Comparative analysis of some models of gene regulation in mixed-substrate microbial growth

Mixed-substrate microbial growth is of fundamental interest in microbiology and bioengineering. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in diauxic growth. In this work, we compare the dynamics of three such models (Narang, 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121; Thattai and Shraiman, 2003. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85(2), 744-754; Brandt et al., 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38, 1004-1013). We show that these models are dynamically similar--the initial motion of the inducible enzymes in all the models is described by the Lotka-Volterra equations for competing species. In particular, the prediction of diauxic growth corresponds to "extinction" of one of the enzymes during the first few hours of growth. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: they are required for their own synthesis, and they inhibit each other. Despite this dynamic similarity, the models vary with respect to the range of dynamics captured. The Brandt et al. model always predicts the diauxic growth pattern, whereas the remaining two models exhibit both diauxic and non-diauxic growth patterns. The models also differ with respect to the mechanisms that generate the mutual inhibition between the enzymes. In the Narang model, mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. The Brandt et al. model superimposes upon this dilution effect an additional mechanism of mutual inhibition. In the Thattai and Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups. For quantitative agreement with the data, all models must be modified to account for specific mechanisms of mutual inhibition, such as inducer exclusion.     

Bacterial gene regulation in diauxic and non-diauxic growth

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.     

Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model

The growth of mixed microbial cultures on mixtures of substrates is a problem of fundamental biological interest. In the last two decades, several unstructured models of mixed-substrate growth have been studied. It is well known, however, that the growth patterns in mixed-substrate environments are dictated by the enzymes that catalyse the transport of substrates into the cell. We have shown previously that a model taking due account of transport enzymes captures and explains all the observed patterns of growth of a single species on two substitutable substrates (J. Theor. Biol. 190 (1998) 241). Here, we extend the model to study the steady states of growth of two species on two substitutable substrates. The model is analysed to determine the conditions for existence and stability of the various steady states. Simulations are performed to determine the flow rates and feed concentrations at which both species coexist. We show that if the interaction between the two species is purely competitive, then at any given flow rate, coexistence is possible only if the ratio of the two feed concentrations lies within a certain interval; excessive supply of either one of the two substrates leads to annihilation of one of the species. This result simplifies the construction of the operating diagram for purely competing species. This is because the two-dimensional surface that bounds the flow rates and feed concentrations at which both species coexist has a particularly simple geometry: It is completely determined by only two coordinates, the flow rate and the ratio of the two feed concentrations. We also study commensalistic interactions between the two species by assuming that one of the species excretes a product that can support the growth of the other species. We show that such interactions enhance the coexistence region.     

Mathematical modeling for mixed culture growth of two bacterial populations with opposite substrate preferences

An unstructured mathematical model is proposed for mixed culture growth of two different bacterial species that exhibit "opposite" substrate preferences in response to the "same" environmental conditions. The model incorporates enzymatic control mechanisms such as induction, repression, and inhibition in the microorganisms as manifested in their preferential utilization of substrates and microbial interactions such as amensalism and competition. The model predicts cell mass, substrate concentrations, dissolved oxygen tension, as well as key enzyme levels. The predictions of the model are compared with experimental data for pure culture growth and for mixed culture growth on two substrates, glucose and citrate, in a batch reactor.     

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.     

Modeling microbial dynamics in heterogeneous environments: growth on soil carbon sources

We have developed a new kinetic model to study how microbial dynamics are affected by the heterogeneity in the physical structure of the environment and by different strategies for hydrolysis of polymeric carbon. The hybrid model represented the dynamics of substrates and enzymes using a continuum representation and the dynamics of the cells were modeled individually. Individual-based biological model allowed us to explicitly simulate microbial diversity, and to model cell physiology as regulated via optimal allocation of cellular resources to enzyme synthesis, control of growth rate by protein synthesis capacity, and shifts to dormancy. This model was developed to study how microbial community functioning is influenced by local environmental conditions in heterogeneous media such as soil and by the functional attributes of individual microbes. Microbial community dynamics were simulated at two spatial scales: micro-pores that resemble 6-20-μm size portions of the soil physical structure and in 111-μm size soil aggregates with a random pore structure. Different strategies for acquisition of carbon from polymeric cellulose were investigated. Bacteria that express membrane-associated hydrolase had different growth and survival dynamics in soil pores than bacteria that release extracellular hydrolases. The kinetic differences suggested different functional niches for these two microbe types in cellulose utilization. Our model predicted an emergent behavior in which co-existence of membrane-associated hydrolase and extracellular hydrolases releasing organisms led to higher cellulose utilization efficiency and reduced stochasticity. Our analysis indicated that their co-existence mutually benefits these organisms, where basal cellulose degradation activity by membrane-associated hydrolase-expressing cells shortened the soluble hydrolase buildup time and, when enzyme buildup allowed for cellulose degradation to be fast enough to sustain exponential growth, all the organisms in the community shared the soluble carbon product and grew together. Although pore geometry affected the kinetics of cellulose degradation, the patterns observed for the bacterial community dynamics in the 6-20 μm-sized micro-pores were relevant to the dynamics in the more complex 111-μm-sized porous soil aggregates, implying that micro-scale studies can be useful approximations to aggregate scale studies when local effects on microbial dynamics are studied. As shown with examples in this study, various functional niches of the bacterial communities can be investigated using complex predictive mathematical models where the role of key environmental aspects such as the heterogeneous three-dimensional structure, functional niches of the community members, and environmental biochemical processes are directly connected to microbial metabolism and maintenance in an integrated model.     

Cybernetic modeling of growth in mixed, substitutable substrate environments: Preferential and simultaneous utilization

Growth of microorganisms on substitutable substrate mixtures display diverse growth dynamics characterized by simultaneous or preferential uptake of carbon sources. This article shows that cybernetic modeling concepts which were successful in predicting diauxic growth patterns can be extended to describe simultaneous consumption of substrates. Thus the growth of Escherichia coli on mixtures of glucose and organic acids such as pyruvate, fumarate, and succinate has been described successfully by the cybernetic model presented here showing both diauxic and simultaneous uptake when observed. The model also describes the changes in utilization patterns that occur under changing dilution rates, substrate concentrations, and models of preculturing. The model recognizes the importance of the synthesis of biosynthetic precursors in cell growth through a kinetic structure that is quite general for any mixture of carbon-energy sources. (c) 1996 John Wiley & Sons, Inc.     

Periphyton growth and diatom community structure in a cooling water pond

Periphyton (Aufwuchs) accumulation was measured on artificial substrates in a pond in central Finland which receives warm cooling-water effluent from a power plant. The growth of periphyton was generally more rapid on the substrates during the first two weeks of colonization near the inflow of the warm water effluent than in the middle of the pond. The maximum accumulation of periphyton was in spring and autumn (dry weight maximum at warm effluent was in spring 3.5 mg DW cm⁻²,2.65 mg AFDW cm⁻²; chlorophyll a maximum 3.96 μg cm⁻² was found in autumn at pond-middle station). During mid-winter months the growth was strongly limited by solar radiation, but the growth was also slow at both stations in the summer months, when the power plant was out of operation. The periphyton accumulation rate was fastest near the water surface and decreased rapidly with increasing depth. A total of 167 diatom species were found in periphyton samples. However, most species were rare; many of the dominants were common to both plankton and periphyton. Species similarity analyses (Jaccard's similarity) between 10 different diatom communities (including periphyton from 9 different types of substrates and phytoplankton) indicated low similarity index values although differences between communities were not significant.     

Carbon source utilization by the marine Dendryphiella species D. arenaria and D. salina

Carbon utilization by the marine Dendryphiella species, D. arenaria and D. salina, was investigated to detect differences in utilization and traits associated with their adaptation to the marine habitat. Fifty-four strains were isolated world-wide and tested for the utilization of various carbon sources using BIOLOG phenotype MicroArray (PM) and for the production of extracellular enzymes on solid culture media and on API ZYM assay strips. PM analysis showed that the fastest growth occurred on several monosaccharides and amino acids, 2-keto-d-gluconic acid, succinamide and turanose. Some polyols were poor carbon sources. However, the two species differed in their utilization rates of carbon sources, forming three major clusters: two separate clusters for D. arenaria and D. salina and a third cluster in which strains of the two species formed separate subclades that correlated with geographic origin. Several carbon sources were also found useful in differentiating the two speices. Dendryphiella salina did not utilize xylitol and quinic acid, whereas D. arenaria grew well on these substrates. The latter failed to grow on sorbitol and grew slowly on mannitol, both were good substrates for the former. There were also no qualitative differences between the extracellular enzymes produced, although laccase and peroxidase activities were confined only to some strains. The physiological similarities exhibited by the two species support the close relationship between D. arenaria and D. salina.     

Decelerating growth in tropical forest trees

The impacts of global change on tropical forests remain poorly understood. We examined changes in tree growth rates over the past two decades for all species occurring in large (50-ha) forest dynamics plots in Panama and Malaysia. Stem growth rates declined significantly at both forests regardless of initial size or organizational level (species, community or stand). Decreasing growth rates were widespread, occurring in 24–71% of species at Barro Colorado Island, Panama (BCI) and in 58–95% of species at Pasoh, Malaysia (depending on the sizes of stems included). Changes in growth were not consistently associated with initial growth rate, adult stature, or wood density. Changes in growth were significantly associated with regional climate changes: at both sites growth was negatively correlated with annual mean daily minimum temperatures, and at BCI growth was positively correlated with annual precipitation and number of rainfree days (a measure of relative insolation). While the underlying cause(s) of decelerating growth is still unresolved, these patterns strongly contradict the hypothesized pantropical increase in tree growth rates caused by carbon fertilization. Decelerating tree growth will have important economic and environmental implications.     

Juvenile growth and palatability in co-occurring, congeneric British herbs

Differential sensitivity (DS) storage dynamics describe a temporal niche axis that determines coexistence of competing taxa through a trade-off between environmental insensitivity and competitive ability at the recruitment stage. In DS storage dynamics, when the relevant environmental factor is low, the more sensitive, better competitor preferentially recruits; when the environmental factor is high, the environmentally sensitive species suffers high mortality and the environmentally insensitive taxon preferentially recruits. A herbivore defense/growth rate trade-off at the seedling/juvenile stage could support this dynamic. We therefore compared juvenile palatability, a measure of anti-herbivore defense, and early growth rate for five congeneric pairs of native British herbs. All five comparisons showed a positive association between average individual growth rate and average palatability to a native slug species. We observed no evidence of associations between early growth rate and adult palatability or between early growth rate and life history strategy (annual vs. perennial). Seed mass was not associated with either early growth rate or with life history strategy whether or not relatedness was taken into account. We offer two explanations as to why we found statistically significant support for a growth rate- defense trade-off when within-species studies so often produce only equivocal results.     

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.     

Diversity of substrate utilization and growth characteristics of sulfate-reducing bacteria isolated from estuarine sediment in Japan

Two different isolation methods, the dilution colony-counting method (colony-isolation) and enrichment culture, were used to isolate sulfate-reducing bacteria (SRBs) from estuarine sediment in Japan. Lactate was used as an electron donor for colony-isolation, and lactate or propionate was used for enrichment culture. All isolates were classified into six different phylogenetic groups according to the 16S rRNA gene-based analysis. The closest relatives of the colony-isolates (12 strains) were species in the genera of Desulfobacterium, Desulfofrigus, Desulfovibrio and Desulfomicrobium. The closest known relative of the lactate-enrichment isolates was Desulfovibrio acrylicus and that of the propionate-enrichment isolates was Desulfobulbus mediterraneus. All isolates were incompletely-oxidizing SRBs. Overall patterns of utilization of electron donors and acceptors, as well as fermentative substrates, differed depending on the affiliation of the strain. Furthermore, even if several strains used the same substrate, the growth rates were often significantly different depending on the strain. It was strongly suggested that various species of SRBs could coexist in the sediment by competing for common substrates as well as taking priority in favorable or specific substrates for each species and the community of SRBs should be able to oxidize almost all major intermediates of anaerobic decomposition of organic matter such as lower fatty acids, alcohols and H2 as well as amino acids. Thus, it was indicated by the phylogenetic and physiological analyses of the isolates that the SRB community composed of diverse lineages of bacteria living in anoxic estuarine sediment should be able to play an extensive role in the carbon cycle as well as the sulfur cycle of the earth.     

The ideal free distribution and bacterial growth on two substrates

A population dynamical model describing growth of bacteria on two substrates is analyzed. The model assumes that bacteria choose substrates in order to maximize their per capita population growth rate. For batch bacterial growth, the model predicts that as the concentration of the preferred substrate decreases there will be a time at which both substrates provide bacteria with the same fitness and both substrates will be used simultaneously thereafter. Preferences for either substrate are computed as a function of substrate concentrations. The predicted time of switching is calculated for some experimental data given in the literature and it is shown that the fit between predicted and observed values is good. For bacterial growth in the chemostat, the model predicts that at low dilution rates bacteria should feed on both substrates while at higher dilution rates bacteria should feed on the preferred substrate only. Adaptive use of substrates permits bacteria to survive in the chemostat at higher dilution rates when compared with non-adaptive bacteria.     

Dynamics of a intraguild predation model with generalist or specialist predator

Intraguild predation (IGP) is a combination of competition and predation which is the most basic system in food webs that contains three species where two species that are involved in a predator/prey relationship are also competing for a shared resource or prey. We formulate two intraguild predation (IGP: resource, IG prey and IG predator) models: one has generalist predator while the other one has specialist predator. Both models have Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type III functional response between IG prey and IG predator. We provide sufficient conditions of the persistence and extinction of all possible scenarios for these two models, which give us a complete picture on their global dynamics. In addition, we show that both IGP models can have multiple interior equilibria under certain parameters range. These analytical results indicate that IGP model with generalist predator has “top down” regulation by comparing to IGP model with specialist predator. Our analysis and numerical simulations suggest that: (1) Both IGP models can have multiple attractors with complicated dynamical patterns; (2) Only IGP model with specialist predator can have both boundary attractor and interior attractor, i.e., whether the system has the extinction of one species or the coexistence of three species depending on initial conditions; (3) IGP model with generalist predator is prone to have coexistence of three species.     

Meristem growth dynamics and branching patterns in the Cladoniaceae

Branching patterns in the lichen family Cladoniaceae are varied and taxonomically important. Branching occurs on the podetium, the erect secondary thallus that characterizes most species in the Cladoniaceae, and is influenced by growth dynamics of the fungal meristem tissue at the apex of the podetium. Branching is primarily the result of meristem divisions, and branching patterns are modified by meristem enlargement, deformation, and torsion. Branching processes are conserved, and early branch ontogeny provides information from which to determine relationships in the Cladoniaceae. Branching is characterized by two major patterns. In one pattern, branches arise from the relatively late divisions of a large meristem (≥100 μm in diameter), whose shape changes during ontogeny. In a second pattern, branches arise from small meristems (<100 μm in diameter), which split early in ontogeny but whose shape does not change. The trend toward reduced meristems that split early in ontogeny is seen as an evolutionary advance in the Cladoniaceae. Some "small meristem" species retain aspects of the "large meristem" habit in early ontogeny, and this provides a clue to their relationships. Patterns of meristem growth dynamics provide a basis for interpreting phylogeny in mycobionts of the Cladoniaceae. Meristem activities in four genera of the Cladoniaceae were compared in order to determine trends in growth dynamics within the family.     

Effects of substrate patterning on cellular spheroid growth and dynamics measured by gradient light interference microscopy (GLIM)

The development of three‐dimensional (3D) cellular architectures during development and pathological processes involves intricate migratory patterns that are modulated by genetics and the surrounding microenvironment. The substrate composition of cell cultures has been demonstrated to influence growth, proliferation and migration in 2D. Here, we study the growth and dynamics of mouse embryonic fibroblast cultures patterned in a tissue sheet which then exhibits 3D growth. Using gradient light interference microscopy (GLIM), a label‐free quantitative phase imaging approach, we explored the influence of geometry on cell growth patterns and rotational dynamics. We apply, for the first time to our knowledge, dispersion‐relation phase spectroscopy (DPS) in polar coordinates to generate the radial and rotational cell mass‐transport. Our data show that cells cultured on engineered substrates undergo rotational transport in a radially independent manner and exhibit faster vertical growth than the control, unpatterned cells. The use of GLIM and polar DPS provides a novel quantitative approach to studying the effects of spatially patterned substrates on cell motility and growth.     

Hyperbolic growth of marine and continental biodiversity through the phanerozoic and community evolution

Among diverse models that are used to describe and interpret the changes in global biodiversity through the Phanerozoic, the exponential and logistic models (traditionally used in population biology) are the most popular. As we have recently demonstrated (Markov, Korotayev, 2007), the growth of the Phanerozoic marine biodiversity at genus level correlates better with the hyperbolic model (widely used in demography and macrosociology). Here we show that the hyperbolic model is also applicable to the Phanerozoic continental biota at genus and family levels, and to the marine biota at species, genus, and family levels. There are many common features in the evolutionary dynamics of the marine and continental biotas that imply similarity and common nature of the factors and mechanisms underlying the hyperbolic growth. Both marine and continental biotas are characterized by continuous growth of the mean longevity of taxa, by decreasing extinction and origination rates, by similar pattern of replacement of dominant groups, by stepwise accumulation of evolutionary stable, adaptable and "physiologically buffered" taxa with effective mechanisms of parental care, protection of early developmental stages, etc. At the beginning of the development of continental biota, the observed taxonomic diversity was substantially lower than that predicted by the hyperbolic model. We suggest that this is due, firstly, to the fact that, during the earliest stages of the continental biota evolution, the groups that are not preserved in the fossil record (such as soil bacteria, unicellular algae, lichens, etc.) played a fundamental role, and secondly, to the fact that the continental biota initially formed as a marginal portion of the marine biota, rather than a separate system. The hyperbolic dynamics is most prominent when both marine and continental biotas are considered together. This fact can be interpreted as a proof of the integrated nature of the biosphere. In the macrosociological models, the hyperbolic pattern of the world population growth arises from a non-linear second-order positive feedback between the demographic growth and technological development (more people - more potential inventors - faster technological growth - the carrying capacity of the Earth grows faster - faster population growth - more people - more potential inventors, and so on). Based on the analogy with macrosociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by a non-linear second-order positive feedback between the diversity growth and community structure complexity. The feedback can work via two parallel mechanisms: 1) decreasing extinction rate (more taxa- higher alpha diversity, or mean number of taxa in a community - communities become more complex and stable - extinction rate decreases - more taxa, and so on) and 2) increasing origination rate (new taxa facilitate niche construction; newly formed niches can be occupied by the next "generation" of taxa). The latter possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the "carrying capacity of the Earth" in demography. As far as new species can increase ecospace and facilitate opportunities for additional species entering the community, they are analogous to the "inventors" of the demographic models whose inventions increase the carrying capacity of the Earth. The hyperbolic growth of the Phanerozoic biodiverstiy suggests that "cooperative" interactions between taxa can play an important role in evolution, along with generally accepted competitive interactions. Due to this "cooperation", the evolution of biodiversity acquires some features of a self-accelerating process. Macroevolutionary "cooperation" reveals itself in: 1) increasing stability of communities that arises from alpha diversity growth; 2) ability of species to facilitate opportunities for additional species entering the community.     

The dynamics of Phanerozoic marine animal diversity agrees with the hyperbolic growth model

Generic diversity dynamics of the Phanerozoic marine animals is far better described by the hyperbolic model, widely used in demography and macrosociology, than by the exponential and logistic models from population dynamics traditionally employed for this purpose. Exponential and logistic models imply zero influence of interactions between taxa on the dynamics of diversity, with the exception of competing for unoccupied ecological space, whereas the hyperbolic model implies non-linear second-order positive feedback in the development of the biota. The hyperbolic human population growth is caused by positive feedback between population size and the rate of technological and cultural development (the more individuals, the more inventors, the more rapid progress, the more rapid growth of the Earth's bearing capacity; the smaller death-rate, the more accelerated growth-rate of the population). Probably there is also non-linear second-order positive feedback between diversity and community structure (the more genera, the higher alpha-diversity, which is defined as average number of genera per community, the more complicated and stable, "buffered" communities, the greater "taxonomic capacity of the environment" and average duration of the existence of genera; extinction rate dencreases, biodiversity growth-rate increases). The simplest mathematical model of biodiversity dynamics based on this assumption is confirmed by empirical data on alpha-diversity dynamics. Progressive complexification of marine communities during the Phanerozoic is also confirmed by the growing evennes of generic abundance distribution in paleocommunities.