— 15.11

Since all eigenvalues of S are located outside of the unit circle (lA12l 1 < 2.4, lA3;41 1 < 1.53, whence lA¿l 1 > 1), then the operator S is not contracting, and this ecosystem does not satisfy the generalised Le Chatelier principle given by inequality (7.4). This result can be interpreted in the sense that in spite of the fact that the carbon cycle in a bog is stable, and the equilibrium exists and is stable, at the same time no fluctuation of carbon inflows is attenuated and can even be amplified. This shows, for instance, that additional carbon, which has entered the system as a result of inflow fluctuation, is not dissipated by outflows, but it is accumulated inside the system. It leads to the increase of equilibrium storages. It means that the equilibrium state of a bog in the temperate zone is very sensitive in relation to the change of carbon input from external sources. The system does not try to keep its internal state, attenuating the external perturbation, but it changes its state in the direction of perturbation, adapting itself to it. The behaviour of the system may be very complex; resonance, non-linear oscillations and even chaos may appear under certain conditions (Zavalishin and Logofet, 2001).

The considered ecosystem has two real inputs with corresponding inflow q1 and q4 (see Fig. 9.3); therefore Sq = Sq1 + Sq4 and Sx* = s1Sq1 + s4Sq4 where i1 = i11 + s21 + s31 + s41 < 0.1 and s4 = s14 + s24 + s34 + s44 < 0.13. In Fig. 9.9 the domains corresponding to normal and paradoxical reactions of a bog in relation to variations of inflows are shown.

One can see that the ecosystem of a bog reacts normally to almost any variations of inflows. Paradoxical reaction is possible if Sq1 and Sq4 have opposite signs.

Fig. 9.9. Domains of normal and paradoxical reactions of the ecosystem on variations of inflows.

9.9. Summary of the ecological important issues

A complex ecosystem can be described as an ecological network, indicating how mass, energy and information are transferred from one component to another within the ecosystem. It is interesting that Patten (1991) has shown that the possible interactions between two components (symbiosis, prey-predator, competition, commensalism, amensalism and indifference) all become more beneficial for both components due to the presence of the network that ensures constant cycling of matter, energy and information.

Various measures of the network organisation have been proposed: MacArthur's diversity index, the trophic diversity, ascendancy, exergy storage and indirect effect relative to direct effect. The four latter have been examined in this context and it was demonstrated that they offer different interpretations of network organisation. It is demonstrated that ascendancy is a good measure of the organisation of the network, but the concept has two shortcomings: it is not dynamic and it does not take into account storages. Exergy has the advantage as the measure of ecosystem organisation that it is able to account for storages and genetic information when exergy is calculated by the method presented in Chapter 5. Furthermore it has been shown that ecological networks are able to deal with almost any realistic input in one way or another.

A thermodynamic analysis of bogs has revealed that they show equilibrium storages. Additional carbon entering the system is not dissipated by outflows but accumulates.

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