Cycles in the two‐sex problem: An investigation of a nonlinear demographic model

A fundamental shortcoming of classic stable population theory is its failure to handle populations differentiated by sex. The classic theory is linear while the two‐sex problem is inherently nonlinear. Previous two‐sex investigations have focused on equilibrium conditions rather than dynamics, and ignored competition between age groups for marriage partners. This study makes a start at analyzing dynamics and models that incorporate competition, which can play an important role in any realistic marriage model and can turn a model with a stable equilibrium sex ratio into one with a cycling equilibrium. As competition for mates increases is the cycle period stable or does it respond more sensitively? Over a wide range of demographic parameters the period at bifurcation is a good predictor of the cycle period for higher levels of competition; however, other cycle characteristics are insufficiently predicted by linear methods and nonlinear methods are needed to complete the picture.

Key words:

• Two‐sex problem
• nonlinear
• limit cycles

Notes

A version of this paper was presented at the annual meeting of the Population Association of America in Toronto, Canada, in May 1990. The author is indebted to Carl Boe, Ron Lee, Robert Pollak, and Ken Wachter for comments and advice beyond value.