If you’ve ever read The Origin of Species, and perused Charles Darwin’s multiform thoughts, you will note one major area of muddle: an incoherent theory of inheritance. More formally Darwin’s theory of evolutionary change via adaptation had within it the assumption that there was heritable variation upon which natural selection could operate. If you have no heritable variation, then natural selection operating on populations has no power to affect changes which persist over the generations. In the 19th century there was no consensus as to the nature of inheritance. The ideas of Jean-Baptiste Lamarck were still influential, and had an impact on Darwin’s early thought. Though some thinkers, such as Francis Galton in an inchoate manner, put forward models of discrete inheritance, by and large the assumption was that traits were passed down from parents in sexual species through blending of the characteristics of the parents. This is an eminently intuitive thesis, and persists down to the present. It is why there the incorrect perception that admixture between light and dark skinned populations will lead to a uniform brown hued future. By analogy to mixing between buckets of paint it is clear that blending eliminates the variation which is the raw material of evolutionary process via natural selection. More formally the variance of the trait decreases by a factor of two every generation under a blending inheritance model.

How did Darwin address this issue? “Provisionally”, in his own words. The fact was that until the discovery of the significance of Gregor Mendel’s work in the early 20th century evolutionary biology had no persuasive mechanism for how the variation which it was dependent upon could be maintained. But the situation was worse than even that. Over at arXiv Alan Rogers has put up a short note, Rate of Adaptive Evolution under Blending Inheritance. He concludes:

Late in the 19th century, two misconceptions

undermined the debate about evolutionary time. One of these—the age of the earth—has been widely discussed. Yet by comparison, its effect was minor. Victorians underestimated the age of the earth by 1 or 2 orders of magnitude. Their theory of heredity implied a far larger error. Had they worked this out, they would have had good reason for skepticism about evolution

Using some straightforward algebraic manipulations Rogers concludes that for a new beneficial mutation the rate of mean increase within the population under a Mendelian model as opposed to a blending scenario is 2 N times greater, where N is the population size. He observes that ” In a population of 10,000 individuals, adaptive evolution would be 20,000 times slower under blending than under Mendelian inheritance, given equal mutational inputs.”

Lord Kelvin had nothing on that.