Chance, Determinism and Biology: Introduction
Note: a wonderful, readable book that covers some material from this
part of the course in more detail than we have time to is: Chance in
Biology: Using Probability to Explore Nature by Mark Denny and Steven
Gaines, Princeton University Press, 2000.
This section of our course deals with unpredictability, a factor which
occurs in every area of the life sciences, and of course in every area
of our lives (weather, traffic conditions, catching the flu, the sex
and genetics of our offspring, when we die). It might be useful in some
circumstances to ignore the aspects of biology that we can't predict,
which means that we take a purely "deterministic" view - there is no
unpredictability in our measurements, or our capacity for determining
the future course of events. We saw one example of this in the Leslie
matrix models for the age structure of a population. Given the initial
age structure of the population x0, and a Leslie matrix P, then at the
next time period the age structure will be P x0. Here, given the
present population structure, we can precisely predict the population
structure one time period later, and in fact at any future time n as we
saw by calculating P^n x0.
However, the Leslie matrix model assumes that all individuals in the
population reproduce and survive exactly consistently according to the
elements of the Leslie matrix, and this doesn't vary in any way. In one
sense, this implies that every individual in the population produces
exactly the same number of offspring as every other individual of the
same age. Clearly this assumption would not hold in reality, where not
only do individuals differ in the capacity to survive and reproduce
(the individual differences which, if heritable, are the basis for the
process of natural selection), but these may vary through time and
space as environmental conditions change. The area of mathematics that
provides us with methods to account for unpredictability is called
"probability". This is closely related to the area of statistics, which
applies probability to questions such as how likely it is that the
outcomes of two experiments will differ or be the same (e.g. do the
outcomes of the experiments differ "significantly") and how we can best
design experiments to evaluate some hypothesis.
Although in this course we will only cover basic probability and
models, in addition to the field of statistics there are many
applications of probability to sub-disciplines of biology that are
absolutely essential. A few examples:
Genomics - this is the application of probability to analyze genetic
sequences, determine differences between sequences, and compare
sequences between different individuals/species. The techniques to do
this utilize computational methods that are part of the general area of
"bioinformatics".
Population genetics - this uses probability to analyze the genetic
structure of a population (just as we have analyzed the age structure
using the Leslie model). The reason probability matters here is the
process by which mating and assortment of genetic material occurs in
many populations - it is not possible to determine exactly what egg and
sperm cells will combine and therefore there is an unpredictable
component to what the next generation will look like. Think of the
simple situation of two birds landing on an island, mating and founding
a population on the island. If by chance a genetically determined
characteristic of the parents is not passed on to the offspring, then
that characteristic will be completely lost from future generations
unless there is a mutation which returns it or an immigrant arrives
with that characteristic and interbreeds. The jargon name for this is
"founder effect". The limited genetics of the small number of founders
of a new population constrain the future genetic composition of the
population.
Disease spread - the entire field of epidemiology deals with how
diseases spread within and between populations. The initial phase of
this is unpredictable - think of the 2003 case of hepatitis A in
Knoxville, which was spread quite unpredictably among some individuals
who ate at a restaurant and not to others. This is associated with the
issue of vaccination - in what circumstances is it likely that without
vaccination a disease will spread and how do you trade off the costs of
this with the side effects and other costs associated with the
vaccination.
Vision - certain organisms have the capacity to perceive images and
movement extremely well under very low light conditions. In this
situation, there are very few photons hitting the cells (say within our
retinas) that respond and pass a neural signal on to the brain. So
photons hit the retina in an unpredictable manner. How then does the
organizms perceive an image under low light, since a decision has to
made as to whether that part of the image is really dark, or that it is
not dark but that a photon from that part of the image by chance has
not hit the retinal cell? This is part of the problem of signal
detection - determining what a signal is in a system with "noise" - a
central problem in sensory perception.