Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Características físicas e químicas do habitat da Biomphalaria tenagophila (Mollusca, Planorbidae)

Foram realizadas mensalmente, através de conchadas aleatórias, coletas de caramujos e de água, em uma pequena represa, visando a contribuir para o conhecimento das características físico-químicas da água e sua possível influência sobre alguns parâmetros, biológicos. Dos 17 fatores analisados, a Alcalinidade e a Condutividade se mostraram positivamente correlacionadas com a densidade de B. tenagophila (r = +0,224 e +0,290), enquanto que CO2 e Acidez se correlacionaram negativamente com densidade (r = -0,592 e -0,601). Alcalinidade e Dureza Total apresentaram valores um pouco acima de 100 mg/l de CaCO3; Condutividade e Cloretos, teores considerados altos para a região (680,1 ± 64,3micronS/cm e 94,9 ± 38,7 mg/l). Os demais fatores, como pH e OD, estiveram dentro dos padrões de águas brutas de abastecimento. As densidades de B. tenagophila foram mais baixas nos seis meses subseqüentes a um longo período de chuvas tortenciais (12 a 30 caramujos/ 90 conchadas/mês) e nos verões chuvosos. Nos meses mais frios de 1980 foram mais elevadas. Os diâmetros médios mensais foram sempre superiores a 13 mm, chegando a 21,4 ± 4,1 mm; mas a média da maioria dos meses girou em torno de 17 mm. Não houve correlação diâmetro/densidade (r = 0,037), nem densidade/temperatura (r = 0,065).

Ecology of sandflies (Diptera: Psychodidae) in a restricted focus of cutaneous leishmaniasis in Northern Venezuela: II. Species composition in relation to habitat, catching method and hour of catching

The ecology of phlebotomine sandflies in an endemic focus of cutaneous leishmaniasis in Northern Venezuela (San Esteban, Carabobo State) was investigated through a year-term study. Three different habitats: viz. a house, a pridomestic area and a sylvatic area, were covered and the species composition, the abundance and occurrence of each species were analyzed in relation to the habitats, catching methods and hour of catching. L. panamensis, L. gomezi and L. ovallesi are the species which bite man, although almost exclusively at night. All of them hide by day and are common in the sylvatic area. Moreover, L. panamensis and L. gomezi successfully approach the house and seem to settle in the peridomestic area. L. shannoni and L. olmeca bicolor also approach and accidentally bite man. L. trinidadensis, L. atroclavata and L. cayennensis are the common non-antrhopophilic species in the area.

Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).

Structured RNAs in the ENCODE selected regions of the human genome.

Functional RNA structures play an important role both in the context of noncoding RNA transcripts as well as regulatory elements in mRNAs. Here we present a computational study to detect functional RNA structures within the ENCODE regions of the human genome. Since structural RNAs in general lack characteristic signals in primary sequence, comparative approaches evaluating evolutionary conservation of structures are most promising. We have used three recently introduced programs based on either phylogenetic-stochastic context-free grammar (EvoFold) or energy directed folding (RNAz and AlifoldZ), yielding several thousand candidate structures (corresponding to approximately 2.7% of the ENCODE regions). EvoFold has its highest sensitivity in highly conserved and relatively AU-rich regions, while RNAz favors slightly GC-rich regions, resulting in a relatively small overlap between methods. Comparison with the GENCODE annotation points to functional RNAs in all genomic contexts, with a slightly increased density in 3'-UTRs. While we estimate a significant false discovery rate of approximately 50%-70% many of the predictions can be further substantiated by additional criteria: 248 loci are predicted by both RNAz and EvoFold, and an additional 239 RNAz or EvoFold predictions are supported by the (more stringent) AlifoldZ algorithm. Five hundred seventy RNAz structure predictions fall into regions that show signs of selection pressure also on the sequence level (i.e., conserved elements). More than 700 predictions overlap with noncoding transcripts detected by oligonucleotide tiling arrays. One hundred seventy-five selected candidates were tested by RT-PCR in six tissues, and expression could be verified in 43 cases (24.6%).

Local adaptation and matching habitat choice in female barn owls with respect to melanic coloration.

Local adaptation is a major mechanism underlying the maintenance of phenotypic variation in spatially heterogeneous environments. In the barn owl (Tyto alba), dark and pale reddish-pheomelanic individuals are adapted to conditions prevailing in northern and southern Europe, respectively. Using a long-term dataset from Central Europe, we report results consistent with the hypothesis that the different pheomelanic phenotypes are adapted to specific local conditions in females, but not in males. Compared to whitish females, reddish females bred in sites surrounded by more arable fields and less forests. Colour-dependent habitat choice was apparently beneficial. First, whitish females produced more fledglings when breeding in wooded areas, whereas reddish females when breeding in sites with more arable fields. Second, cross-fostering experiments showed that female nestlings grew wings more rapidly when both their foster and biological mothers were of similar colour. The latter result suggests that mothers should particularly produce daughters in environments that best match their own coloration. Accordingly, whiter females produced fewer daughters in territories with more arable fields. In conclusion, females displaying alternative melanic phenotypes bred in habitats providing them with the highest fitness benefits. Although small in magnitude, matching habitat selection and local adaptation may help maintain variation in pheomelanin coloration in the barn owl.

Variation in habitat suitability does not always relate to variation in species' plant functional traits.

Habitat suitability models, which relate species occurrences to environmental variables, are assumed to predict suitable conditions for a given species. If these models are reliable, they should relate to change in plant growth and function. In this paper, we ask the question whether habitat suitability models are able to predict variation in plant functional traits, often assumed to be a good surrogate for a species' overall health and vigour. Using a thorough sampling design, we show a tight link between variation in plant functional traits and habitat suitability for some species, but not for others. Our contrasting results pave the way towards a better understanding of how species cope with varying habitat conditions and demonstrate that habitat suitability models can provide meaningful descriptions of the functional niche in some cases, but not in others.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Comparing population distributions from bin-aggregated sample data: an application to historical height data from France

This paper develops a methodology to estimate the entire population distributions from bin-aggregated sample data. We do this through the estimation of the parameters of mixtures of distributions that allow for maximal parametric flexibility. The statistical approach we develop enables comparisons of the full distributions of height data from potential army conscripts across France's 88 departments for most of the nineteenth century. These comparisons are made by testing for differences-of-means stochastic dominance. Corrections for possible measurement errors are also devised by taking advantage of the richness of the data sets. Our methodology is of interest to researchers working on historical as well as contemporary bin-aggregated or histogram-type data, something that is still widely done since much of the information that is publicly available is in that form, often due to restrictions due to political sensitivity and/or confidentiality concerns.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.