**3.3 Case study; eco-exergy analysis of lake Baikal state**

The first works were fulfilled with the use of mathematic models. Different sensitivity of under-ice and open water plankton communities to contaminant additions was demonstrated. This can be related to different structural exergy content in plankton community. Exergy buffer capacity seems to be a more realistic measure for pliability of ecosystem reaction to external factors than biomass buffer capacity (Silow, 1998, 1999). In field researches the structural exergy of benthic communities at control (pristine) site, and in the region of Baikalsk Pulp and Paper Combine wastewaters discharge region at the same depths and kind of sediments was shown to differ strongly (structural exergy in polluted area was much lower than in pristine one), while biomass and total exergy behaved in not such an expressive way (Silow & Oh, 2004; Silow. 2006). The next step was the analysis of

different trophic groups responded differently to different water types reflecting

Eco-Exergy and Specific Eco-Exergy were used to characterize the state of the community during the recovery process after damage to the benthic communities caused by ecological engineering Yangtze River, China (Zhang et al., 2009). Changes of the macro-benthic community structure (Venice lagoon, Italy) over almost 70 years were pictured, showing a sharp decrease in its diversity and system efficiency, estimated with the use of exergy

The idea to use exergy as an indicator of ecosystem health was proposed by S.E. Jørgensen (1992, 1999, 2002, 2006a,b), but the first applications of exergy as an ecosystem health indicator were fulfilled with mathematical models. Mathematical modelling with the use of exergy was shown to be applicable to explain ecosystem reactions (Jørgensen & Padisak, 1996), and to facilitate the estimation of parameters of models. The first pioneer papers describing the application of exergy indicators for natural aquatic ecosystems were published in 1997 (Xu et al., 1997; Marques et al., 1997). In 1998 the first application of exergy analysis to the results of field and laboratory experiments with real aquatic ecosystem was published (Silow, 1998). This work was continued by few more publications (Xu et al., 1999a, 1999b; Silow & Oh, 2004). The possibility to use such parameters as structural exergy and exergy for estimation of ecosystem state and its changes under various external influences was demonstrated for real natural and experimental ecosystems. These parameters were shown to reflect the state of ecosystem and they can indicate the degree of ecosystem adaptation, decreasing when important for ecosystem functioning components were depressed or eliminated. S.E. Jørgensen (2006a) proposed to use Eco-Exergy, specific Eco-Exergy and ecological buffer capacities as Ecological indicators for ecosystem

Exergy is now often used for eutrophication assessment (Xu et al., 1999, 2001, 2011a; Fonseca et al., 2002; Marques et al., 2003; Ye et al., 2007), for ecological engineering purposes (Nunneri et al., 2008), for ecosystem health assessment (Vassallo et al., 2006; Libralato et al., 2006; Xu et al., 2011b). Exergy and specific exergy indices as Ecological indicators of the trophic state of lake ecosystems were tested on a set of lakes (Ludovisi & Poletti, 2003). The

The first works were fulfilled with the use of mathematic models. Different sensitivity of under-ice and open water plankton communities to contaminant additions was demonstrated. This can be related to different structural exergy content in plankton community. Exergy buffer capacity seems to be a more realistic measure for pliability of ecosystem reaction to external factors than biomass buffer capacity (Silow, 1998, 1999). In field researches the structural exergy of benthic communities at control (pristine) site, and in the region of Baikalsk Pulp and Paper Combine wastewaters discharge region at the same depths and kind of sediments was shown to differ strongly (structural exergy in polluted area was much lower than in pristine one), while biomass and total exergy behaved in not such an expressive way (Silow & Oh, 2004; Silow. 2006). The next step was the analysis of

ecosystem maturity was estimated for Lake Trasimeno (Ludovisi et al., 2005).

**3.3 Case study; eco-exergy analysis of lake Baikal state** 

characteristics of target ecosystems (Park et al., 2006).

**3.2.3 Eco-exergy as an ecosystem health indicator** 

development and health assessment.

(Pranovi et al., 2008).

exergy and structural exergy of plankton community response to different chemical stressors analyzed in mesocosms experiments. Results obtained with mesocosms and microcosms demonstrate structural exergy decrease in experiments proportionally to a value of the added toxicant concentration, while other parameters (biomasses of components, total biomass of community, total exergy) fluctuated (Silow & Oh, 2004; Silow. 2006). Here we present the results of exergy calculations for natural plankton community of the lake Baikal.

Yearly average values of structural exergy during 1951–1999 fluctuated around their longterm average within the limits "long-term average ± mean square deviation" (154,9±26,0) without any trends. More interesting is the picture for total eco-exergy for the same period. It demonstrates well expressed linear trend of increase with r2 = 0.31 (Fig. 2).

We have also analysed the long-term dynamics of exergetic parameters for four limnological seasons at Baikal: inverted stratification (limnological Winter, under-ice season, February – April), spring overturn (limnological Spring, ice melting, May – June), direct stratification (limnological Summer, July – October), fall overturn (limnological Autumn, November – January)1. Analysis of eco-exergy and structural exergy behaviour during different seasons cleared that the positive trend of eco-exergy is observed during limnological Summer (Fig. 3, 4).

Dynamics of pelagic plankton biomass in Baikal for 1951-1999 is given in Fig. 2. There is neither expressed directional change of total biomass, nor changes of biomasses of different components (only slight positive trend of zooplankton biomass). Long-term oscillations of individual components are easily observed. Taking into account all discussed above and remembering the relative constancy of the total biomass of pelagic plankton, we can try to explain the tendency of its exergy to increase according to three listed above strategies (EL8 – increase of biomass, increase of network, increase of information). According to the first strategy it is the primary production increase, based on the mass development of small sized alga in summer period. Actually it is observed in the lake (Izmesyeva & Silow, 2010). According to the second strategy it might be some recently observed structural changes in the plankton community (Hampton et al., 2008; Moore et al., 2009; Silow, 2010), and the third startegy is realized through the growth of share of larger zooplankton, like Cladocerans (Pislegina & Silow, 2010). Total biomass of plankton community and its individual components remains constant, while the total exergy of the community tends to increase. This increase can be explained with the principles of S.E. Jørgensen (section 2.1) – the principles of exergy maximization (EL9 and EL10) via the growth of solar exergy consuming capacity, sophistication of ecosystem networking and increase of ecosystem information storage (EL8).

The calculated values of structural exergy for different seasons in the lake Baikal plankton for the second half of XX century, on the basis of long-term monitoring data, fluctuate within their natural limits (long-term average ± mean square deviation) and do not demonstrate any positive or negative trends (Fig. 2, Fig. 4). It points to the lack of expressed unfavourable changes in the lake Baikal pelagic.

<sup>1</sup> Lake Baikal is dimictic lake, characterized by two periods of stratification – inverted, when upper layer (0-50 m) of water has the temperature 0–1 ºC, layer 50-250 m – 1-4 ºC, direct, when temperature of upper layer decreases from 12 ºC at surface to 5-6 ºC at 50 m, layer 50-250 m – 4-5 ºC, and two overturns with temperature at 0-250 m is about 4 ºC. Below 250 m temperature is constant about 3,3 ºC.

Some Applications of Thermodynamics for Ecological Systems 331

February-April

0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0

0,0 50,0 100,0 150,0 200,0 250,0

0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0 160,0

0,0 50,0 100,0 150,0 200,0 250,0

different seasons.

1951

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Fig. 3. Long-term dynamics of total exergy (g detritus eq·m-3) of lake Baikal plankton for

1975

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R2 = 0,42

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1951

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May-June

1975

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Fig. 2. Long-term dynamics of year-average biomasses of components (mg·m-3), exergy (g detritus eq·m-3) and structural exergy of lake Baikal plankton. Dotted line – long-term average.

40,0 50,0 60,0 70,0 80,0 90,0

330 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

total biomass zooplankton biomass phytoplankton biomass

0,00 100,00 200,00 300,00 400,00 500,00 600,00 700,00 800,00 900,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0 100,0

0,0

average.

1951

1954

1957

1960

1963

1966

1969

1972

Fig. 2. Long-term dynamics of year-average biomasses of components (mg·m-3), exergy (g detritus eq·m-3) and structural exergy of lake Baikal plankton. Dotted line – long-term

1975

1978

1981

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50,0

100,0

150,0

200,0

250,0

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Structural exergy

1975

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Eco-Exergy

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R2 = 0,31

1987

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February-April

Fig. 3. Long-term dynamics of total exergy (g detritus eq·m-3) of lake Baikal plankton for different seasons.

Some Applications of Thermodynamics for Ecological Systems 333

while overturn seasons exergy is lower – 142,5 and 139,4 for spring and fall overturns. It means summer community is much more resistant to external disturbances than under-ice one, and during overturns Baikal is especially sensitive to pollution and other kinds of human impact. It is in good concordance with previously obtained results of our experiments with mathematical models (Silow et al., 1995, 2001; Silow, 1999) and

One of the characteristic features of ecosystems behaviour are cyclic changes of component biomasses and numbers. They are observed both in natural objects and in artificial ecosystems. Application of Lotka - Volterra and energy flow models to systems containing more than two components demonstrates reducing of oscillation amplitude and stabilization of components parameters at fixed levels (Limburg, 1985; Ruan, 2001; Mougi Nishimura, 2007). Some researchers make their systems to oscillate via chaotic (Stone & He,

Another fact hardly simulated with the use of existing approaches is "paradox of plankton" coexisting of two or more species in the same ecological niche (Hutchinson, 1961). To explain it researchers are forced to find any, though very small differences in ecological characteristics of these species, such as optimal temperatures or oxygen contents, growth rates, nutrient thresholds for growth, mortality (Ebenhöh, 1988), time and duration of mass development (Nikolaev, 1986), albeit the last can be not the cause but effect of coexistence.

> *<sup>X</sup> <sup>k</sup> XA* 2

 *constNXA* where *A* - food, *X* - component biomass, *N* - general organic matter content in closed system,

*dXXNkX*

This equation is identical to those used for description of autocatalytic processes, where component *X* serves as catalyst for self-creation from substance *A*. Such autocatalytic and self-reproduction units can be regarded in cycles called hypercycles (Eigen & Schuster,

Ecosystem also can be described as hypercycle, where every next trophic level obtains material from previous level to reproduce itself as autocatalyst. Example of such structure is given in Fig. 5. Phytoplankton obtains nutrients from bacteria to create organic matter with the use of external energy (solar irradiation). Zooplankton feeding on phytoplankton obtains organic matter for growth. Bacteriae in turn get food supply from zooplankton corpses and faeces. Of course, this scheme is idealized as bacteriae obtain food from

*<sup>A</sup> <sup>d</sup> <sup>X</sup>* (22)

)( . (23)

mesocosms (Silow et al., 1991; Silow & Oh, 2004).

2007) or stochastic (Abta et al., 2008) behaviour of its components.

Nicolis & Prigozhin (1977) basing on the following suggections:

*dt dX*

*k, d* - growth and death rate coefficients, obtained

**4. Hypercycles** 

**4.1 Description of models** 

1979).

Fig. 4. Long-term dynamics of structural exergy of lake Baikal plankton for different seasons.

As we know from above (sections 3.1, 3.2.4) structural exergy reflects ecosystem health and ability of it to withstand to external influences, e.g. human impact. It is seen from Fig. 4 average long-term under-ice structural exergy (157,2) is practically equal to long-term yearaverage (154,9), summer structural exergy (175,9) is sufficiently higher than year-average , while overturn seasons exergy is lower – 142,5 and 139,4 for spring and fall overturns. It means summer community is much more resistant to external disturbances than under-ice one, and during overturns Baikal is especially sensitive to pollution and other kinds of human impact. It is in good concordance with previously obtained results of our experiments with mathematical models (Silow et al., 1995, 2001; Silow, 1999) and mesocosms (Silow et al., 1991; Silow & Oh, 2004).

## **4. Hypercycles**

332 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

February-April

0,0 50,0 100,0 150,0 200,0 250,0

0,0 50,0 100,0 150,0 200,0 250,0

0,0 50,0 100,0 150,0 200,0 250,0

0,0 50,0 100,0 150,0 200,0 250,0

seasons.

1951

1953

1955

1957

1959

1961

1963

1965

1967

1969

Fig. 4. Long-term dynamics of structural exergy of lake Baikal plankton for different

1971

1973

As we know from above (sections 3.1, 3.2.4) structural exergy reflects ecosystem health and ability of it to withstand to external influences, e.g. human impact. It is seen from Fig. 4 average long-term under-ice structural exergy (157,2) is practically equal to long-term yearaverage (154,9), summer structural exergy (175,9) is sufficiently higher than year-average ,

1975

1977

1979

1981

1983

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1998

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May-June

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1998

One of the characteristic features of ecosystems behaviour are cyclic changes of component biomasses and numbers. They are observed both in natural objects and in artificial ecosystems. Application of Lotka - Volterra and energy flow models to systems containing more than two components demonstrates reducing of oscillation amplitude and stabilization of components parameters at fixed levels (Limburg, 1985; Ruan, 2001; Mougi Nishimura, 2007). Some researchers make their systems to oscillate via chaotic (Stone & He, 2007) or stochastic (Abta et al., 2008) behaviour of its components.

Another fact hardly simulated with the use of existing approaches is "paradox of plankton" coexisting of two or more species in the same ecological niche (Hutchinson, 1961). To explain it researchers are forced to find any, though very small differences in ecological characteristics of these species, such as optimal temperatures or oxygen contents, growth rates, nutrient thresholds for growth, mortality (Ebenhöh, 1988), time and duration of mass development (Nikolaev, 1986), albeit the last can be not the cause but effect of coexistence.

### **4.1 Description of models**

Nicolis & Prigozhin (1977) basing on the following suggections:

$$\begin{array}{c} A + X \xrightarrow{k} 2X\\ X \xrightarrow{d} X\\ A + X = N = \text{const} \end{array} \tag{22}$$

where *A* - food, *X* - component biomass, *N* - general organic matter content in closed system, *k, d* - growth and death rate coefficients, obtained

$$\frac{dX}{dt} = kX(N-X) - dX\,\,. \tag{23}$$

This equation is identical to those used for description of autocatalytic processes, where component *X* serves as catalyst for self-creation from substance *A*. Such autocatalytic and self-reproduction units can be regarded in cycles called hypercycles (Eigen & Schuster, 1979).

Ecosystem also can be described as hypercycle, where every next trophic level obtains material from previous level to reproduce itself as autocatalyst. Example of such structure is given in Fig. 5. Phytoplankton obtains nutrients from bacteria to create organic matter with the use of external energy (solar irradiation). Zooplankton feeding on phytoplankton obtains organic matter for growth. Bacteriae in turn get food supply from zooplankton corpses and faeces. Of course, this scheme is idealized as bacteriae obtain food from

Some Applications of Thermodynamics for Ecological Systems 335

fluctuations, cased by increase of community size and complexity (Fowler, 2009). It may be connected with the competition for resources (in our case – for nutrients, released by bacteria), as in many works similar results were obtained. For example, in system of two plant populations, competing for one nutrient (Damgaard, 2004), two predators, competing for one prey (Saleem et al., 2003; Yu et al., 2011), three microbial populations, competing for

> Phytopl ankton

> > Zooplan kton

Fig. 5. Idealized scheme of ecosystem as hypercycle. Blue arrows – flows of energy and matter between ecosystem components, green – self-reproduction of components, yellow arrow – income of low entropy (high exergy) energy from external source (Sun), dotted arrows – dissipation of energy in the form of high entropy (low exergy) heat energy.

It is now becoming clear that the movement away from thermodynamic equilibrium, and the subsequent increase in organization during ecosystem growth and development, is a result of system components and configurations that maximize the flux of useful energy and the amount of stored exergy. Both empirical data, as well as theoretical models, support these conclusions. Exergy is widely used in ecology to analyze theoretical problems and to solve applied tasks. The most perspective use of exergy parameters in recent ecology is the

resources (Li, 2001).

**5. Conclusion** 

use of them as ecosystem health indicators.

Bacterio plankton

phytoplankton extracellular products and dead phytoplankton cells, zooplankton can consume not only phytoplankton but also bacteriae etc. Nevertheless this scheme represents the most important ways of energy and matter transfer in closed ecosystem including producers, consumers and reducers. Dynamics of components is determined by following system of equations

$$\begin{aligned} \text{dx}\_1 \mid dt &= f(\mathbf{x}\_1, \boldsymbol{\mu}\_1, \boldsymbol{\phi}(\mathbf{x}\_3)) - \mathbf{g}(\mathbf{x}\_1, \boldsymbol{\phi}(\mathbf{x}\_2)), \\ \text{dx}\_2 \mid dt &= f(\mathbf{x}\_2, \boldsymbol{\mu}\_2, \boldsymbol{\phi}(\mathbf{x}\_1)) - m(\mathbf{x}\_2), \qquad . \end{aligned} \tag{24}$$

$$\text{dx}\_3 \mid dt = f(\mathbf{x}\_3, \boldsymbol{\mu}\_3, \boldsymbol{\phi}(\mathbf{x}\_2)) - m(\mathbf{x}\_3),$$

where *xi* - biomasses, *f* - growth functions, *m* - death functions, *g* - grazing function, effectiveness of energy and matter conversion (for phytoplankton - relation between bacteriae concentration and nutrients availability) between components, *φ* - effectiveness of grazing, - maximum growth rate. Indices *i* mean: 1 - phytoplankton, 2 - zooplankton, 3 bacteriae. Function parameters were calculated at the ecosystem stability condition *dxi/dt=0.*  Also we have investigated a system including two species of phytoplankton (*x11, x12*) competing for nutrient supply and two species of zooplankton (*x21, x22*), and bacteriae (Fig. 6). Starting biomasses for these newly introduced species at stability state were *x12=0,33·x11*, *x22=0,1·x21*. System was described by the following equations:

$$\begin{aligned} dx\_{11} &\wedge dt = f(\mathbf{x}\_{11}, \boldsymbol{\mu}\_{11}, \boldsymbol{\phi}(\mathbf{x}\_{3}), \tilde{\xi}(\mathbf{x}\_{11}, \mathbf{x}\_{12})) - \mathbf{g}(\mathbf{x}\_{11}, \boldsymbol{\phi}(\mathbf{x}\_{21})), \\ dx\_{12} &\wedge dt = f(\mathbf{x}\_{12}, \boldsymbol{\mu}\_{12}, \boldsymbol{\phi}(\mathbf{x}\_{3}), \tilde{\xi}(\mathbf{x}\_{12}, \mathbf{x}\_{11})) - \mathbf{g}(\mathbf{x}\_{12}, \boldsymbol{\phi}(\mathbf{x}\_{22})), \\ dx\_{21} &\wedge dt = f(\mathbf{x}\_{21}, \boldsymbol{\mu}\_{21}, \boldsymbol{\phi}(\mathbf{x}\_{11})) - m(\mathbf{x}\_{21}), \\ dx\_{22} &\wedge dt = f(\mathbf{x}\_{22}, \boldsymbol{\mu}\_{22}, \boldsymbol{\phi}(\mathbf{x}\_{12})) - m(\mathbf{x}\_{22}), \\ dx\_{3} &\wedge dt = f(\mathbf{x}\_{3}, \boldsymbol{\mu}\_{3}, \boldsymbol{\phi}(\mathbf{x}\_{21}, \mathbf{x}\_{22})) - m(\mathbf{x}\_{3}), \end{aligned} \tag{25}$$

where - competition for nutrients function.

### **4.2 Behaviour of models**

Dynamics of model (24) after external influence shows its returning to the stability point. Such behaviour is characteristic for stable non-linear systems (Gnauck, 1979).

There are no oscillations in this system, it always returns to stable state after initial biomasses changes. To make the system oscillate it is necessary to imitate input of nutrients or toxicants into it (Fig. 7). We can remind similar situation obtained by group of R. Pal et al. (2009). Their phytoplankton – zooplankton – nutrients model (with much more sophisticated mathematics, than ours) demonstrated oscillations under toxification. In other works oscillations of ecosystem components were caused by externally driven forces (oscillating environment) (Eladydi & Sacker, 2006; Koszalka et al., 2007). Hypercycles with not more than three components are shown to remain stable with equilibrium concentrations of components regardless with initial concentrations (Köppers, 1985).

Model (25) demonstrates oscillation behaviour around stability point but never reaches it (Fig. 8). It is in good accordance, e.g. with the biomass fluctuations and species population

phytoplankton extracellular products and dead phytoplankton cells, zooplankton can consume not only phytoplankton but also bacteriae etc. Nevertheless this scheme represents the most important ways of energy and matter transfer in closed ecosystem including producers, consumers and reducers. Dynamics of components is determined by following

), <sup>3</sup> ()) <sup>2</sup> (, <sup>3</sup> , <sup>3</sup> (/ <sup>3</sup>

where *xi* - biomasses, *f* - growth functions, *m* - death functions, *g* - grazing function,

effectiveness of energy and matter conversion (for phytoplankton - relation between bacteriae concentration and nutrients availability) between components, *φ* - effectiveness of

bacteriae. Function parameters were calculated at the ecosystem stability condition *dxi/dt=0.*  Also we have investigated a system including two species of phytoplankton (*x11, x12*) competing for nutrient supply and two species of zooplankton (*x21, x22*), and bacteriae (Fig. 6). Starting biomasses for these newly introduced species at stability state were *x12=0,33·x11*,

)), <sup>22</sup> (, <sup>12</sup> ()) <sup>11</sup> , <sup>12</sup> (), <sup>3</sup> (, <sup>12</sup> , <sup>12</sup> (/ <sup>12</sup>

Dynamics of model (24) after external influence shows its returning to the stability point.

There are no oscillations in this system, it always returns to stable state after initial biomasses changes. To make the system oscillate it is necessary to imitate input of nutrients or toxicants into it (Fig. 7). We can remind similar situation obtained by group of R. Pal et al. (2009). Their phytoplankton – zooplankton – nutrients model (with much more sophisticated mathematics, than ours) demonstrated oscillations under toxification. In other works oscillations of ecosystem components were caused by externally driven forces (oscillating environment) (Eladydi & Sacker, 2006; Koszalka et al., 2007). Hypercycles with not more than three components are shown to remain stable with equilibrium

*xfdtdx xxgxxx*

*xfdtdx xxgxxx*

)), <sup>21</sup> (, <sup>11</sup> ()) <sup>12</sup> , <sup>11</sup> (), <sup>3</sup> (, <sup>11</sup> , <sup>11</sup> (/ <sup>11</sup>


*xmxxfdtdx*

*x22=0,1·x21*. System was described by the following equations:

), <sup>3</sup> ()) <sup>22</sup> , <sup>21</sup> (, <sup>3</sup> , <sup>3</sup> (/ <sup>3</sup>

Such behaviour is characteristic for stable non-linear systems (Gnauck, 1979).

concentrations of components regardless with initial concentrations (Köppers, 1985).

Model (25) demonstrates oscillation behaviour around stability point but never reaches it (Fig. 8). It is in good accordance, e.g. with the biomass fluctuations and species population

*xmxxxfdtdx*


*xfdtdx xmx*

*xfdtdx xmx*

), <sup>22</sup> ()) <sup>12</sup> (, <sup>22</sup> , <sup>22</sup> (/ <sup>22</sup>

), <sup>21</sup> ()) <sup>11</sup> (, <sup>21</sup> , <sup>21</sup> (/ <sup>21</sup>

*xmxxfdtdx*

), <sup>2</sup> ()) <sup>1</sup> (, <sup>2</sup> , <sup>2</sup> (/ <sup>2</sup>

*xxgxxfdtdx*

)), <sup>2</sup> (, <sup>1</sup> ()) <sup>3</sup> (, <sup>1</sup> , <sup>1</sup> (/ <sup>1</sup>

. (24)


. (25)

system of equations

grazing,

where 

**4.2 Behaviour of models** 

fluctuations, cased by increase of community size and complexity (Fowler, 2009). It may be connected with the competition for resources (in our case – for nutrients, released by bacteria), as in many works similar results were obtained. For example, in system of two plant populations, competing for one nutrient (Damgaard, 2004), two predators, competing for one prey (Saleem et al., 2003; Yu et al., 2011), three microbial populations, competing for resources (Li, 2001).

Fig. 5. Idealized scheme of ecosystem as hypercycle. Blue arrows – flows of energy and matter between ecosystem components, green – self-reproduction of components, yellow arrow – income of low entropy (high exergy) energy from external source (Sun), dotted arrows – dissipation of energy in the form of high entropy (low exergy) heat energy.
