In this paper, we will put some timely network approaches, used in "cultural evolutionary theory" (CET) to the test, comparing their specific explanatory power. CET applies Darwinian principles to understand how traits like language, technology and norms spread, mutate, and persist. We evaluate four CET network models: (a) Phylogenetic Trees, (b) Death-Birth Networks, (c) Interaction Graphs and (c) Trait Networks. (a) excel at modeling vertical transmission but struggle with horizontal exchange. (b) reveal feedback between network structure and trait evolution but oversimplify edge dynamics (c) capture dynamic trait transmission but are often quite complicated. (d) effectively model co-evolving traits but neglect social agents.

We then evaluate these different models against the background of four classical philosophy of science explanations: Causal-Mechanical, Statistical Relevance, Unificationist and Pragmatic explanations. Each model has strengths and weaknesses concerning each kind of explanation. This comparative analysis illuminates which approaches best explain different aspects of CET.