State-space models for stochastic and seasonal fluctuations of vole and shrew populations in east-central Illinois

Small mammal populations fluctuate erratically and exhibit seasonal and multi-annual variations in abundance. The decomposition of population dynamics into seasonal fluctuations, stochastic trends, and residuals helps to quantify environmental stochasticity of population dynamics. We used basic structural model (BSM), a state-space time series model, to decompose and de-trend 25 years of monthly live-trapping data for Microtus ochrogaster, M. pennsylvanicus, and Blarina brevicauda in east-central Illinois, USA. We further used Bayesian state-space models (BSSM) to determine the structure of within-year and between-year density dependent feedbacks in the stationarized residuals from the BSM for the three species. The BSM and spectral analysis identified significant seasonal fluctuations for the B. brevicauda populations. All populations of the three species exhibited strong stochastic fluctuations, but those of M. ochrogaster and B. brevicauda displayed greater environmental stochasticity than that of M. pennsylvanicus. The BSSM analysis indicates that M. pennsylvanicus was subject to density-dependence with a 4-month time lag, whereas the M. ochrogaster and B. brevicauda populations displayed 18- and 10-month delayed density-dependence, respectively. Moreover, spectral analysis suggests that none of the species exhibited multi-annual cyclic population fluctuations. Thus, both environmental stochasticity and density-dependence appeared to play significant roles in the population dynamics. State-space models are a promising tool for analyzing long-term monthly population time series.