Biomedical Engineering Reference
In-Depth Information
sex of the fly is male—assuming no external forces have been at work to affect the natural balance of
fruit fly sex. Probability, the likelihood that an event will occur, is expressed as the ratio of the
number of favorable outcomes in the set of outcomes divided by the total number of possible
outcomes. Similarly, a stochastic system involves or shows random behavior.
Despite the apparent randomness at the organism level, when the same events are viewed at the
population and ecosystem levels, they often appear as deterministic behaviors. That is, they have an
outcome that can be predicted because all of its causes are either known or are the same as those of
previous events. The concepts of evolution and chaos theory describe patterns in apparently random
events that appear systematic and predictable over several generations. Chaos theory describes the
unpredictability inherent in every system, in which apparently random changes occur because of a
system's extreme sensitivity to small differences in initial conditions. A small increase in the earth's
average temperature may drastically alter life on earth over several centuries, for example.
Mutations, chance mating, random environmental pressures, and the relative contribution of parents
to the genotype of their offspring all lend themselves to statistical interpretation. An important
distinction in biological systems is that some processes or measurements are either present or absent
(discrete), while others are variable within some range (continuous). For example, a particular
nucleotide is either at a location within a sequence or it isn't, just as a pea from one of Mendel's
sweet pea plants either was round or wrinkled. In contrast, the expression of a gene, as measured by
the fluorescence of a spot on a microarray slide, may range from absent to weak or pronounced. For
example, consider a patient genetically predisposed to adult onset or Type II Diabetes. In many
cases, by altering their behavior to include a low-calorie diet and regular exercise, a patient can
control the symptoms of the disease—and presumably the expression of some genes. As such,
bioinformatics methods encompass not only traditional statistics, but probability and stochastic
processes, with both continuous and discrete variables.
Progress
Many advances in statistics were rooted in anecdotal observations that predated the development of
formal mathematical proofs or models. For example, the first model of Mendel's work, Punnet
Squares (see
Figure 6-1
), was developed about 50 years after Mendel's original observations. R.C.
Punnet developed the model to illustrate the range of possible allele pairings, and to calculate the
probability of each pairing. Using Mendel's mating of pea plants with round and wrinkled peas,
Punnet's model predicts that the offspring will have four genotypes and a probability ratio of:
1 RR : 2 Rr : 1 rr
Figure 6-1. Probability and Punnet Squares. The model illustrates how the
relative probability of a genotype relates to a given genotype mating.
