Abstracts

Evolution of Species and Ecosystems: Theoretical Analysis and Computer-Assisted Modeling

There were applied methods of stationary stochastic process for the analysis of bird number time series.

Number (density) of birds was counted on the integrated area of forests and on the integrated area of all researched places.

The autocorrelation plot for the change of bird number during the 12 - year’s period was obtained. Autocorrelation and partial autocorrelation coefficients were counted (greatest autocorrelation coefficient R=0,63; greatest partial autocorrelation coefficient R=0,63).

It was not found characteristics of Auto Regressive and Moving-Average models, e.g. limited length of autocorrelation and partial autocorrelation functions. So we have chosen the Auto Regressive Integrated Moving-Average model, (ARIMA).

The ecological sense of parameters consists of reflection of periodicity of change of bird number during annual and long-term period. Moving average can be used, so it is known that smoothing help to reduce fluctuations of an empirical regression line, (Bioindication: theory, methods, applications, 1994).

The model is:
xt = xt-1+at - Θ at-1, where x - prognosticating variable of an autoregression, a - moving average, and Θ - parameters of integrated model.

Validity of the model has been tested on truncated sequences of data (10-year's). The forecast was calculated forward for two years and was compared with empirical data. There was obtained correlation between the empirical data and forecast for forests (Spearman’s rank correlation coefficient R=0,81) and smaller relationships for the integrated areas (R=0,53). The plot shows insignificant autocorrelations of the residuals. It was obtained likeness of the forecast and the trend, obtained by us earlier, of small decreasing number of birds.

The ARIMA model can be useful for the analysis and forecasting number of birds. We thank V.G. Ivliev for number of bird fond data.

Note. Abstracts are published in author's edition

|Home Page| |English Part|

Go to Home