Diversity of the biosphere

Life on Earth is represented by a huge number of diverse forms, and it is necessary to maintain all this diversity. This is one of the main thermodynamic roles of solar energy. Otherwise, from the point of view of classic thermodynamics, the film of life would have to be homogenous, and, moreover, life would not have occurred at all. Nevertheless, life exists and its diversity is very high. In order to resolve this contradiction we suggest a simple thermodynamic model (see also Svirezhev and Svirejeva-Hopkins, 1997).

Let the biota (the living matter of the biosphere) be subdivided by 1 sets. These sets could be interpreted as different hierarchical taxonomic units: biomes, ecosystems, communities and species. We assume that every ith set contains Ni virtual biPosphere "particles", so that the total number of particles in the biota is equal to N = £1=1 Ni. Generally speaking, the particles must differ from each other, but, as a first approximation, we assume that they are equal. In particular, they all have a unique mass, so that the sets differ from each other only by mass.

Let us assume that at some initial moment the particles were mixed up in some "pre-biosphere" substance, and this "pre-biosphere" system had no structure. How could such an ordered structure as the biosphere have arisen? We think that it is the result of the work of a demon named Ecodemo1, from the famous Maxwell family of demons (Fig. 4.2). He distributes the biosphere particles among the boxes, removing them from the "pre-biosphere" pool. As a result, each ith box contains Ni particles. In this way a new structure arises, which may be called biota. The transition from a fully mixed system ("pre-biosphere chaosP") to the "structured" biosphere is accompanied by the entropy reduction DS = — sN £1=1 Pi ln Pi, where s is the specific entropy of the mass unit of some "pre-biosphere" substance. In our case this substance is a mixture of chemical elements from which living matter can be constructed: 106 molecules of CO2 + 90 molecules of H2O + 16 molecules of NO3 + 1 molecule of PO4 + a few molecules of some mineral elements (Odum, 1971a,b). Note that when we speak about the "mixture", we do not mean a real physical mixture, but some likely sum of elements already in existence but—very importantly—still not reacting with each other so that "living matter" is still not formed. Since the specific molar entropies of CO2, H2O (vapour), NO3 and PO4 are equal to 214, 154, 256 and 301 (all the values are expressed in J/mol K), and their molar masses are 44,

18, 62 and 95 g, respectively, then

= 214 X 106 + 154 X 90 + 256 X 16 + 1 X 301 S = 44 X 106 + 18 X 90 + 62 X 16 + 1 X 95

This value can also be considered as entropy of 1 g of protoplasm, that is a primary non-structured living matter, from which Ecodemon has to construct the structured biosphere. One-gram portions of protoplasm are our biosphere particles.

Let us consider the following cyclic process: every year a certain amount of new biomass, DN, is created, and, since the biosphere is at steady state, the same amount of dead organic matter is decomposed. It is obvious that the value of DN is equal to the net annual production of the biosphere, NPP. The decomposition process is accompanied by a release of heat, which is equal to the enthalpy of DN. If DN is expressed in the units of dry biomass (d.w.), and the enthalpy of 1 g d.w. is equal to h = 18.9 X 103 J/g, then NPP = h DN (J). If we assume the entropy production is equal to the thermal effect divided by temperature T, then DS = (NPP)/T where T = 288 K is the annual mean planetary temperature.

We assume (and this is our basic hypothesis) that this entropy production is balanced by the entropy decrease in the process of the creation of new biomass. The decrease has to be equal to information entropy. In other words, the value of NPP is the annual work performed by Ecodemon, which feeds on the enthalpy.

If we keep in mind that I = — (1/ln2)£n=1 Pi ln Pi is the information entropy or diversity of the system and NPP = s DNI ln 2 then


Since h = 18.9 X 103 J/g and s < 5.55 J/g then I < 17 bits.

Let us estimate the probability of spontaneous creation of the biosphere. It is equal to

i.e. is very small. But if the contemporary biosphere is a result of a sufficiently large number of attempts L, in accordance with a simple probabilistic model (Chernavsky and Chernavskaya, 1984), the probability of its creation will be equal to

L Pr

How to evaluate the number of attempts? The photosynthetic biosphere with vegetation existed during approximately the last 109 years (Rutten, 1971). The mean time of the biosphere renovation is equal to t = B/NPP where NPP = 1.2 X 1017 g d.w./year is the annual net production and B is the total biomass of the biosphere equal to 1.8 X 1018 g d.w. (Svirezhev et al., 1985). Then t = 15 years, and if we assume that one attempt is nothing else than one cycle of the biosphere renovation, then L = 109/15 < 6.7 X 107 = 0.66 X 108, and

Thus, the probability of the biosphere creation is close to 1. In other words, there is nothing surprising in the existence of the contemporary biosphere.

It is also very interesting that the probability Pr depends neither on the mass of the biosphere nor on its productivity (you can see it from the formula for '). The probability Pr depends only on two factors:

1. Work of the climatic machine, which determines the Earth temperature.

2. Composition of input components for construction of living matter; namely, the composition determines the value of s.

Photosynthesis reaction uses two gases as basic substance for the formation of living matter: carbon dioxide and water vapour. Certainly, we can imagine other hypothetical reactions, which would use other elements and substances (for instance, silicon instead of carbon), but this would give other values of s and, as a consequence, other values of diversity. As a result, the probabilities of existence of such virtual biospheres would differ from the similar probability for the really existing one.

Note, however, that the probability PrL nevertheless depends in an implicit way on the total mass of the biosphere and its productivity because the number of attempts (L) is defined by these values.

Knowing the value of ', the number of components (elements, elementary units, etc.) of the biosphere could be estimated. If these elements are relatively independent and they occur with almost the same frequencies, then ' = log2n and the number of elements n = 2' = 217 < 2 X 105. It is interesting that this number is close to the number of biological species on our planet. An impression appears that our Ecodemon uses species as boxes. However, if the elementary units within the biosphere are organised in "hard" structures (like trophic chains and trophic levels) with the exponential distributions of frequencies Pi, then 1 < I, i.e. the number of different sorts of these elementary units would be relatively small.

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