Hoyle’s Critique of Neo-Darwinian Theory and the Impact of Heavy-Tailed Distributions

Physicist and astronomer Fred Hoyle has repeatedly criticized Neo-Darwinism as a flawed theory because of mathematical and statistical problems. His comments have been used by creationists and other opponents of the theory, even though he himself did not support their views. In this paper Hoyle’s critique of one aspect of Neo-Darwinism is analyzed to see what merits it may have. The conclusion is that while Hoyle’s mathematics is impeccable, and thus his critique based on them has merit, he did not carry his own reasoning far enough and specifically failed to consider the possibility of large variations in selective value. This may have been due to his belief that such variations would be extremely unlikely, due to an assumption that such variations would be governed by a normal distribution. However, if a heavy-tailed distribution is involved, such variations become feasible. The net result is that evolution in its early stages may have involved large jumps, which, though infrequent, would move it along. The objective of this study is to analyze the impact of Hoyle’s results and how they are affected by modern knowledge of heavy-tailed distributions.