2Pi log2 PP

Using the data from Table 4.2 we can calculate the corresponding value of information (per letter), its cost and redundancy:

1. For productivity: (I(1))P = 3.61 bits, Cf = 1.32, Rf = 0.24.

2. For living biomass: (I(1))B = 3.27 bits, Cf = 1.5, Rf = 0.33.

3. For dead organic matter: (I(1))D = 4.13 bits, CD = 1.17, RD = 0.16.

These values show that information about the biome productivity, living biomass and dead organic matter is more valuable than the information about the distribution of the biome areas. Information about the distribution of living biomass has the maximal cost

It is necessary to say a few words about information at the global and regional levels of scaling. If we keep in mind that the total number of species in the contemporary biosphere is equal to n < 106, then information per species at the zero level of description and the global scale is equal to (I(0)) B = log2(106) < 19.9 bits. At this level of description all specimens of a community differ from each other only by one indication, namely, by its membership of one or another species. However, as we saw above, if the biosphere is represented as a composition of higher taxonomic units (biomes), which in turn represent the composition of species, i.e. words are formed by groups of letters representing species, then the information per word is less than 19.9 bits. The same effect is observed when we estimate the amount of information per species for some taxonomic unit, which is lower than the biosphere.

The point is that when we describe a community belonging to some ecotype (for instance, either an aquatic community in a lake, or a plant community of some biome, etc.) then the alphabet may be significantly shorter. Then the amount of information per letter will be less than in the previous case. This seeming loss of information is a result of its redundancy at this "regional" or "local" level in comparison with the global level. In fact, the information about all the species present in the biosphere is absolutely redundant when we describe some regional or local community. Here we need only the information about those species, which are typical for some of the considered locality. Note that the "lost" information is not actually lost; it is usually used to extract the locality from the biosphere.

Let us consider the following example. The number of different plant species typical for the Russian dry steppe is equal to 150. Then the information per species contained in the botanical description of any steppe community (list of species) is equal to (I(0))R = log2150 < 7.23 bits.

Finally, we can give another interpretation of these results. Indeed, what is implied the value of information equal to 19.9 bits per species? Note that this is a global value. Since a considered system is the Globe then this statement is equivalent to the following: the probability to find even one (and more) individuals of given species at any arbitrary point on the Globe is equal to 2~199. The same probability, but calculated for the list of steppe species (150) and the region of the Russian steppe, will be equal to 227 23. An analogous interpretation occurs for biomes. At the zero level of description the probability to find one and more plants representing one (of 30) given biome at any point of land is equal to 2_I< '. At the first level, when we know the area of each biome, the same probability but calculated for one plant will be higher, 22I( ', I(1) < I(0). Hence, the greater is the area of a certain biome, the higher is the probability to meet its representative at any arbitrary point.

At the second level the probability to find a pair of plants representing a given pair of biomes in the close vicinity of any point of land is equal to 2—/(2) /2. It is also higher than the previous probability.

In addition to area each biome can be characterised by either productivity, or living biomass or dead organic matter. Then the corresponding probabilities Prp,B,D = 2—(/(1))P,B,D are the probabilities to find at any point of land a plant with characteristics which are typical for a given biome. Note that all these statements can be paraphrased as ".the probability to find a plant-representative of any arbitrary biome at a given point of land."

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