Nonlinearity in Bacterial Population Dynamics: Proposal for Experiments for the Observation of Abrupt Transitions in Patches

An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions in spite of the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental set-up suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation as in Lin et al., Biophys. J. {\bf 87}, 75 (2004) and Perry, J. R. Soc. Interface {\bf 2}, 379 (2005) but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters.Comment: 5 figure

Particle Statistics and Population Dynamics

We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical patch size problem. We analize both cases in which the particles are considered fermions and bosons and show using exact analitical methods that, while the Fermi-Dirac statistics leads to certain extinction for any refuge size, the Bose-Eistein statistics allows survival even for the minimal refuge

Periodically Varying Externally Imposed Environmental Effects on Population Dynamics

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatio-temporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.Comment: 7 pages, 8 figures, include

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure

An application of the generalized Poisson difference distribution to the Bayesian modelling of football scores

The analysis of sports data, in particular football match outcomes, has always produced an immense interest among the statisticians. In this paper, we adopt the generalised Poisson difference distribution (GPDD) to model the goal difference of football matches. We discuss the advantages of the proposed model over the Poisson difference (PD) model which was also used for the same purpose. The GPDD model, like the PD model, is based on the goal difference in each game which allows us to account for the correlation without explicitly modelling it. The main advantage of the GPDD model is its flexibility in the tails by considering shorter as well as longer tails than the PD distribution. We carry out the analysis in a Bayesian framework in order to incorporate external information, such as historical knowledge or data, through the prior distributions. We model both the mean and the variance of the goal difference and show that such a model performs considerably better than a model with a fixed variance. Finally, the proposed model is fitted to the 2012-13 Italian Serie A football data and various model diagnostics are carried out to evaluate the performance of the model

Net-charge probability distributions in heavy ion collisions at chemical freeze-out

We explore net charge probability distributions in heavy ion collisions within the hadron resonance gas model. The distributions for strangeness, electric charge and baryon number are derived. We show that, within this model, net charge probability distributions and the resulting fluctuations can be computed directly from the measured yields of charged and multi-charged hadrons. The influence of multi-charged particles and quantum statistics on the shape of the distribution is examined. We discuss the properties of the net proton distribution along the chemical freeze-out line. The model results presented here can be compared with data at RHIC energies and at the LHC to possibly search for the relation between chemical freeze-out and QCD cross-over lines in heavy ion collisions.Comment: 21 pages, 6 figure

A graphical theory of competition on spatial resource gradients

Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations which lead to coexistence in a uniform environment may favor alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes

Range expansion of an invasive species through a heterogeneous landscape - the case of American mink in Scotland

ACKNOWLEDGEMENTS We would like to thank Scottish Natural Heritage, particularly Iain Macleod and Rob Raynor, for data and funding.We are grateful to the Game and Wildlife Conservation Trust, especially Jonathan Reynolds, Vincent Wildlife Trust and Scottish Mink Initiative for supplying data of mink presence and to the Centre for Ecology and Hydrology for the Land Cover Map data. XL acknowledges support from NERC grant NE/J01396X/1Peer reviewedPublisher PD

Heterologous expression of the avirulence gene ACE1 from the fungal rice pathogen Magnaporthe oryzae

The ACE1 and RAP1 genes from the avirulence signalling gene cluster of the rice blast fungus Magnaporthe oryzae were expressed in Aspergillus oryzae and M. oryzae itself. Expression of ACE1 alone produced a polyenyl pyrone (magnaporthepyrone), which is regioselectively epoxidised and hydrolysed to give different diols, 6 and 7, in the two host organisms. Analysis of the three introns present in ACE1 determined that A. oryzae does not process intron 2 correctly, while M. oryzae processes all introns correctly in both appressoria and mycelia. Co-expression of ACE1 and RAP1 in A. oryzae produced an amide 8 which is similar to the PKS-NRPS derived backbone of the cytochalasans. Biological testing on rice leaves showed that neither the diols 6 and 7, nor amide 8 was responsible for the observed ACE1 mediated avirulence, however, gene cluster analysis suggests that the true avirulence signalling compound may be a tyrosine-derived cytochalasan compound.Government of Egypt ScholarshipThe School of Chemistry at the University of Bristol and the Mark Evans ScholarshipKano State Government NigeriaMacArthur FoundationBayero UniversityNigerian Petroleum Technology FundMalaysian Govenment ScholarshipEP/F066104/

Evidence for enzyme catalysed intramolecular [4+2] Diels-Alder cyclization during the biosynthesis of pyrichalasin H

Cytochalasans are highly complex fungal metabolites which exhibit diverse biological activities. Little is known of the chemical steps involved in the construction of the tricyclic core, which consists of an octahydro-isoindole skeleton fused to a macrocyclic ring. Here, using a directed gene knockout and complementation strategy, we show that PyiF is implicated as the proposed intramolecular [4+2] Diels-Alderase required for construction of the tricyclic core of pyrichalasin H 1. © 2020 The Royal Society of Chemistry