Green oak leaf roller moth dynamics: An application of discrete time mathematical models

Discrete mathematical model is selected for description of green oak leaf roller (Tortrix viridana L.) population dynamics. Experimental data set from Rubtsov [Rubtsov, V.V., 1992. Models of Oscillation Processes in Forest Ecosystems, Forest Institute, Moscow, Russian Federation, p. 39 (in Russian)] is analyzed from the standpoint of phenomenological theory of forest insect population dynamics [Isaev, A.S., Khlebopros, R.G., Nedorezov, L.V., Kiselev, V.V., Kondakov, Yu. P., 1984. Dynamics of Forest Insects Populations, USSR, Nauka, Novosibirsk, p. 224 (in Russian); Isaev, A.S., Khlebopros, R.G., Nedorezov, L.V., Kiselev, V.V., Kondakov, Yu.P., Soukhovol'sky, V.G., 2001. Population Dynamics of Forest Insects, Russian Federation, Nauka, Moscow, p. 347 (in Russian)]. For checking hypotheses confidence for fitting of experimental time series, Moran-Ricker model, Maynard Smith-Slatkin model, and some others are used. Selection of statistical criteria for estimating parameter's values is discussed. In addition, probabilities of realizations of several dynamical regimes are estimated.