A Darwinian model of cultural replication over the continuum of Weismannian and Lamarckian inheritance

Universal Darwinism argues that entities capable of multiplication, variation and inheritance evolve by natural selection. Besides genetic reproduction implementing Weismannian inheritance, other adaptive systems were proposed to support Darwinian evolution, most notably culture, assuming autonomous cultural replicators akin to genes. Culture, on one hand, lacks direct template copying and inherits acquired changes, while on the other its overall behaviour is Darwinian as languages attest. The properties of culture setting it apart from biological evolution suggests a Lamarckian, while its overall behaviour a Weismannian interpretation, which is often coined as "the duality of cultural replication". According to canonical Darwinism, Lamarckian and Weismannian inheritance are disjunct mechanisms and only the latter is sufficient to maintain cumulative evolution. We resolve this apparent contradiction via a mathematical model of cultural information replication. We model the inheritance of information, cultural or genetic, as a successive set of template-based transformations of digital information between generations. We demonstrate that Lamarckian and Weismannian inheritance form a continuum and that both can reconstruct information stably for an indefinite time. Our formalism naturally unifies Lamarckian and Weismannian inheritance, proving that cultural replication, in theory, can approximate the fidelity of genetic replication. We claim that (well-defined) Lamarckian inheritance is an adequate low-level model of culture and can support population-level Darwinian evolution. We discuss the implications of our results to bridge the gap between the Lamarckian and Darwinian explanations of cultural evolution.