A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

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.     

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.     

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.     

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.     

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.     

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'.     

The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation

The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.     

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.     

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.     

Evolution of hemocyte concentration in the melanogaster subgroup species

We explore two possible hypotheses about the ecological factors driving the evolution of hemocyte load in insects. The first is parasite infection risk, its variability and the genetic diversity of parasites. The other supposes that all the other factors of environmental stress drive the evolution through a pleiotropic selection on metabolic rate. The two hypotheses are tested with data on hemocyte load and ecology of six Drosophila species of the melanogaster subgroup. Hemocyte load correlates significantly with the parasite-driven selection index, but not with the stress selection index. The result being based on too little data to conclude definitely, this work must be considered more as a methodological research based on published results on insect physiology immunity and ecology rather than an empirical evidence of such a relationship.     

Conservation and control strategies for the wolf (Canis lupus) in western Europe based on demographic models

Securing the long-term acceptance of large carnivores such as the wolf (Canis lupus) in Europe and North America raises a difficult challenge to conservation biologists: planning removals to reduce depredations on livestock while ensuring population viability. We use stochastic-stage-structured population models to investigate wolf population dynamics and to assess alternative management strategies. Among the various management strategies advocated by agencies, zoning that involves eliminating wolves outside a restricted area should be designed with caution, because probabilities of extinction are extremely sensitive to the maximum number of packs that a zone can support and to slight changes in stage specific survival probabilities. In a zoned population, viability is enhanced more by decreasing mortality rates in all classes than by increasing wolf zone size. An alternative to zoning is adaptive management, where there is no limit on pack number but population control can be operated whenever some predefined demographic conditions are met. It turns out that an adaptive management strategy that removes a moderate percentage (10%) of the population following each year of more than 5% of total population growth would provide visible actions addressing public concerns while keeping extinction probability low.     

A reappraisal of the geographical distribution of the genus Pseudouroplectes Lourenço (Scorpiones: Buthidae) in Madagascar

We review aspects of the distributional patterns of Malagasy scorpions belonging to the endemic genus Pseudouroplectes (family Buthidae), restricted to dry forests formations in the south and southwest. One species is described here as new to science. We propose that the observed distributional pattern of members of this genus is not only a consequence of recent ecological features of the landscape, but also of historical biogeographical factors associated with the antiquity of this scorpion lineage.     

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.     

Biology and population dynamics of Porcellionides sexfasciatus (Crustacea,Isopoda, Oniscidea)

The biology and the population dynamics of Porcellionides sexfasciatus Budde-Lund (1879) were studied on a field and carried out at Garat Naam (Kasserine, Tunisia) from July 1996 to June 1998. The reproduction exhibited a seasonal pattern extending from February/March to October/November. The juveniles appeared in the population from April to November. Size frequency distributions were analysed and 14 cohorts were recognised during the sampling period. Six cohorts were identified at the first sampling and eight new ones on the other samplings. Among these latter cohorts, three were tracked till they disappeared. Minimum average length of new cohorts ranged from 3.07 +/- 0.35 mm to 3.47 +/- 0.2 mm. Maximum average length of cohorts was 10.42 mm. P. sexfasciatus is a semi-annual species (females producing two or three broods per year), with iteroparous and amphogenes females (females reproducing twice or more in their life and producing both males and females), and bivoltine life cycle (two generations per year). The females are able to produce two broods, in the laboratory, without new mating. Fecundity and fertility, corresponding to the number of eggs or embryos per brood, appeared positively correlated with females' size. Although oscillating throughout the year, the sex ratio was often in equilibrium.     

A new look at genome size,evolutionary duration and genetic variation in salamanders

Salamanders have some of the largest genomes among vertebrates, and also some of the lowest reported levels of genetic diversity. Paedomorphs, in particular, have the largest genomes on average among urodela, and display exceptionally low levels of nucleotide and protein variation. Here, we address the question of genetic variation in relation to genome size in eight different salamander families. Using the rag1 gene as a probe for evolutionary rates, we found that rates of substitution are exceptionally low in obligate paedomorphs (neotenes) and other salamander species. Substitution rates in some cases are as low as those reported for cartilaginous fish, which have the slowest mutation rates recorded so far in vertebrates. Confirming and extending an earlier study, we also found that genome size is correlated with phylogenetic age in Plethodontidae, indicating a more general trend in genome size evolution in urodela. The Plethodontidae, furthermore, display much higher levels of genetic variance than the obligate neotene families, consistent with greater habitat heterogeneity in terrestrial salamanders. Finally, we present the first direct evidence of a gene, rag1, whose substitution rate is negatively associated with genome size. Based on these and other observations, we propose a hypothesis according to which mutation rates in nuclear genes tend to increase as genome size decreases during the course of vertebrate evolution.     

An agent-based model of sleeping sickness: simulation trials of a forest focus in southern Cameroon

An agent-based model (AMB) used to simulate the spread of Human African Trypanosomiasis is presented together with the results of simulations of a focus of the disease. This model is a completely spatialized approach taking into account a series of often overlooked parameters such as human behaviour (activity-related movements), the density and mobility of the disease vectors--tsetse flies (Glossina spp.)--and the influence of other tsetse feeding hosts (livestock and wild animal populations). The agents that represent humans and tsetse flies move in a spatially structured environment managed by specialized location agents. Existing compartmental mathematical models governed by differential equations fail to incorporate the spatial dimension of the disease transmission. Furthermore, on a small scale, transmission is unrealistically represented by entities less than one. This ABM was tested with data from one village of the Bipindi sleeping sickness focus (southern Cameroon) and with obtained realistic simulations of stable transmission involving an animal reservoir. In varying different spatial configurations, we observe that the stability of spread is linked to the spatial complexity (number of heterogeneous locations). The prevalence is very sensitive to the human densities and to the number of tsetse flies initially infected in a given location. A relatively low and durable prevalence is obtained with shortening the phase I. In addition, we discuss some upgrading possibilities, in particular the linkage to a Geographical Information System (GIS). The agent-based approach offers new ways to understanding the spread of the disease and a tool to evaluate risk and test control strategies.     

Phenotypic and genetic divergence among harbour porpoise populations associated with habitat regions in the North Sea and adjacent seas

Determining the mechanisms that generate population structure is essential to the understanding of speciation and the evolution of biodiversity. Here, we investigate a geographical range that transects two habitat gradients, the North Sea to North Atlantic transition, and the temperate to subpolar regions. We studied the harbour porpoise (Phocoena phocoena), a small odontocete inhabiting both subpolar and temperate waters. To assess differentiation among putative populations, we measured morphological variation at cranial traits (N = 462 individuals) and variation at eight microsatellite loci for 338 of the same individuals from Norwegian, British and Danish waters. Significant morphological differentiation reflected the size of the buccal cavity. Porpoises forage in relatively shallow waters preying mainly on benthic species in British and Danish waters, and on mesopelagic and pelagic fish off the coast of Norway. We suggest that the observed differentiation may be explained by resource specialization and either adaptation or developmental responses to different local habitats.