STABILITY OF TERRESTRIAL ECOSYSTEMS TO PLANT PESTS: AN AXIOMATIC APPROACH
Gleb Vasechko

Introduction

This report has been inspired by the book of M.Bunge (1973) who strenuously agitates for the usage of the axiomatic approach in every branch of science (province). This author supposes that the usage of the approach is an evidence of maturity of a province; it is a means that imparts a province with lucidity and excludes contradictions from it. In fact, every scientists in his thinking uses some general ideas, but they often are not realized clearly being as though in the subconscious mind. They are divers even in peoples working with the same problems that results in misunderstanding in the scientific media. On the other hand, when axiomatic systems are used in a province, a scientist is able to choose one, which likes him, or to invent own one. If scientists would not hide their disposition to the used by them system, the level of misunderstanding in their media would be definitely less. By such means, in thinking of a person and in collective thinking, the lucidity would be achieved, whereas contradictions would be excluded.

M.Goldstein and J.Goldstein (1978) put a question why disputes among scientists of diverse schools within the same province are often futile. Such a misunderstanding is thought to be a consequence of vague ideas as to foundations of scientific thinking. Just an axiomatic approach allows offering clearly inapparent foundations of knowledge, to reveal contradictions among the schools on the profound level, and to draw them together. Hence, an axiomatic approach is a means of synthesis of paradigms. The latter are considered as scientific subcultures.

M.Bunge (1973) has paid attention on the fact that the idea of systematization of knowledge by the usage of axioms is in the mainstream of Western thinking, and this approach has been used by Euclid, Aristotle, Newton, Descartes, Darwin and many other scientists.

The trend to systemize the main ideas (they are referred to as "laws", "axioms", "principles", "postulates") is characteristic for every province, but no everywhere they constitute a perfect system. The ideal in this respect was achieved else in the ancient time in the field of geometry. Other mathematical provinces are close to it. It might be that a province becomes an "exact sciences" only in the case if it has a perfect axiomatic system. In biology, perfect axiomatic systems are in theory of evolution and genetics. The provinces, which will be used for developing of the present set of axioms, in particular population ecology of animals, are far behind theory of evolution and genetics.

What is an axiom? Let an axiom be a description of an important property of the phenomena, with which a given province operates. An axiom is a product of analysis of these phenomena, rather than a priori declaration. M.Bung (1973, Ch.8) reminds the sense of this word in the Old Greek language - an inquiry. That is why, a scientist proposing a concept as an axiom hopes to excite a discussion on the part of the scientific media rather than to take it on trust.

The axioms should be organized in a system (a set) with the aim of entire characteristics of a province. This feature endures them with an ability of mutual control, and therefore helps to exclude contradictions. Also, it determines the number of axioms in a system. This number needs to be not too little, because some phenomena discussed in a given province would be unexpected. This number needs to be not too much because some axioms would be unused at explaining of phenomena in a province. Axioms need to be free from secondary detail, and to indicate necessary conditions, at which the phenomena postulated by an axiom take place (Conditio sine qua non). These conditions are known as prerequisites.

There exist the view that it needs to reveal a "structure" of a system, which is described by a given province. The structure is implied as important (fundamental, stable) relations among components of this system operating coherently. Our conscious expects that every system has such a structure. However, until our knowledge is not perfect, the relations appear to be chaotic. Proposition of a set of axioms is an attempt to bring Order in Chaos.

In this context, it should turn to rather enigmatic term a "paradigm." In a province, it operates a number of paradigms (Kuhn, 1970). When publishing data of studies, it is getting the good form to point out the paradigm, which is used as the ground in a given study. In a result, a matter of a report gets more comprehensible. It seems, a paradigm is some proximity of a set of axioms.

What is a benefit of an axiomatic approach to a province apart of the better understanding among scientists? A system of axioms gives an advice to a scientist what is a probable "key" factor, which determines trends of a process in question. This advice helps to make a true choice in difficulties. The reality of such difficulties has been expressed frankly by W.R.Henson (1968, p.37) in the following words: "One's choice of strategy in any investigation I suppose, more in nature of art than of science."

What is the province, for which an axiomatic approach is proposed? The term "stability of ecosystems to plant pests" has not been found out by the author in literature. Therefore, let us begin with the known term "stability of an ecosystem." According to the definition given by R.E.Ricklefs (1976, Ch.18), this is a property to resist plant pests (PPs) or tolerate effects caused by them. Let it be a "general stability of an ecosystem." The province under question is a part of this general stability. As a preliminary, let us determine it as a property to tolerate changing induced by plant pests (PPs) or to resist them. The term "PPs" embraces species of invertebrate and vertebrate animals as well as phytopathogens, which have been recorded as being harmful for plants worthy protection with the position of human interest.

It is proposed to use an axiomatic approach in the province under question, which will be referred to as "ecosystem stability to plant pests" (ESPPs). Here is an outline of the situation, which bears a direct relation to a subject of the present report: "In the "Origin of Species" Ch.Darwin stated that man does not know how the numbers of a single species are controlled in nature. A century later this statement needs little modification:

The mechanisms responsible for cycles in populations still remain a biological mystery. Similarly, the factors determining the natural dispersal and migration of organisms, including pests, are little understood. We are almost equally ignorant of the genetic and evolutionary mechanisms operating in the adaptation of pests to their habitats.

Parasites, predators, and pathogens have been used successfully against several pests, but the mechanisms of parasite-host, predator-prey, and pathogen-host population interactions remain vague."

This passage has been quoted from the fundamental book by E.P.Knipling, 1979, The Basic Principles of Insect Population Suppression and Management. In turn, this is the citation from the report "Restoring of Quality of our Environment" prepared for the President's Science Advisory committee (1965, pp.41-42).

This outline of the situation was prepared on a centenary of the Ch.Darwin's book. Nevertheless, on the forthcoming 150-year anniversary of the book, it seems, "this statement needs little modification." Probably, an attempt to use an axiomatic approach in this province would contribute to better understanding of "mechanisms" operating in it.

This report is a synthesis of the mainly well known ideas of population ecology of herbivores, epidemiology of phytopathogens and a number of other provinces that allows to explain ESPPs. The novel features of this synthesis are as follow:

• The selection of the ideas with the aim to choice the most important among them, which are able to serve as axioms.
• The attempt to determine the conditions, at which every of axioms is adequate, i.e. their prerequisites; this intention gives a possibility to associate the ideas, which before appeared to be unrelated or competing one with other.
• Some modification of these ideas with the aim of their association.

The axioms and their components will be codified. The aim of the codification consists in not only economy of a place for subsequent description and better orientation in the contents, but also as a means of the usage of this information in hypothetical computerization of this province. One may dream about the situation when this province would operate formulae, and it gets an exact science.

An axiom is only a hypothesis as M.Bunge (1973) says. A hypothesis is no more than an attempt to explain a phenomenon under study. Good hypotheses induce such an interest in the scientific media that it appears attempts to disprove them. To win recognition, hypotheses need to be well argued. Therefore, they are accompanied by an array of evidences (Part II).

Summing up, a set of axioms to be useful should meet some requirements, as follows:

• Relation to knowledge, which does not excite doubt in its true; in the given case, this is the Ch.Darwin's theory of evolution.
• The set of axioms embraces as far as possible all the domain of a province when explaining its phenomena.
• The axioms do not contradict each other.
• Composition of a set of Axioms is limited by the domain of a province.
• The axioms are interconnected that imparts the set of them by property of a system eliciting absence or surfeit of the components.
• To indicate the boundary conditions, within which the statements exposed in Axioms are true.