Ecosystem as a text: information analysis of the global vegetation pattern

Abstract

Let us consider a text, which is written in the English language. At the zero level of perception (or description), we know only the number of symbols ( n=29: 26 letters, 1 blank, 1 comma and 1 full stop). Then the information per symbol I (0) log 2 29≈4.85 bits. At the second level of perception we take into account the frequencies of the symbols (letters); then I (1)≈4.03 bits. At the next levels we take into account double, triple, etc. correlations, i.e., words of two letters, three letters, etc., so that the information per letter are I (2)/2≈3.32 bits, I (3)/3≈3.10 bits,…. The redundancy of information, R ( i) , and its cost, C ( i) , are equal to R (0)=0, R (1)=0.15, R (2)=0.30, R (3)=0.35, and C (0)=1, C (1)=1.18, C (2)=1.43, C (3)=1.54. Let us consider a description of the global vegetation pattern (GVP). At the zero level of description we have a number of significant biomes or vegetation types, n. In accordance with Bazilevich n=30, then I (0) log 2 30≈4.9 bits. At the second level we take into account the relative areas covered by biomes. Then I (1)≈4.41 bits, R 1=0.1, and C 1=1.11. At the next level of description we consider the spatial correlations between different pairs of biomes, then I (2)/2≈3.6 bits, R 2=0.265, and C 2=1.36. Note that in addition to their areas, the biomes are also characterised by three parameters: annual productivity P i , living biomass B i and dead organic matter D i . Weighting them in relation to biome area σ i we define the frequencies p i P =P iσ i/ ∑ i=1 30 P iσ i,p i B =B iσ i/ ∑ i=1 30 B iσ i and p i D =D iσ i/ ∑ i=1 30 D iσ i . The description in terms of productivity, living or dead organic matter can be considered as description at the first level with information per letter defined as (I (1)) P, B, D =− ∑ i=1 n p i P, B, D log 2 p i P, B, D . Then (1) for productivity: ( I (1)) P=3.61 bits, C 2 P=1.32, R 2 P=0.24; (2) for living biomass: ( I (1)) B=3.27 bits, C 2 B=1.5, R 2 B=0.33; (3) for dead organic matter: ( I (1)) D=4.13 bits, C 2 D=1.17, R 2 D=0.16. One can see that information about the biome productivity, living biomass and dead organic matter is more valuable than the information about the biome areas distribution. Information about the distribution of living biomass has the maximal cost ( C 2 B=1.5).