For an introduction to "Dual Inheritance Theory" (DIT), see the page on Wikipedia titled Dual inheritance theory.
This is basically Memetics without the "M" word from my perspective - and since one of the primary points of memetics is to provide some nice terminology for those who study cultural evolution, I think that sucks.
The page contains a list of differences between DIT and memetics.
It claims memetics focuses on replicators, while DIT allows looser forms of cultural transmission. A complete theory of cultural evolution should obviously include those systems with low-fidelity transmission. They are evidently capable of cumulative adaptations, if used in conjunction with error correction.
However, IMO, memetics doesn't insist on high fidelity transmission, any more than genetics does. Rather what is needed for cumulative adaptations is Shannon mutual information between ancestors and distant descendants. High mutation rates don't invalidate evolutionary theory. They are just high mutation rates. That is true for both genetic and cultural evolution - for both genetics and memetics.
The idea that memetics is concerned with high fidelity replicators probably comes from Richard Dawkins - since he says things rather like that.
The idea that genetics is concerned with high fidelity replicators probably comes from the idea that genetics is the study of DNA - which is usually a high-fidelity replicator in biology. However, I take a broader perspective. Biology is the study of life - but that doesn't just include organisms made of DNA. It includes all living things, everywhere - including aliens, and virtual life, and future synthetic life. Genetics is the study of inheritance in living things. That need not necessarily involve high fidelity transmission of data - though it had better involve high fidelity transmission of information, or cumulative adaptations (and life) are impossible.
So, the idea that memetics is tied to the notion of high fidelity replicators comes from a fundamental misconception people have about the nature of biology and genetics.
Genetics shouldn't necessarily imply high fidelity data replication - and so neither should memetics, which is just genetics applied to culture.
DIT is mostly a rechristening of memetics, minus its widespread terminology, and supposed connotations of high-fidelity transmission.
Update: I revisit this Wikipedia article here.
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