Conditions for Global Dynamic Stability of a Class of Resource-Bounded Model Ecosystems

This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are ‘resource bounded’ in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka–Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of ‘explicit conditions’ on the basis of a notion of ‘uniform diagonal dominance’ for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.     

A Dynamical Study of a Cellular Automata Model of the Spread of HIV in a Lymph Node

We conduct a mathematical study of a cellular automata model of the spread of the HIV virus in a lymph node. The model was proposed by Zorzenon dos Santos and Coutinho and captures the unique time scale of the viral spread. We give some rigorous mathematical results about the time scales and other dynamical aspects of the model as well as discuss parameter and model changes and their consequences.     

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.     

In vitro separation of a rose chimera

“Fairmount 1 thorny” (“FM1 thorny”) (a Rosa multiflora Thunb ex. J. Murr.) and a thornless sport of “FM1 thorny” (“Fairmount 1” (“FM1”)) were established in vitro to investigate chimeral segregation under various levels of BA and to obtain a pure thornless rose. While the chimeral thornless sport was expected to segregate in vitro and yield both thorny and thornless plantlets, “FM1 thorny” was to yield only thorny plants. “FM1” segregated in vitro into its constituent genotypes and yielded thorny and thornless plantlets, suggesting that “FM1” is chimeral. “FM1 thorny” produced only thorny plants in vitro. These results indicate that the “FM1 thorny” clone was not chimeral (pure thorny) and that the thornless regenerates of “FM1” did not develop via somaclonal variation. There was a significant linear relationship between increasing BA concentration and the percentage of thorny plants. Among a population of 690 tissue culture derived plants from all the BA experiments, 6 plants were classified as pure thornless plants 1 year later.     

C-Terminal 23 kDa polypeptide of soybean Gly m Bd 28 K is a potential allergen

Gly m Bd 28 K is a major soybean (Glycine max Merr.) glycoprotein allergen. It was originally identified as a 28 kDa polypeptide in soybean seed flour. However, the full-length protein is encoded by an open reading frame (ORF) of 473 amino acids, and contains a 23 kDa C-terminal polypeptide of as yet unknown allergenic and structural characteristics. IgE-binding (allergenic potential) of the Gly m Bd 28 K protein including the 23 kDa C-terminal portion as well as shorter fragments derived from the full-length ORF were evaluated using sera from soy-sensitive adults. All of these sera contained IgE that efficiently recognized the C-terminal region. Epitope mapping demonstrated that a dominant linear C-terminal IgE binding epitope resides between residues S256 and A270. Alanine scanning of this dominant epitope indicated that five amino acids, Y260, D261, D262, K264 and D266, contribute most towards IgE-binding. A model based on the structure of the subunit of soybean -conglycinin revealed that Gly m Bd 28 K contains two cupin domains. The dominant epitope is on the edge of the first -sheet of the C-terminal cupin domain and is present on a potentially solvent-accessible loop connecting the two cupin domains. Thus, the C-terminal 23 kDa polypeptide of Gly m Bd 28 K present in soy products is allergenic and apparently contains at least one immunodominant epitope near the edge of a cupin domain. This knowledge could be helpful in the future breeding of hypoallergenic soybeans.Abbreviations Ara h 1 Arachis hypogaea allergen 1 - Ara h 3 Arachis hypogaea allergen 3 - BCA Bicinchoninic acid - Gly m Bd 28 K Glycine max band 28 kDa allergen - Gly m Bd 30 K Glycine max band 30 kDa allergen - Gly m Bd 68 K Glycine max band 68 kDa allergen - IgE Immunoglobulin E     

Utilisation of cardiac pacemakers over a 20-year period: Results from a nationwide pacemaker registry

The implantation of cardiac pacemakers has become a well-established therapy for conduction disorders and sinus node dysfunction. In many countries pacemaker registries have been initiated in order to collect information on patient characteristics, trends in numbers and the types of pacemakers used, to identify problematic devices, and for safety monitoring. For this utilisation study the Central Pacemaker Patients Registration (CPPR) from the Netherlands Pacemaker Registry Foundation (CPPR-SPRN) containing data collected for more than 20 years was used. During this period nearly 97,000 first pacemakers were implanted. Analyses show an increase in the rate of implanted devices. The change in pacemaker type from VVI to DDD, followed by biventricular stimulation, is reflected by the number of simultaneously implanted leads, which is partly a consequence of cardiac resynchronisation therapy. Our data demonstrate that indications for implantation and type of pacemaker are comparable with other European countries.     

Turing Pattern Formation with Two Kinds of Cells and a Diffusive Chemical

We study a three-variable Turing system with two kinds of cells and a diffusive chemical, considering the formation and maintenance of fish skin patterns with multiple pigment cells. The two types of cells are produced from undifferentiated cells. They inhibit the supply rate of the other cell type, forming local clusters of the same cell type. In addition, the cells of one type can be maintained only in the presence of a diffusive chemical produced by the other cell type, resulting in the coexistence of two cell types in heterogeneous spatial patterns. We assume linear interaction among cells and the chemical, and cell supply rates constrained to be positive or zero. We derive the condition for diffusion-driven instability. In one-dimensional model, we examine how the wavelength of the periodic pattern depends on parameters. In the two-dimensional model, we study the condition for spot, stripe or reversed spot pattern to emerge (pattern selection). We discuss heuristic criteria for the pattern selection.     

Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.     

Production of a thermostable extracellular lipase by Kluyveromyces marxianus

Kluyveromyces marxianus was grown in submerged culture in a complex medium with several potential inducers of lipolytic activity (triacylglycerols, fatty acids). The highest extracellular lipolytic enzyme production (about 80 U ml^–1 in 3 d) was obtained when the medium was supplemented with 2 g urea l^–1 plus 5 g tributyrin l^–1. Addition of surfactants (1 g l^–1) did not improve production. The lipase had a high thermal stability in aqueous solution (73% residual activity after 9 d at 50 °C, 16 min half-life time at 100 °C). It was also stable at acidic pH and showed good tolerance to organic solvents (70% residual activity after 2 d in n-hexane of cyclohexane).     

Advanced backcross QTL analysis of a hard winter wheat × synthetic wheat population

Advanced backcross quantitative trait locus (AB-QTL) analysis was used to identify QTLs for yield and yield components in a backcross population developed from a cross between hard red winter wheat (Triticum aestivum L.) variety Karl 92 and the synthetic wheat line TA 4152-4. Phenotypic data were collected for agronomic traits including heading date, plant height, kernels per spike, kernel weight, tiller number, biomass, harvest index, test weight, grain yield, protein content, and kernel hardness on 190 BC₂F_2:4 lines grown in three replications in two Kansas environments. Severity of wheat soilborne mosaic virus (WSBMV) reaction was evaluated at one location. The population was genotyped using 151 microsatellite markers. Of the ten putative QTLs identified, seven were located on homoeologous group 2 and group 3 chromosomes. The favorable allele was contributed by cultivated parent Karl 92 at seven QTLs including a major one for WSBMV resistance, and by the synthetic parent at three QTLs: for grain hardness, kernels per spike, and tiller number. Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture.     

The Evolution of Virulence in RNA Viruses under a Competition–Colonization Trade-Off

RNA viruses exist in large intra-host populations which display great genotypic and phenotypic diversity. We analyze a model of viral competition between two viruses infecting a constantly replenished cell pool. We assume a trade-off between the ability of the virus to colonize new cells (cell killing rate or virulence) and its local competitiveness (replicative success within coinfected cells). We characterize the conditions that allow for viral spread by means of the basic reproductive number and show that a local coexistence equilibrium exists, which is asymptotically stable. At this equilibrium, the less virulent competitor has a reproductive advantage over the more virulent colonizer reflected by a larger equilibrium population size of the competitor. The equilibria at which one virus outcompetes the other one are unstable, i.e., a second virus is always able to permanently invade. We generalize the two-virus model to multiple viral strains, each displaying a different virulence. To account for the large phenotypic diversity in viral populations, we consider a continuous spectrum of virulences and present a continuum limit of this multiple viral strains model that describes the time evolution of an initial continuous distribution of virulence without mutations. We provide a proof of the existence of solutions of the model equations, analytically assess the properties of stationary solutions, and present numerical approximations of solutions for different initial distributions. Our simulations suggest that initial continuous distributions of virulence evolve toward a distribution that is extremely skewed in favor of competitors. At equilibrium, only the least virulent part of the population survives. The discrepancy of this finding in the continuum limit with the two-virus model is attributed to the skewed equilibrium subpopulation sizes and to the transition to a continuum. Consequently, in viral quasispecies with high virulence diversity, the model predicts collective virulence attenuation. This result may contribute to understanding virulence attenuation, which has been reported in several experimental studies.     

Discovery of a unique Mycobacterium tuberculosis protein through proteomic analysis of urine from patients with active tuberculosis

Identification of pathogen-specific biomarkers present in patients' serum or urine samples can be a useful diagnostic approach. In efforts to discover Mycobacterium tuberculosis (Mtb) biomarkers we identified by mass spectroscopy a unique 21-mer Mtb peptide sequence (VVLGLTVPGGVELLPGVALPR) present in the urines of TB patients from Zimbabwe. This peptide has 100% sequence homology with the protein TBCG_03312 from the C strain of Mtb (a clinical isolate identified in New York, NY, USA) and 95% sequence homology with Mtb oxidoreductase (MRGA423_21210) from the clinical isolate MTB423 (identified in Kerala, India). Alignment of the genes coding for these proteins show an insertion point mutation relative to Rv3368c of the reference H37Rv strain, which generated a unique C-terminus with no sequence homology with any other described protein. Phylogenetic analysis utilizing public sequence data shows that the insertion mutation is apparently a rare event. However, sera from TB patients from distinct geographical areas of the world (Peru, Vietnam, and South Africa) contain antibodies that recognize a purified recombinant C-terminus of the protein, thus suggesting a wider distribution of isolates that produce this protein.     

Molecular characterization of a ring X chromosome in a male with short stature

We report the molecular characterization of a ring X chromosome that was transmitted from a mother to a male who has short stature and minor dysmorphic features. This represents only the second reported ring X chromosome in a male. The ring is derived from breakage within the Xp pseudoautosomal region (PAR) and just proximal to the Xq PAR. The total amount of deleted material is 700-900 kb DNA and includes six known transcribed genes. Interestingly, SHOX, a gene implicated in short stature, is not deleted from the ring chromosome. Possible pathogenetic explanations for the patient's clinical features include insufficient dosage of deleted genes, a position effect on SHOX expression, and cell death during development because of ring chromosome nondisjunction. The findings are also relevant to observations made of "complete" ring chromosomes.     

Prey Selection,Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System

A model is developed to describe the interaction between a predator and two prey types located in different regions. Conditions for stability and persistence are analysed. The effects of harvesting the predators are investigated by making the predator mortality rate habitat dependent. Results demonstrate that for any given set of parameter values there is a value of the intrinsic preference of the predator for each prey type at which the system undergoes a Hopf bifurcation. Above this critical value the system evolves towards a stable equilibrium, whereas below it, stable limit cycles arise by Hopf bifurcations. Simulations demonstrate that the presence of demographic stochasticity may destabilise oscillatory populations, thereby causing population extinctions. An application of the model to the foraging behaviour of North Sea cod is described. It is shown that if the preferred prey is more productive, it is likely that the equilibrium will be stable, whereas if the less preferred prey is more productive, populations are likely to display cycles and in the stochastic case become extinct. As cod fishing mortality is increased, the point of bifurcation and region of parameter space for which the system is unstable decreases. An increased understanding of how cod behave may enable fish stocks to be managed more successfully, for example by indicating where marine reserves should be placed.     

Ranging behavior of Mahale chimpanzees: a 16 year study

We have analyzed the ranging patterns of the Mimikire group (M group) of chimpanzees in the Mahale Mountains National Park, Tanzania. During 16 years, the chimpanzees moved over a total area of 25.2 or 27.4 km², as estimated by the grid-cell or minimum convex polygon (MCP) methods, respectively. Annually, the M group used an average of 18.4 km², or approximately 70 %, of the total home-range area. The chimpanzees had used 80 % of their total home range after 5 years and 95 % after 11 years. M group chimpanzees were observed more than half of the time in areas that composed only 15 % of their total home range. Thus, they typically moved over limited areas, visiting other parts of their range only occasionally. On average, the chimpanzees used 7.6 km² (in MCP) per month. Mean monthly range size was smallest at the end of the rainy season and largest at the end of the dry season, but there was much variability from year to year. The chimpanzees used many of the same areas every year when Saba comorensis fruits were abundant between August and January. In contrast, the chimpanzees used several different areas of their range in June. Here range overlap between years was relatively small. Over the 16 years of the study we found that the M group reduced their use of the northern part of their range and increased their frequency of visits to the eastern mountainous side of their home range. Changes in home-range size correlated positively with the number of adult females but not with the number of adult males. This finding does not support a prediction of the male-defended territory model proposed for some East African chimpanzee unit-groups.