Author1 Edit

It is extremely difficult to find a clear and precise statement of the theory of evolution

Author2 Edit

A popular tautology is that presented by Volterra's model of competition (Volterra and d'Ancona 1935). It assumes that two popUlations grow in a limited system such that, eventually, increase in one population produces a decline of the other. These conditions are presented as constants in the LotkaVolterra equations, from which a strictly mathematical logic shows that two results may be obtained: one population or the other disappears. Because the argument is logically derived from the assumptions, it is tautological. Nevertheless, the argument has received considerable attention, possibly because the conclusions, which are evident in a verbal statement, are more difficult for us to see in the mathematical form.

This tautology might form the deductive portion of a combined theory, but this would require that the axioms be phrased as testable theories. Andrewartha and Birch (1954) maintain that this is impossible: one can determine the necessary constants only by fitting the results of the competition experiment to the general form of the equations. Thus the results must be predicted from the results themselves. A more acceptable phrasing is that the results are classified in terms of the model. The verification offered by Gause (1935) represents a post facto correspondency with the model, not its proof. Hardin (1960) points out that the third possible outcome, survival of both populations, could only indicate a misclassification; that is, that the original conditions were not met. He states that the principle is untestable and tautological, but suggests that it may be useful in ordering our thoughts. Cole (1960) was quick to point out that Hardin had thus raised the tautology to a dogma

Author3 Edit

Tautologies may be useful logical aids, but they cannot replace true theories. Unless ecologists are careful to distinguish the two, their confusion may produce a body of thought resting on metaphysical rationale rather than empirical, predictive science.

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