Hidden parameters of time series of the forest insects’ population dynamics and patterns of formation of insect complexes

The paper considers approaches to the use of some additional (hidden) parameters to analyze population dynamics of forest insects. The study presents the analysis of data on the population dynamics of phyllophagous insects of Scots pine obtained during a long-term continuous monitoring (1979–2016) of five phyllophagous species on the territory of the Krasnoturansk pine forest (south of Krasnoyarsk Territory), data on abundance dynamics of insects in forest stands in Switzerland (Oberengadin valley), and data on abundance dynamics of the Siberian silkworm Dendrolimus sibsiricus Tschetv. in the taiga forests of Siberia. To analyze the features of the population dynamics we used the rank distribution of the long-term density of species in a particular habitat, the characteristics of the distribution of individuals on trees, considered from the point of view of the model of second order phase transitions, as well as the parameters of autoregressive equations for the dynamics of the population, with the account of the order of autoregression, the sign of the model coefficients, and the stability margin. It is shown that the indicators of competition between species in a community are weakly related to the changes in population density in the community, and the competition coefficient b can be considered as an independent indicator of the state of the community. The use of the hidden parameter b makes it possible to estimate the competition between species in the insect complex in the Krasnoturansk pine forest and between species in the complex of the species of insects in the larch forests of the Alps. Using a phase transition model of the second kind, it is shown that the dispersal of the species on the accounting units (trees) on the trial plot is of a group nature and, therefore, the pest has an increased effect on some trees. The possibility of using autoregressive equations to describe the dynamics of the populations of certain species is considered. It is shown, that AR-models describe well enough the dynamics of the population size in various natural boundaries. Coefficients of AR-equations and the values of the stability margin of these equations can be considered hidden parameters of dynamics. The «hidden» patterns of the population dynamics characterize the long-term dynamics of the number of forest insect communities. The long-term properties of insect populations are considered with the help of these “hidden” parameters (not directly measured). These parameters must be taken into account when assessing the type of species dynamics. With the help of “hidden” indicators, it is possible to obtain additional information about the properties and dynamics of the studied populations. 

1. Baltensweiler W. Zeiraphera griceana Hubner (Lepidoptera, Tortricedae) in the European Alps. A contribution to the problem of cycles. Can. Entomol, 1964, vol. 96, nо. 5, рр. 792–800.

2. Baltensweiler W. The folivore guild on larch (Larix decidua) in the Аlps. Y. Baranchikov, W. Mattson, F. Hain, T. Payne (eds.). Forest insect guilds: patterns of interaction with host trees. USDA Forest Service. General Technical Report NE-153, 1991, рр. 145–164. (In Russ.)

3. Bazykin A.D. Nonlinear dynamics of interacting populations. Moscow; Izhevsk: Institute of Computer Studies, 2003. 368 p. (In Russ.)

4. Boldaruev V.O. Population dynamics of the Siberian silkmoth and its parasites. Ulan-Ude: Buryat. Books, 1969. 162 p. (In Russ.)

5. Box G.E.P., Jenkins G.M. Time series analysis: forecasting and control. San Francisco: Holden-Day, 1970. 784 p. (In Russ.)

6. Bratus A.S., Novozhilov A.S., Platonov A.P. Dynamical systems and models in biology. M.: Fizmatlit, 2010. 400 p. (In Russ.)

7. Gaiduk A.R., Belyaev V.E., Pyavchenko T.A. Automatic control theory: examples and problems. St. Petersburg: Lan, 2001. 464 p. (In Russ.)

8. Hayashi F. Econometrics. M: Business, 2017. 728 p. (In Russ.)

9. Hemming R.W. Digital filters. M.: Nedra, 1987. 221 p. (In Russ.)

10. Isaev A.S., Khlebopros R.G., Kondakov Yu.P., Nedorezov L.V., Kiselev V.V. Soukhovolsky V.G. Population dynamics of forest insects. Moscow: Nauka, 2001. 374 p. (In Russ.)

11. Isaev A.S., Palnikova E.N., Soukhovolsky V.G., Tarasova O.V. Population dynamics of phyllophagous forest insects: models and forecasts. Moscow: KMK Publishing House, 2015. 262 p. (In Russ.)

12. Isaev A.S., Soukhovolsky V.G., Tarasova O.V., Palnikova E.N., Kovalev A.V. Forest insect population dynamics, outbreaks and global warming effects. N.Y.: Wiley and Sons, 2017. 286 p.

13. Kim D.P. Theory of automatic control. Moscow: Fizmatlit, 2007, vol. 1. 312 p. (In Russ.)

14. Landau L.D. On the theory of phase transitions. JETP, 1937, vol. 7, pp. 19–32. (In Russ.)

15. Magarran E. Ecological diversity and its measurement. M.: Mir, 1992. 184 p. (In Russ.)

16. Palnikova E.N., Sviderskaya I.V., Soukhovolsky V.G. Pine looper in Siberian forests. Novosibirsk: Nauka, 2002. 252 p. (In Russ.)

17. Pareto V. Cours d'Économie Politique. Lausanne: F. Rouge, 1896, vol. I. 430 p.; 1897, vol. II. 426 p. (In Russ.)

18. Pareto V. Compendium of General Sociology. Moscow: Ed. House of the Higher School of Economics, 2008. 511 p.

19. Podkorytova O.A., Sokolov M.V. Time series analysis. M.: Yurayt, 2016. 266 p. (In Russ.)

20. Royama T. Analytical population dynamics. L.: Chapman and Hall, 1992. 371 p.

21. Soukhovolsky V.G., Baranchikov Yu.N. Methods for the quantitative assessment of the species diversity of communities. Entomological research in Siberia, 1998, iss. 1, рр. 44–54. (In Russ.)

22. Volterra V. Mathematical theory of the struggle for existence. M.; Izhevsk: Institute for Computer Research, 2004. 288 p. (In Russ.)

23. Zipf G.K. Human behavior and the principle of least effort. Cambridge, MA: Addison-Wesley, 1949. 573 p.