As an extension of weed threshold models in which crop losses are based on weed density, an alternative model for grass weeds in cereal crops is proposed that incorporates the theoretical importance of selection for herbicide resistance, initial weed population frequency, and weed seed dispersal. Simulations suggest optimum weed population levels (thresholds) for maintaining genotypes that are susceptible to control practices and which minimize crop yield reductions. Weed population frequency, in combination with dispersal and competitive traits may determine optimum weed management strategies/Model simulations indicate that understanding how agricultural practices select for “weedy” traits (e.g. herbicide resistance, competitive ability, dispersal potential) may be important in determining weed density thresholds.

A minimal model for predator-prey interaction in a composite environment is presented and analysed. We first consider free migrations between two patches for both interacting populations, and then the particular cases where only one-directional migration is allowed and where only one of the two populations can migrate. Our findings indicate that in all cases the ecosystem can never disappear entirely, under the model assumptions. The predator-free equilibrium and the coexistence of all populations are found to be the only feasible stable equilibria. When there are only one-directional migrations, the abandoned patch cannot be repopulated. Other equilibria then arise, with only prey in the second patch, coexistence in the second patch, or prey in both patches but predators only in the second one. For the case of sedentary prey, with predator migration, the prey cannot thrive alone in either of the two environments. However, predators can survive in a prey-free patch due to their ability to migrate into the other patch, provided prey is present there. If only the prey can migrate, the predators may be eliminated from one patch or from both. In the first case, the patch where there are no predators acts as a refuge for the survival of the prey.

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces.In this paper we investigate a mathematical model that has beenshown to display these structures when solved numerically. The model consists of an ordinarydifferential equation coupled with a partial differential equation involving a first-orderhyperbolic aging term together with nonlinear degenerate diffusion. The system is shown toadmit global weak solutions.

The Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) at the University of Hawaii's Institute for Astronomy is a funded project to repeatedly survey the entire visible sky to faint limiting magnitudes (mR ~ 24). It will be composed of four 1.8m diameter apertures each outfitted with fast readout orthogonal transfer Giga-pixel CCD cameras. A single aperture prototype telescopes has achieved first-light in the second half of 2006 with the full system becoming available a few years later. Roughly 60% of the surveying will be suitable for discovery of new solar system objects and it will cover the ecliptic, opposition and low solar-elongation regions. In a single lunation Pan-STARRS will detect about five times more solar system objects than the entire currently known sample. Within its first year Pan-STARRS will have detected 20,000 Kuiper Belt Objects and by the end of its ten year operational lifetime we expect to have found 107 Main Belt objects and achieve ~90% observational completeness for all NEOs larger than ~300m diameter. With these data in hand Pan-STARRS will revolutionize our knowledge of the contents and dynamical structure of the solar system.

In the next generation surveys, the discovery of moving objects can be successful only if an observation strategy and the identification/orbit determination procedure are appropriate for the diverse apparent motions of the target sub-populations. The observations must accurately measure the displacement over a short interval of time; observations believed to belong to the same object have to be connected into tracklets. Information contained in tracklets is in most cases not sufficient to compute an orbit: two or more of them must be identified to provide an orbit. We have developed a method for recursive identification of tracklets allowing an unbiased orbit determination for all sub-populations and efficient enough to cope with the data flow expected from the next generation surveys. The success of the new algorithms can be easily measured only in a simulation, by consulting a posteriori some “ground truth”.

We present here the results of a simulation of the orbit determination for one month of operations of the future Pan-STARRS survey, based upon a Solar System Model with a downsized population of Main Belt asteroids and a full size populations of Trojans, NEO, Centaurs, Comets and TNO. The results indicate that the method already developed and tested to find identifications of NEO and Main Belt asteroids are directly applicable to Trojans. The more distant objects often require modified algorithms, fitting orbits with only 4 parameters in a coordinate system specially adapted to handle very short arcs of observations. These orbits are mostly used as intermediate results, allowing to find full solutions as more tracklets are identified.

When the number density of detections is as large as expected from the next generation surveys, both joining observations into tracklets and identifying tracklets can produce some false results. The only reliable way to remove them is a procedure of tracklet/identification management. It compares the tracklets and the identifications with a complex logic, allowing to discard almost all the false tracklets and all the false identifications. However, the distant objects still present a challenge for orbit determination: they require three tracklets in separate nights. If this requirement is met we have found no problem in achieving an unbiased orbit determination for all populations. Further work will lead to more advanced simulations, in particular by introducing a realistic model for astrometric and photometric errors.

The population ecology of ticks is fundamental to the spatial and temporal variation in the risk of infection by tick-borne pathogens. Tick population dynamics can only be fully understood by quantifying the rates of the demographic processes, which are influenced by both abiotic (climatic) factors acting on the free-living tick stages and biotic (host) responses to the tick as a parasite. Within the framework of a population model, I review methods and results of attempts to quantify (1) rates of tick development and the probability of diapause, (2) the probability of questing for hosts by unfed ticks, (3) the probability of ticks attaching to a host, and (4) tick mortality rates. Biologically, these processes involve the physiological and behavioural response of ticks to temperature, moisture stress and day length that result in specific patterns of seasonal population dynamics and host relationships. Temperate and tropical patterns will be illustrated with reference mostly to Ixodes ricinus and Rhipicephalus appendiculatus, respectively.

We present a simulation population model for the African tick Rhipicephalus appendiculatus, based on previous analyses of the mortality factors most closely correlated with observed population changes at 11 sites in equatorial and South Africa. The model incorporates temperature-dependent rates of egg production and development, climate-driven density-independent mortality rates, particularly during the adult-larval stage, and density-dependent regulation of both nymphs and adults. Diapause is also included for tick populations in southern Africa. The model successfully describes both the seasonality and annual range of variation in numbers of each tick stage observed at each of 4 test sites in Uganda, Burundi and South Africa. Sensitivity analysis showed that the final version of the model is robust to 4-fold variation in most parameter values (that were per force based on informed guesses), but is more sensitive to the regression coefficients determining density-dependent interstadial mortality (that were derived from analysis of field data). The model is able to predict the seasonality of ticks from a site in Kenya where a full prior population analysis was not possible because only adults and nymphs had been counted. The model is potentially applicable to other species of ticks, both tropical and temperate, to predict tick abundance and seasonality as risk factors for tick-borne diseases.

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

In the present paper we study three aspects in the theory of non-homogeneous Markov systems under the continuous-time formulation. Firstly, the relationship between stability and quasi-stationarity is investigated and conditions are provided for a quasi-stationary structure to be stable. Secondly, the concept of asymptotic attainability is studied and the possible regions of asymptotically attainable structures are determined. Finally, the cyclic case is considered, where it is shown that for a system in a periodic environment, the relative structure converges to a periodic vector, independently of the initial distribution. Two numerical examples illustrate the above theoretical results.

The development of simple models for describing the population dynamics of species with overlapping generations is briefly described. The paper then presents a minimally complex simulation model for tsetse populations in which seasonally varying density-independent mortality, generally applied only to the adult stage, is combined with density dependence acting on both puparia and adults. Density dependence regulates population size within limits determined by an interaction between the strength of the density-dependent relationships and the variability of the seasonal density independence. Population data sets for Glossina palpalis and G. morsitans in Nigeria, and G. pallidipes in Kenya are adequately described by the model. Relationships discovered between the density-independent mortality and climatic variables for the Lambwe Valley data set allow predictions of population changes in other sites on the basis of their climatic conditions. Attempts to predict changes in the population of G.pallidipes in Somalia highlight the difficulties of this exercise. A tsetse's demographic response to climate may vary from region to region, making extensive predictions from local data sets difficult. There seems, however, no need to make more complex models to describe observed changes in tsetse populations.

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.