  Feldman and Karlin conjectured that the number of isolated fixed points for
deterministic models of viability selection and recombination among n possible
haplotypes has an upper bound of 2^n - 1. Here a proof is provided. The upper
bound of 3^{n-1} obtained by Lyubich et al. (2001) using Bezout's Theorem
(1779) is reduced here to 2^n through a change of representation that reduces
the third-order polynomials to second order. A further reduction to 2^n - 1 is
obtained using the homogeneous representation of the system, which yields
always one solution `at infinity'. While the original conjecture was made for
systems of viability selection and recombination, the results here generalize
to viability selection with any arbitrary system of bi-parental transmission,
which includes recombination and mutation as special cases. An example is
constructed of a mutation-selection system that has 2^n - 1 fixed points given
any n, which shows that 2^n - 1 is the sharpest possible upper bound that can
be found for the general space of selection and transmission coefficients.
