**3. Simulation of prokaryotic communities via the Haploid Evolutionary Constructor**

Through the use of the HEC software tool, we have simulated a number of biological models of the functioning and evolution of unicellular haploid organism communities [37]. Inter alia, the correspondence of the modeling results to biological data as well as previously published mathematical models has been illustrated. We estimated the key parameters of the model, regarding cell size, number of substrates required for cell division and other factors based on *E.coli* cell information [40].

replaceability. In case of non-compensatory nutrition strategy, the deficiency of any substrate cannot be compensated by the extra concentration of other substrates. This case satisfies

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It is known that the change of conditions on Earth shows a certain cyclism. Its sources are geophysical and astronomical cyclic processes [41,42]. As a result, the input of matter and energy into the ecosystem tends to change. To keep the common value of this flow constant, the ecosystem must conduct an evolutionary search for new sources of matter and energy [6,43]. Hence, the "learning ability" of the ecosystem becomes a critical parameter. The horizontal gene transfer (HGT) in prokaryotic populations is a relatively easy way to carry out such "learning". The simulation showed that the trophic structure of a community imposes substantive restrictions on the benefits of the HGT – a long-term effect is possible only in case of HGT between populations, whose metabolisms are sufficiently rich and flexibly adjustable (compensatory trophism). For populations with simplified metabolisms (non-compensatory trophism), the HGT offers only localized advantages. This contradicts the assumption that the major trend of prokaryotes evolution is individual genome simplification, compensated by relationship amplification in the bacterial community. Such simplification in the long term

The simulation showed dramatically better adaptivity of trophic rings with compensatory (ТRC) trophism in comparison with non-compensatory ones. The fixation of beneficial mutations even in one TRC population improved stability of the entire system, significantly extending its lifetime, i.e. offering an additional chance to wait out the starvation, or even completely saved the ТRS from extinction due to the metabolism optimization. Nevertheless, many taxa in the world are unable to compensate one resource with another on a broad scale. Why is the major trend of the evolution on Earth increasing biodiversity by means of progres‐ sive specialization, rather than the formation of biota based on several taxa-generalists? Let us assume that "learning ability" is a critical parameter for evolution within an ecosystem. Subsequently, in case of a low biodiversity level in an ecosystem with compensatory trophism, it is entirely possible that new sources of energy and matter will never be found. In fact, the probability of finding such sources is higher in ecosystems that preserve a high level of biodiversity until extinction. Then, if the value of the initial nutrient flow is recovered, a new source will be added, providing the ecosystem with resources for further progressive evolu‐ tion. Therefore, in the long term Liebig's systems have an advantage over Rubel's. It should be noted that this advantage has, as with all evolutionary processes, a nondeterministic, stochastic nature, while the stability of the advantage is determined. Thus, when biodiversity is high, the system may die out for stochastic reasons. This matches paleontological informa‐ tion. A permanent rotation of hegemonic biotas, without sacrificing comparably small amounts of epibiotic ecosystems, accumulating virtually the entire range of biochemical activities (cyanobacterium tufts, alkalophilic communities), is observed in the fossil records.

**3.2. Evolutionary trends of genome sophistication and simplification**

One of the most important periods in the evolution of life on Earth is eukaryotic cell formation [44]. The comparative study involving genome-wide information for bacteria, archaea and

Liebig's law of the minimum.

leads to the death of the community.

**Figure 7.** Scheme of the choice of the lysogenic or lytic scenarios.

To verify the modeling approach, a number of basic models were considered, and the obtained results confirmed correspondence to both classical models and experimental information [38]. Thus, the models examined proved the biological adequacy of the HEC and its applicability for a wide range of population, genetic and ecological problems.

### **3.1. Modeling of biodiversity dynamics and adaptability in bacterial communities**

The evolutionary success of a biological system relates to the balance of two characteristics: its stability (ability to preserve its structure and homeostasis despite changes in the environment) and its adaptability –ability to preserve an evolutionary flexibility in response to uncontrolled environmental changes. Traditionally, communities that are more complex are considered to be more stable, but there can be exceptions. The study of model dynamics, when the population size growth of one species depends on the population size of others species in the community, confirms that increased complexity leads to the improvement of stability only when commun‐ ity connectivity increases at the same time.

We maintained a comparative simulation of stability dynamics, the adaptability and biodi‐ versity of trophic closed communities with compensatory and non-compensatory metabolism (according to Rubel and Liebig respectively). The trophic strategies formulas representing these laws [eq.3,4] are mentioned in the HEC models description. The deficiency or low concentration of a nonspecific substrate in the environment leads to population extinction for both strategies. However, in case of compensatory nutrition strategy, the deficiency (a low concentration, but not a complete lack) of a nonspecific substrate in the environment can partly be compensated by the high concentration of specific substrates. This satisfies Rubel's law of replaceability. In case of non-compensatory nutrition strategy, the deficiency of any substrate cannot be compensated by the extra concentration of other substrates. This case satisfies Liebig's law of the minimum.

It is known that the change of conditions on Earth shows a certain cyclism. Its sources are geophysical and astronomical cyclic processes [41,42]. As a result, the input of matter and energy into the ecosystem tends to change. To keep the common value of this flow constant, the ecosystem must conduct an evolutionary search for new sources of matter and energy [6,43]. Hence, the "learning ability" of the ecosystem becomes a critical parameter. The horizontal gene transfer (HGT) in prokaryotic populations is a relatively easy way to carry out such "learning". The simulation showed that the trophic structure of a community imposes substantive restrictions on the benefits of the HGT – a long-term effect is possible only in case of HGT between populations, whose metabolisms are sufficiently rich and flexibly adjustable (compensatory trophism). For populations with simplified metabolisms (non-compensatory trophism), the HGT offers only localized advantages. This contradicts the assumption that the major trend of prokaryotes evolution is individual genome simplification, compensated by relationship amplification in the bacterial community. Such simplification in the long term leads to the death of the community.

The simulation showed dramatically better adaptivity of trophic rings with compensatory (ТRC) trophism in comparison with non-compensatory ones. The fixation of beneficial mutations even in one TRC population improved stability of the entire system, significantly extending its lifetime, i.e. offering an additional chance to wait out the starvation, or even completely saved the ТRS from extinction due to the metabolism optimization. Nevertheless, many taxa in the world are unable to compensate one resource with another on a broad scale. Why is the major trend of the evolution on Earth increasing biodiversity by means of progres‐ sive specialization, rather than the formation of biota based on several taxa-generalists? Let us assume that "learning ability" is a critical parameter for evolution within an ecosystem. Subsequently, in case of a low biodiversity level in an ecosystem with compensatory trophism, it is entirely possible that new sources of energy and matter will never be found. In fact, the probability of finding such sources is higher in ecosystems that preserve a high level of biodiversity until extinction. Then, if the value of the initial nutrient flow is recovered, a new source will be added, providing the ecosystem with resources for further progressive evolu‐ tion. Therefore, in the long term Liebig's systems have an advantage over Rubel's. It should be noted that this advantage has, as with all evolutionary processes, a nondeterministic, stochastic nature, while the stability of the advantage is determined. Thus, when biodiversity is high, the system may die out for stochastic reasons. This matches paleontological informa‐ tion. A permanent rotation of hegemonic biotas, without sacrificing comparably small amounts of epibiotic ecosystems, accumulating virtually the entire range of biochemical activities (cyanobacterium tufts, alkalophilic communities), is observed in the fossil records.

#### **3.2. Evolutionary trends of genome sophistication and simplification**

To verify the modeling approach, a number of basic models were considered, and the obtained results confirmed correspondence to both classical models and experimental information [38]. Thus, the models examined proved the biological adequacy of the HEC and its applicability

Infestation

Later, If environmental conditions become more optimal, partial transition of a population in lytic form is possible

Cells are in optimal conditions

Infected population Lytic cycle:

Part of cells perish (up to 100%), with phages raising.

Number of phages raised after lysis depends on virulence, which in its turn, is defined by alleles of phage genes.

The evolutionary success of a biological system relates to the balance of two characteristics: its stability (ability to preserve its structure and homeostasis despite changes in the environment) and its adaptability –ability to preserve an evolutionary flexibility in response to uncontrolled environmental changes. Traditionally, communities that are more complex are considered to be more stable, but there can be exceptions. The study of model dynamics, when the population size growth of one species depends on the population size of others species in the community, confirms that increased complexity leads to the improvement of stability only when commun‐

We maintained a comparative simulation of stability dynamics, the adaptability and biodi‐ versity of trophic closed communities with compensatory and non-compensatory metabolism (according to Rubel and Liebig respectively). The trophic strategies formulas representing these laws [eq.3,4] are mentioned in the HEC models description. The deficiency or low concentration of a nonspecific substrate in the environment leads to population extinction for both strategies. However, in case of compensatory nutrition strategy, the deficiency (a low concentration, but not a complete lack) of a nonspecific substrate in the environment can partly be compensated by the high concentration of specific substrates. This satisfies Rubel's law of

**3.1. Modeling of biodiversity dynamics and adaptability in bacterial communities**

for a wide range of population, genetic and ecological problems.

**Figure 7.** Scheme of the choice of the lysogenic or lytic scenarios.

ity connectivity increases at the same time.

Cells are in pessimal conditions

Infected population Lysogenic cycle:

122 Biodiversity - The Dynamic Balance of the Planet

Phage genes are appended to population genome (genetic spectra vector), which leads to a prophage origin.

Further lifecycle of infected population is the same with ordinary polymorphic population.

> One of the most important periods in the evolution of life on Earth is eukaryotic cell formation [44]. The comparative study involving genome-wide information for bacteria, archaea and

eukaryotes suggest that the microbial eukaryotic domains could not be inherited from the ancestors of mitochondria and plastids, but were borrowed from other bacteria [45]. In such a case, the origin of eukaryotes is a consequence of the autonomism of one member of the complex synotrophic prokaryotic community through the looping back of major regulatory interactions. It is considered that such autonomism is the result of symbiosis of several types of prokaryotes, and it is fairly probable that the entire series of HGT between symbionts took place.

**Final population size**

extinct, as did 12 other populations.

0,0E+00

1,0E+07

2,0E+07

3,0E+07

**Population size (cells)**

4,0E+07

5,0E+07

6,0E+07

7,0E+07

**Number Genotype (scheme)**

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1 P30 4.86 · 107

2 P24 4.85 · 107

3 P28 2.94 · 107

4 P23 2.94 · 107

5 P27 2.94 · 107


18-33 P2 0

18-33 P3 0

**Table 1.** The final distribution of the population sizes after long-term evolution (over 15000 generations) of the trophic system. In the genotype scheme, a green bar represents gene presence in this position (first 3 positions represent 1-3 specific genes of substrate utilization, latter 3 positions represent 1-3 specific genes of substrate synthesis). The table shows that the first and most populous populations are the populations with a "complete genome" P30, next are populations with an "almost complete genome". Some start populations (P1-P3) became

0 2500 5000 7500 10000 12500 15000

**Figure 9.** The evolution of a trophic system where new populations form due to HGT. After 7000-8000 generations,

populations with metabolically rich genomes that quickly replace other populations have formed.

**Time (generations)**

**Total size (individuals)**

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**level**

#### *3.2.1. Genome amplification*

By applying the HEC, we investigated the evolution of a community, which at the beginning of computations constituted a trophic ring, in which each of the three populations consumed and produced precisely one specific substrate. For example, the first population produced the substrate consumed by the second, and the second produced the substrate consumed by the third population, etc. (Figure 8).

**Figure 8.** The trophic ring scheme consisted of three populations at start time (left) and after 15000 generations (right).

During calculations with a certain probability between cells of different populations (10-7 per generation per cell), HGT could take place. As a result, new populations, either consuming a larger number of specific substrates or producing a larger number of specific products would be formed. It was found, that in the longer term (after 10000–15000 generations), the population with the "most complete genome" (i.e. populations consuming and producing the maximum possible number of specific substrates in the given trophic system), or the population with an "almost complete genome" gain an extreme biomass advantage at the specified conditions. Namely, at modetare genome-length-penalty level values (0.01-0.05), and with stable poor environmental conditions (nonspecific substrate concentration in the inflow is around 10-4 mM, i.e. at the survival minimum for parent population cells) (Table 1). In the long-term, such populations replaced all other populations from the trophic system ("outsider" populations either died or reached a maximum number in the environment that hovered around 10-100 individuals) (Figure 9).

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eukaryotes suggest that the microbial eukaryotic domains could not be inherited from the ancestors of mitochondria and plastids, but were borrowed from other bacteria [45]. In such a case, the origin of eukaryotes is a consequence of the autonomism of one member of the complex synotrophic prokaryotic community through the looping back of major regulatory interactions. It is considered that such autonomism is the result of symbiosis of several types of prokaryotes, and it is fairly probable that the entire series of HGT between symbionts took

By applying the HEC, we investigated the evolution of a community, which at the beginning of computations constituted a trophic ring, in which each of the three populations consumed and produced precisely one specific substrate. For example, the first population produced the substrate consumed by the second, and the second produced the substrate consumed by the

**Figure 8.** The trophic ring scheme consisted of three populations at start time (left) and after 15000 generations

During calculations with a certain probability between cells of different populations (10-7 per generation per cell), HGT could take place. As a result, new populations, either consuming a larger number of specific substrates or producing a larger number of specific products would be formed. It was found, that in the longer term (after 10000–15000 generations), the population with the "most complete genome" (i.e. populations consuming and producing the maximum possible number of specific substrates in the given trophic system), or the population with an "almost complete genome" gain an extreme biomass advantage at the specified conditions. Namely, at modetare genome-length-penalty level values (0.01-0.05), and with stable poor environmental conditions (nonspecific substrate concentration in the inflow is around 10-4 mM, i.e. at the survival minimum for parent population cells) (Table 1). In the long-term, such populations replaced all other populations from the trophic system ("outsider" populations either died or reached a maximum number in the environment that hovered around 10-100

15000 generations

P3 P2

S3

S2 N

P25

P21 P22 P23 P24

P26 P27 P28 P29

> P17 P18 P19

P20 P14

P32 P31

P15 P16

P13 P12 P11 P10 P9 P8 P7 P6 P5 P4

P1

P30

P33

S1

place.

*3.2.1. Genome amplification*

124 Biodiversity - The Dynamic Balance of the Planet

third population, etc. (Figure 8).

N

S1 S2

S3

individuals) (Figure 9).

P1

P3

(right).

P2

**Table 1.** The final distribution of the population sizes after long-term evolution (over 15000 generations) of the trophic system. In the genotype scheme, a green bar represents gene presence in this position (first 3 positions represent 1-3 specific genes of substrate utilization, latter 3 positions represent 1-3 specific genes of substrate synthesis). The table shows that the first and most populous populations are the populations with a "complete genome" P30, next are populations with an "almost complete genome". Some start populations (P1-P3) became extinct, as did 12 other populations.

**Figure 9.** The evolution of a trophic system where new populations form due to HGT. After 7000-8000 generations, populations with metabolically rich genomes that quickly replace other populations have formed.

#### *3.2.2. Genome simplification*

We have also simulated the processes of gene loss due to a higher genome-length penalty (0.1-0.25) for the environment in which a single metabolically complete population is presented ab initio (the genetic analogue of P30 from Table 1). During the iteration process, both gene loss and HGT compensating deletions could occur. It was demonstrated, that a strong genome reproduction tendency is observed in both suitable and unsuitable environmental conditions. The most primitive populations, possessing just two utilization genes (one for nonspecific and the other for specific substrates), replaced other populations.

Therefore, the selective advantage of the "metabolically rich" populations emerged under pessimal conditions and was a combination of autonomism (lower dependence on specific substrate concentration in the environment) and egoism (cells of an autonomous population on average secrete less specific substrates into the environment and consume them independ‐ ently). The selection supports autonomizing populations, however their formation causes the degradation of the trophic ring into an alliance of autonomous populations, accompanied by a "trail" of small nonautonomous populations. The simulation showed that HGT, in case of poor environmental conditions, actually transforms the collective metabolism of a trophic ring to the metabolism of separate populations, which in general conforms the scenario [46] of eukaryotes formation in symbiogenesis.

However, if conditions are optimal, cells reduced their genome successfully, as well as reducing the time necessary for the reproduction. This fact was observed during the experi‐ ment repeatedly [47,48].

#### **3.3. Evolutionary trends in prokaryotic communities influenced by phages**

To study phage infection influence on possible evolutionary tendencies, models of prokaryotic community infection were constructed. The model from 2.2 (a trophic ring consisting of three populations) was used as a basic model. The horizontal transfer and gene loss processes were stochastically generated during simulations. The addition of a phage population to the community led to an infestation of all populations, while the proportion of infected cells depended on the phage concentration in the environment. The infection fundamentally changed the dynamics of the community, inhibiting the growth or even destroying fast growing populations (following the infection of a lytic pathway), and as a result supported less competitive populations in such conditions. For example, a series of numerical experi‐ ments showed that, in pessimal conditions, environments can displace the populations that are far from having a metabolically complete genome (Figure 10). This presents a contrast to the tendency of genome amplification in such conditions as noted above (ref. 2.2).

It should be noted that the given results of numerical simulations are stochastic in nature. In a number of numeric experiments, infection led to death of the entire community, or the community died before the infection due to the fast growth of unduly primitive populations. Changes in evolutionary tendencies do not always take place either. Consequently, our results show that phage infection of a community can, but does not necessarily, change its evolution‐

**Figure 11.** Population size dynamics of a community in optimal conditions. For some time species formation takes place within the system due to HGT and gene loss, but at the 10000th iteration an infection occurs. Shortly afterwards, all populations become extinct, except the population with a metabolically complete genome infected by the phage.

**Figure 10.** Population size dynamics in pessimal environmental conditions. For some, a species formation takes place in the system due to HGT and gene loss, but an infection occurred at the 10000th iteration. Shortly afterwards, most of the populations became extinct. Surviving populations did not have a metabolically complete genome. Furthermore, among the survivors there were populations with extremely primitive genomes (lower scheme in figure). In the ge‐

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nome figures, the black bar represents the phage gene, i.e. all survived populations are phage carriers.

**3.4. Simulation of prokaryotic communities implementing synthesis strategy according to**

The model of genetic regulation of protein biosynthesis (Figure 12), suggested by F.Jacob and J. Monod [49], and mathematically studied by D.S. Chernavsky and his colleagues [50], is of a

ary tendency.

trigger nature.

**the molecular triggers principle**

Possible changes in evolutionary tendencies in case of a phage infection have also been discovered for communities in optimal environmental conditions. Figure 11 shows the survival of a population with a metabolically complete genome – the worst adapted population in the community before the moment of infection. The periodic nature of both prokaryotic and phage population size curves is explained by spontaneous transition of a part of cells to a lytic form, followed by death or the forming of new phages due to lysis.

*3.2.2. Genome simplification*

126 Biodiversity - The Dynamic Balance of the Planet

We have also simulated the processes of gene loss due to a higher genome-length penalty (0.1-0.25) for the environment in which a single metabolically complete population is presented ab initio (the genetic analogue of P30 from Table 1). During the iteration process, both gene loss and HGT compensating deletions could occur. It was demonstrated, that a strong genome reproduction tendency is observed in both suitable and unsuitable environmental conditions. The most primitive populations, possessing just two utilization genes (one for nonspecific and

Therefore, the selective advantage of the "metabolically rich" populations emerged under pessimal conditions and was a combination of autonomism (lower dependence on specific substrate concentration in the environment) and egoism (cells of an autonomous population on average secrete less specific substrates into the environment and consume them independ‐ ently). The selection supports autonomizing populations, however their formation causes the degradation of the trophic ring into an alliance of autonomous populations, accompanied by a "trail" of small nonautonomous populations. The simulation showed that HGT, in case of poor environmental conditions, actually transforms the collective metabolism of a trophic ring to the metabolism of separate populations, which in general conforms the scenario [46] of

However, if conditions are optimal, cells reduced their genome successfully, as well as reducing the time necessary for the reproduction. This fact was observed during the experi‐

To study phage infection influence on possible evolutionary tendencies, models of prokaryotic community infection were constructed. The model from 2.2 (a trophic ring consisting of three populations) was used as a basic model. The horizontal transfer and gene loss processes were stochastically generated during simulations. The addition of a phage population to the community led to an infestation of all populations, while the proportion of infected cells depended on the phage concentration in the environment. The infection fundamentally changed the dynamics of the community, inhibiting the growth or even destroying fast growing populations (following the infection of a lytic pathway), and as a result supported less competitive populations in such conditions. For example, a series of numerical experi‐ ments showed that, in pessimal conditions, environments can displace the populations that are far from having a metabolically complete genome (Figure 10). This presents a contrast to

**3.3. Evolutionary trends in prokaryotic communities influenced by phages**

the tendency of genome amplification in such conditions as noted above (ref. 2.2).

followed by death or the forming of new phages due to lysis.

Possible changes in evolutionary tendencies in case of a phage infection have also been discovered for communities in optimal environmental conditions. Figure 11 shows the survival of a population with a metabolically complete genome – the worst adapted population in the community before the moment of infection. The periodic nature of both prokaryotic and phage population size curves is explained by spontaneous transition of a part of cells to a lytic form,

the other for specific substrates), replaced other populations.

eukaryotes formation in symbiogenesis.

ment repeatedly [47,48].

**Figure 10.** Population size dynamics in pessimal environmental conditions. For some, a species formation takes place in the system due to HGT and gene loss, but an infection occurred at the 10000th iteration. Shortly afterwards, most of the populations became extinct. Surviving populations did not have a metabolically complete genome. Furthermore, among the survivors there were populations with extremely primitive genomes (lower scheme in figure). In the ge‐ nome figures, the black bar represents the phage gene, i.e. all survived populations are phage carriers.

**Figure 11.** Population size dynamics of a community in optimal conditions. For some time species formation takes place within the system due to HGT and gene loss, but at the 10000th iteration an infection occurs. Shortly afterwards, all populations become extinct, except the population with a metabolically complete genome infected by the phage.

It should be noted that the given results of numerical simulations are stochastic in nature. In a number of numeric experiments, infection led to death of the entire community, or the community died before the infection due to the fast growth of unduly primitive populations. Changes in evolutionary tendencies do not always take place either. Consequently, our results show that phage infection of a community can, but does not necessarily, change its evolution‐ ary tendency.

#### **3.4. Simulation of prokaryotic communities implementing synthesis strategy according to the molecular triggers principle**

The model of genetic regulation of protein biosynthesis (Figure 12), suggested by F.Jacob and J. Monod [49], and mathematically studied by D.S. Chernavsky and his colleagues [50], is of a trigger nature.

This model describes a system consisting of two genes, G1 and G2, which synthesize regulators P1 and P2, which are suppressors of G2 and G1 respectively. This genetic system has at least two stable stationary states – gene G1 or gene G2 is expressed within the system. The probability of transit (a switch) from one stationary state to another is caused by disturbing factors (for example, by adding of one of the regulators to the system), which enables us to suggest the trigger nature of this system.

We have conducted a series of computer simulations and have illustrated the possibility of a trigger mode appearing in this model, depending on the gene network parameter values [eq. 7], and physiological, population and ecological parameters.We have demonstrated that the modes of gene networks functioning inside the organism taking into account restrictions on organism, population and ecological levels, may considerably differ from the modes predicted based on analysis of mathematical models of these networks. For instance, in the molecular trigger model [eq.7] the saddle point (S1=S2=c) is an unstable stationary state. However, in our model we showed the probability of the system stabilizing precisely in such a state despite the fact that the initial data differed from this state. Such stabilization is possible due to additional factors, including limited cell wall permeability, which limits the effect of substrate switchers.

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As can be seen from the above, the models we built suggest an **additional epigenetic mecha‐ nism of the functioning mode stability of persistence gene networks**. Such mechanisms were theoretically and experimentally developed by, for example, R.N. Tchuraev and colleagues [52,53]. Via our models, we have also obtained examples the stability persistence of gene network functioning. That is true even in cases when the gene network structure in itself supposes both the presence of several such modes. The possibility of switching between these modes have also been obtained through this models. **Such mechanisms can, on the one hand, explain the "nonworking" of artificial genetic constructions during experiments, when they should work according to the calculations** *in silico*. On the other hand, these mechanisms are

The "Haploid Evolutionary Constructor" (HEC) software provides modeling of evolutionary and population processes in prokaryotic communities adjusted for the genetic structure of the population, trophic relationships between populations and the influence of environmental conditions (Figure 13). The special feature of the HEC is the approach that enables the modeling of structure variable systems, which in fact provides for the possibility to vary the number of populations, genes, and other variables and parameters immediately during simulations. This makes it possible to model the processes of the gene loss and horizontal transfer between cells, as well as the companion processes of speciation. Together, they open up possibilities for the modeling of bacterial community evolution and their population and ecological dynamics.

We have compared two trophic strategies of prokaryotes: compensatory and non-compensa‐ tory nutrition. It has been shown that compensatory systems are more stable under hard environmental conditions. The beneficial mutations in such prokaryotic communities often extend the lifetime of the community significantly. The compensatory systems are more stable in continuously varying conditions from the viewpoint of preserving and growing biomass, while the non-compensatory systems are more stable when it comes to conserving biodiversity [54]. In this way, both strategies have their evolutionary advantages and disadvantages.

of significant evolutionary importance and require further study.

**4. Conclusion**

Neither of them dominate absolutely.

**Figure 12.** Scheme of synthesis of two enzymes according to Jacob and Monod.

By applying the HEC, a model of a trophic community with one nonspecific substrate N1, consisting of one population and synthesizing two specific substrates S1 and S2 has been built. The synthesis constants for these substrates are noted as *d1* and *d2* respectively. The synthesis strategy for the cells in the population is described through the gene network – the molecular trigger. The mathematical model of the corresponding gene network is given below [eq.7]. Liebig's non-compensatory strategy has been used as the trophic strategy.

$$\begin{cases} \frac{dS\_i}{dt} = \underbrace{\frac{\overline{d}\_i}{\mathbf{1} + \mathbf{S}\_j^{\overline{\gamma}}}}\_{\mathbf{1} + \mathbf{S}\_j^{\overline{\gamma}}} - \mathbf{S}\_i\\ \frac{dS\_j}{dt} = \underbrace{\frac{\overline{d}\_j}{\mathbf{1} + \mathbf{S}\_j^{\overline{\gamma}}}}\_{\mathbf{1} + \mathbf{S}\_j^{\overline{\gamma}}} - \mathbf{S}\_j \end{cases} \tag{7}$$

Where *di* ¯and *<sup>d</sup> <sup>j</sup>* ¯ – are mean values of the *di* and *dj* traits in the population.

The parametric analysis of this model has been reported in many studies e.g. in [51]. In particular, it is shown that if γ≥2 and certain values of *di* ¯/*<sup>d</sup> <sup>j</sup>* ¯ *>g*, the system takes on the properties of trigger. There are two stable critical points on the phase plane of the system, between which a labile saddle point is situated. The meaning of the g parameter is bifurca‐ tional, while the bifurcation is of a trigger nature (saddle forms).

We have conducted a series of computer simulations and have illustrated the possibility of a trigger mode appearing in this model, depending on the gene network parameter values [eq. 7], and physiological, population and ecological parameters.We have demonstrated that the modes of gene networks functioning inside the organism taking into account restrictions on organism, population and ecological levels, may considerably differ from the modes predicted based on analysis of mathematical models of these networks. For instance, in the molecular trigger model [eq.7] the saddle point (S1=S2=c) is an unstable stationary state. However, in our model we showed the probability of the system stabilizing precisely in such a state despite the fact that the initial data differed from this state. Such stabilization is possible due to additional factors, including limited cell wall permeability, which limits the effect of substrate switchers.

As can be seen from the above, the models we built suggest an **additional epigenetic mecha‐ nism of the functioning mode stability of persistence gene networks**. Such mechanisms were theoretically and experimentally developed by, for example, R.N. Tchuraev and colleagues [52,53]. Via our models, we have also obtained examples the stability persistence of gene network functioning. That is true even in cases when the gene network structure in itself supposes both the presence of several such modes. The possibility of switching between these modes have also been obtained through this models. **Such mechanisms can, on the one hand, explain the "nonworking" of artificial genetic constructions during experiments, when they should work according to the calculations** *in silico*. On the other hand, these mechanisms are of significant evolutionary importance and require further study.
