A note on pair-formation functions

In this paper, we take a closer look at two harmonic mean functions [1, 2] and two minimum functions (moving dominance function [3] and group-specific minimum function), in two sex multigroup populations. Comparisons between these functions are focused on proportionate mixing. We show that under some special conditions, the two harmonic mean functions are identical; and under the mixing framework of Castillo-Chavez and Busenberg [4], the two minimum functions are also identical (for both proportionate and nonproportionate mixing). Simulations of a simple demographic model with the four functions are also performed to confirm the above mentioned identity and to illustrate the behavior of these functions.