**1. Introduction**

Life on Earth exists in the form of interacting communities of two types: populations and ecosystems. Populations maintain reproduction and Darwinian selection. Substance and energy exchange both with the environment and between populations is one of the major functions of ecosystems, which, as a result, enables the necessary conditions for organism reproduction [1–3]. Consequently, it is reasonable to consider any evolutionary process both in terms of population and in terms of ecosystems. Therefore, the evolutionary success of any given genotype carrier is related not only to fixation in population, but also the influence of such a population on functioning of the ecosystem. It is impossible to understand patterns of certain species' evolution without considering the trophic structure of the ecosystem, as a part of which they exist. An ecosystem enables the sparing use of environmental resources by setting up various linear or branched trophic chains [4]. When several linear chains or their branches integrate, a trophic cycle can arise, which enables reproduction of one or another resource [5–7]. On the other hand, an unusable resource – a metabolic cul-de-sac – can arise in ecosystems, which is buried or removed by the flow [8–10].

Symbiotic relationships are widespread in ecosystems, and especially specific to prokaryot‐ ic communities. These communities often have taxonomical diversity and are character‐ ized by a complicated trophic chain with a certain extent of closeness. Specific traits of

© 2014 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

prokaryotes, such as a pinotrophy diet, small cell size and low speed, lead to an organ‐ ism's inability to escape from the surrounding environment quickly, and to the "biogenic desert" problem [11], when organisms that inhabit the center of a high-density popula‐ tion have to go hungry due to lack of nutrients. Therefore, the characteristic feature of prokaryotic ecosystems is **metabolism integration** – from the close association of single organisms of different species [12] to spatially-structured, trophically highly-closed ecosystems of meromictic [13] and soda lakes [14], and, after all, global biogeochemical cycles of the biosphere [15]. The large majority of prokaryotes in nature exist as a part of communities with a complicated structure – bacterial mats or biofilms, whose common metabolite pool often forms a complete cycle [15,16]. The presence of such cycles optimiz‐ es community members' metabolism. Trophic rings, within which metabolic products of one species or strain are used or can in certain conditions be used for food by others, are revealed in bacterial biofilms and in complex metabolic graphs, reconstructed on the basis of metagenomic projects [17,18].

population simultaneously. However, it should be noted that the large majority of these methods (like the other population genetics methods) are focused on diploid organism

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

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

113

Methods of "portrait" (individual-oriented, agent-based) modeling [34–36] bridge the gap between individual characteristics and community structure, evolving as a consequence of some or other rules of interactions between individuals. These approaches are illustrative enough, but may have a high computational complexity (ideally, they require a detailed description of every individual in the population). Besides, most of them are static, i.e. during calculations their structure can be changed only within the limits predetermined by the developer. As a result, if modern computer capacity is sufficient for modeling of a population of diploid organisms with sexual reproduction (whereas the effective size of such populations is generally no more than 100-1000 individuals), then direct simulation modeling is often problematic for the modeling of a population of haploid organisms, particularly bacteria (the


where the number of alleles can be changed during the simulation process.

**2. Haploid Evolutionary Constructor methodology description**

With due consideration to the abovementioned requirements of the evolutionary and popu‐ lation process modeling tool, we previously developed a modeling method and software package "Haploid evolutionary constructor" (HEC) [37,38]. The HEC provides tools to simulate the functioning of a haploid organism population network, trophically linked with substrate-product relationships under the environmental effect. This modeling approach provides a means of simultaneously describing the prokaryotic community at various levels of its biological organization: genetic, metabolic, population and ecological, flexibly varying the degree of description detail at any level. During the model simulation, each population may vary both its size and genetic diversity due to selection and mutations. The key feature of this methodology is the ability to model such evolutionary and population processes that require an intense structure rearrangement of a model during simulation. Such processes contain, for example, horizontal genetic transfer and speciation. Besides, the methodology offers the possibility to describe the polymorphism of one or several genes in a population,

In summary, the HEC provides comprehensive study of the bacterial community model, analyzing the dynamics of changes in allelic frequency, the population size, the concentration of metabolites, the community trophic structure and its evolution, including stochastic genetic

During model simulation via the HEC, the number of populations reached 300, with an approximate total 1020 individuals, the size of distinct population came to 1018, with around

The HEC methodology provides modeling and simulation of biological and evolutionary processes in trophically linked communities of unicellular haploid organisms. Figure 1 shows

– 107 different genotypes (up to 4000–15000 different genotypes within one population in

individuals).

population modeling (generally, with sexual reproduction).

effective size of bacterial populations is 106

case of multiple polymorphism of 10–15 genes).

factors.

106

Close bacterial association in biofilms enhances the probability of horizontal gene transfer between different bacteria, which enable them to obtain new features [19–21]. The impor‐ tance of the horizontal transfer is supported by recently discovered natural vectors for cloning exogenes in prokaryotic genomes – integrons and superitegrons [22,23]. There‐ fore, most prokaryotes exist as a part of communities. A wide variety of prokaryotes are unable to grow in pure culture (uncultured prokaryotes) confirms this [24]. The evolution of such highly-integrated communities has its qualitative specific factors and cannot be reduced to the evolution of distinct populations composing them. Thus, while the reproduc‐ tion rate of prokaryotes is exceptionally high, an experimental study of prokaryotic evolution is difficult, as it requires the study of the whole prokaryotic community. Accordingly, the mathematical modeling of evolutionary processes, adjusted for different types of trophic interactions, spatial distribution of organisms, genetic structure of popula‐ tions, speciation, different reproduction schemes, environmental influence and other factors, is one of the main methods for the study of the evolutionary process. The modeling of evolution is one of the primary challenges of 21st century biology, mathematics and computer science.

Traditional approaches to evolutionary and population process modeling include meth‐ ods of population dynamics [25,26] and methods of population genetics [27,28]. Popula‐ tion dynamics modeling methods describe population size changes through time subject to environmental conditions, trophic interactions between populations and other features, but as a rule, population genetic structure changes cannot be studied using these methods. As to population genetics methods, they are generally based on methods of the probability theory and mathematical statistics [29–31]. They allow for studying the evolution of population genetic structure, but do not provide means for the modeling of the popula‐ tion dynamics process in detail.

Further development of modeling and simulation methods led to so-called "hybrid" methods [32,33], which allow us to investigate changes both in the size and genetic structure of a population simultaneously. However, it should be noted that the large majority of these methods (like the other population genetics methods) are focused on diploid organism population modeling (generally, with sexual reproduction).

prokaryotes, such as a pinotrophy diet, small cell size and low speed, lead to an organ‐ ism's inability to escape from the surrounding environment quickly, and to the "biogenic desert" problem [11], when organisms that inhabit the center of a high-density popula‐ tion have to go hungry due to lack of nutrients. Therefore, the characteristic feature of prokaryotic ecosystems is **metabolism integration** – from the close association of single organisms of different species [12] to spatially-structured, trophically highly-closed ecosystems of meromictic [13] and soda lakes [14], and, after all, global biogeochemical cycles of the biosphere [15]. The large majority of prokaryotes in nature exist as a part of communities with a complicated structure – bacterial mats or biofilms, whose common metabolite pool often forms a complete cycle [15,16]. The presence of such cycles optimiz‐ es community members' metabolism. Trophic rings, within which metabolic products of one species or strain are used or can in certain conditions be used for food by others, are revealed in bacterial biofilms and in complex metabolic graphs, reconstructed on the basis

Close bacterial association in biofilms enhances the probability of horizontal gene transfer between different bacteria, which enable them to obtain new features [19–21]. The impor‐ tance of the horizontal transfer is supported by recently discovered natural vectors for cloning exogenes in prokaryotic genomes – integrons and superitegrons [22,23]. There‐ fore, most prokaryotes exist as a part of communities. A wide variety of prokaryotes are unable to grow in pure culture (uncultured prokaryotes) confirms this [24]. The evolution of such highly-integrated communities has its qualitative specific factors and cannot be reduced to the evolution of distinct populations composing them. Thus, while the reproduc‐ tion rate of prokaryotes is exceptionally high, an experimental study of prokaryotic evolution is difficult, as it requires the study of the whole prokaryotic community. Accordingly, the mathematical modeling of evolutionary processes, adjusted for different types of trophic interactions, spatial distribution of organisms, genetic structure of popula‐ tions, speciation, different reproduction schemes, environmental influence and other factors, is one of the main methods for the study of the evolutionary process. The modeling of evolution is one of the primary challenges of 21st century biology, mathematics and

Traditional approaches to evolutionary and population process modeling include meth‐ ods of population dynamics [25,26] and methods of population genetics [27,28]. Popula‐ tion dynamics modeling methods describe population size changes through time subject to environmental conditions, trophic interactions between populations and other features, but as a rule, population genetic structure changes cannot be studied using these methods. As to population genetics methods, they are generally based on methods of the probability theory and mathematical statistics [29–31]. They allow for studying the evolution of population genetic structure, but do not provide means for the modeling of the popula‐

Further development of modeling and simulation methods led to so-called "hybrid" methods [32,33], which allow us to investigate changes both in the size and genetic structure of a

of metagenomic projects [17,18].

112 Biodiversity - The Dynamic Balance of the Planet

computer science.

tion dynamics process in detail.

Methods of "portrait" (individual-oriented, agent-based) modeling [34–36] bridge the gap between individual characteristics and community structure, evolving as a consequence of some or other rules of interactions between individuals. These approaches are illustrative enough, but may have a high computational complexity (ideally, they require a detailed description of every individual in the population). Besides, most of them are static, i.e. during calculations their structure can be changed only within the limits predetermined by the developer. As a result, if modern computer capacity is sufficient for modeling of a population of diploid organisms with sexual reproduction (whereas the effective size of such populations is generally no more than 100-1000 individuals), then direct simulation modeling is often problematic for the modeling of a population of haploid organisms, particularly bacteria (the effective size of bacterial populations is 106 -109 individuals).

With due consideration to the abovementioned requirements of the evolutionary and popu‐ lation process modeling tool, we previously developed a modeling method and software package "Haploid evolutionary constructor" (HEC) [37,38]. The HEC provides tools to simulate the functioning of a haploid organism population network, trophically linked with substrate-product relationships under the environmental effect. This modeling approach provides a means of simultaneously describing the prokaryotic community at various levels of its biological organization: genetic, metabolic, population and ecological, flexibly varying the degree of description detail at any level. During the model simulation, each population may vary both its size and genetic diversity due to selection and mutations. The key feature of this methodology is the ability to model such evolutionary and population processes that require an intense structure rearrangement of a model during simulation. Such processes contain, for example, horizontal genetic transfer and speciation. Besides, the methodology offers the possibility to describe the polymorphism of one or several genes in a population, where the number of alleles can be changed during the simulation process.

In summary, the HEC provides comprehensive study of the bacterial community model, analyzing the dynamics of changes in allelic frequency, the population size, the concentration of metabolites, the community trophic structure and its evolution, including stochastic genetic factors.

During model simulation via the HEC, the number of populations reached 300, with an approximate total 1020 individuals, the size of distinct population came to 1018, with around 106 – 107 different genotypes (up to 4000–15000 different genotypes within one population in case of multiple polymorphism of 10–15 genes).
