August 19, 2005 | David F. Coppedge

Why Mathematical Formalism Eludes Evolutionary Theory

An important mathematical tool used by evolutionists has been discredited.  To study life history evolution (i.e., the changes over time in a population’s reproductive age, maximum size, age at death, etc.) evolutionists have relied on Charnov’s concept of life history invariants.  These invariants, which are “dimensionless ratios of two life history traits—for instance, age at maturity and average length of life,” according to Gerdien de Jong writing in Science,1 have been a staple of evolutionary models, providing generalizations “leading to an understanding of universal life history strategies.”  Now, warns de Jong about work by Nee et al. in the same issue,2 the principal method of detecting life history invariants has been called into question.  “The authors have determined that the approach is misleading, throwing the very existence of the concept into doubt.”  (Emphasis added in all quotes.)
    Ratios can fall on a straight line when plotted, suggesting a mathematical relationship, but Nee et al. have demonstrated that the relationships are figments of the method and not necessarily real.  The same data plotted between groups of animals might yield a straight line, for instance, but when plotted within isolated groups of animals can yield lines offset from one another.  “The regression analysis is therefore misleading,” de Jong says.  The same problem can exist within other biological models.  Are the patterns real, therefore, or contrived?  Are they meaningful in evolutionary terms?

Life history evolution is not the only field where invariants or universal constants are proposed.  The Universal Temperature Dependence of metabolism proposal asserts that the metabolism of all organisms can be described by a single equation.  Scaling laws (as, for instance, basic metabolic rate scale as mass to the power 3/4) are called universal over all life.  This hankering for universal explanations has been criticized not only on technical grounds but also for ignoring biology and the variation between organisms.  Interesting biology might not be in life history invariants but in biological variation.

De Jong illustrates, for example, that two species of fish in the same habitat can have completely different ratios of sex to social rank.  De Jong doesn’t go so far as to argue that it is a waste of time to look for mathematical relationships in biology, just that “We should be wary of treating an average across species as an explanatory general life history invariant.”


1Gerdien de Jong, “Evolution: Is Invariance Across Animal Species Just an Illusion?”, Science, Vol 309, Issue 5738, 1193-1195, 19 August 2005, [DOI: 10.1126/science.1117591].
2Nee et al., “The Illusion of Invariant Quantities in Life Histories,” Science, 2005 309: 1236-1239.

Evolutionists desperately want their theories to be considered scientific, but the language of science is mathematics.  They should recall the difference between the hard sciences and biology, as expressed by the Harvard Law: “Under the most rigorously controlled conditions of pressure, temperature, volume, humidity, and other variables, the organism will do as it *@#&! well pleases.”  The deception is even worse when evolutionary psychologists measure human behavior according to Koestler’s Ratomorphic Fallacy, treating people like lab rats, or when they try to describe altruism, whether in humans or bacteria, in terms of the equations of game theory.  One of the ugliest of recent examples involved anthropologists trying to measure the evolution of anti-Semitism (see 07/19/2005).
    Read the quote at the top right of this page again.  Is there anything in evolutionary biology that even comes close to Kepler’s Laws or Newton’s Laws in generality and formal structure?  Scientific research papers on evolution often contain equations, formulas, and graphs (e.g., 07/21/2005), but if even some of the most basic observable ratios of characteristics between present-day animals can produce misleading relationships, why should anyone trust relationships inferred between dead things lost in imaginary evolutionary prehistory?  If the “interesting biology” lies in variation, no pattern of evolution can be rigorously inferred.  Thus, evolutionists in their formalisms commit the fallacy of statistics, fooling and being fooled.

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