The Effect of the G 1 - S transition Checkpoint on an Age Structured Cell Cycle Model

Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model''s results are discussed.     

Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution

The effect of dispersal on population size and stability is explored for a population that disperses passively between two discrete habitat patches. Two basic models are considered. In the first model, a single population experiences density-dependent growth in both patches. A graphical construction is presented which allows one to determine the spatial pattern of abundance at equilibrium for most reasonable growth models and rates of dispersal. It is shown under rather general conditions that this equilibrium is unique and globally stable. In the second model, the dispersing population is a food-limited predator that occurs in both a source habitat (which contains a prey population) and a sink habitat (which does not). Passive dispersal between source and sink habitats can stabilize an otherwise unstable predator-prey interaction. The conditions allowing this are explored in some detail. The theory of optimal habitat selection predicts the evolutionarily stable distribution of a population, given that individuals can freely move among habitats so as to maximize individual fitness. This theory is used to develop a heuristic argument for why passive dispersal should always be selectively disadvantageous (ignoring kin effects) in a spatially heterogeneous but temporally constant environment. For both the models considered here, passive dispersal may lead to a greater number of individuals in both habitats combined than if there were no dispersal. This implies that the evolution of an optimal habitat distribution may lead to a reduction in population size; in the case of the predator-prey model, it may have the additional effect of destabilizing the interaction. The paper concludes with a discussion of the disparate effects habitat selection might have on the geographical range occupied by a species.     

The effect of intragenic recombination on the number of alleles in a finite population

A two-site infinite allele model is constructed to study the effect of intragenic recombination on the number of neutral alleles and the distribution of their frequencies in a finite population. The results of theory and Monte Carlo simulation of the two-site model demonstrate that intragenic recombination significantly increases the mean and variance of the number of alleles when the rates of mutation and recombination are as large as the reciprocal of the population size. Data from natural populations indicate that this may be a significant process in generating variation and determining its distribution.     

Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a sample of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n; and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.     

Evidence for the non-quasispecies evolution of RNA viruses [corrected

The quasispecies model of RNA virus evolution differs from those formulated in conventional population genetics in that neutral mutations do not lead to genetic drift of the population, and natural selection acts on the mutant distribution as a whole rather than on individual variants. By computer simulation, we show that this model could be inappropriate for many RNA viruses because the neutral sequence space may be too large to allow the formation of a quasispecies distribution. This view is supported by our analysis of gene sequences from vesicular stomatitis virus, which is considered a prototype RNA virus quasispecies. Our results are relevant to the evolution of RNA systems in general.     

A stochastic model of the distribution of unequal competitors between resource patches

We present a stochastic model of individuals' movements between two patches of resources. The population is made up of two types of individual with differing competitive abilities, and two types of movements occur, with individuals moving either to increase their intake rate or at random. Several previous models have used simulations to evaluate the likely distribution of individuals. We instead derive equations for the equilibrium distribution of the population, which can be solved numerically. This avoids the need to choose an initial distribution for the population, and enables us to obtain the probability with which rare events occur. This may not be possible when simulations are used, since a rare event may not occur at all. We find that when random movements are rare, an increase in the rate of random movements out of a patch can increase the number of individuals on that patch. We consider an approximation to the model with rare random movements, which provides an explanation for this phenomenon.     

人为引入和气候变化对灰喜鹊未来分布的影响

气候变化和人为引种正在改变世界物种的分布格局,对生态系统中的关键物种构建分布模型,有助于理解全球气候变化背景下物种的分布变化规律,并预测其对生态系统的潜在影响。灰喜鹊(Cyanopica cyanus)是重要的食虫鸟类,对控制虫害、维持森林生态系统的稳定性具有重要意义,由于人为引种等原因,目前灰喜鹊已在其自然分布地外建立了多处可自我维持的种群。基于气候生态位理论,使用最大熵模型构建了自然分布地模型、引入地模型及综合分布模型等3种模型,模拟灰喜鹊在当前时期、2050s时期及2070s时期的潜在适生区,并以此分析灰喜鹊的分布格局与变化趋势。结果表明：(1)当前时期,自然分布地种群的适生区主要分布于华北、华中和华东地区,而引入地种群的适生区则主要分布于华南和西南地区;(2)在未来气候变化的背景下,各模型结果均表明灰喜鹊有显著的扩张趋势,自然分布地种群主要表现为向高纬度、高海拔地区扩散,截至2070s时期,适生区的质心向北偏东25°方向移动了229.16 km,而引入地种群扩张趋势较缓,截至2070s时期,质心仅向北偏东46°方向移动了67.69 km;(3)从适宜值方面来看,自然分布地模型中...     

Formation and maintenance of discrete wild rabbit (Oryctolagus cuniculus) population systems in arid Australia: Habitat heterogeneity and management implications

Abstract The wild rabbit (Oryctolagus cuniculus L.) is a significant pest in arid and semi‐arid Australia, where erratic rainfall and irregular pasture growth cause population sizes to oscillate, increasing virtually without limit and then crashing during drought conditions. Vacant habitat patches can be rapidly recolonized from nearby patches in high rainfall years. Using two adjoining rabbit population systems in arid and semi‐arid south‐west Queensland, this study evaluates patterns of population differentiation and proposes a mechanism that may lead to the formation of multiple rabbit population systems in the same locality. Using the combined haplotype frequency data from both a local and regional study, estimates of genetic exchange among local populations are considered in conjunction with ecological data to evaluate the significance of habitat attributes (and their spatial distribution) on the local distribution of rabbit populations, both within and between two adjacent population systems. A tentative model is proposed to explain the observed differences in population structure between the two adjoining systems. Under this model, population structure at specific locations is determined primarily by the availability of areas suitable for prolonged colonization and the quality of the intervening habitat that dictates the degree of isolation between locations and therefore the probability of recolonization following local extinctions. It is also suggested that the current rabbit distribution may be a function of the flexibility of behavioural responses in rabbits to the level of spatial heterogeneity of favourable habitats within the two regions.     

A unifying framework for chaos and stochastic stability in discrete population models

 In this paper we propose a general framework for discrete time one-dimensional Markov population models which is based on two fundamental premises in population dynamics. We show that this framework incorporates both earlier population models, like the Ricker and Hassell models, and experimental observations concerning the structure of density dependence. The two fundamental premises of population dynamics are sufficient to guarantee that the model will exhibit chaotic behaviour for high values of the natural growth and the density-dependent feedback, and this observation is independent of the particular structure of the model. We also study these models when the environment of the population varies stochastically and address the question under what conditions we can find an invariant probability distribution for the population under consideration. The sufficient conditions for this stochastic stability that we derive are of some interest, since studying certain statistical characteristics of these stochastic population processes may only be possible if the process converges to such an invariant distribution. Received 15 May 1995; received in revised form 17 April 1996     

A semiparametric test to detect associations between quantitative traits and candidate genes in structured populations

MOTIVATION: Although population-based association mapping may be subject to the bias caused by population stratification, alternative methods that are robust to population stratification such as family-based linkage analysis have lower mapping resolution. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate genes and traits of interest. The association between a candidate gene and a quantitative trait is often evaluated via a regression model with inferred population structure variables as covariates, where the residual distribution is customarily assumed to be from a symmetric and unimodal parametric family, such as a Gaussian, although this may be inappropriate for the analysis of many real-life datasets. RESULTS: In this article, we proposed a new structured association (SA) test. Our method corrects for continuous population stratification by first deriving population structure and kinship matrices through a set of random genetic markers and then modeling the relationship between trait values, genotypic scores at a candidate marker and genetic background variables through a semiparametric model, where the error distribution is modeled as a mixture of Polya trees centered around a normal family of distributions. We compared our model to the existing SA tests in terms of model fit, type I error rate, power, precision and accuracy by application to a real dataset as well as simulated datasets.     

Exploring rarity using a general model for distribution and abundance

We describe a simple model for changes in the distribution and abundance of a metapopulation and use it to explore the conditions leading to different types of rarity. The model suggests that localized populations (those with low patch occupancy but high local abundance) arise from low dispersal, low heterogeneity in extant population size, and frequent local extinctions relative to the potential for recolonization. Scarce populations (with low distribution and abundance) arise when relative local extinction rate is low to moderate and heterogeneity is high or successful dispersal is relatively low. Sparse populations (widespread, but with low local abundance) arise when relative local extinction rate is very low and either spatial heterogeneity or mortality through unsuccessful dispersal is high. In sparse or common species, there may be unstable as well as stable equilibria, implying a threshold distribution and abundance for persistence. The model supports a general correlation between distribution and abundance and suggests that persistence may be threatened by dispersal rates being either too high or too low. The model provides a new perspective on rarity and suggests a simple theoretical foundation for understanding the population-dynamic mechanisms that determine distribution and abundance.     

PREDICTING ADAPTATION UNDER MIGRATION LOAD: THE ROLE OF GENETIC SKEW

Quantitative genetics models have been used to predict the constraints on local adaptation caused by gene flow between populations under migration–selection balance. One key assumption of this approach is that genetic values within a population are normally distributed. Gene flow, however, may generate distributions that are skewed toward the immigrant's mean value. If the response to selection from a skewed distribution is different from that expected under the assumption of normality, models may result in inaccurate predictions. We use individual-based computer simulations to explore this problem, comparing our results to a recent model developed by Hendry et al. (2001) . We show that this model underestimates the equilibrium divergence between populations at migration–selection balance. The extent of this underestimation is correlated with the amount of genetic skew generated by migration and is partly explained by the fact that the analytical model ignores direct selection against hybrid phenotypes. We also show that all else being equal, response to selection in a population with a skewed distribution of genotypes is greater than in a population with normally distributed genotypes. The production of skew under migration–selection balance, however, is itself dependent upon the genetic architecture, with greater deviations from normality produced when alleles contributing to population differentiation have very different effect sizes. We find that both the skew and discrepancies between the models are greatest at intermediate migration rates and moderate to strong selection, which is exactly the region of parameter space that is most empirically relevant.     

Incorporating evolutionary processes into a spatially-explicit model: exploring the consequences of mink-farm closures in Denmark

In this paper, we present an individual-based cellular lattice model, which is based on a real landscape (Denmark). The model predicts the distribution of free-ranging mink from data collated on the geographic locations of fur farms, the number of breeding mink kept per farm, and a range of parameters regarding escape, reproduction, mortality, and dispersal. When evolution was incorporated in the model, the results showed that the degree of adaptation within the free-ranging mink population is likely to vary spatially, with lower adaptation in areas where farm mink density is highest (due to the greater number of escaping mink). We used the model to explore the potential consequences of closing mink farms, or limiting escapes from them, on the evolutionary ecology of the free-ranging population and found that depending upon the paramaterisation of the evolutionary processes, several different outcomes are possible. Closing mink farms may result in a crash of the free-ranging population, or alternatively it may result in the establishment of a better-adapted, truly feral population that may ultimately outnumber the population that was present before farm closures. The main purpose of this paper is to raise awareness of the potential importance of evolutionary processes for the naturalisation of mink in Denmark, and to highlight the need for further work. Future field studies should be targeted to reduce the uncertainty in key parameters, allowing the development of an improved version of this model that can be used to generate management recommendations. More generally, we believe that further work linking evolutionary and population biology is required particularly in an applied context. There are likely to be many further scenarios where evolutionary processes may hold the key to understanding both population and community dynamics.     

The Effect of an Upper Limit to Population Size on Persistence Time

For a population with density-independent vital rates in a randomly varying environment, previous authors have calculated the probability that population size will first drop to some specified (arbitrary) low level at a given time (the first passage time distribution (FPTD), which may be interpreted as a distribution of extinction times). In this paper, we study the FPTD For a stochastic model of density-independent population growth which includes a hard upper limit to population size. We discuss the conditions under which this distribution may be approximated by the FPTD of a Wiener process with a reflecting boundary condition, for which an exact calculation is presented in an appendix. We compare the FPTD of the new model with its counterpart in the model without an upper limit. The most important effects of introducing the upper limit are: (a) ultimate extinction becomes certain; (b) if the long run growth rate in the absence of the upper boundary was small but positive, extinction within ecologically significant times is likely; (c) for larger values of the long run growth rate, persistence over ecologically significant times is almost certain. We discuss the implications of result (b) for conservation. Result (c) establishes that "density-vague" regulation can produce persistent, but bounded, populations.     

THE EVOLUTIONARILY STABLE PHENOTYPE DISTRIBUTION IN A RANDOM ENVIRONMENT

In an unpredictably changing environment, phenotypic variability may evolve as a “bet-hedging” strategy. We examine here two models for evolutionarily stable phenotype distributions resulting from stabilizing selection with a randomly fluctuating optimum. Both models include overlapping generations, either survival of adults or a dormant propagule pool. In the first model (mixed-strategies model) we assume that individuals can produce offspring with a distribution of phenotypes, in which case, the evolutionarily stable population always consists of a single genotype. We show that there is a unique evolutionarily stable strategy (ESS) distribution that does not depend on the amount of generational overlap, and that the ESS distribution generically is discrete rather than continuous; that is, there are distinct classes of offspring rather than a continuous distribution of offspring phenotypes. If the probability of extreme fluctuations in the optimum is sufficiently small, then the ESS distribution is monomorphic: a single type fitted to the mean environment. At higher levels of variability, the ESS distribution is polymorphic, and we find stability conditions for dimorphic distributions. For an exponential or similarly broad-tailed distribution of the optimum phenotype, the ESS consists of an infinite number of distinct phenotypes. In the second model we assume that an individual produces offspring with a single, genetically determined phenotype (pure-strategies model). The ESS population then contains multiple genotypes when the environmental variance is sufficiently high. However the phenotype distributions are similar to those in the mixed-strategies model: discrete, with an increasing number of distinct phenotypes as the environmental variance increases.     

The combination of population pharmacokinetic studies

Pharmacokinetic data consist of drug concentrations with associated known sampling times and are collected following the administration of known dosage regimens. Population pharmacokinetic data consist of such data on a number of individuals, possibly along with individual-specific characteristics. During drug development, a number of population pharmacokinetic studies are typically carried out and the combination of such studies is of great importance for characterizing the drug and, in particular, for the design of future studies. In this paper, we describe a model that may be used to combine population pharmacokinetic data. The model is illustrated using six phase I studies of the antiasthmatic drug fluticasone propionate. Our approach is Bayesian and computation is carried out using Markov chain Monte Carlo. We provide a number of simplifications to the model that may be made in order to ease simulation from the posterior distribution.     

Demographic and ecogeographic factors limit wild grapevine spread at the southern edge of its distribution range

The spatial distribution of plants is constrained by demographic and ecogeographic factors that determine the range and abundance of the species. Wild grapevine (Vitis vinifera ssp. sylvestris) is distributed from Switzerland in the north to Israel in the south. However, little is known about the ecogeographic constraints of this species and its genetic and phenotypic characteristics, especially at the southern edge of its distribution range in the Levant region. In this study, we explore the population structure of southern Levantine wild grapevines and the correlation between demographic and ecogeographic characteristics. Based on our genetic analysis, the wild grapevine populations in this region can be divided into two major subgroups in accordance with a multivariate spatial and ecogeographical clustering model. The identified subpopulations also differ in morphological traits, mainly leaf hairiness which may imply adaptation to environmental stress. The findings suggest that the Upper Jordan River population was spread to the Sea of Galilee area and that a third smaller subpopulation at the south of the Golan Heights may represent a distinguished gene pool or a recent establishment of a new population. A spatial distribution model indicated that distance to water sources, Normalized difference vegetation index, and precipitation are the main environmental factors constraining V. v. sylvestris distribution at its southern distribution range. These factors in addition to limited gene flow between populations prevent further spread of wild grapevines southwards to semi‐arid regions.     

The natural variability of vital rates and associated statistics

The first concern of this work is the development of approximations to the distributions of crude mortality rates, age-specific mortality rates, age-standardized rates, standardized mortality ratios, and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution. The Lexis diagram is seen to make direct use of the result. It is suggested that in a variety of cases, it will be satisfactory to approximate the distribution of the number of deaths given the population size, by a Poisson with mean proportional to the population size. It is further suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths, with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits.     

Potential Distribution of Dengue Fever Under Scenarios of Climate Change and Economic Development

Dengue fever is the most important viral vector-borne disease with ~50 million cases per year globally. Previous estimates of the potential effect of global climate change on the distribution of vector-borne disease have not incorporated the effect of socioeconomic factors, which may have biased the results. We describe an empirical model of the current geographic distribution of dengue, based on the independent effects of climate and gross domestic product per capita (GDPpc, a proxy for socioeconomic development). We use the model, along with scenario-based projections of future climate, economic development, and population, to estimate populations at risk of dengue in the year 2050. We find that both climate and GDPpc influence the distribution of dengue. If the global climate changes as projected but GDPpc remained constant, the population at risk of dengue is estimated to increase by about 0.28 billion in 2050. However, if both climate and GDPpc change as projected, we estimate a decrease of 0.12 billion in the population at risk of dengue in 2050. Empirically, the geographic distribution of dengue is strongly dependent on both climatic and socioeconomic variables. Under a scenario of constant GDPpc, global climate change results in a modest but important increase in the global population at risk of dengue. Under scenarios of high GDPpc, this adverse effect of climate change is counteracted by the beneficial effect of socioeconomic development.