**4. Conclusion**

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

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].

*<sup>γ</sup>* - *Si*

*<sup>γ</sup>* - *S <sup>j</sup>*

and *dj*

The parametric analysis of this model has been reported in many studies e.g. in [51]. In

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‐

*mRNA2*

(7)

¯/*<sup>d</sup> <sup>j</sup>* ¯ *>g*, the system takes on the

traits in the population.

*mRNA1*

trigger nature of this system.

128 Biodiversity - The Dynamic Balance of the Planet

Where *di*

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

Liebig's non-compensatory strategy has been used as the trophic strategy.

*dt* <sup>=</sup> *di* ¯ 1 + *S <sup>j</sup>*

{ *d Si*

¯and *<sup>d</sup> <sup>j</sup>* ¯ – are mean values of the *di*

particular, it is shown that if γ≥2 and certain values of *di*

tional, while the bifurcation is of a trigger nature (saddle forms).

*d S <sup>j</sup> dt* <sup>=</sup> *<sup>d</sup> <sup>j</sup>* ¯ 1 + *Si* 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. Neither of them dominate absolutely.

We have studied the importance of gene horizontal transfer and loss during the evolution of the prokaryotic communities depending on ecological conditions. The models have shown the genesis of autonomous populations with rich intrinsic cellular metabolism in pessimal conditions. However, their genome is unstable, and the metabolically complete populations lose genes if conditions improve. This evolutionary tendency may be overcome by the addition of phages to the system. Moreover, the result is of a stochastic nature. We suggest that this shows the potential role of bacteriophages in the genesis of eukaryotes [55].

**Abbreviations**

HEC – Haploid Evolutionary Constructor

Sergey A. Lashin1,2\*, Yury G. Matushkin1

US89468.xml;US8818555

\*Address all correspondence to: lashin@bionet.nsc.ru

This work is supported by the following grants:VI.61.1.2,Russian Foundation for Basic

Evolution, Biodiversity and Ecology in Microbial Communities: Mathematical Modeling and Simulation with…

1 Department of Systems Biology, Institute of Cytology and Genetics, Novosibirsk, Russia

2 Faculty of Natural Science, Novosibirsk State University, Novosibirsk, Russia

[1] Kamshilov MM. Evolution of the Biosphere. Mir Publishers; 1976. p. 269.

[3] Zherikhin V V. Biocoenotic regulation of evolution. Paleontol. J. 1986;(1):3–12.

[4] Odum EP. Basic ecology. Saunders College Pub.; 1983 [cited 2013 Nov 5]; Available from: http://agris.fao.org/agris-search/search/display.do?f=1989/US/

[5] Begon M, Harper J, Townsend C. Ecology. In 2 volumes Мoscow: Mir. 1989 [cited 2013 Nov 5]; Available from: http://scholar.google.ru/scholar?clus‐

[6] Vernadsky V. Chemical Structure of the Earth's Biosphere and Its Environment. 1965 [cited 2013 Nov 5]; Available from: http://scholar.google.ru/scholar?clus‐

[2] Margalef R. The Looks of the Biosphere. Мoscow: Nauka; 1992.

ter=6815279472378442327&hl=ru&as\_sdt=2005&sciodt=0,5#0

ter=3535744253151054862&hl=ru&as\_sdt=2005&sciodt=0,5#0

, Alexandra I. Klimenko1,2, Valentin V. Suslov1

and

http://dx.doi.org/10.5772/58302

131

Research (12-07-00671, 13-04-00620),SB RAS integration project №47.

HGT – Horizontal Gene Transfer

**Acknowledgements**

**Author details**

**References**

Nikolay A. Kolchanov1,2

The study of a trigger-type gene network (two mutually repressing operons) has shown that special characteristics of intracellular factors are able to stabilize states that are defined as being unstable during the mathematical analysis of continuous gene network models. Therefore, alongside ecological and population genetics modeling, the HEC can be used for research on the competition and evolution of gene networks in populations, as well as for the optimization of gene network parameters for certain environmental conditions. The gene network model can be described as a synthesis strategy, while the criterion of optimality and selection mechanisms are trophic strategies.

**Figure 13.** Graphical user interface of the HEC.
