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Nature of equilibria and effects of drug treatments in some simple viral population dynamical models.

We examine some simple mathematical models which have been recently employed to predict the evolution of population dynamical systems involving virus particles. They include: (1) A general two-component antibody-viral system; (2) A simplified two-component model for HIV-1 dynamics (3) An HIV-1 three-component model including virions and (4) A four-component HIV-1 dynamical model which includes both latently and actively infected cells. For each system we find equilibrium points and analyse their local stability properties in order to obtain a global phase portrait. Analytical methods are complemented with numerical solutions. In all four models there are at most two equilibrium points for physically meaningful values of the variables. As the viral growth rate parameter increases through a critical value, a transcritical bifurcation occurs. One critical point (P1) is always found at zero viral or infected cell levels and non-zero antibody or uninfected cell levels. For parameter values in their usual ranges, P1 is either an asymptotically stable node or a saddle point. When the critical point P2 occurs at biologically meaningful values, it is either an asymptotically stable node or an asymptotically stable spiral point. For all three HIV-1 models, the values of the parameters at which P2 makes a transition to physically meaningful values are precisely those at which P1 changes from an asymptotically stable node to an unstable saddle point. The global pictures for all four models are similar and examples are represented graphically. No limitcycle solutions were found in any of the models for parameter values in their usual ranges. In the four-component HIV-1 model, the effects of varying each parameter are found and conditions under which P2 changes from spiral point to node are investigated numerically. The effects of reverse transcriptase inhibitors and protease inhibitors, two classes of drugs used to treat HIV-1 infection, are examined in the three-component model for early HIV-1 dynamics.

HIV Antibodies↗

Small population effects in stochastic population dynamics.

The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results.

Ecosystem↗

The effects of climatic patterns and agricultural practices on the population dynamics of Culex tritaeniorhynchus in Asia.

Annual population curves for C. tritaeniorhynchus are presented for representative localities distributed from Pakistan, east through Southeast Asia and the Philippines and north to Japan and Korea. In the dry temperature (Pakistan) and colder maritime climates (Japan and Korea). C. tritaeniorhynchus populations apparently overwintered as hibernating adults, while in the warmer maritime climates (Okinawa and Taiwan), gonotrophic activity and larval development continued throughout the winter months. In these climatic types, the population curves closely paralleled the annual temperature curves. In the tropical climates, however, temporal population patterns were closely related to available moisture either in the form of annual precipitation and/or rice irrigation. The extremely variable environmental conditions tolerated C. tritaeniorhynchus throughout its distribution attests to the physiological and ecological plasticity of this species and suggests that further ecological and genetic studies may reveal marked clinical variances among selected biological parameters.

Agriculture↗

Trypanosoma cruzi: analysis of the population dynamics of heterogeneous mixtures.

Utilizing the previously reported inter-clonal differences in total DNA/organism, flow cytometry was used to analyze the population dynamics of Trypanosoma cruzi clone mixtures growing in liquid medium or vertebrate cells. The growth of clone mixtures in liquid medium can be described by unique parameters reflecting exponential growth rate (r), stationary phase population density (1/k), and the interaction between the clones (h). The relative numbers of each clone in the population change rapidly with time and the results are in quantitative agreement with mathematical models of competitive population growth. The relationship between the parameters for T. cruzi is such that, in general, there is no dynamic equilibrium with coexistence of clones with different growth rates; under all culture protocols, the faster growing clone will prevail. A computer simulation of the vertebrate cell cycle of T. cruzi suggests that clone mixtures grow relatively independently; the basic attributes of the model were substantiated experimentally. Although wide fluctuations in the proportion of each clone released occurred, the faster growing clone again predominated. Finally, these results underline the importance of working with well-defined clones in the laboratory to avoid inconsistencies and paradoxical results and stress the importance of the rapid isolation of single cell clones from clinical specimens when studying the relationship of the parasite to human disease.

Animals↗

Direct and indirect effects of sublethal toxicant exposure on population dynamics of freshwater rotifers: a modeling approach.

Ecotoxicological assessments commonly consider the direct effects of anthropogenic toxicants on the survival, growth, and reproduction of organisms. However, toxicants also may have indirect effects on aquatic communities by altering species interactions such as predation and competition. Such indirect effects are often mediated by changes in animal behavior, and contribute to uncertainty in predicting the environmental effects of toxicants. In an attempt to better understand indirect effects, a modeling approach was used to simulate the population dynamics of the predatory rotifer Asplanchna girodi and six prey species of herbivorous rotifers in response to sublethal concentrations (110, 190 or 330 mg/l) of pentachlorophenol (PCP). Simulations were performed assuming three different toxicant effect scenarios: behavioral toxicity alone, reproductive toxicity alone, or both behavioral and reproductive toxicity. Population growth rates (G(r)), maximum population densities (D(max)), and the percent of carrying capacity at D(max) (%K) were calculated for A. girodi and each prey species for each effect scenario and toxicant concentration. Similar qualitative results were obtained regardless of which prey species was exploited by A. girodi. Toxicant effects on predator and prey population densities appeared to be the dominant cause of both direct and indirect toxicant effects, and behavioral toxicity was a redundant endpoint relative to reproductive toxicity. These results suggest that assessing toxicant effects on the population growth of individual species may provide sufficient data to predict toxicant effects on species interactions as well.

Animals↗

Adaptive feeding across environmental gradients and its effect on population dynamics.

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.

Adaptation, Physiological↗

Molecular monitoring of microbial population dynamics during operational periods of anaerobic hybrid reactor treating cassava starch wastewater.

This study characterized the microbial community and population dynamics in an anaerobic hybrid reactor (AHR) treating cassava starch wastewater. Methanogens and nonmethanogens were followed during the start-up and operation of the reactor, and linked to operational and performance data. Biomass samples taken from the sludge bed and packed bed zones of the AHR at intervals throughout the operational period were examined by 16S rRNA fluorescence in situ hybridization (FISH). The start-up seed and the reactor biomass were sampled during the feeding of the wastewater with a chemical oxygen demand (COD) value of 8 g L(-1) and a hydraulic retention time (HRT) of 8 days. These samples were characterized by the predominance of cells with long-rod morphology similar to Methanosaeta spp. Following a sharp operational change, accomplished by increasing the COD concentration of the organic influent from 8 to 10 g L(-1) and reducing the HRT from 8 to 5 days, there was a doubling of the organic loading rate, a reduction of the COD removal efficiency, as well as decreased methane content in the biogas and an accumulation of total volatile acids in the reactor. Moreover, this operational change resulted in a significant population shift from long-rod Methanosaeta-like cells to tetrad-forming Methanosarcina-like cells. The distributions of microbial populations involved in different zones of the AHR were determined. The results showed that nonmethanogens became the predominant population in both sludge and the packed bed zone. However, the percentage of methanogens in the packed bed zone was higher than that in the sludge bed zone. This higher percentage of methanogens was likely caused by the fact that the packed bed zone provided a suitable environmental condition with an appropriate nutrient availability for methanogen growth.

Bacteria, Anaerobic↗

A dynamic population of excitable cells: the taste receptor cells.

Taste receptor cells (TRCs) represent an unique opportunity to study a dynamic population of excitable cells that undergoes two basic neurobiological processes: postnatal development and cell turnover. We have begun to investigate the functional properties of TRCs and how they mature over time by applying the patch-clamp technique to single cell in taste buds isolated from mouse vallate papilla during postnatal development. We have focussed our attention on a well-defined functional group of taste cells, called Na/OUT cells, and on their voltage-gated K+, and Cl- currents (I(K) and I(Cl), respectively). As in neurons, I(K) and I(Cl) underlie action potential waveform and firing properties in these cells. By analyzing the relative occurrence of I(K) and I(Cl) among cells, we found that in adult mice three different electrophysiological phenotypes of Na/OUT cells could be detected: cells with only I(K) (K cells); cells with both I(K) and I(Cl) (K + Cl cells); and cells with I(Cl) (Cl cells). On the contrary, at early developmental stages (2-4 postnatal day, PD) there were no Cl cells, which appeared at PD 8. The analysis of the changes in current amplitude (which continuously increased in developing cells) during postnatal development suggested that Cl cells and K + Cl cells likely represented a single functional line different from K cells. In addition, electrophysiological data were consistent with the interpretation that Cl cells derived from some K + Cl cells by suppression of I(K). The dynamics of the expression of I(K) and I(Cl) during postnatal development likely reflects a mechanism that could also operate during turnover.

Action Potentials↗

[Mathematical modeling of population dynamics of unstable plasmid-containing bacteria during continuous cultivation in a chemostat].

A structural approach to studying the regularities of the population dynamics of unstable recombinant bacterial strains in a chemostat was elaborated. The approach is based on the mathematical modeling of cell distribution in a population with different numbers of plasmid copies. The effect of decreased selective preference of plasmidless variants of the recombinant strain in the chemostat, which is related to a decrease in the number of plasmid copies in cells upon long-term incubation was analyzed. It is shown that the time of half-elimination of plasmids from the bacterial population in the steady state in the chemostat T1/2 does not depend on the maximum number of plasmid copies in cells N but is determined only by the mean time of generation g and the probability of the loss of one plasmid copy tau. The dependence of the preference of bacterial plasmidless variants on the efficiency of expression of genes cloned into plasmids in chemostat was analyzed using the recombinant strain E. coli Z905, whose plasmids pPHL-7 contain cloned genes for the luminescence system of marine luminescing bacteria Photobacterium leiognathi.

Bioreactors↗

Population dynamics of rumen microbes using modern techniques in rumen enhanced solid incubation.

The microbial ecology of the rumen is very complex. Different species of bacteria, protozoa, and fungi are involved in digestion of plant material in ruminants. In spite of complicated interrelationships among the various groups of microorganisms in the rumen ecosystem, Bacteria and Archaea are believed to play a major role because of their numerical predominance and metabolic diversity. In this work we are presenting the results for microbial population dynamics of rumen microbes during two-stage anaerobic digestion of grass. The reactors were inoculated with fresh rumen content. Fluorescent in situ hybridization, confocal laser scanning microscopy and epifluorescence microscopy were employed for microbial investigation. It was observed that Bacteria dominated in the hydrolytic reactor (1st stage) whereas Archaea were predominant in the methanogenic reactor (2nd stage). The stability of the methanogenic reactor was result of the dominance of Methanosaeta species (mainly the filamentous type).

Animals↗

[Experimental and mathematical modeling of population dynamics of rhizospheric bacteria under conditions of cadmium stress].

The method of membrane filters was used to study the population dynamics of bacteria belonging to the genera Arthrobacter, Flavobacterium, and Klebsiella in barley (Hordeum vulgare) rhizosphere under conditions of cadmium stress (5-15 mg Cd/g soil). Mathematical modeling allowed us to demonstrate that the phytoprotective effect is implemented via the following succession of events: the bacteria synthesize phytohormones (IAA and ethylene)-->root excretory activity increases-->the number of the bacteria in the rhizoplane grows-->the flux of bacteria migrating from the rhizoplane to the rhizosphere increases-->the number of bacteria binding cadmium ions in the rhizosphere grows-->the amount of free ions entering the plant decreases. Among the bacteria studied, K. mobilis 880 displayed the highest migration and immobilization activity and the best survival rate under conditions of cadmium stress. Consequently, K. mobilis 880 is recommended for use in biopreparations for stimulating plant growth under conditions of heavy metal pollution.

Agriculture↗

Life-history strategies and population dynamics of abomasal nematodes in Svalbard reindeer (Rangifer tarandus platyrhynchus).

The observation that the total abundance of adult nematodes in the abomasum of Svalbard reindeer increases between October and April suggests adaptation to cope with the Arctic winter. Here we investigate the extent to which selection has led to similar life-history strategies in the 3 most numerous trichostrongyle species. The life-histories are found to differ markedly. We use flexible statistical models for the abundance and dispersion of parasites in the host population. One of the taxa, Marshallagia marshalli, was most abundant and had its highest egg output in the winter. In contrast, the abundance of the most common taxa, Ostertagia gruehneri, m. gruehneri was stable or declined from autumn to late winter, and the closely related taxa, O. gruehneri, m. arcticus, showed a similar over winter drop. The faecal egg output of these 2 taxa was highest in summer, as found in temperate trichostrongyle species. Despite the apparent contamination of summer pastures with O. gruehneri, calves showed negligible burdens until their second summer and the abundance of infection reached an asymptote within their third year. In contrast, the abundance of M. marshalli in calves showed a rapid increase over the first summer and by late winter was similar to peak levels found in adults (8000 worms). This increase could not be accounted for by the developing abomasum larvae population and is therefore evidence for transmission over the winter for this taxa. While M. marshalli showed little between-year variation, O. gruehneri showed 2-fold fluctuation in the abundance of infection. O. gruehneri may therefore play a role in the fluctuating population dynamics of the host. Since there was no apparent decline in abundance with host age in any of the 3 taxa there was no evidence of reindeer mounting an immune response.

Abomasum↗

Reconciling genetic expectations from host specificity with historical population dynamics in an avian brood parasite, Horsfield's Bronze-Cuckoo Chalcites basalis of Australia.

Mitochondrial DNA (mtDNA) is being used increasingly to explore the evolution of host specificity in avian brood parasites. A stable coevolutionary equilibrium between multiple phylogenetically unrelated hosts and a brood parasitic species predicts that mtDNA diversity in the parasite should be relatively deep and phylogenetically structured. Also, the different intraspecific clades resulting from parasitism to multiple sympatric hosts should themselves occur sympatrically. However, mtDNA diversity in brood parasites is as susceptible to effects of historical population dynamics as in any species. We demonstrate the relevance of these dynamics to the use of mtDNA in understanding coevolution between an Australian brood-parasite, Horsfield's Bronze-Cuckoo Chalcites basalis and its hosts, Malurus fairy-wrens and Acanthiza thornbills. Previous ecological and behavioural analyses argue that Malurus- and Acanthiza-specific host races exist in C. basalis. Yet mtDNA diversity in C. basalis is low and phylogenetically unstructured (mean sequence divergence 0.15 +/- 0.07%, range 0.00%-0.31%) and tests of mtDNA neutrality and range expansion vs. population stability (Tajima's D, Fu & Li's F* and D*, Fu's F(S), mismatch analyses) all indicate that C. basalis has expanded its range very recently, probably within the last few tens of thousands of years following climatic amelioration after a peak of aridity in the late Pleistocene. The low mtDNA diversity and its lack of phylogenetic structure in C. basalis deny the existence of evolutionarily long-term stable host races in C. basalis but not the possibility of recently evolved ones. They highlight the need for renewed behavioural and ecological study of the relationship between C. basalis and its hosts. Our findings illustrate the need to understand the evolutionary context in which a brood parasite and its hosts have evolved if mtDNA data are to be used in testing hypotheses concerning the origin and maintenance of host specificity. They also add to the growing body of work illustrating the use of mismatch analyses and Fu's F(S) in detecting range expansions.

Animals↗

Population dynamics of male-killing and non-male-killing spiroplasmas in Drosophila melanogaster.

The endosymbiotic bacteria Spiroplasma spp. are vertically transmitted through female hosts and are known to cause selective death of male offspring in insects. One strain of spiroplasma, NSRO, causes male killing in Drosophila species, and a non-male-killing variant of NSRO, designated NSRO-A, has been isolated. It is not known why NSRO-A does not kill males. In an attempt to understand the mechanism of male killing, we investigated the population dynamics of NSRO and NSRO-A throughout the developmental course of the laboratory host Drosophila melanogaster by using a quantitative PCR technique. In the early development of the host insect, the titers of NSRO were significantly higher than those of NSRO-A at the first- and second-instar stages, whereas at the egg, third-instar, and pupal stages, the titers of the two spiroplasmas were almost the same. Upon adult emergence, the titers of the two spiroplasmas were similar, around 2 x 10(8) dnaA copy equivalents. However, throughout host aging, the two spiroplasmas showed strikingly different population growth patterns. The titers of NSRO increased exponentially for 3 weeks, attained a peak value of around 4 x 10(9) dnaA copy equivalents per insect, and then decreased. In contrast, the titers of NSRO-A were almost constant throughout the adult portion of the life cycle. In adult females, consequently, the titer of NSRO was significantly higher than the titer of NSRO-A except for a short period just after emergence. Although infection of adult females with NSRO resulted in almost 100% male killing, production of some male offspring was observed within 4 days after emergence when the titers of NSRO were as low as those of NSRO-A. Based on these results, we proposed a threshold density hypothesis for the expression of male killing caused by the spiroplasma. The extents of the bottleneck in the vertical transmission through host generations were estimated to be 5 x 10(-5) for NSRO and 3 x 10(-4) for NSRO-A.

Animals↗

Population dynamics of "null" and Thy1lo lymphocytes in mouse bone marrow: genesis of cells with natural killer cell lineage characteristics.

The population dynamics of "null" small lymphocytes lacking B and T lineage markers in mouse bone marrow have been examined using a combination of immunolabeling and hydroxyurea (HU) deletion techniques. The binding of the B lineage-associated mAb, 14.8, and anti-Thy1.2 to bone marrow cells has been detected radioautographically. Null cells lacking 14.8 and Thy1.2 determinants (14.8- Thy1-) formed a substantial subset (12-14%) of bone marrow small lymphocytes, representing 0.5 x 10(6) cells per femur (2-3% of nucleated cells). HU treatment revealed an exceptionally rapid turnover of the null small lymphocyte population (T1/2, 7.5 hr) compared with 14.8+ cells (T1/2, 20.5 hr) and Thy1+ cells (T1/2, 53 hr). Small lymphocytes bearing low intensities of Thy1 (Thy1lo) were also rapidly renewed (T1/2, 28 hr) whereas those with high intensities of Thy1 (Thy1hi) were renewed only slowly (T1/2, 123 hr). During ontogeny, null small lymphocytes first appeared in the fetal liver by Day 11 and the fetal spleen by Day 16, but increased rapidly in the bone marrow in early postnatal life. Double immunolabeling techniques demonstrated that 10% of null small lymphocytes in the bone marrow expressed NK1.1 antigen, while larger proportions bound to tumor (YAC.1) cells in vitro and displayed Fc receptors. The NK1.1-bearing fraction of null small lymphocytes in bone marrow was depleted by HU treatment only after an initial delay. NK1.1 was also expressed on subsets of Thy1lo cells and Thy1hi cells. The results have revealed the continuous production in mouse bone marrow of null and Thy1lo small lymphocytes, totaling 1-3 x 10(7) cells/day and 1.2 x 10(6) cells/day, respectively. The findings suggest that the large-scale production of null lymphocytes in mouse bone marrow includes the genesis of NK lineage cells which express NK1.1 and Thy1lo during a period of terminal maturation.

Age Factors↗

Emergence of drug-resistant influenza virus: population dynamical considerations.

Given the considerable challenges to the rapid development of an effective vaccine against influenza, antiviral agents will play an important role as a first-line defense if a new pandemic occurs. The large-scale use of drugs for chemoprophylaxis and treatment will impose strong selection for the evolution of drug-resistant strains. The ensuing transmission of those strains could substantially limit the effectiveness of the drugs as a first-line defense. Summarizing recent data on the rate at which the treatment of influenza infection generates resistance de novo and on the transmission fitness of resistant virus, we discuss possible implications for the epidemiological spread of drug resistance in the context of an established population dynamic model.

Acetamides↗

[Effect of sodium salicylate on the population dynamics of a rhizospheric strain of Pseudomonas aureofaciens in soil and on wheat roots].

The effect of sodium salicylate on the population dynamics of the rhizobacterium Pseudomonas aureofaciens BS1393 and its variant bearing the naphthalene biodegradation plasmid pBS216 was studied in the wheat rhizoplane and adjacent soil. Optimum salicylate concentration for the maintenance of the plasmid-bearing strain and for the normal growth of wheat was found to be 250 micrograms/g soil. When the soil was supplemented with salicylate, the population of P. aureofaciens BS1393(pBS216) in the wheat rhizoplane and adjacent soil was, respectively, 4- and 20-fold higher than that of the parent strain lacking the plasmid.

Chromatography, High Pressure Liquid↗

Population dynamics of HTLV-I infection: a discrete-time mathematical epidemic model approach.

Human T-cell Leukaemia Virus Type I (HTLV-I) is a retrovirus that causes Adult T-cell Leukaemia (ATL). The transmission routes of HTLV-I are (i) from infected mothers to their newborn babies, (ii) from infected males (husbands) to females (their wives) by long-term sexual intercourse, and (iii) from infected females (wives) to males (their husbands). Eshima et al. (2001) analysed a continuous-time HTLV-I model with no age structure in the population. In this paper, we consider the population dynamics of HTLV-I infection in a discrete-time mathematical model incorporating an age structure. The necessary and sufficient condition for the extinction of HTLV-I is derived from the mathematical model. A simulation of the HTLV-I infection based on the model demonstrates a rapid reduction of the HTLV-I infection proportion in Japan.

Adolescent↗