Geochemical turnovers can circulate without participation of biological compartments, but their rate is much higher because of such participation. For calcium circulation it is especially right, since mainly the sedimentation of calcium salts is a result of calcium absorption and accumulation in animal and plant bodies (skeletons of corals and higher animals, shells of mollusks, etc.), which are concentrated on the seabed after the organisms' death. The influence of living organisms is not so important for the water cycling, but higher plants essentially accelerate it. They play the role of peculiar 'pumps', sucking out water from soil and returning it to the atmosphere in the course of transpiration.
Historically, the biological component is embedded into the abiotic cycles. It was based on peculiarities of these preceding cycles, changed them, and, finally, formed new biochemical 'nutrient' cycles, which are much faster and localized. Sometimes they are called small or biological cycles. Now all matter flows within the Earth proceed under significant influence of biological compartments. From the Cambrian period, biota became an important geological factor, which has formed the modern face of the Earth.
Both big (geological) cycling and small (biological) cycling function under the influence of the external source of solar energy.
The totality of living organisms, unified by participation in the biogeochemical cycles, is called biosphere. This term was proposed, in a slightly different sense, by J.-B. Lamarck in 1802. The modern meaning of the word was proposed by E. Suess in 1875. The theory of biosphere was essentially developed by V. I. Vernadsky (during 1927-44), who especially studied links between biotic and abiotic components and considered the role of humanity in the current biosphere functioning.
The borders of the biosphere in space are determined by the location of biogenic elements, involving biogeo-chemical cycles. It covers all the territory of the Earth, and it is limited from the top by the upper board of the troposphere (8-16 km of altitude) and from the bottom by the lower board of sedimentary rocks in the lithosphere (2-3 km of depth) and deepest oceanic depressions (11 km of depth). Thus, geometrically, it is really a sphere of thickness of about 20-30 km. Most of the organisms concentrate in the much thinner geographical shell, which includes the lowest layer ofthe troposphere and the upper layers of the lithosphere and hydrosphere (not deeper than 200 m). The biochemical cycling functions mainly in this shell of Earth.
The biosphere is the biggest object, which can be called an ecological system. The next, lower level of ecological systems is represented by big territorial and functional units with more or less homogeneous structure. The systems include, besides biological populations, abiotic compartments: 'soil-ground' (edaphotop) and atmosphere (clymatop). For the biological part of the object, a special term 'biocoenose' was introduced by T. Mobius in 1877. Later the term was translated into English as ecosystem by A. G. Tansley in 1935, who also modernized the concept by emphasizing of systems nature of biological societies. Concurrently, the concept of biocoenose was developed by V. N. Sykachev in 1940, who proposed the term 'biogeocoenose' for the system, including not only biological objects, but also its direct abiotic environment. The last term is more preferable for description of territorial biosphere units, whereas the ecosystem can be understood as an ecological system of any scale. Biogeocoenose is a system of many populations of different species (biocoenose) acting in a relatively homogeneous abiotic environment (biotop) and characterized by relatively stable biogeochemical cycling. Biogeocoenoses (and corresponding types of cycling) can be classified by the type of natural conditions for forests, grasslands, marshes, lakes, aquatic ecosystems, etc.
Extraction of next levels of ecological organization, associated with separate biogeochemical cycles, is not evident. There are many concepts realizing the functional (consortium, coenoelement, etc.) or territorial (parcella, gap, locus, etc.) approach. In any case, the existence of elementary cycles, formed by dominant population of plant-autotroph species and satellite species of plants, animals, and microorganisms, is considered as an ascertained fact. For such an abstract elementary cycle, the term 'coenome' can be used (for more details, see later).
Although biological cycling of each biogenic element is characterized by its own properties (see Carbon Cycle, Oxygen Cycle, Nitrogen Cycle, Phosphorus Cycle, Calcium Cycle, and Sulfur Cycle), all of the elements include migration of biomass in food webs. Transfer of the matter in the course of the cycling involves the following main steps: absorption and accumulation by living organisms of elements from abiotic environment; distribution of the matter among organisms as a result of herbivory, predation, and parasitism; territorial migration of organisms; formation of dead organic matter (DOM or mortmass) as a result of excretion and death of organisms; decomposition of the mortmass and return of the elements to the abiotic environment.
In accordance with the place, occupied by species in the food webs, they are usually divided into three main groups: producers (which use external energy, solar or inorganic chemical, and realize biosynthesis: generate organic matter), consumers (which use chemical energy of living tissue of other organisms), and reducers (which use chemical energy of mortmass and do its biodegradation: decomposition to simple inorganic agents). A classification of such organisms was initially proposed by A. L. Lavoisier in 1792 and then, in another form, was developed by W. Pfeffer in 1886.
The main players in the nutrient cycling are producers and reducers. The former are an 'engine' of the cycling; they involve elements from the abiotic environment in the turnover and send them further in the composition of permanently generating high-energetic organic matter.
The reducers 'close' the cycling; they return the elements to the abiotic environment, where they can be used by producers again. Abiotic decomposition takes place, but its intensity is very low. Without producers available elements would concentrate in the biomass and leave the environment; cycling would stop, and life development would end. The simplest artificial stable ecosystems, functioning in closed flasks, included populations of producers (unicellular algae) and reducers (bacteria and fungus).
Theoretically it is possible to envision producers, independently realizing the function of reducing with respect to their own biomass. But in reality this possibility is not realized. This fact can be explained by the absence of evolutionary reasons of forming 'self-sufficient' organisms, if the hypothesis about the origin of heterotrophs (consumers and reducers) before producers is correct. Stable biological cycles could form gradually, during the process of co-adaptation of producers and reducers. Close symbiosis and species peculiarity are typical for relations between producers and reducers.
The most common flows of matter in the biosphere, including food chains and abiotic topical ways, are presented in Figure 2. There are four ecosystems of different nature in the Figure 2: terrestrial; shelf; open sea; deep-sea black geyser. The core cycle for each ecosystem is cycling 1: 'producers-mortmass-reducers-inorganic salts-producers'. For the terrestrial ecosystem it can be written: 'producers-litter-reducers-soil-producers'; for the water one: 'producers-sediments-reducers-water-producers'. The cycles are initiated by the producer block, which transform the solar energy to the chemical one in the course of the photosynthetic process. It is the most rapid and mainframe cycle in the biosphere; its dynamic properties are considered below.
The amount of different biogenic elements in cycling is determined mainly by features of the environment. The intensity of cycling depends on properties of the producer block. The additional loop 2 reflects the role of the consumer block. The energy and matter flow through it are approximately 10 times less than directly from the producers to the mortmass, but the consumers, influencing the producer block, 'bootstrap' the turnover. Similarly, loop 3, involving the block of consumers of second order and also 10 times less intensive than loop 2, contributes to increasing intensity of the total cycling. In Figure 2 for the marine ecosystems the blocks of producers, reducers, and consumers are marked by the first letters P, R, and C, respectively.
Elements' Pathways: Terrestrial Ecosystems
The terrestrial biogeocoenose, in addition to the blocks, involved in the described main cycle, includes the atmospheric block. Flows 1-6, connecting this block with others, are internal flows of the biogeocoenose. The importance of the cycle formed by flows 1 and 2 is close to importance of the central cycle 1. The main source of carbon for photosynthetic plants is carbonic gas from atmosphere. In contrast, in the course of respiration, plants send off carbonic gas and consume oxygen. Also, as shown in Figure 1, plants play important role in passing water from soil to atmosphere (the process of transpiration).
Flow 3 describes the process of respiration of other members of biocoenose: consumers and reducers. Another way of sending carbonic gas (and other chemical substances) from plant body to atmosphere is fire, produced by such natural factors as thunderbolt (flow 4). Connections between soil and atmosphere are reflected in flows 5 and 6: precipitation, soil respiration, and diffusion.
Interaction between soil and upper lithosphere (which is considered as a part of the biosphere, but not of biogeocoenoses) is described by flows 7 (lixiviation), 8 (leakage, mineralization, fossilization), and 9 (thermal water circulation).
Elements' Pathways: Marine Ecosystems
Aquatic biogeocoenoses have the same principal 'cybernetic' structure, but with special role of the water environment. The latter plays the functional role of soil (or, more precisely, soil solution), which stores ions and 'feeds' producers, and, partially, the role of atmosphere, which delivers carbonic gas and oxygen to living organisms. Connections between water environment and real atmosphere are pictured by flows 10 (precipitations), 11 (diffusion), and 12 (evaporation). The hydrosphere is also connected with the upper lithosphere by flows 13 (dissolution) and 14 (fossilization of sediments).
It is important to stress that total biomass of marine ecosystems is much less (approximately 800 times) of the terrestrial one (about 5 x 109t contrary to 4000 x 109t). At the same time the primary production of marine ecosystem is only 4 times less. It is explained by much more intensive matter cycling in the ocean. Correspondingly, the matter involved in marine and terrestrial cycles is similar (about 215 x 109 and 270 x 109t correspondingly). Apart from similarity of the primary production (170 x 109 and 60 x 109t), it is explained by intensive migration of gas substances among the atmosphere and the ocean. Biomass of marine ecosystems is renewed many times during a year.
The marine ecosystems can be divided into shelf or sublittoral (functioning on the shelf, shallow coastal part of the sea) and open sea (connected with open deep-sea territories). The former are much richer in energy and biomass, and are characterized by much more intensive nutrient cycling. This fact is explained by possibility of photosynthesis in the sea floor (the bottom is above the photosynthetic horizon, which lies at a depth of about 200 m) and easiness of involving the mortmass, concentrating in the seabed, in the cycling.
Open-sea ecosystems are characterized by two types of nutrient cycling. The first is connected with surface water, which includes not only producers, but also reducers, 'intercepting' diving particles of mortmass. This cycle, naturally, is not closed, because an essential part of the mortmass falls to the bottom. Return of this matter to the ecosystem is difficult because of (1) bottom conditions, which are adverse for the life and, particularly, for reducer's activity; and (2) the usual absence of ways of transportation of biogenic elements from the bottom to the layers under the photosynthetic horizon. As a result, the biogenic elements are concentrated in the bottom sediments, and the process of fossilization (flow 14) is much more intensive in the open sea than in the shelf.It leads to much more essential losses of biogenic elements in this type of biological cycles.
The upper cycle, in its part, usually can be divided into two forms. The first, in a depth of 25-40 m, is characterized by the best conditions for photosynthesis, but limited by deficiency in accessible biogenic elements, which are mainly results of local reducers' activity. The second form of cycling is connected with producers' activity in a depth of 70-90 m, where photosynthesis cannot be so intensive, but the reducers are much better provided by nutrition, which come in from above, from the upper cycle, and from below, as a result of turbulent diffusion.
The richest marine ecosystems are observed in the territories where cold sea currents lift deep water to the surface or where local conditions promote mixing of water layers (e.g., near coral reefs). In other words, open-sea ecosystems function better, if the second, bigger cycle, including deep-water sediments, is closed.
The shelf and open-sea ecosystems are unified, naturally, by the water; these are mixed by currents and winds. Besides, there is a transfer of biogenic elements from the shelf to open sea (flow 15), where they are utilized by the upper-water reducers or accumulated by bottom sediments.
A special type of marine nutrient cycling is typical for the so-called rift life concentrations or 'oases'. They were discovered in 1977 and are located around abyssal rifts, where deep-sea thermal springs occur. Such abyssal rift ecosystems are based on populations of microbial chemo-synthetic producers, which use chemical energy, not solar, for organic matter production . Flow 16 represents the movement (with lifting hot water) of high-energy substances (mainly hydrogen sulfide) from lithosphere to ocean water. The ecosystems can include many organisms, consumers and reducers, adapted to these special conditions: worms, pogonophors, mollusks, fishes, etc. Some of these organisms are in symbiotrophic relations with chemosynthetic bacteria, which live in their bodies.
Probably, rift ecosystems can function without contacts with other parts of biosphere, although they are not really isolated and, particularly, can participate in enrichment of seawater by organic substance. There is an opinion that biogeochemical cycling, characterized for the rift ecosystems, has some common properties with the first cycling, formed in the Earth on the stage of hydrogen-helium atmosphere.
A basic element for formal description of biological cycling is a model of elementary turnover. A special term 'coenome' can be proposed for such elementary biogeocoenotic cyclic element. The coenome can include one or several populations of producers (as a source of energy and a kernel of the association); reducers, that close biogeochemical cycles; and consumers that stimulate energetic processes in the system. According to V. N. Sukachev, producers can be subdivided into three general groups: edificators (determinators), co-edificators, and assectators. Coenome species are characterized by some level of co-adaptation. The main features of cross-population relations in a coenome are the following: a low level of competition, as a result of effective separation of niches; high-developed mutualism, especially, in pairs 'producer-reducer'; and an optimal (from energetic reasons) level of trophic relationship. Naturally, the areas of ecological optimum of coenome species must have a common part.
Biogeocoenose may be characterized by one dominant coenome, but usually it is also possible to recognize some minor coenomes in its structure. If biogeocoenose is characterized by two or more dominant coenomes, it is amphicoenoses. In general, most natural ecosystems are superposition of several coenomes as a result of spatial heterogeneity, exogenic factors, etc.
The principal scheme of matter and energy flows in coenome (without consumers) is represented in Figure 3. The symbols x, y, p, q denote contents of some chemical element, respectively, in the biomass of producers, in the biomass of reducers, in the mortmass, and in the inorganic matter, accessible for producers. Characteristic intensity of the element cycling is symbolized by M. The coefficient a (0 < a < 1) determines what part of the element does escape the populations of producers as organic matter, and the coefficient A (0 < A < 1) determines the same for populations of reducers.
The cyclic structure of a coenome illustrates the importance of positive feedback in food webs which exists simultaneously with negative feedback circuits in usual competition and trophic relations. This nontrivial 'cybernetic' structure of ecosystem permits its capacity of fast development in appropriate conditions, concurrently with the capacity of homeostasis.
The simplest closed model of matter cycling in a coenome (the firm lines in Figure 3) can be designed on the basis of Lotka-Volterra models. Without describing effects of saturation and self-limitation of populations, it can be written as follows:
dx/dt — aqx - bx dp/dt — abx + Asy - ryp dy/dt — rpy - sy dq/dt — (1 - a)bx +(1 - A)sy - aqx
The coefficients b and s are the death rates of producers and reducers; a and r estimate intensity of use, respectively, of inorganic matter by producers and mortmass by consumers. The model does not
p y determine the stable values x and y, but only their ratio: x/y = (1 — X)s/ab. It is explicable both from the mathematical point of view (the sum (x + y + p + q) does not change during the process) and by biological reasons (the model describes closed circulation of the element) that the element amount in the cycle is determined by some external factors. Under natural assumptions that a > b, r > s, system of equations in  is stable, but not asymptotically.
A more realistic model can be obtained by the use of the equations with Michaelis-Menten functions in the right-hand members:
dx/dt — A(cq/(x + cq) -b/A)x dp/dt — abx + Asy - Rhpy/(y + hp)
dy/dt — R(hp/(y + hp) - s/R)y dq/dt — (1 - a)bx +(1 - A)sy - Acqx/ (x + cq)
System  dictates the same parameter M = abx and the same ratio between biomasses of populations, as in model . However, in this case, the quantities p and q depend on population sizes.
For the energetic flows in coenome (the dotted lines in Figure 3), it is possible to write, similarly to the model , the following system:
dix-/dt = (E — ab — <x )ex dep / dt = abex + Asey — Rhepey / (ey + hep) — <pep  dey/dt = (7Rhep/(ey + hep) — As — <y )ey where the variables ex, ey, ep estimate energy in the biomass of producers, reducers, and mortmass, respectively; <xex, <yey, <jpep are energy losses for each group; E ex is the intensity of the energy flow into populations of producers; 7 (0 < 7 < 1) is the part of the dead biomass energy, which passes to the energy of the reducers' biomass.
The first equation of the system  does not depend on others. The condition of existing steady nonzero value ex (which depends on initial conditions) is <rx = E — ab. The conditions of positivity of the steady state are 7 > As/R, <y < 7R — AS.
The problem of interrelation between the matter and energy flows in the coenome can be considered with the use of the variables fly, flp, which are the measures of energy per biomass unit ofproducers, reducers, and mort-mass, respectively. The variables can be described by the equation dflx/dt — (E - ab - ax dfip/dt — h(R - s)(l - A)f3x + h(R - s) jRs ftp
Figure 3 Matter and energy flows in a coenome.
The variables flx, flp, fly can be used as measures of the level of organization (or thermodynamic instability) of a p
p a y population biomass. It is possible to interpret system  as the model of information transformation in the coenome, if the term 'information' is used as a synonym of negentropy.
The flows of matter, energy, and information in the models - are ultimately determined by producer activity. In some way, the variables x, ex, and are external parameters of the models, which should be described by some additional equations. A possibility to estimate the steady values of these coordinates has to be studied on the basis of other reasons; for example, one can use the Liebig law. Concentration of noncritical ions in soil does not influence productivity, and even inhibits it in the case of too high concentration. A scale of cycling is determined not only by the amount of accessible bioelements, but also by the biochemical properties of soil.
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