Figure 4. A cultural trait modifying the evolution of a genetic trait.
When the T trait is transmitted by Mendelian inheritance and the N trait is transmitted culturally, assorting and selection may lead to gene-culture polymorphisms. We took the parameter set α 1 = 0.83, α 2 = 0.24, b 0 = 0, b 1 = b 2 = 0.5, b 3 = 1, c 0 = 0, c 3 = 1, σ 1 = −0.01, and σ 2 = −0.82 and varied pairs of parameters as indicated. A. Cultural transmission affects equilibria: c 1 and c 2 varied between 0 and 1, and the equilibrium approached from initial frequencies near the x 1−x 2 edge is indicated by color. Polymorphisms exist in the orange region. In B and D, we considered the transmission parameters indicated by the black star in A: c 1 = 0.4 and c 2 = 0.31. In C and E, we used the Mendelian transmission parameters indicated by the white star in A: c 1 = 0.5 and c 2 = 0.5. B. Selection parameters that produce a polymorphism are shown in orange. C. When both traits show Mendelian transmission, no stable polymorphisms exist for any combination of selection levels. D. The assorting parameter combinations that produce a gene-culture polymorphism are shown in orange. E. When both traits show Mendelian transmission, polymorphisms do not exist for any combination of assorting parameters.