When can a population spreading across sink habitats persist?

We consider populations with time-varying growth rates living in sinks. Each population, when isolated, would become extinct. Dispersal-induced growth (DIG) occurs when the populations are able to persist and grow exponentially when dispersal among the populations is present. We provide a mathematical analysis of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates and non-symmetric migration which are assumed to be piecewise continuous. We also consider a stochastic model with random variation of growth rates and migration. This work extends existing results of the literature on the DIG effects obtained for periodic continuous growth rates and time independent symmetric migration.

Untangling the role of temporal and spatial variations in persistence of populations

We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, 1-ɛ>0 or -(1+ɛ)<0. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the second half of the period, that we refer as the (±1) model. In the absence of migration, the population goes to 0 exponentially fast in each environment. In this paper, we show that, when the period is sufficiently large, a small dispersal between the two patches is able to produce a very high positive exponential growth rate for the whole population, a phenomena called inflation. We prove in particular that the threshold of the dispersal rate at which the inflation appears is exponentially small with the period. We show that inflation is robust to random perturbation, by considering a model where the values of the growth rate in each patch are switched at random times: we prove that inflation occurs for low switching rate and small dispersal. We also consider another stochastic model, where after each period of time T, the values of the growth rates in each patch is chosen randomly, independently from the other patch and from the past. Finally, we provide some extensions to more complicated models, especially epidemiological and density dependent models.

Interspecific density-dependent model of predator–prey relationship in the chemostat

The objective of this study is to analyze a model of competition for one resource in the chemostat with general interspecific density-dependent growth rates, taking into account the predator–prey relationship. This relationship is characterized by the fact that the prey species promotes the growth of the predator species which in turn inhibits the growth of the first species. The model is a three-dimensional system of ordinary differential equations. With the same dilution rates, the model can be reduced to a planar system where the two models have the same local and even global behavior. The existence and stability conditions of all steady states of the reduced model in the plane are determined according to the operating parameters. Using the nullcline method, we present a geometric characterization of the existence and stability of all equilibria showing the multiplicity of coexistence steady states. The bifurcation diagrams illustrate that the steady states can appear or disappear only through saddle-node or transcritical bifurcations. Moreover, the operating diagrams describe the asymptotic behavior of this system by varying the control parameters and show the effect of the inhibition of predation on the emergence of the bistability region and the reduction until the disappearance of the coexistence region by increasing this inhibition parameter.

Study of performance criteria of serial configuration of two chemostats

This paper deals with thorough analysis of serial configurations of two chemostats. We establish an in-depth mathematical study of all possible steady states, and we compare the performances of the two serial interconnected chemostats with the performances of a single one. The comparison is evaluated under three different criteria. We analyze, at steady state, the minimization of the output substrate concentration, the productivity of the biomass and the biogas flow rate. We determine specific conditions, which depend on the biological parameters, the operating parameters of the model and the distribution of the total volume. These necessary and sufficient conditions provide the most efficient serial configuration of two chemostats versus one. Complementarily, this mainly helps to discern when it is not advisable to use the serial configuration instead of a simple chemostat, depending on: the considered criterion, the operating parameters fixed by the operator and the distribution of the volumes into the two tanks.

Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model

This paper deals with a mathematical analysis of two-steps model of anaerobic digestion process, including dynamics of soluble microbial products (SMP). We propose to investigate effects of the new variable SMP on qualitative properties of the process in different generic cases. Equilibria of the model are graphically established considering qualitative properties of the kinetics and, their stability are proved theoretically and/or verified by numerical simulations. It will shown that the model has a rich qualitative behavior as equilibria bifurcation and multi-stability according to the considered bifurcation parameter.

Operating diagram of a flocculation model in the chemostat

International audience

The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species.

L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

Effect of different modes of erbium:yttrium aluminum garnet laser on shear bond strength to dentin

OBJECTIVES

The aim of this study was to evaluate the effect of different surface treatments on the shear bond strength (SBS) of resin composites to dentin using total etch dentin bonding adhesives.

MATERIALS AND METHODS

Sixty extracted human molars were flattened to obtain dentin surfaces. The samples were divided into three groups (n = 20): Group I: 37% phosphoric acid + optibond FL + resin composite; Group II: Erbium:yttrium aluminum garnet (Er:YAG) laser (medium short pulse [MSP] mode, 120 mJ/10 Hz) + optibond FL + resin composite; Group III: Er:YAG laser (quantum square pulse [QSP] mode, 120 mJ/10 Hz) + optibond FL + resin composite. After the specimens were prepared, the SBS test was performed at a crosshead speed of 0.5 mm/min. The fractured specimens were examined under a stereomicroscope to evaluate the fracture pattern. Statistical analyses were performed with one-way ANOVA and Tukey's honestly significant difference tests. One sample of treated dentin surface from each group was sputter-coated with gold, and scanning electron microscope (SEM) images were captured.

RESULTS

Acid etching showed significantly higher SBS than the other groups (P < 0.05). However, the difference between Er:YAG MSP and QSP mode groups was not statistically significant (P > 0.05). SEM images of the acid-etched dentin surface showed opened dentinal tubule with a regular surface, but Er:YAG MSP mode treated surface was irregular. The surface treated with Er:YAG QSP mode represented wide dentinal tubules with a clean and flat surface.

CONCLUSION

Using different modes (MSP and QSP) of Er:YAG laser for dentin surface treatment before application of total etch adhesives is still not an sufficient alternative compared to acid etching.

The operating diagram of a model of two competitors in a chemostat with an external inhibitor

Understanding and exploiting the inhibition phenomenon, which promotes the stable coexistence of species, is a major challenge in the mathematical theory of the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor. The model is a four-dimensional system of ordinary differential equations. Using general monotonic growth rate functions of the species and absorption rate of the inhibitor, we give a complete analysis for the existence and local stability of all steady states. We focus on the behavior of the system with respect of the three operating parameters represented by the dilution rate and the input concentrations of the substrate and the inhibitor. The operating diagram has the operating parameters as its coordinates and the various regions defined in it correspond to qualitatively different asymptotic behavior: washout, competitive exclusion of one species, coexistence of the species around a stable steady state and coexistence around a stable cycle. This bifurcation diagram which determines the effect of the operating parameters, is very useful to understand the model from both the mathematical and biological points of view, and is often constructed in the mathematical and biological literature.

Asymmetric dispersal in the multi-patch logistic equation

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been fully analyzed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated with dispersal is either favorable or unfavorable to total population abundance. We pay special attention to the case of asymmetric dispersal, i.e., the situation in which the dispersal rate from patch 1 to patch 2 is not equal to the dispersal rate from patch 2 to patch 1. We show that this asymmetry can have a crucial quantitative influence on the effect of dispersal.

Generalised approach to modelling a three-tiered microbial food-web

The complexity of the anaerobic digestion process has motivated the development of complex models, such as the widely used Anaerobic Digestion Model No. 1. However, this complexity makes it intractable to identify the stability profile coupled to the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). In a previous study this model was simplified and reduced to its very backbone to describe a three-tiered chlorophenol mineralising food-web, with its stability analysed numerically using consensus values for the various biological parameters of the Monod growth functions. Steady-states where all organisms exist were always stable and non-oscillatory. Here we investigate a generalised form of this three-tiered food-web, whose kinetics do not rely on the specific kinetics of Monod form. The results are valid for a large class of growth kinetics as long as they keep the signs of their derivatives. We examine the existence and stability of the identified steady-states and find that, without a maintenance term, the stability of the system may be characterised analytically. These findings permit a better understanding of the operating region of the bifurcation diagram where all organisms exist, and its dependence on the biological parameters of the model. For the previously studied Monod kinetics, we identify four interesting cases that show this dependence of the operating diagram with respect to the biological parameters. When maintenance is included, it is necessary to perform numerical analysis. In both cases we verify the discovery of two important phenomena; i) the washout steady-state is always stable, and ii) a switch in dominance between two organisms competing for hydrogen results in the system becoming unstable and a loss in viability. We show that our approach results in the discovery of an unstable operating region in its positive steady-state, where all three organisms exist, a fact that has not been reported in a previous numerical study. This type of analysis can be used to determine critical behaviour in microbial communities in response to changing operating conditions.

A density-dependent model of competition for one resource in the chemostat

This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived. The bifurcations of steady states according to interspecific interference parameters are analyzed in a particular case of density-dependent growth rates which are usually used in the literature. The operating diagrams show how the model behaves by varying the operating parameters and illustrate the effect of the intra- and interspecific interference on the disappearance of coexistence region and the occurrence of bi-stability region. Concerning the small enough interspecific interference terms, we would shed light on the global convergence towards the coexistence steady state for any positive initial condition. When the interspecific interference pressure is large enough this system exhibits bi-stability where the issue of the competition depends on the initial condition.

Competition for a single resource and coexistence of several species in the chemostat

We study a model of the chemostat with several species in competition for a single resource. We take into account the intra-specific interactions between individuals of the same population of micro-organisms and we assume that the growth rates are increasing and the dilution rates are distinct. Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria. Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium. Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species. The operating diagram describes the asymptotic behavior of this model with respect to control parameters and illustrates the effect of the intra-specific competition on the coexistence region of the species.

Investigation of Blood Compatibility of PMEA Coated Extracorporeal Circuits

In this study, the blood compatibility of the PMEA-coated and uncoated hollow fibers was investigated using poly(2-methoxyethyl acrylate) PMEA-coated (X-coating, Terumo Corp., Japan) and uncoated (Capiox SX 18, Terumo Inc., Japan) oxygenators. Total protein, human serum albumin, fibrinogen, erythrocyte, leukocyte and platelets loss quantities were detected on blood samples taken in five different times during cardiopulmonarybypass (CPB) such as; baseline (T1), during CPB (T2), end of CPB (T3), after protamine injection (T4) and intensive care (T5). The average loss of fibrinogen for uncoated and PMEA-coated fiber surfaces was 1.34 and 0.25 g/L, respectively. After operation protein desorption assayfrom the PMEA-coated and uncoated fiber surfaces were examined, and significant protein desorption differences were found as 1.46 and 5.70 mg/dL, respectively. More platelet aggregation was observed for the uncoated fibers. Also for platelet loss quantities, significant differences were found as 116,000 and 36,000 cell/mm3,respectively,for uncoated and PMEA-coated fibers. Less bleeding was observed in the patients operated with oxygenator containing PMEA-coated fibers; more and longer postoperative haemorrhaging were observed when uncoated circuits have been used; fibrinogen losses caused longer blood clotting times. Differences in adsorbed protein quantities on hollow fiber surface and denaturation were examined by the aid of STM images, which showed that more proteins existed in the sample solution of uncoated fiber surfaces.

A model of a syntrophic relationship between two microbial species in a chemostat including maintenance

Many microbial ecosystems can be seen as microbial 'food chains' where the different reaction steps can be seen as such: the waste products of the organisms at a given reaction step are consumed by organisms at the next reaction step. In the present paper we study a model of a two-step biological reaction with feedback inhibition, which was recently presented as a reduced and simplified version of the anaerobic digestion model ADM1 of the International Water Association (IWA). It is known that in the absence of maintenance (or decay) the microbial 'food chain' is stable. In a previous study, using a purely numerical approach and ADM1 consensus parameter values, it was shown that the model remains stable when decay terms are added. However, the authors could not prove in full generality that it remains true for other parameter values. In this paper we prove that introducing decay in the model preserves stability whatever its parameters values are and for a wide range of kinetics.

Predicting coexistence of plants subject to a tolerance-competition trade-off

Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such a characterization. In the model plant species compete for sites where each site has a fixed stress condition. Species differ both in stress tolerance and competitive ability. Stress tolerance is quantified as the fraction of sites with stress conditions low enough to allow establishment. Competitive ability is quantified as the propensity to win the competition for empty sites. We derive the deterministic, discrete-time dynamical system for the species abundances. We prove the conditions under which plant species can coexist in a stable equilibrium. We show that the coexistence conditions can be characterized graphically, clearly illustrating the trade-off between stress tolerance and competitive ability. We compare our model with a recently proposed, continuous-time dynamical system for a tolerance-fecundity trade-off in plant communities, and we show that this model is a special case of the continuous-time version of our model.

The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out as well as the analysis of the local and global stability of the equilibria. We demonstrate, under general assumptions of monotonicity which are relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.

Oscillations in a Prey-Predator-Superpredator System

The behaviour of a food chain with three populations of the type prey-predator-superpredator is studied in the case where the growth rates of the three populations are highly diversified. The analysis shows that the system can have high-frequency oscillations, due to the interaction between prey and predator, which arise during a low-frequency cycle, due to the interaction between predator and superpredator. Using an averaging method, the dynamics of the superpredator is determined, during the high-frequency oscillations of the prey and predator.

Global dynamics of the chemostat with different removal rates and variable yields

In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone growth functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. We construct a Lyapunov function which reduces to the Lyapunov function used by S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growth functions are of Michaelis-Menten type and the yields are constant. Various applications are given including linear, quadratic and cubic yields.

Clinical impact and biomaterial evaluation of autologous platelet gel in cardiac surgery

We compared the clinical efficacy of autologous platelet gel (APG) and gelatine (CONT), including biomaterial evaluation. In a prospective, randomized, controlled trial, 64 patients undergoing complex coronary artery bypass graft (CABG) surgery and/or aortic surgery, in whom the surgeon was able to identify a bleeding site for which conventional means to stop bleeding were impractical or proved unsuccessful, were enrolled. Aortic punch biopsy from each patient was harvested in explant cell (EC) culture media. Hemostasis success for the “oozing” category was 89% in APG and 60% in CONT (p< 0.05). For the “heavy bleeding” category, the success rates were 92% in APG and 45% in CONT (p<0.01). Contact of gelatine inhibited EC proliferation and APG increased cell cycling and EC quantity. Phagocytic capacity (PC) was significantly higher in the APG group (p<0.001). APG was significantly better than CONT with respect to hemostatic success rate, effects on wound healing and increased resistance to infection (PC).

Qualitative simulation of genetic regulatory networks using piecewise-linear models

In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

Intracytoplasmic sperm injection versus in vitro fertilization for patients with a tubal factor as their sole cause of infertility: a prospective, randomized trial

OBJECTIVE

To compare the efficacy of intracytoplasmic sperm injection and IVF in women with a tuboperitoneal factor as their sole cause of infertility.

DESIGN

Prospective, randomized study.

SETTING

Hacettepe University Assisted Reproduction Unit, Ankara, Turkey.

PATIENT(S)

Seventy-six consecutively seen patients with tuboperitoneal factor infertility were randomized on an alternate basis to undergo either intracytoplasmic sperm injection (38 patients and cycles) or IVF (38 patients and cycles).

INTERVENTION(S)

Intracytoplasmic sperm injection and IVF.

MAIN OUTCOME MEASURE(S)

Fertilization, implantation, and clinical pregnancy rates.

RESULT(S)

A comparable number of oocytes and embryos were obtained with intracytoplasmic sperm injection and IVF. The two-pronuclei fertilization rates per metaphase II oocyte or mature cumulus-oocyte complex were similar in the two groups. The numbers of total and grade I embryos transferred also were similar. Comparisons of intracytoplasmic sperm injection and IVF did not reveal any statistically significant differences in individual implantation rates (38.75% +/- 24.46% and 34.58% +/- 16.97%, respectively) clinical pregnancy rates per cycle (21.05% and 21.05%, respectively), or take-home infant rates (18.42% and 15.79%, respectively). The type of procedure performed was not a significant predictor of clinical pregnancy.

CONCLUSION(S)

When a decision is made to proceed with an assisted reproductive technique in patients with a tubal factor as their sole cause of infertility, IVF should be the initial treatment of choice.