which can be easily created by copying and pasting. For example, to add more childrent to P1 and P2, select C and Color_C, and while holding the CTRL key down, drag them a little. You can also copy C and Color_C, then paste them in another place. If you hook one of the disconnected links up to C you have created a grandchild. You could duplicate P2 and Color_P2 to hook up the other disconnected link to. Using these simple operations you can build up any kind of family tree you want.

Belief networks are very powerful tools for genetic analysis. They can model multiple genes, interacting genes, indeterminate family trees, mutations, phenotypes that depend on genotypes in a complex or probabilistic way, etc.