Life can be considered as existing in its own space of possibilities (a 'space of life'). Mathematically, this space can be called as a 'phase space'. Potential wells in this nonlinear space are occupied by different forms of life; they are the so-called ecological 'niches' (see Ecological Niche). Usually the niche of species is defined as a set of environmental factors corresponding to the needs of the species. A linear world (without sources of energy) would have no niches. The inflow of energy creates or allows to create wells in the life space, where life can consolidate. The situation is similar to the physical picture of the world; elementary particles, probably, exist in potential wells and the world space is furrowed by some fundamental processes (e.g., the energy conservation law can be approximate, and leaking energy furrows space).
Evolution is a process of optimization. Biological systems evolve to a steady state or, in other words, optimize some criterion (Lyapunov's function), looking for a potential well (a niche) in a phase space. One of the optimization criteria is entropy production, which must be minimal in a state of dynamic equilibrium in accordance with the Glansdorff-Prigogine theorem.
In a niche, the system possess properties of homeosta-sis; after small distortions, it will return to the initial state. The evident discrete character of the steady states' set produces separateness of niches. Heterogeneity of the life space explains existence of strictly separated species and other taxonomic units. Living organisms are substantially casts of their niches. There are many examples of convergence, when similarity of niches leads to similarity of organization of living beings.
Tendency of nonlinear systems to keep in equilibrium is well known as a general systems property of 'equifinality', postulated by L. Bertalanfy. It is a spontaneous reaction of the system; it is an important factor of evolution, but it does not direct the life progress. Optimality does not mean progressive character; the level of amoeba fitness is not lower than that ofman. Evolution uses the gradient method, which allows finding a local extremum only; for improving living conditions, species must jump over unacceptable ones. According to I. Prigogine, self-organization is a process of step-by-step loss of stability. The change of a steady state can be a result of either essential external influence upsetting the system from a previous equilibrium and forcing it to transit to a new one, or a gradual change of system parameters leading to a change of the phase space topology, to disappearance of the current steady state. Both of these ways were combined during life history; the model corresponds to the saltation conception about evolution as a sequence of catastrophes. External influences (geological, cosmic, anthropogenic) cause disappearance and reorganization of niches. New niches stimulate evolution of their potential hosts, which fill them because of reproductive abilities producing 'pressure of life' (see Figure 3). Species, which have lost their niches, should progress or become extinct.
In accordance with another topological model, catastrophes (and accompanying biological innovations) create new dimensions of the life space. In the niche (a point of local minimum), a new dimension appears; correspondingly, the host of the niche loses its stability and gets a possibility to find a better position in a new direction. At the result of such step-by-step changes, the development trajectory of the species is formed as a chain of orthogonal line segments. The path of progress can be compared with a 'bobsleigh track'.
Can evolution proceed under the constant conditions of environment? Darwinism does not exclude this possibility; the development of life organization can go on in the course of successive small improvements (decreasing entropy), but this movement is very slow. Usually it does not presuppose essential change of phase space topology; although it can sometimes stimulate radical changes: for example, the development of photosynthesis brought to the oxygen revolution and total reorganization of the system of niches. As a rule, a host of a stable niche slowly evolves and can meet competition only from the side ofkindred species or, quite rarely, introduced ones. The Black Queen hypothesis about the necessity of permanent improvement of all species (''to stop means to die'') is not true for stable niches. This fact is illustrated by the existence of a great number of primitive species formed millions and billions of years ago. For continuation of the race, it is necessary to change topology of the phase space, to disturb the system.
Relatively fast evolution of life has become possible because of general instability of niches. The history of life is a sequence of actions of forming and filling niches. As a result of divergence, niches bifurcate; the process of'niche proliferation' takes place. Quite fast processes of niches interaction are ecological successions, when niches regularly change and supplement each other. Often infill of a niche creates a number of new ones, and, importantly, the complexity of the derived niches is usually higher than that of the initial one. It creates prerequisites for progressive evolution of life, an increase of its complexity. Newer forms of life produce newer local worlds, up to virtual worlds in the human mind, which are entirely real as both processes in brains and a plan for the real world change. Man with his imaginary worlds creates principally new powerful niches, particularly, for the development of artificial 'electronic beings'.
Principally, the evolution process concerns not separate organisms, but the biosphere as a whole. The optimality of organisms is not an absolute value; it has a sense in the context of environment including other organisms. In other worlds, self-organization of life cannot be understood at the level of organisms; it is necessary to consider the general life space, separated species in corresponding niches, and their interference.
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