Non-Traditional Approach to Estimation of Ecological Models Parameters (On Examples of Larch Bud Moth and Pine Looper Moth Population Dynamics)
L. V. Nedorezov
Center for Interdisciplinary Studies of Environmental Problems, Russian Academy of Sciences, Nabereznaya Kutuzova, 14, Saint-Petersburg, 191187 Russian Federation
Keywords: динамика численности популяций, временные ряды, математическая модель, оценка параметров, серая лиственничная листовертка, сосновая пяденица, population dynamics, time series, mathematical model, parameter estimation, larch bud moth, pine looper moth
Abstract
In current publication, a non-traditional approach to estimation of parameters of ecological models is considered. Within the framework of this approach it is not necessary to construct loss-function or likelihood function. The basic idea of method is as follows: first of all, basic requirements to model and to deviate between theoretical (model) and empirical datasets must be formulated. After that, respective statistical criteria must be selected, and with the help of these statistical criteria, a feasible set in space of model parameters must be determined (where all statistical criterions demonstrate required results). Within the limits of this feasible set must be found elements with strongest properties. These elements can be used as estimations of model parameters. Constructions of feasible sets for Moran - Ricker model with and without time lag and ELP-model were demonstrated on examples of larch bud moth (Zeiraphera diniana Gn.) and pine looper moth (Bupalus piniarius L.) time series. Results of approximation are discussed. For a time series of population dynamics of larch budworm it was found that feasible sets are not empty for the model Moran - Ricker without delay and with delay of one year. At the same time, the analysis of properties of elements of admissible sets showed that among them there are no properties that match the prevailing biological understanding of the dynamics of the Zeiraphera diniana Gn. The resulting estimation allowed taking into account the delay of one year to receive treatment with a cycle length of 18 with two maxima. However, almost all statistical tests gave negative results. These results indicate that the delay in the self-regulation mechanisms of action of more than one year. Given way to simultaneously estimate the parameters of the population dynamics model of pine looper for related time series. The analysis shows that there is every reason for the claim that the observed mode - cyclic short cycle length of two years.
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