Подход на уровне отдельной особи в экологии

УДК 574.3

Я. Ухманский

Центр экологических исследований Польскай Академии Наук, Ломианки, Польша
E-mail: januch@cbe-pan.pl

Ключевые слова: теоретическая экология, индивидуальные модели


J. Uchmañski

Centre for EcologicalResearchPolishAcademy of Sciences, £omianki, Poland,
E-mail: januch@cbe-pan.pl

Key words: theoretical ecology, individual-based models

The classical theoretical ecology applies state variable models. This approach assumes that the dynamics of ecological systems can adequately be described by developing appropriate differential or difference equations. In this case, state variable is represented by densities of the component populations of a system, and the rate of change in the state variable is a function of the state variable itself. Due to this approach, theoretical ecology could use the most recent achievements of the mathematical theory of dynamic systems, including the theory of deterministic chaos, but this did not lead to an essential turning-point in understanding of the dynamics of ecological systems. We would even say that it caused some crisis in ecological theory. This is reflected in the fact that classical ecological theory cannot explain well documented facts such as population cycles, yielded contradicting hypotheses in community ecology, and finally caused that ecology, as compared with other fields of biology, became little attractive to mathematicians. I believe that individual-based approach may be a remedy for this crisis of theoretical ecology.

Individual-based approach in ecology represents the way of thinking about ecological processes that primarily considers the fates of individuals in ecological systems. Traditional ecology is centered upon the dynamics of ecological systems. It can be described by different variables. The most natural variable is the number of individuals in populations forming an ecological system. Individual-based approach applied to the dynamics of an ecological system analyses the properties of individuals and interactions among individuals, and then uses them as a basis for explanation of changes in sizes of populations in ecological systems.

Individual-based approach as a young discipline and also of a great potential to the future development of theoretical ecology, requires many discussions. For example, various authors define it in different ways. Some consider that each model with a little more information about individuals than in classical models is individual-based model, whereas for others, individual-based models must conform to very restrictive assumptions. As a result of publications and discussions at conferences, a set of problems important to individual-based approach in ecology emerged over the recent ten or so years. In addition to the general question why to apply individual-based approach when describing the dynamics of ecological systems, the basic problems involve growth of individuals, competition and resource partitioning among competing individuals, individual variability, weight distribution in even-aged populations, population dynamics generated by individual-based models. Moreover, the usefulness of the individual-based approach for addressing applied issues has become an important question.

The use of individual-based models, which are more complicated and more difficult to develop and analyse than classical models, can be reasonable only when these two approaches yield differential results for the same ecological system. If this is the case in general is not yet clear. The opinions are divided. Some argue that individual-based approach generate results that differ from those of the classical mathematical ecology. Others are of an opposite opinion. They suggest that such views are premature, or that there is a continuous transition between these two types of modelling, that they are complementary to one another, as each of them offers an adequate description at a different level of the ecological system considered. Closely related to these general problems is the question whether it is possible to construct a classical model corresponding to a given individual-based model.

Description of the growth of individuals is an important component of the majority of individual-based models. Typically, the so-called growth equations are used. The most general form of such an equation is a balance equation which assumes that the growth rate of an individual until maturity can be considered as a difference between the rates of assimilation and respiration. However, individual growth is something more than an increase in body weight and immediate transformation of the assimilated food. Organisms accumulate the assimilated energy, and transform it with some delay. Growth also involves the development of structure. For plants and some animals, this aspect of growth is well described by so called fractal models of growth. This type of modelling is based on the description of growth as a process of the summation of similar structures.

Growth equations do not solve all the problems involved in the description of individuals living together. It is easy to notice that they differ in size, even if they are of the same age. Most often these differences are due to competition among individuals. Competition means partitioning, typically unequal, of resources. There are quite good ways of describing competition in plants. They use the so called zones of influences or Thiesen polygons. The only problem is that the shape of weight distribution in even-aged plant populations (also in sessile animals) depends not only on population density, intensity of competition and the degree of its asymmetry but also on the distribution of individuals in space, which may obliterate the effects of the other factors.

Population dynamics is the oldest field of the application of individual-based approach in ecology. However, the application of individual-based models is most chaotic in this field. Most often a very detailed question is asked. To answer it, very complex models are used, developed just to answer this one specific question, and most often these are models with a mixed structure, a large part of them conforming to the rules used in classical ecology. It is difficult then to evaluate the output of the model and to compare it with the outputs of other models. In spite of a seeming animation in this field of ecological applications of individual-based approach, we still cannot answer many basic questions referring, for example, to the ways of regulation in populations made up of individuals that differ from one another.

For a long time, the individual-based approach was traditionally used to describe forest dynamics. Another kind of the application of the individual-based approach was shown by Baveco in 1998. He used this approach to solve the problems concerned with protection of tree frogs and root voles in heterogeneous agricultural landscape of the Netherlands. The model answers the question concerning factors promoting populations persistence of these species, as well as makes predictions about their future survival in face of different scenarios of habitat transformation.

One of the greatest programs for restoration ecology concerns the Everglades region of South Florida, USA. This programme uses a mathematical model simulating the fates of animal species most important to Florida ecosystems at different hydrological regimes. The model, which is called ATLSS (Across Trophic Level System Simulation), is a complex simulation model set up of many submodels describing biotic and abiotic components of the environment.

The model ATLSS gave rise to discussion about fundamental problems concerning individual-based approach in ecology. The authors of the ATLSS have emphasised that one of the most important arguments for applying individual-based models is the fact that individuals making up a population do not live in a uniform habitat. If so, we cannot use classical models that assume identical environmental conditions for all individuals of a local population. The audience, in turn, asked questions about the possibility of verification of such complex models. This is a very important question, not answered so far. On the one side, attempts are made to construct a unified and relatively easily available program. On the other side, the authors of individual-based models prefer to construct models on their own from the beginning, and to verify them by using their own experience and knowledge of the object of the model.

Intense application of computer simulations and visualization of their outputs creates a danger that individual-based models will turn ecology into «virtual ecology». Instead of continuing traditional methods used in natural sciences, which are based on developing and testing hypotheses, we may construct a computer model of each, even very complex, ecological system.

Zoocenosis — 2005
 Біорізноманіття та роль зооценозу в природних і антропогенних екосистемах: Матеріали ІІІ Міжнародної наукової конференції. – Д.: Вид-во ДНУ, 2005. – С. 162-164.