Evolutionary theory famously predated the emergence of genetics by decades. Initially there was some conflict between the heirs of Charles Darwin and the first geneticists in terms of their mechanistic understanding of how evolutionary process occurs. Within a few decades though genetics and evolutionary biology were synthesized so that the former came to be integral toward understanding the processes and parameters which shape the character of the latter (see The Genetical Theory of Natural Selection). E.g., imagine attempting to understand the origins and maintenance of sexual reproduction without any genetic understanding of the determination of sex and its implications for transmission.
But obviously genes are not everything when it comes to phenotypes. In particular with humans, there are complex behaviors and social interactions which seem to be persistent, and perhaps adaptive, which may not be directly contingent upon any simple genotype-phenotype map. 
This is not to say that cultural and behavioral traits have no genetic basis. To give an example, religion is a complex phenomenon which is both universal and does not seem directly encoded in one’s genes. The search for a “god gene” is futile, because religion as a phenotype is mediated by innumerable other phenotypes, which themselves have complex genetic bases.
Though culture is contingent upon genes, exhibits a character which is separable from genetic evolution. In particular, dual inheritance theory explicitly acknowledged that human cultural variation over time and space is a function of the interaction between both cultural and genetic evolution. Though there are similarities between the two, and in fact the field of cultural evolution consciously utilizes much of the same formalism as population and quantitative genetics, the modes of inheritance and nature of the origination and perpetuation of variation of the two differ a great deal.
As a rule of thumb you can posit that genetic evolution is relatively slow and torpid in relation to cultural evolution, which is protean and quicksilver. Consider that lactase persistence or high altitude adaptations are the two fastest we know for human genetics, and they occur on 1,000 year time scales. Over a 1,000 year time scale takes you from Julius Caesar to Otto the Great. It takes you from first of the Mycenaean, to Athens of Pericles.
The differences between culture and genes are important to keep in mind when one is making predictions. I’m a big fan of the Eric Kaufmann book, Shall the Religious Inherit the Earth?: Demography and Politics in the Twenty-First Century. The model outlined within the book, higher fertility for religious people, ergo, the reemergence of religion, is logically plausible. But I always must remind me people that the same concerns were prevalent in France before 1850, with the arrival of more traditional Roman Catholics into a milieu which had notably secularized and undergone early demographic transition. Why is France today not a uniformly Catholic republic? First, there is history. The migration of Muslims from North Africa. But even more important, cultural evolution, as the descendants of Spaniards, Poles, and Italians, secularized.
There is though a difference between description, and formal modeling. The field of cultural evolution attempts to do the latter. There are several lay and specialist introductions to the field (just click some of the book links and you’ve find them all). It’s worth attempting to grapple with the domain in a more systematic way, because that’s the only way you can make predictions which make sense of the diversity we see around us.
A new preprint is an interesting addition to the literature, Gene-culture co-inheritance of a behavioral trait:
Human behavioral traits are complex phenotypes that result from both genetic and cultural transmission. But different inheritance systems need not favor the same phenotypic outcome. What happens when there are conflicting selection forces in the two domains? To address this question, we derive a Price equation that incorporates both cultural and genetic inheritance of a phenotype where the effects of genes and culture are additive. We then use this equation to investigate whether a genetically maladaptive phenotype can evolve under dual transmission. We examine the special case of altruism using an illustrative model, and show that cultural selection can overcome genetic selection when the variance in culture is sufficiently high with respect to genes. Finally, we show how our basic result can be extended to nonadditive effects models. We discuss the implications of our results for understanding the evolution of maladaptive behaviors.
The most relevant section is probably 3.2 Model 2: Cultural prisoner’s dilemma. If you don’t know what the Price Equation is, read the original paper. It will induce some clarity.
The fact that more variance in culture in relation to genes allows for selection to act more powerfully on culture, and arguably in a maladaptive manner from the gene-centric perspective, is no surprise. This preprint adds more precision and clarity. For adaptation to occur there needs to be heritable variation. One reason that cultural group selection is more plausible than genetic group selection is that genetic variation across demes is often very low. The Fst between racial groups may be 0.10 to 0.30, but it is not very common for such Fst values to be realized between two groups genuinely in competition. More often neighboring populations have much lower Fst values, though ancient DNA is suggesting that 0.05 to 0.10 values were maintained in some areas 5 to 10 thousand years ago. A simple population genetic rule of thumb is that one needs to have less than one migrant between two populations per generation for their genetic variation to increase, rather than decrease. In other words, minimal gene flow on a general scale quickly reduces between group genetic variance.
In contrast, cultural variation can be maintained because migrants can switch cultures, or, their genetic progeny can adopt the culture of one the parents in totality. In this way the later Ottoman Sultans and Umayyad rulers of Al-Andalus had been genetically transformed by generations of mixing with concubines derived from Europeans or Caucasians (i.e., those from the Caucasus), while remaining culturally very Turk and Arab respectively.
As noted in the preprint, this formal/theoretical avenue of research will allow for the development of a robust empirical research program. The data is out there.
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