A note on pair-formation functions

In this paper, we take a closer look at two harmonic mean functions and two minimum functions (moving dominance function 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, 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. (C) 2000 Elsevier Science Ltd.