BY A. W. F. EDWARDS†+ Department of Genetics, University of Cambridge
Genetics is the study of the biological relations between parent and offspring. Some of the observed similarities are due to the environmental influence of parent on offspring, or of a similar environment on both, whilst others are due to the transmission of matter, influential in the moulding of the offspring, by the parental zygotes. Classical genetic theory tells us that genes, spaced along chromosomes in the nucleus of a cell, and transmitted from parent to offspring, control the development of the individual.
Opportunities for physical models in genetics are many: from those showing the behaviour of chromosomes at meiosis, to those portraying the most recent advances, such as the model of the bacteriophage, or of the double- spiral structure of DNA. But we will concern ourselves here with a model of much wider application: the mathematical model 'probability'.
The concept of probability is very widely used in genetics. It is used in mathematical models of populations and of evolutionary changes, in techniques--such as in the sample-recapture method of estimating population size, in statistical tests, and in the mathematical model of the segregation of characters. It is this particular model that we will analyse.
Gregor Mendel was the first person to examine the segregation of characters critically, and his extensive experiments led him to formulate his famous Law of Segregation of genes. Not only did he observe that the segregation ratios, as we now call them, were integral ratios such as one-to-one, or three- to-one, but he also put forward the concept of a gene to explain how such segregations arose. Upon the foundation that he laid geneticists have built a statistical model which is compatible with the observed segregation ratios.
This model is wholly based on the concept of probability. We postulate that a crossover in a certain part of a chromosome will occur with probability p1, that a certain centromere will go to a certain nucleus at division with probability p2, and so on. Then we compound our postulated probabilities according to the mathematical laws of probability, and obtain expectations for the segregation ratios. Finally, knowing the observed segregation ratios, we derive estimates for p1, p2, . . . by an approved statistical technique, and we are left with a probability model describing a biological process.
We must now digress into a consideration of what we mean by a model: How does it differ from a description, or a law? Must it have a logical structure? May we logically draw any conclusions from one?
First, a model need not be physical: it can be mathematical, or it can exist merely in the mind of the scientist. For example, when Laplace writes 'in____________________