Density-dependent population regulation detected in short time series of saproxylic beetles
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Understanding the regulation of natural populations has been a long-standing problem in ecology. Here we analyze the population dynamics of 17 species of saproxylic beetles in Shizuoka Prefecture, Japan collected over 11–12 years using autoregressive integrated moving average (ARIMA) models. We first examined the dynamics for indications of the order of the ARIMA models and evaluated the time series to determine that it was not simply a random, white noise sequence. All species dynamics were not mere random noise, and ARIMA models up to lag 3 were considered. The best model was selected from the possible ones using several criteria: model convergence, weak residual autocorrelation, the small sample AIC must be among the smallest that were not significantly different, and the lag indicated by the cutoff values in the detrended partial autocorrelation function. We found significant and nearly significant direct density-dependence for 14 of the 17 species, varying from −0.709 and stronger. The characteristic return rates were strong and only one species had a weak return rate (>0.9), implying that these species were strongly regulated by density-dependent factors. We found that populations with higher order ARIMA models (lag 2 and 3) had weaker return rates than populations with ARIMA models with only one lag, suggesting that species with more complex dynamics were more weakly regulated. These results contrast with previous suggestions that 20+ years are needed to detect density dependence from population time series and that most populations are weakly regulated.
KeywordsARIMA model Autoregressive model Equilibrium density Moving average model Stability Time lag
We acknowledge the assistance of Mrs. N. Kiritani for collecting beetles every early morning during the study. Appreciation also goes to Drs. H. Amano, K. Fujii, Y. Higashiura, O. Imura, S. Masaki, T. Namba, M. Takada, S. Tanaka, K. Togashi, T. Royama, K. Yamamura and J. Yukawa for helpful comments made on an earlier draft of the manuscript. We also appreciate Dr. H. Makihara for identification of longicorn species and useful comments on biology.
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