A note on pair-formation functions

In this paper, we take a closer look at two harmonic mean functions [1,2] a nd two minimum functions (moving dominance function [3] and group-specific minimum function), in two-sex multigroup populations. Comparisons between t hese functions are focused on proportionate mixing. We show that under some special conditions, the two harmonic mean functions are identical; and und er the mixing framework of Castillo-Chavez and Busenberg [4], the two minim um functions are also identical (for both proportionate and nonproportionat e mixing). Simulations of a simple demographic model with the four function s are also performed to confirm the above mentioned identity and to illustr ate the behavior of these functions. (C) 2000 Elsevier Science Ltd. All rig hts reserved.