Cyclically stable populations∗

This is a revision of a paper presented at the 1993 Annual Meeting of the Population Association of America. The work was supported by grants R01 HD19145 and R01 HD28443 from the Center for Population Research (NICHD), and benefited from the assistance of Robin M. Weinick, comments from Kenneth W. Wachter, and support provided by NICHD grant P30 HD06268 to the Hopkins Population Center.

The cyclically stable population relaxes the stable population assumption of fixed vital rates and replaces it with the assumption of a recurring sequence of schedules of vital rates. From any point (or stage) in one cycle of the sequence to the same stage in the next cycle, the cyclically stable population grows at a constant rate (λ). While the age composition of the cyclically stable population is different at different stages of the same cycle, it always has the same age composition at the same stage of every cycle. The essential dynamics of the cyclically stable model are captured by its birth projection matrix (BPM). The dominant eigenvalue of the BPM is growth rate A, and the right eigenvector associated with λ gives the within cycle‐birth sequence.

An important special case occurs when λ = 1, and a cyclically stationary population arises. Such populations challenge simplistic ideas about “Zero Population Growth.”; A population projection based on the sets of rates observed in the United States, 1970–90, shows a cyclically stationary population arising in less than 100 years. While it experiences no long term growth, that cyclically stationary population exhibits fluctuations in total size and considerable variability in age structure.

Key words:

• Cycles
• stable population
• zero growth

Notes

This is a revision of a paper presented at the 1993 Annual Meeting of the Population Association of America. The work was supported by grants R01 HD19145 and R01 HD28443 from the Center for Population Research (NICHD), and benefited from the assistance of Robin M. Weinick, comments from Kenneth W. Wachter, and support provided by NICHD grant P30 HD06268 to the Hopkins Population Center.