Mutational randomness as conditional independence and the experimental vindication of mutational Lamarckism

The Modern Synthesis enshrined natural selection as the driver of adaptive evolution mainly by eliminating competing explanations. One of the eliminated competitors was Lamarckism, particularly 'mutational Lamarckism', a hypothesis according to which mutations may be directed towards producing phenotypes that improve the performance of the organism in a particular environment. Contrary to this hypothesis, the Modern Synthesis' view claims that mutations are 'random', even though the precise meaning of the term was never formally explicated. Current evidence seemingly in favour of the existence of legitimate cases of mutational Lamarckism has revitalized interest to seek a clarification of the meaning of the term 'random' in this context. Herein we analyse previous definitions of random mutations and show that they are deficient in three ways: either they are too wide, or too narrow, or dyadic. We argue that the linguistic expression 'random mutation' refers to a triadic rather than a dyadic relationship, propose a new, formal and precise definition based on the probabilistic concept of conditional independence, and finally provide examples of its application. One important consequence of our analysis is that the genomic specificity of the mutational process is not a necessary condition for the existence of mutational Lamarckism.