Background/Question/Methods Regularly fluctuating populations are of great interest to ecologists. Density dependent processes are often invoked to explain fluctuations, but fluctuations in “obligate biennial” plants can occur in the absence of density dependence. We review explanations and models for regularly fluctuating populations with an emphasis on demographic time-lags in plant life cycles. As a detailed example, we explore alternative models to explain population cycling in Warea carteri, an annual mustard endemic to Florida’s Lake Wales Ridge. We used independent data to model the life cycle of W. carteri and compared the projected trajectories to observed trajectories (up to 16 years) of plants in 74 patches in three populations. The model is based on an annual time step and four stages (recently produced seeds, seeds in the seed bank, seedlings, and adults) with seven transitions, summarized by five vital rates (seed bank survival, fecundity contribution to the seed bank, fecundity contribution to seedlings, germination, plant survival). It includes variation in the amount of fecundity and the degree of seed dormancy. Fluctuations of both observed and modeled populations were evaluated using analyses of subordinate eigenvalues, power spectra, autocorrelation, amplitude, and damping.

Results/Conclusions Observed W. carteri populations showed strong cycling with significantly negative one-year autocorrelations and positive two-year autocorrelations. Damping ratios and oscillation periods were approximately two. Consistent estimates of power spectrum analysis confirmed a dominant two-year cycle. Observed amplitude was higher in the more frequently burned populations, and reached its maximum one year after fire and then dampened. Deterministic modeling and elasticity analyses indicated that delayed germination (for one year) may explain biennial population cycling. Demographic variation of stochastic models showed similar cycling with slower dampening than deterministic models, but still had lower amplitudes (especially 3-4 years post-fire) than observed populations. Stochastic simulations with higher levels of variation in model parameters were most successful in producing typical fluctuations. We conclude that the biennial cycle in W. carteri is likely caused by the delay in seed germination, which creates two overlapping cohorts of plants, much like a strict biennial. Fire initiates the cycle by killing aboveground individuals and promoting germination of seedlings in the first post-fire year. Regular cycles in other species, including annuals that have overlapping cohorts, could also be caused by demographic delays. Our use of matrix models to explore hypotheses for observed phenomena could be expanded to many ecological questions.