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Siberian Journal of Forest Science

2015 year, number 3

Modeling of Forest Dynamics

F. S. Berezovskaya1, G. P. Karev2
1Howard University, 2400 Sixth Street, NW, Washington, D.C., 20059 US
2National Center for Biotechnology Information U.S. National Institute of Health, Building 38 A, Bethesda, MD, 20894 USA
Keywords: самоизреживание, неоднородная популяция, мальтузианская модель гибели, эргодичность, self-thinning, heterogeneous population, Malthusian model of death, ergodicity

Abstract >>
The concept of describing the process of self-thinning stands is considered from the standpoint of the general theory and methods of modeling the dynamics of biological populations and communities. Heterogeneity is one of the fundamental factors that determine the population dynamics of both the evolutionary time, and at the level of the lifetime of one generation. The study of various well-known formulas of one-species stands self-thinning in the frameworks of theory of non-homogeneous population models showed that these formulas are the solutions of the simplest Malthusian model of heterogeneous population death with different initial distributions of Malthusian parameter (intensity of death). It is shown that all the above formulas describe the self-thinning of stands as essentially the same Malthusian process of death, but under different conditions, which in summary form are taken into account in the initial distribution. Applied research methods of Malthusian dynamics of inhomogeneous models study allow us to refine the known formulas of self-thinning and build a number of new, choosing a suitable initial intensity distribution death. The proposed methods allow testing of various hypotheses on the initial distribution of the amount of tree loss for various stands. It is shown that an alternative approach to addressing the diversity of crops may be based on a multi-stage model of Leslie and use to simulate a modified version of the Poletaev’ model. A simple model constructed that operates with only three stages of stand development, but it is sufficient for reliable real and calculated data. We found that the inclusion of stand’s heterogeneity even in a very simplified form is not only necessary, but also to a certain extent is sufficient for constructing adequate models of self-thinning stands.

Growth of Forest Stands as Analogue of Production Process in Economic Systems: E2E-Model

V. G. Soukhovolsky1, Yu. D. Ivanova2
1V. N. Sukachev Institute of Forest, Russian Academy of Sciences, Siberian Branch, Akademgorodok, 50/28, Krasnoyarsk, 660036 Russian Federation
2Institute of Biophysics, Russian Academy of Sciences, Siberian Branch, Akademgorodok, 50/50, Krasnoyarsk, 660036 Russian Federation
Keywords: лесные насаждения, рост, чистая первичная продукция, динамика, моделирование, forest stands, growth, NPP, dynamics, modeling

Abstract >>
An economic-ecological model (E2E-model) is proposed to describe the growth of plants. The process of growth of forest stand phytomass is considered within the E2E model as an analogue of the production process in economics. As a capital K in E2E models are considered non-photosynthetic phytomass components - stem, roots and branches. The role of labor L satisfies leaves (or needles), in which the process of photosynthesis occurs. Produced by the process of photosynthesis, energy is partially consumed for the current «consumption» of plants and partly «invested» and is transformed into a new phytomass, which is distributed between non-photosynthetic components of trees and their photosynthetic apparatus. The death of the trees in the stand during growth in the E2E model is considered as an analogue of capital depreciation (aging equipment, etc.) in the production process. For a complete description of the process of energy production and phytomass during photosynthesis entered the equation describing the synthesis of phytomass, describes the principles of distribution obtaining resources to meet the current energy needs of plants and for investments in new phytomass, the principles of investment allocation to reproduction «capital» - phytomass trunks roots and branches, and reproduction of «labor» - leaves or needles of trees. The proposed approach to the description of the growth in forest stand as an analogue of production may be regarded as competitive in relation to the autocatalytic growth models - different clones of Verhulst equation. In comparison with the autocatalytic growth models, E2E-growth models allow description of a number of phenomena observed in the forest (such as the death of trees) and not be explained in terms of autocatalytic models. Calculation of biomass of dead wood in the plantation opens the possibility of using the E2E model to describe the process of transformation of dead wood decomposers (fungi, bacteria, insects), as well as to determine the amount of forest fuel and the risk of forest fires.

Analysis of Tree Stand Horizontal Structure Using Random Point Field Methods

O. P. Sekretenko1, P. Y. Grabarnik2
1V. N. Sukachev Institute of Forest, Russian Academy of Sciences, Siberian Branch, Akademgorodok, 50/28, Krasnoyarsk, 660036 Russian Federation
2Institute of Physicochemical and Biological Problems in Soil Science, Russian Academy of Sciences, Institutskaya str., 2, Pushchino, Moscow Oblast, 142290 Russian Federation
Keywords: горизонтальная структура древостоя, случайные точечные поля, пространственная статистика, экологическое моделирование, естественное изреживание насаждения, tree stand horizontal structure, random point fields, spatial statistics, ecological modeling, natural forest thinning

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This paper uses the model approach to analyze the horizontal structure of forest stands. The main types of models of random point fields and statistical procedures that can be used to analyze spatial patterns of trees of uneven and even-aged stands are described. We show how modern methods of spatial statistics can be used to address one of the objectives of forestry - to clarify the laws of natural thinning of forest stand and the corresponding changes in its spatial structure over time. Studying natural forest thinning, we describe the consecutive stages of modeling: selection of the appropriate parametric model, parameter estimation and generation of point patterns in accordance with the selected model, the selection of statistical functions to describe the horizontal structure of forest stands and testing of statistical hypotheses. We show the possibilities of a specialized software package, spatstat, which is designed to meet the challenges of spatial statistics and provides software support for modern methods of analysis of spatial data. We show that a model of stand thinning that does not consider inter-tree interaction can project the size distribution of the trees properly, but the spatial pattern of the modeled stand is not quite consistent with observed data. Using data of three even-aged pine forest stands of 25, 55, and 90-years old, we demonstrate that the spatial point process models are useful for combining measurements in the forest stands of different ages to study the forest stand natural thinning.

Modeling and Analysis of Horizontal Structure of a Mixed Tree Stands (On Example of Sample Plots in the «Bastak» Nature Reserve in the Middle Amur River Area)

A. N. Kolobov1, E. S. Lonkina2, E. Ya. Frisman1
1Institute for Complex Analysis of Regional Problems, Russian Academy of Sciences, Far Eastern Branch, Sholom-Aleykhem str., 4, Birobidzhan, 679016 Russian Federation
2State Nature Reserve «Bastak», Sholom-Aleykhem str., 69a, Birobidzhan, 679016 Russian Federation
Keywords: древостой, горизонтальная структура, пространственные данные, индивидуально-ориентированная модель, конкуренция, tree stand, horizontal structure, spatial data, individual-based model, competition

Abstract >>
The results of the research model and real data spatial distribution of trees in single-species, ages and mixed stands are studied. Modeling of the horizontal structure of the stand was based on a computer simulation model. Investigation of the horizontal structure of the stand allows drawing of conclusions about the processes of intraspecific and interspecific competition. It is shown that the model used to generate spatial data model reflects the basic mechanisms of stacked-mosaic structure of the stand, which is observed in natural communities. It allows future use of this model to study the characteristics of the formation of the spatial structure of mixed forest communities, developing under the influence of internal (competition) and external (logging, windfalls, herbivores, etc.) factors. Statistical analysis of the tree spatial distribution for shade-tolerant and light-loving species relative to each other showed that, on average, around an arbitrarily chosen shade-tolerant tree species, there is an area within which the opportunity to meet the tree light-loving species is less than it would be under their random placement. Around an arbitrarily chosen «large» tree of shade-tolerant species there is an area within which the opportunity to meet the «small» or «medium» light-loving tree species is less than would have been at their random placement. It is shown that the mutual arrangement of «large» light-loving trees and «small», «medium» shade-tolerant trees is no different from a random allocation. As a result of competitive processes of spatial arrangement for light-loving tree species is determined by the placement of shade-tolerant trees. Location of light-loving trees does not affect the location of shade-tolerant trees. The relative placement of different types of shade-tolerant trees, especially spruce, fir and pine, are independent of each other.

Cellular-Automata Model of the Dwarf Shrubs Populations and Communities Dynamics

A. S. Komarov, E. V. Zubkova, P. V. Frolov
Institute of Physicochemical and Biological Problems in Soil Science, Russian Academy of Sciences, Institutskaya str., 2, Pushchino, Moscow Oblast, 142290 Russian Federation
Keywords: имитационная модель, популяции растений, клеточные автоматы, L-системы, динамика биосистем, кустарнички, simulation model, plant populations, cellular automatons, L-systems, biosystem dynamics, dwarf shrubs

Abstract >>
The probabilistic cellular-automata model of development and long-time dynamics of dwarf shrub populations and communities is developed. It is based on the concept of discrete description of the plant ontogenesis and joint model approaches in terms of probabilistic cellular automata and L-systems by Lindenmayer. Short representation of the basic model allows evaluation of the approach and software implementation. The main variables of the model are a number of partial bushes in clones or area projective cover. The model allows us to investigate the conditions of self-maintenance and sustainability population under different environmental conditions (inaccessibility of the territory for settlement, mosaic moisture conditions of soil and wealth). The model provides a forecast of the total biomass dynamics shrubs and their fractions (stems, leaves, roots, fine roots, fruits) on the basis of the data obtained in the discrete description of ontogenesis and further information on the productivity of the plant fractions. The inclusion of the joint dynamics of biomass of shrubs and soil in EFIMOD models cycle of carbon and nitrogen to evaluate the role of shrubs in these circulations, especially at high impact, such as forest fires and clear cutting, allow forecasting of the dynamics of populations and ecosystem functions of shrubs (regulation of biogeochemical cycles maintaining biodiversity, participation in the creation of non-wood products) with changing climatic conditions and strong damaging effects (logging, fires); and application of the models developed to investigate the stability and productivity of shrubs and their participation in the cycle of carbon and nitrogen in different climatic and edaphic conditions.

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.

Energy Balance of Forage Consumption by Phyllophagous Insects: Optimization Model

O. V. Tarasova, I. I. Kalashnikova, V. V. Kuznecsova
Siberian Federal University, Prospekt Svobodny, 79, Krasnoyarsk, 660041 Russian Federation
Keywords: насекомые-филлофаги, корм, потребление, модели, эффективность, цены потребления, phyllophagous insects, forage, consumption, models, efficiency, consumption costs

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The model of optimal food consumption by phytophagous insects proposed, in which the metabolic costs are presented in the form of two components - the cost of food utilization and costs for proper metabolism of the individuals. Two measures were introduced - the «price» of food conversion and the «price» of biomass synthesis of individuals to assess the effectiveness of food consumption by caterpillars. The proposed approach to the description of food consumption by insects provides the exact solutions of the equation of energy balance of food consumption and determining the effectiveness of consumption and the risk of death of the individual. Experiments on larvae’s feeding in laboratory conditions were carried out to verify the model. Caterpillars of Aporia crataegi L. (Lepidoptera, Pieridae) were the research subjects. Supply-demand balance, calculated value of the environmental price of consumption and efficiency of food consumption for each individual were determined from experimental data. It was found that the fertility of the female does not depend on the weight of food consumed by it, but is linearly dependent on the food consumption efficiency index. The greater the efficiency of food consumption by an individual, the higher its fertility. The data obtained in the course of experiments on the feeding caterpillars Aporia crataegi were compared with the data presented in the works of other authors and counted in the proposed model of consumption. Calculations allowed estimation of the critical value of food conversion price below which the energy balance is negative and the existence of an individual is not possible.

Modeling of Pheromone Communication System of Forest Lepidopterous Insects. II. Model of Female Searching by Male

A. V. Kovalev, P. E. Volkova
International Scientific Center for Study of Extreme Men States Krasnoyarsk Scientific Center, Russian Academy of Sciences, Siberian Branch, Akademgorodok, 50, Krasnoyarsk, 660036 Russian Federation
Keywords: лесные чешуекрылые насекомые, поиск самки самцом, феромоны, система коммуникации, управление, forest lepidopterous insects, female searching by mail, pheromones, communication system, management

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We propose an agent-based simulation model search. This model allows us to evaluate the effectiveness of different males-females pheromone search strategies for Lepidoptera. In the model, we consider the simplest case of the search, when the pheromone has only one chemical component. It is assumed that the insects are able to detect the pheromone molecules and the sensory cells generate action potentials in contact with the pheromone for some time. Thereafter pheromone molecule is inactivated. This behavior can be regarded as a memory of individual. Proportion of individuals who have reached the source is selected as an integral indicator of the search efficiency. To evaluate the effectiveness, numeric experiments were performed in different conditions: random walk, search algorithm without memory, and algorithm with memory and return mechanism. The resulting effectiveness of source localization by insects for flight in turbulent flows is ~ 70 %, which corresponds to experiments with live specimens in literature. In this case, proposed pheromone search algorithm is quite simple, which makes it biologically correct. Conducted modeling calculations can be the starting point for planning of field observations and pest monitoring systems using pheromone traps.

Basic Trends of Game Mammal Population Dynamics in the Russian Middle Amur River Area: The Observation and Simulation Results

E. Ya. Frisman, O. L. Revutskaya, G. P. Neverova
Institute for Complex Analysis of Regional Problems Russian Academy of Sciences, Far Eastern Branch, Sholom-Aleykhem str., 4, Birobidzhan, 679016 Russian Federation
Keywords: промысловые млекопитающие, Среднее Приамурье России, тенденции динамики численности популяции, экологическая емкость, математическое моделирование, game mammals, Middle Amur river area of Russia, trends of population dynamics, ecological capacity, mathematical modeling

Abstract >>
The detailed analysis was completed on long-term population dynamics data of different game mammals conducted in the region of the Middle Amur. The study showed that when a certain stability of the majority of the total number of game animals throughout the Jewish Autonomous Region (the coefficient of Malthus model for the entire period of observation a little more than 1, except for the lynx, kolinsky and squirrel) from the mid 90s of the last century indicates a steady downward trend in population numbers, especially in areas where hunting occurs (Malthus model coefficients less than 1). Perhaps the reason for the decline was the increase in the amount of poaching in the 90s due to the deteriorating socio-economic situation in the country. Impression of a certain stability in the JAR as a whole due to the position of animals in protected areas. For all considered commercial species in the reserve there is a clear tendency for the number. For such species as the kolinsky, squirrel and bears, the maximum possible model number lower than the maximum number of accounting was observed during the study period. For populations of other game animals it can be assumed that the status of their ecological niches, i.e. habitat resources (supply of food, the size of the range, availability and propagation of the growth of the offspring, etc.) are relatively stable. The relation between the amount of natural reproduction of «local» populations and their replenishment quantities due to external migration was studied in detail. Maintaining the number of target species is determined by migratory activity. The presence of protected areas helps to maintain and even some increase the population numbers, but it is clearly insufficient. It’s necessary to expand the territories free from the hunt and the transition to the strategies of hard periodic limitations of hunting populations experiencing depressive mode of population dynamics.

The Method for Determination of Parameters of the Phenomenological Continual Model of Soil Organic Matter Transformation

S. I. Bartsev, A. A. Pochekutov
Institute of Biophysics, Russian Academy of Sciences, Siberian Branch, Akademgorodok, 50/50, Krasnoyarsk, 660036 Russian Federation
Keywords: органическое вещество почвы, континуальная модель трансформации органического вещества почвы, почвенное дыхание, гумификация, минерализация, soil organic matter, continual model of soil organic matter transformation, soil respiration, humification, mineralization

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A possible method for experimental determination of parameters of the previously proposed continual mathematical model of soil organic matter transformation is theoretically considered in this paper. The previously proposed by the authors continual model of soil organic matter transformation, based on using the rate of matter transformation as a continual scale of its recalcitrance, describes the transformation process phenomenologically without going into detail of microbiological mechanisms of transformation. Thereby simplicity of the model is achieved. The model is represented in form of one differential equation in first-order partial derivatives, which has an analytical solution in elementary functions. The model equation contains a small number of empirical parameters which generally characterize environmental conditions where the matter transformation process occurs and initial properties of the plant litter. Given the values of these parameters, it is possible to calculate dynamics of soil organic matter stocks and its distribution over transformation rate. In the present study, possible approaches for determination of the model parameters are considered and a simple method of their experimental measurement is proposed. An experiment of an incubation of chemically homogeneous samples in soil and multiple sequential measurement of the sample mass loss with time is proposed. An equation of time dynamics of mass loss of incubated homogeneous sample is derived from the basic assumption of the presented soil organic matter transformation model. Thus, fitting by the least squares method the parameters of sample mass loss curve calculated according the proposed mass loss dynamics equation allows to determine the parameters of the general equation of soil organic transformation model.