The second, more substantive problem is that the analogy between genes and culture is not very deep. The two are similar in that important information is transmitted between individuals. Both systems create patterns of heritable variation, which in turn implies that the population-level properties of both systems are important. Population-level properties require broadly Darwinian methods for analysis. But this just about exhausts the similarities. The list of differences is much larger. Culture is not based on direct replication but upon teaching and imitation. The transmission of culture is temporally extended. It is not necessarily particulate. Psychological processes have a direct impact on what is transmitted and remembered. These psychological effects can produce complex adaptations in the absence of natural selection. Users of the meme concept seem to us to believe that it does more work than it really does.
Firstly, there are no complex adaptations in the absense of selection. Unless one argues that some selective processes are somehow "unnatural" I see no case against this thesis. Boyd and Richerson are arguing, I think - that intelligent design by humans can produce complex adaptations. However, this misses the basic and fundamental point of Campbell and many others that brain function depends on natural selection on multiple levels - selection between axon and dendrite spikes, selection between synapses, selection between ideas - and so on.
Boyd and Richerson argue that transmission of culture is "temporally extended" - while transmission of genes is not. This is false, I think, since transmission of genes is also "temporally extended". Organisms typically acquire genes throughout their lifespan as they acquire genomes from parasites and mutualist symbionts. Gene transmission is often a long, drawn-out process involving temporally extended phenomena - including parental care. The idea that transmission of genes is not "temporally extended" seems wrong in just about every way.
Boyd and Richerson argue that psychological processes have a direct impact on what is transmitted in cultural evolution - but not in organic evolution. This too, is mistaken. Psychological processes have a direct impact on what is transmitted in organic evolution too. In particular mate choice, and habits affecting parasite transmission affect gene transfer in a big way - if you are squeamish about rotting food you will probably wind up with a different set of parasites from someone who is afraid of social contact.
Both organic inheritance and cultural inheritance use high-fidelity template copying - and a range of other types of more sloppy and low-fidelity inheritance. Any idea that organic inheritance is entirely based on "direct replication" is mistaken - and the idea that some types of organic inheritance are not based on genes is using the molecular biology conception of a "gene" - which seems pretty irrelevant to me. The molecular biology conception of a "gene" is not what memetics is based on.
To recap a little, in my preferred terminology, "gene" is a general term for a piece of heritable information - and "genetics" is the science of heredity. That means that memes are a type of gene. To say "the analogy between genes and culture is not very deep" makes no sense from this perspective. It isn't an "analogy" in the first place - a meme is a type of gene. Memes can't be too different from genes - a meme is a kind of gene.
Basically, all of Boyd and Richerson's objections seem to be based on misunderstandings to me. Now, maybe this is the fault of memeticists, for not explaining these issues more clearly. However, these points aren't new objections that I'm raising - they are all in the memetics literature. The failure of academics to understand memes remains an ongoing, frustrating issue. This is now the internet era. Scientific differences can be discussed and explored online. Such differences of opinion should mostly fade in the face of the truth.
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