$$ \frac{\lambda^9 (\lambda - 1)^3 (2\lambda - (1 + b_f - \mu))^2}{4} = 0 $$

Since three of these eigenvalues are equal to one, the equilibrium is unstable or neutrally stable for all parameters. This makes intuitive sense since the fitness of all four alleles in both sexes is equivalent in the absence of culture.

## B.6 Stability of the $B_4$ equilibrium with culture lost

To determine the stability of this equilibrium, I calculated the characteristic equation for the system given by Equations 7 and 8 evaluated where $y_{f40} = y_{m40} = 1$.

$$ \frac{\lambda^9 (\lambda - 1)^3 (2\lambda - (1 + b_f - \mu))^2}{4} = 0 $$

Since three of these eigenvalues are equal to one, the equilibrium is unstable or neutrally stable for all parameters. This makes intuitive sense since the fitness of all four alleles in both sexes is equivalent in the absence of culture.