Effect of variable surrounding on species creation

We constructed a model of speciation from evolution in an ecosystem consisting of a limited amount of energy recources. The species possesses genetic information, which is inherited according to the rules of the Penna model of genetic evolution. The increase in the number of the individuals of each species depends on the quality of their genotypes and the available energy resources. The decrease in number of the individuals results from genetic death or maximum-age reaching by the individual. The amount of energy resources is represented by a solution of the differential logistic equation, where the growth rate of the amount of the energy resources has been modified to include the number of individuals from all species in the ecosystem under consideration. The fluctuating surrounding is modelled with the help of the function V(x, t) = 1/4 x4 + 1/2 b(t)x2, where x represents phenotype and the coefficient b(t) shows the cos(omega t) time dependence. The closer the value x of an individual to the minimum of V(x, t), the better adapted its genotype to the surrounding. We observed that the life span of the organisms strongly depends on the value of the frequency omega. It becomes shorter the more frequent the changes of the surrounding. However, there is a tendency for the species that have a higher value of the reproduction age aR to win the competition with the other species. Another observation is that small evolutionary changes of the inherited genetic information lead to spontaneous bursts of the evolutionary activity when many new species may appear in a short period.     

A mathematical derivation of size spectra in fish populations

Taking into account a predator/prey size ratio in a size-structured population model leads to a partial derivative equation of which we study the properties. By expliciting the structure of the attractor of this equation, it is shown that a simple mechanism, size-based opportunistic predation, can explain the stability in the shape of size spectra observed in various marine ecosystems.     

Mass extinctions,biodiversity explosions and ecological niches

The logistic model proposed by Courtillot and Gaudemer to describe the growth of biodiversity during geological ages is more explored here and further developed. A new parameterisation is first proposed. Another expression of this model is obtained by introducing a new variable representing the number of ecological niches. It appears that the rates of increase of biodiversity during Jurassic and Cretaceous periods is quite different from other ones. The classical literature essentially focuses on possible extinction mechanisms, but explosions in biodiversity must be more precisely explored. For this purpose, on the basis of data analysis through different expressions of the logistic model, different ecological mechanisms can be assumed (e.g., qualitative and quantitative niches changes, possible appearance of new kinds of ecological relationships, such as 'niche-sharing', which involves coexistence or cooperation), even if genetic processes must also be involved. Finally, we emphasise the astonishing speed of biological diversification following a 'catastrophic' mass extinction. We could refer to this feature as 'catastrophic biological diversification'.     

Community diversity and total abundance: Quantitative predictions from competition niche theory

Lotka–Volterra niche competition theory (LVNCT) is based on Lotka–Volterra competition equations with competition coefficients between pairs of species determined by the intensity of their niche overlap though the MacArthur–Levins niche overlap formula. Here I study analytically and numerically the predictions of LVNCT concerning total abundance and biodiversity, measured by the Shannon equitability index. Firstly, a set of simplifying assumptions that render the LVNCT amenable of analytical treatment are considered. In particular I derive an approximated formula for the total abundance, as the inverse of the mean value of the interspecific competition coefficients, which works pretty well both for the transient and steady regime and for a wide range of the typical niche width σ. Secondly, I analyze, by means of simulations, the effect of relaxing the above simplifying assumptions when considering more realistic conditions. It turns out that the approximated formula for the total abundance is quite robust and its potential implications for management are discussed. I also analyze the predicted relationship between community productivity and diversity.     

Individual-based spatially-explicit model of an herbivore and its resource: the effect of habitat reduction and fragmentation

We present an individual-based, spatially-explicit model of the dynamics of a small mammal and its resource. The life histories of each individual animal are modeled separately. The individuals can have the status of residents or wanderers and belong to behaviorally differing groups of juveniles or adults and males or females. Their territory defending and monogamous behavior is taken into consideration. The resource, green vegetation, grows depending on seasonal climatic characteristics and is diminished due to the herbivore's grazing. Other specifics such as a varying personal energetic level due to feeding and starvation of the individuals, mating preferences, avoidance of competitors, dispersal of juveniles, as a result of site overgrazing, etc., are included in the model. We determined model parameters from real data for the species Microtus ochrogaster (prairie vole). The simulations are done for a case of an enclosed habitat without predators or other species competitors. The goal of the study is to find the relation between size of habitat and population persistence. The experiments with the model show the populations go extinct due to severe overgrazing, but that the length of population persistence depends on the area of the habitat as well as on the presence of fragmentation. Additionally, the total population size of the vole population obtained during the simulations exhibits yearly fluctuations as well as multi-yearly peaks of fluctuations. This dynamics is similar to the one observed in prairie vole field studies.     

Contribution to the logistic theory of growth: temporal structure and growth potential

The analysis of a structured population according to three (juvenile, mature and senescent) cellular states is carried out within the framework of Delattre's transformation systems theory. Growth in number, with the dissymmetry of cell divisions, is determined by an autocatalysis process under the constraint of the availability of a source. Two models are presented: their dynamics results in a growth of the exponential type or of the sigmoidal type, respectively. In the sigmoidal case, the logistic equation (Richards-Nelder's function with adjunction of a lower asymptote Y not equal to 0) fits satisfactorily the simulated data of the total cell number Y. The growth potential is defined as the instantaneous capacity of autocatalysis, which is expressed in relation to the present 'mitotic resources' (source + non-senescing mature cells). The acceleration variations d2Y/dt2 are in close agreement with the growth potential gradient. The analysis is then generalized to other population structuring. As a result, the logistic equation can be interpreted in terms of a formal model of growth of a structured population submitted to autocatalysis and competition.     

Permanence induced by life-cycle resonances: the periodical cicada problem

Periodical cicadas are known for their unusually long life cycle for insects and their prime periodicity of either 13 or 17 years. One of the explanations for the prime periodicity is that the prime periods are selected to prevent cicadas from resonating with predators with submultiple periods. This paper considers this hypothesis by investigating a population model for periodical predator and prey. The study shows that if the periods of the two periodical species are not coprime, then the predator cannot resist the invasion of the prey. On the other hand, if the periods are coprime, then the predator can resist the invasion of the prey. It is also shown that if the periods are not coprime, then the life-cycle resonance can induce a permanent system, in which no cohorts are missing in both populations. On the other hand, if the periods are coprime, then the system cannot be permanent.     

Cytomechanics of cell deformations and migration: from models to experiments

A cytomechanical model bas been proposed to analyse cell-cell interactions and cell migration through chemotaxis. We consider as the leading assumption that the cell cortical tension is locally modified by the protrusive activity of neighbour cells and binding of chemoattractant molecules to membrane receptors respectively. The model derives from the one initially proposed by Alt and Tranquillo (1995), which successfully describes experimentally observed cyclic autonomous cell shape changes. It is based on force balance equations coupling intracellular hydrostatic pressure and cell cortex contraction. Considering the protrusive dynamics of L929 fibroblats observed by videomicroscopy, we simulated the influence of neighbouring protrusions on a cell spontaneous pulsating behaviour. We further investigated the role of an extracellular gradient as another kind of external stimulus. The model illustrates how binding of chemoattractant molecules can induce a cell morphological instability that, above an intracellular stress threshold, will break the cell-substratum attachment. As a result, realistic cell chemotaxis can be simulated.     

Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations

The Lotka–Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state. Such path is known as turnpike property. Some experiments are performed to observe such turnpike phenomenon in the hunting problem. Based on the turnpike property, we implement a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.     

Avoiding toxic prey may promote harmful algal blooms

Blooms of freshwater cyanobacteria are a worldwide spread environmental issue. Despite toxin producing planktonic species are generally expected to be poor competitors for resources, dense blooms of toxic cyanobacteria, such as Microcystis, do often occur in nature. Experimental results suggest that the formation of such blooms is promoted by the predatory activity of zooplankton. In fact, such predator grazes on both the nontoxic and toxic species despite the toxicity of the latter actually inhibits its growth. We model this phenomenon through a Lotka–Volterra reaction–diffusion system. Our goal is to investigate the coupled role of toxicity and zooplankton's predation in the persistence of the toxic prey and to study the mechanisms behind the formation of spatially local toxic blooms. It is known that the classical Lotka-Volterra system consisting of one prey and one predator never exhibits pattern formation. In this paper, we show that the introduction of a toxic prey may destabilize the spatially homogeneous coexistence and trigger spatial pattern formation. We also show that local blooms more likely occur when predators avoid the toxic prey and when the strength of the toxicity is of an intermediate level.     

Non-invasive detection of respiratory muscles activity during assisted ventilation

The instantaneous pressure applied by the respiratory muscles [Pmus(t)] of a patient under ventilatory support may be continuously assessed with the help of a model of the passive respiratory system updated cycle by cycle. Inspiratory activity (IA) is considered present when Pmus goes below a given threshold. In six patients, we compared IA with (i) inspiratory activity (IAref) obtained from esophageal pressure and diaphragmatic EMG and (ii) that (IAvent) detected by the ventilator. In any case, a ventilator support onset coincides with an IA onset but the opposite is not true. IA onset is always later than IAref beginning ((0.21 +/- 0.10 s) and IA end always precedes IAref end (0.46 +/- 0.16 s). These results clearly deteriorate when the model is not updated.     

Odor intensity of binary mixtures of odorous compounds

This paper presents the MBO model for the perceived intensity of odour mixtures. This model is based on an equation previously reported by our team, intended to model the whole stimulus-response intensity curve of pure odorous compounds. The MBO model was applied to a set of published data, and compared to other published models. The results show a high modelling efficiency of the MBO model compared to other proposed equations, especially for binary mixtures exhibiting significant asymmetry of intensity for different ratios of the two components. Furthermore, the MBO model includes parameters specific to the respective effects of each component in the mixture, which may help to clarify the masking and synergy effects that are often sought in odour mixtures.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

Modeling the batch bacteriocin production system by lactic acid bacteria by using modified three-dimensional Lotka–Volterra equations

Different batch cultures of Lactococcus lactis CECT 539, a nisin-producing strain, were carried out in culture media prepared with whey and mussel processing wastes. From these cultures, a reasonable system of differential equations, similar to the three-dimensional Lotka–Volterra two predators-one prey model, was set up to describe, for the first time, the relationship between the absolute rates of growth, pH drop and nisin production.Thus, the nisin production system was described as a three-species (pH, biomass and nisin) ecosystem. In this case, both nisin and biomass production were considered as two pH-dependent species that compete for the nitrogen source. Excellent agreement (R² values ≥0.9885) resulted between model predictions and the experimental data, and significant values for all the model parameters were obtained. The developed model was demonstrated (R² values ≥0.9874) for five batch cultivations of the strains L. lactis CECT 539 in MRS broth and Lactobacillus sakei LB 706 (sakacin A producer), Pediococcus acidilactici LB42-923 (pediocin AcH producer), L. lactis ATCC 11454 (nisin producer) and Leuconostoc carnosum Lm1 (leuconocin Lcm1 producer) in TGE broth. These results suggest that the batch bacteriocin production system in these culture media can be successfully described by using the Lotka–Volterra approach.     

Conservation of secondary structure in 5 S ribosomal RNA: a uniform model for eukaryotic, eubacterial, archaebacterial and organelle sequences is energetically favourable

The most commonly accepted secondary structure models for 5S RNA differ for molecules of eubacterial origin, where the four-helix model of Fox and Woese is generally cited, and those of eukaryotic origin, where a fifth helix is assumed to exist. We have carefully aligned all available sequences from eukaryotes, eubacteria, chloroplasts, archaebacteria and plant mitochondria. We could thus derive a unified secondary structure model applicable to all 5S RNA sequences known to-date. It contains the five helices already present in the eukaryotic model, extended by additional segments that were not previously assumed to be universally present. One of the helices can be written in two equilibrium forms, which could reflect the existence of a flexible, dynamic structure. For the derivation of the model and the estimation of the free energies we followed a set of rules optimized to predict the tRNA cloverleaf. The stability of the unified model is higher than that of nearly all previously proposed sequence-specific and general models.     

Large ecosystems in transition: Bifurcations and mass extinction

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently the first of its kind to include a feedback mechanism coupling climate and population dynamics. Moreover, we take into account self-limitation effects. The model explains the coexistence of many species, yet also displays the possibility of catastrophic bifurcations, where all species become extinct under the influence of abiotic factors. We show that as these factors change there are different regimes of ecosystem behavior, including a possibly chaotic regime when abiotic influences are sufficiently strong.     

Analytical theory of species abundance distributions of a random community model

We review the history and recent progress of the analytical theories of a random community models. In particular, we focus on a global stability analysis of replicator equations with random interactions and species abundance distributions based on statistical mechanics.     

Étude expérimentale de la nutrition d'un copépode commun (Temora stylifera Dana). Effets de la température et de la concentration de nourriture

The ingestion rate of phytoplankton by adult Temora stylifera Dana changes with concentration of algae and with temperature. From the experimental results, two types of curves were fitted to the data. The effects of these two variables are generally considered independently in grazing models. Thus, the maximal ingestion parameter of the relationship between ingestion and phytoplankton concentration is expressed as a function of temperature. It is therefore possible to formulate simultaneously the effect of these two factors. This formulation of grazing, after normalization of units, can be easily generalized to other filter-feeding copepods.     

Multi-compartmental modelling and experimental design for glucose transport studies in insulin-resistant rats

Many pathologies are associated with abnormalities of glucose metabolism or with perturbations of its transport (type 2 diabetes or insulin-resistance). The pre-diabetic state is characterised by a state of insulin-resistance, in others words a defect of glucose transport in insulin-sensible tissues, such as muscles and adipose tissues. The mathematical modelling of experimental data can be an excellent method to explore the mechanisms implied in the studied biological phenomenon. Thus, starting from a symbolic formulation like the compartmental modelling, it can be possible to develop a theoretical basis for the observation and to consider the best-adapted experiments for the study. We showed with mathematical models that [123I]-6-deoxy-6-iodo-D-glucose (6-DIG), shown as a tracer of glucose transport in vitro, could point out this transport abnormality. To quantify the insulin resistance, we estimated the fractional transfer coefficients of 6-DIG from the blood to the organs. We realised many studies to lead to a satisfying model; special attention has been paid to the precision of the parameter to select the best model. The results showed that by associating experimental data obtained with 6-DIG activities and an adapted mathematical model, discriminating parameters (in and out fractional transfer coefficients) between the two groups (control and insulin-resistant rats) could be pointed out.