Total Analysis of Population Time Series: Estimation of Model Parameters and Identification of Population Dynamics Types

  • Lev V. Nedorezov
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


Current publication is devoted to the problem in identifying the type of population dynamics (on an example of green oak tortrix (Tortrix viridana L.)). For fitting of time series of tortrix fluctuations (Korzukhin and Semevsky, Sin-ecology of forest. Gidrometeoizdat, Saint-Petersburg, 1992), generalized discrete logistic model was used. Results of model parameter estimations obtained with ordinary least squares (OLS) and method of extreme points (MEP) (Nedorezov. Chaos and Order in Population Dynamics: Modeling, Analysis, Forecast. LAP Lambert Academic Publishing, Saarbrucken. 2012. p. 352; Nedorezov. J. Gen. Biol. 73(2), 114–123, 2012; Nedorezov. Biophysics 61(1), 149–154, 2016) were compared. It was assumed that the model demonstrates good correspondence to time series if and only if deviations between time series and model trajectory satisfy with several statistical tests. It was shown that model with OLS estimations of parameters cannot be used for fitting of time series. Analyses of four various variants of MEP estimations were provided, and it was obtained that observed dynamic regime of population dynamics isn’t cyclic (if length of cycle is less than 1500 years). For the selected dynamic regimes, a rapid decrease in values of auto-correlation functions with further small fluctuations near zero level was observed. It means that forecasting the change in population size for short or long time periods is practically impossible.


Population dynamics Generalized discrete logistic model Green oak tortrix fluctuations 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lev V. Nedorezov
    • 1
  1. 1.Research Center for Interdisciplinary Environmental Cooperation RASSaint-PetersburgRussia

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