Adjusting Simon's optimal two-stage design for heterogeneous populations based on stratification or using historical controls

In many cancer studies, the population under consideration is highly heterogeneous in terms of clinical, demographical, and biological covariates. As the covariates substantially impact the individual prognosis, the response probabilities of patients entering the study may strongly vary. In this case, the operating characteristics of classical clinical trial designs heavily depend on the covariates of patients entering the study. Notably, both type I and type II errors can be much higher than specified. In this paper, two modifications of Simon's optimal two-stage design correcting for heterogeneous populations are derived. The first modification assumes that the patient population is divided into a finite number of subgroups, where each subgroup has a different response probability. The second approach uses a logistic regression model based on historical controls to estimate the response probabilities of patients entering the study. The performance of both approaches is demonstrated using simulation examples.     

Inferring the parameters of the neutral theory of biodiversity using phylogenetic information and implications for tropical forests

We develop a statistical method to infer the parameters of Hubbell's neutral model of biodiversity using data on local species abundances and their phylogenetic relatedness. This method uses the approximate Bayesian computation (ABC) approach, where the data are summarized into a small number of informative summary statistics. We used three statistics: the number of species in the sample, Shannon H index of evenness and Shao and Sokal's B ₁ index of phylogenetic tree imbalance. Our approach was found to outperform previous methods, illustrating the potential of ABC methods in ecology. Applying it to four large tropical forest tree data sets, the best-fit immigration rates m were found to be two orders of magnitude smaller and regional diversities θ larger than previously reported for the same data. This implies that neutral-compatible regional pools of tropical trees should extend over continental scales, and that m measures, in this context, mostly the frequency of long-distance dispersal events.     

Fundamental Identifiability Limits in Molecular Epidemiology

Viral phylogenies provide crucial information on the spread of infectious diseases, and many studies fit mathematical models to phylogenetic data to estimate epidemiological parameters such as the effective reproduction ratio (R_e) over time. Such phylodynamic inferences often complement or even substitute for conventional surveillance data, particularly when sampling is poor or delayed. It remains generally unknown, however, how robust phylodynamic epidemiological inferences are, especially when there is uncertainty regarding pathogen prevalence and sampling intensity. Here, we use recently developed mathematical techniques to fully characterize the information that can possibly be extracted from serially collected viral phylogenetic data, in the context of the commonly used birth-death-sampling model. We show that for any candidate epidemiological scenario, there exists a myriad of alternative, markedly different, and yet plausible “congruent” scenarios that cannot be distinguished using phylogenetic data alone, no matter how large the data set. In the absence of strong constraints or rate priors across the entire study period, neither maximum-likelihood fitting nor Bayesian inference can reliably reconstruct the true epidemiological dynamics from phylogenetic data alone; rather, estimators can only converge to the “congruence class” of the true dynamics. We propose concrete and feasible strategies for making more robust epidemiological inferences from viral phylogenetic data.     

扎龙湿地不同生境芦苇种群根茎数量特征及动态

采用单位土体取样,计测长度和生物量的调查与统计方法,对扎龙湿地保护区4个生境芦苇种群根茎数量特征进行比较分析。结果表明,芦苇5月10日左右返青后进入营养生长期,根茎长度6—8月份缓慢增加,8—10月份显著增加,后期是前期的3.5—10.3倍,生长季中后期是种群新根茎补充和生长的主要时期,不仅实现了种群空间扩展,并为营养繁殖储备更多繁殖芽;根茎生物量和干物质贮量6—8月份逐渐减少,8—10月份又逐渐增加,均以生长季末期的10月份最大,并均显著地(P0.05)高于其他月份,种群根茎养分的消耗主要供给根茎芽的萌发和幼株生长,根茎养分的储藏又为翌年种群的更新及扩展提供物质保障,种群对地下根茎存在明显的养分"超补偿性"贮藏现象。种群根茎长度和生物量均以湿生生境最大,依次为旱生生境、水生生境,盐碱生境最小,根茎干物质贮量以旱生生境最大,依次为湿生生境、水生生境,盐碱生境最小。种群根茎长度与返青后实际生长时间之间均较好地符合直线函数关系,种群根茎生物量和干物质贮量与生长时间之间较好地符合二次曲线函数关系,R2在0.804—0.997之间,拟合方程均达到了显著或极显著(P0.01)水平。4个生境芦苇种群在根茎长度、生物量、干物质贮量等数量特征均表现出由遗传因素控制的比较稳定的季节动态规律,在生境间的差异及其差异序位又均基本稳定,均表现出明显的土壤因子环境效应,其中土壤含水量、有机质、速效氮为正向驱动,p H、速效磷为负向驱动,土壤含水量、p H对根茎数量特征的驱动作用更突出。     

Unravelling Escherichia coli dynamics close to the maximum growth temperature through heterogeneous modelling

Aims:  Previous work showed that the exponential phase of Escherichia coli K12 MG1655, grown in Brain Heart Infusion broth at temperatures close to its maximum growth temperature, is disturbed. Based on plate count data, microscopic images and literature, the existence of a heat-resistant subpopulation was hypothesized. Here, this hypothesis is mathematically explored via a heterogeneous model.
Methods and Results:  A heat-sensitive and a heat-resistant subpopulation are considered. A large fraction of the population is inactivated, while the remaining smaller fraction is able to resist (or adapt to) the inimical temperature and grows. A heterogeneous model that encloses a growth model (resistant population) and an inactivation model (sensitive population) is used to describe the global population dynamics. Most experimental data can be predicted when taking parameter uncertainty via Monte Carlo simulation into account.
Conclusions:  The heterogeneous model accurately describes disturbed growth curves at superoptimal temperatures, except for high initial cell densities.
Significance and Impact of the Study:  This study strengthens the hypothesis of the existence of a (small) heat-resistant subpopulation in typical inoculum cultures of E. coli K12 MG1655.     

The evolution of parasite host range in heterogeneous host populations

Theory on the evolution of niche width argues that resource heterogeneity selects for niche breadth. For parasites, this theory predicts that parasite populations will evolve, or maintain, broader host ranges when selected in genetically diverse host populations relative to homogeneous host populations. To test this prediction, we selected the bacterial parasite Serratia marcescens to kill Caenorhabditis elegans in populations that were genetically heterogeneous (50% mix of two experimental genotypes) or homogeneous (100% of either genotype). After 20 rounds of selection, we compared the host range of selected parasites by measuring parasite fitness (i.e. virulence, the selected fitness trait) on the two focal host genotypes and on a novel host genotype. As predicted, heterogeneous host populations selected for parasites with a broader host range: these parasite populations gained or maintained virulence on all host genotypes. This result contrasted with selection in homogeneous populations of one host genotype. Here, host range contracted, with parasite populations gaining virulence on the focal host genotype and losing virulence on the novel host genotype. This pattern was not, however, repeated with selection in homogeneous populations of the second host genotype: these parasite populations did not gain virulence on the focal host genotype, nor did they lose virulence on the novel host genotype. Our results indicate that host heterogeneity can maintain broader host ranges in parasite populations. Individual host genotypes, however, vary in the degree to which they select for specialization in parasite populations.     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

Multi-list methods using incomplete lists in closed populations

Multi-list methods have become a common application of capture-recapture methodology to estimate the size of human populations, and have been successfully applied to estimating prevalence of diabetes, human immunodeficiency virus (HIV), and drug abuse. A key assumption in multi-list methods is that individuals have a unique "tag" that allows them to be matched across all lists. This article develops multi-list methodology that relaxes the assumption of a single tag common to all lists. Estimates are found using estimating functions. An example illustrates its application for estimating the prevalence of diabetes, and a simulation study investigates conditions under which the methodology is robust to different list and population sizes.     

Predicting community structure in snakes on Eastern Nearctic islands using ecological neutral theory and phylogenetic methods

Predicting species presence and richness on islands is important for understanding the origins of communities and how likely it is that species will disperse and resist extinction. The equilibrium theory of island biogeography (ETIB) and, as a simple model of sampling abundances, the unified neutral theory of biodiversity (UNTB), predict that in situations where mainland to island migration is high, species-abundance relationships explain the presence of taxa on islands. Thus, more abundant mainland species should have a higher probability of occurring on adjacent islands. In contrast to UNTB, if certain groups have traits that permit them to disperse to islands better than other taxa, then phylogeny may be more predictive of which taxa will occur on islands. Taking surveys of 54 island snake communities in the Eastern Nearctic along with mainland communities that have abundance data for each species, we use phylogenetic assembly methods and UNTB estimates to predict island communities. Species richness is predicted by island area, whereas turnover from the mainland to island communities is random with respect to phylogeny. Community structure appears to be ecologically neutral and abundance on the mainland is the best predictor of presence on islands. With regard to young and proximate islands, where allopatric or cladogenetic speciation is not a factor, we find that simple neutral models following UNTB and ETIB predict the structure of island communities.     

Identifying outlier loci in admixed and in continuous populations using ancestral population differentiation statistics

Finding genetic signatures of local adaptation is of great interest for many population genetic studies. Common approaches to sorting selective loci from their genomic background focus on the extreme values of the fixation index, F_ST, across loci. However, the computation of the fixation index becomes challenging when the population is genetically continuous, when predefining subpopulations is a difficult task, and in the presence of admixed individuals in the sample. In this study, we present a new method to identify loci under selection based on an extension of the F_ST statistic to samples with admixed individuals. In our approach, F_ST values are computed from the ancestry coefficients obtained with ancestry estimation programs. More specifically, we used factor models to estimate F_ST, and we compared our neutrality tests with those derived from a principal component analysis approach. The performances of the tests were illustrated using simulated data and by re‐analysing genomic data from European lines of the plant species Arabidopsis thaliana and human genomic data from the population reference sample, POPRES.     

Detecting sex-linked genes using genotyped individuals sampled in natural populations

We propose a method, SDpop, able to infer sex-linkage caused by recombination suppression typical of sex chromosomes. The method is based on the modeling of the allele and genotype frequencies of individuals of known sex in natural populations. It is implemented in a hierarchical probabilistic framework, accounting for different sources of error. It allows statistical testing for the presence or absence of sex chromosomes, and detection of sex-linked genes based on the posterior probabilities in the model. Furthermore, for gametologous sequences, the haplotype and level of nucleotide polymorphism of each copy can be inferred, as well as the divergence between them. We test the method using simulated data, as well as data from both a relatively recent and an old sex chromosome system (the plant Silene latifolia and humans) and show that, for most cases, robust predictions are obtained with 5 to 10 individuals per sex.     

Semiparametric estimation of animal abundance using capture-recapture data from open populations

A semiparametric partially linear model for the size of an open population is proposed and inference is conducted using weighted martingale estimating equations. This extends a previous nonparametric approach to modeling capture-recapture data for open populations with frequent capture occasions. Analytic expressions for the large sample variances are derived and these are confirmed in a simulation study. The method is illustrated on monthly penguin banding data collected over 6 years.     

Revealing the demographic histories of species using DNA sequences

Various methodological approaches using molecular sequence data have been developed and applied across several fields, including phylogeography, conservation biology, virology and human evolution. The aim of these approaches is to obtain predictive estimates of population history from DNA sequence data that can then be used for hypothesis testing with empirical data. This recent work provides opportunities to evaluate hypotheses of constant population size through time, of population growth or decline, of the rate of growth or decline, and of migration and growth in subdivided populations. At the core of many of these approaches is the extraction of information from the structure of phylogenetic trees to infer the demographic history of a population, and underlying nearly all methods is coalescent theory. With the increasing availability of DNA sequence data, it is important to review the different ways in which information can be extracted from DNA sequence data to estimate demographic parameters.     

The adaptive dynamics of altruism in spatially heterogeneous populations

Abstract.— We study the spatial adaptive dynamics of a continuous trait that measures individual investment in altruism. Our study is based on an ecological model of a spatially heterogeneous population from which we derive an appropriate measure of fitness. The analysis of this fitness measure uncovers three different selective processes controlling the evolution of altruism: the direct physiological cost, the indirect genetic benefits of cooperative interactions, and the indirect genetic costs of competition for space. In our model, habitat structure and a continuous life cycle makes the cost of competing for space with relatives negligible. Our study yields a classification of adaptive patterns of altruism according to the shape of the costs of altruism (with decelerating, linear, or accelerating dependence on the investment in altruism). The invasion of altruism occurs readily in species with accelerating costs, but large mutations are critical for altruism to evolve in selfish species with decelerating costs. Strict selfishness is maintained by natural selection only under very restricted conditions. In species with rapidly accelerating costs, adaptation leads to an evolutionarily stable rate of investment in altruism that decreases smoothly with the level of mobility. A rather different adaptive pattern emerges in species with slowly accelerating costs: high altruism evolves at low mobility, whereas a quasi-selfish state is promoted in more mobile species. The high adaptive level of altruism can be predicted solely from habitat connectedness and physiological parameters that characterize the pattern of cost. We also show that environmental changes that cause increased mobility in those highly altruistic species can beget selection-driven self-extinction, which may contribute to the rarity of social species.     

Characterising model dynamics using sparse grid interpolation: Parameter estimation of cholera

Sparse grid interpolation is a popular numerical discretization technique for the treatment of high dimensional, multivariate problems. We consider the case of using time-series data to calibrate epidemiological models from both phenomenological and mechanistic perspectives using this computational tool. By capturing the dynamics underlying both global and local spaces, our algorithm identifies potentially optimal regions of the parameter space and directs computational effort towards resolving the dynamics and resulting fits of these regions. We demonstrate how sparse grid interpolants can be effectively deployed to fit available data and discriminate between competing hypotheses to explain the current cholera epidemic in Yemen.     

Ethical issues associated with HIV phylogenetics in HIV transmission dynamics research: A review of the literature using the Emanuel Framework

The reduced costs of DNA sequencing and the use of such data for HIV‐1 clinical management and phylogenetic analysis have led to a massive increase of HIV‐1 sequences in the last few years. Phylogenetic analysis has shed light on the origin, spread and characteristics of HIV‐1 epidemics and outbreaks. Phylogenetic analysis is now also being used to advance our knowledge of the drivers of HIV‐1 transmission in order to design effective interventions. However, HIV phylogenetic analysis presents unique ethical challenges, which have not been fully explored. This review presents an analysis of what appear to be key ethical issues in HIV phylogenetics in the hope of stimulating further conceptual and empirical work in this rapidly emerging area. We structure the review using the Emanuel Framework, a systematic, holistic framework, which has been adapted for use in developing countries, which bear the brunt of the HIV‐1 pandemic.     

Probabilistic methods outperform parsimony in the phylogenetic analysis of data simulated without a probabilistic model

To understand patterns and processes of the diversification of life, we require an accurate understanding of taxon interrelationships. Recent studies have suggested that analyses of morphological character data using the Bayesian and maximum likelihood Mk model provide phylogenies of higher accuracy compared to parsimony methods. This has proved controversial, particularly studies simulating morphology‐data under Markov models that assume shared branch lengths for characters, as it is claimed this leads to bias favouring the Bayesian or maximum likelihood Mk model over parsimony models which do not explicitly make this assumption. We avoid these potential issues by employing a simulation protocol in which character states are randomly assigned to tips, but datasets are constrained to an empirically realistic distribution of homoplasy as measured by the consistency index. Datasets were analysed with equal weights and implied weights parsimony, and the maximum likelihood and Bayesian Mk model. We find that consistent (low homoplasy) datasets render method choice largely irrelevant, as all methods perform well with high consistency (low homoplasy) datasets, but the largest discrepancies in accuracy occur with low consistency datasets (high homoplasy). In such cases, the Bayesian Mk model is significantly more accurate than alternative models and implied weights parsimony never significantly outperforms the Bayesian Mk model. When poorly supported branches are collapsed, the Bayesian Mk model recovers trees with higher resolution compared to other methods. As it is not possible to assess homoplasy independently of a tree estimate, the Bayesian Mk model emerges as the most reliable approach for categorical morphological analyses.     

The diffusive spread of alleles in heterogeneous populations

The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c = 2 square root of (rD), that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations.     

Census data aggregation decisions can affect population‐level inference in heterogeneous populations

1. Conservation and population management decisions often rely on population models parameterized using census data. However, the sampling regime, precision, sample size, and methods used to collect census data are usually heterogeneous in time and space. Decisions about how to derive population‐wide estimates from this patchwork of data are complicated and may bias estimated population dynamics, with important implications for subsequent management decisions.
2. Here, we explore the impact of site selection and data aggregation decisions on pup survival estimates, and downstream estimates derived from parameterized matrix population models (MPMs), using a long‐term dataset on grey seal (Halichoerus grypus) pup survival from southwestern Wales. The spatiotemporal and methodological heterogeneity of the data are fairly typical for ecological census data and it is, therefore, a good model to address this topic.
3. Data were collected from 46 sampling locations (sites) over 25 years, and we explore the impact of data handling decisions by varying how years and sampling locations are combined to parameterize pup survival in population‐level MPMs. We focus on pup survival because abundant high‐quality data are available on this developmental stage.
4. We found that survival probability was highly variable with most variation being at the site level, and poorly correlated among sampling sites. This variation could generate marked differences in predicted population dynamics depending on sampling strategy. The sample size required for a confident survival estimate also varied markedly geographically.
5. We conclude that for populations with highly variable vital rates among sub‐populations, site selection and data aggregation methods are important. In particular, including peripheral or less frequently used areas can introduce substantial variation into population estimates. This is likely to be context‐dependent, but these choices, including the use of appropriate weights when summarizing across sampling areas, should be explored to ensure that management actions are successful.

     

Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics

Biological networks of large dimensions, with their diagram of interactions, are often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a model reduction method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a “reduced” and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival and apoptotic pathways.