Mathematics and the Genome
2. Mathematics
and Classical Genetics (The Early Days)
From ancient times breeders of animals and plants were aware that progeny resemble
their parents. Why did it take so long to pin down the ideas of inheritance we
know of today? The answer seems to be that animal breeders did not have the paradigm
of the scientific method to obtain insight. The leap forward that Mendel appears
to have made was the mathematical analysis (statistical analysis) of his experimental
data, obtaining connections between the phenotype (physical appearance) of the
peas he bred experimentally with a conceptual model of how these phenotypes were
related to an explanation of a genetic mechanism that explained what experimenters
were observing.
Mendel performed a dramatic series of experiments that shed light on the fact
that the traits that were inherited from parents were not blended versions of
those of the parents but rather determined by unchanging factors. Today we think
of these factors as the genes that reside on the chromosomes. Interestingly, Mendel
had studied mathematics in Vienna, including a course with Christian Johann Doppler
(1803-1853), who, though he is best known as a physicist, actually held a university
appointment at one time in mathematics. Doppler emphasized Newtonian thinking
as an approach to doing science, an approach that is related to today's use of
mathematical modeling. Although Mendel's work was presented publicly in 1865 and
published in 1866, surprisingly little notice was taken of it. Only with the rediscovery
of his ideas about 1900 (by Hugo de Vries (Dutch), Carl Correns (German) and Erich
von Tschermak (Austrian)) were steps towards a beginning theory of genetics organized.
Ironically, there has been considerable recent work to try to understand exactly
how Mendel thought about what the results of his experiments meant, and whether
or not some of the data he produced was too good to be true! Furthermore, as time
has gone on we now know there are exceptions to all of Mendel's laws.
- Introduction
- Mathematics
and Classical Genetics (The Early Days)
- Mathematics
and Clasical Genetics (1900-1953)
- Molecular
Genetics (1953-Present)
- Near
and Far (Strings)
- Near
and Far (Trees)
- The
Wider Picture and the Future
- References
