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Abstract
Previous experience in the development of the mathematical theory of biological evolution, has helped the authors toward their theory of cultural evolution. In this review a constant comparison between the two evolutions, in both directions, has led to an interdisciplinary understanding. Cultural transmission is discussed in detail and the ten major modes of transmission are enunciated; cultural traits are defined and the variance within, as well as between, groups considered. Cultural and environmental selection as well as complex transmission are further aspects leading the authors to the conclusion, that in spite of gross oversimplification, their theory is essential for a rigorous qualitative investigation of cultural evolution.