Stochastics Group - Mathematical Institute
- University of Tübingen

Bioinformatics, Biomathematics and Biostochastics

Bioinformatics does not aim to lay down fundamental
mathematical laws that govern biological systems parallel to those
laid down in physics. At this stage the main utility of
Bioinformatics is in the creation
of tools that investigators can use to analyze data.
For example, biologists need tools for the statistical assessment
of the similarity between two or more DNA or protein sequences, for
finding genes in genomic DNA, and for estimating differences in how
genes are expressed in different tissues. Important areas in Bioinformatics
work on the development and the optimization of corresponding data
bases, algorithms and program packages.
Biomathematics works mainly on the mathematical description and
investigation of biological phenomena. The aim is a general mathematical
modelling and mathematical analysis of biological systems similar to
the laws known from physics. The probably most simple example is the
exponential growth of populations (N'=cN). In contrast to physics such
laws are still long way from being determined for biological
systems. In its original meaning Biomathematics mainly considers
deterministic approaches, most of them from the area of
Differential Equations and Dynamical Systems.
Biostochastics pays attention to the fact that many biological
phenomena are partly or even completely determined by randomness.
Although the relevance of randomness in biology (for example in evolution)
was seen quite early (Darwin, Mendel, Hardy-Weinberg), more complex
probabilistic models have been intensively studied only recently, also
due to the relative late development of stochastics. Fundamental progress
could be made only after the theory of Stochastic Processes and the
theory of Stochastic Integration was sufficiently developed. For
example the theory of Branching Processes fundamentally contributed
to the understanding of biological population growth up to the
Polymerase Chain Reaction (PCR). Another typical example is
the Coalescent Theory going back to Kingman (1982), a theory on
ancestral trees which is still influencing the movement of population
genetics. The number of publications in journals on probability
theory with connection to biology increased since 1980 drastically and
documents the importance of Biostochastics. Moreover, Biostochastics
forms the basis for a profound statistical analysis of biological data.
Here the connection to Bioinformatics becomes in particular obvious.