An alternative formulation of the birth function in a two-sex model

The inconsistency in Lotka's stable population model (two different intrinsic growth rates for the two sexes) arises from the fact that he considers two equations (for male and female births), and not because his equation for one sex does not involve the other. Many authors in the past have erroneously put emphasis on the latter point and modified Lotka's equations for male and female births. Since sex ratio at birth is constant, two independent equations for male and female births cannot exist. The correct approach is to attempt to form an equation for all births. The author followed this approach in his earlier works on the problem, but his birth functions were formulated from axiomatic considerations. The present paper provides a new birth function which has an intuitively appealing physical interpretation, and for which the interaction between the sexes is empirically determined from the data.