Summary: Chapter 4
Discrete Time Markov Chain
Models in the Biosciences
In this Chapter, we review some basic discrete time Markov chain models used in the
biosciences. In Section 4.1 we discuss models in genetics.
4.1 Genetic Models
4.1.1 Mendelian Genetics
One of the greatest scientific achievements of the past 200 years was due to Gregor
Mendel who, in his work on the inheritance traits of pea plants, founded the science of
genetics. Mendel predicted that each gene (although there was not even a notion that
we had something called genes in his day) could come in multiple different alleles.
The different observable traits would then depend upon which different types of alleles
were possessed. For example, in his work on pea plants Mendel predicted that there
were alleles for, among others: tall and dwarf plants, round and wrinkled seeds, and
yellow and green seeds.
To come to his conclusions, Mendel made the following series of experiments and
observations. First, if he took tall plants that had been bred from a line of only
tall plants, and cross-bred them with dwarf plants that had been bred from a line of
only dwarf plants, then the resulting plants were all tall. Next, he took these plants
and produced a second generation of plants. In this second generation, roughly a