High Precision U/Th Dating of First Polynesian Settlement

Previous studies document Nukuleka in the Kingdom of Tonga as a founder colony for first settlement of Polynesia by Lapita peoples. A limited number of radiocarbon dates are one line of evidence supporting this claim, but they cannot precisely establish when this event occurred, nor can they afford a detailed chronology for sequent occupation. High precision U/Th dates of Acropora coral files (abraders) from Nukuleka give unprecedented resolution, identifying the founder event by 2838±8 BP and documenting site development over the ensuing 250 years. The potential for dating error due to post depositional diagenetic alteration of ancient corals at Nukuleka also is addressed through sample preparation protocols and paired dates on spatially separated samples for individual specimens. Acropora coral files are widely distributed in Lapita sites across Oceania. U/Th dating of these artifacts provides unparalleled opportunities for greater precision and insight into the speed and timing of this final chapter in human settlement of the globe.     

Increased Y-chromosome resolution of haplogroup O suggests genetic ties between the Ami aborigines of Taiwan and the Polynesian Islands of Samoa and Tonga

The Austronesian expansion has left its fingerprint throughout two thirds of the circumference of the globe reaching the island of Madagascar in East Africa to the west and Easter Island, off the coast of Chile, to the east. To date, several theories exist to explain the current genetic distribution of Austronesian populations, with the “slow boat” model being the most widely accepted, though other conjectures (i.e., the “express train” and “entangled bank” hypotheses) have also been widely discussed. In the current study, 158 Y chromosomes from the Polynesian archipelagos of Samoa and Tonga were typed using high resolution binary markers and compared to populations across Mainland East Asia, Taiwan, Island Southeast Asia, Melanesia and Polynesia in order to establish their patrilineal genetic relationships. Y-STR haplotypes on the C2 (M38), C2a (M208), O1a (M119), O3 (M122) and O3a2 (P201) backgrounds were utilized in an attempt to identify the differing sources of the current Y-chromosomal haplogroups present throughout Polynesia (of Melanesian and/or Asian descent). We find that, while haplogroups C2a, S and K3-P79 suggest a Melanesian component in 23%-42% of the Samoan and Tongan Y chromosomes, the majority of the paternal Polynesian gene pool exhibits ties to East Asia. In particular, the prominence of sub-haplogroup O3a2c* (P164), which has previously been observed at only minimal levels in Mainland East Asians (2.0-4.5%), in both Polynesians (ranging from 19% in Manua to 54% in Tonga) and Ami aborigines from Taiwan (37%) provides, for the first time, evidence for a genetic connection between the Polynesian populations and the Ami.     

Bayesian Nonparametric Modeling for Comparison of Single-Neuron Firing Intensities

Summary .  We propose a fully inferential model-based approach to the problem of comparing the firing patterns of a neuron recorded under two distinct experimental conditions. The methodology is based on nonhomogeneous Poisson process models for the firing times of each condition with flexible nonparametric mixture prior models for the corresponding intensity functions. We demonstrate posterior inferences from a global analysis, which may be used to compare the two conditions over the entire experimental time window, as well as from a pointwise analysis at selected time points to detect local deviations of firing patterns from one condition to another. We apply our method on two neurons recorded from the primary motor cortex area of a monkey's brain while performing a sequence of reaching tasks.     

Bayesian Modeling of Joint Regressions for the Mean and Covariance Matrix

An important problem in agronomy is the study of longitudinal data on the growth curve of the weight of cattle through time, possibly taking into account the effect of other explanatory variables such as treatments and time. In this paper, a Bayesian approach for analysing longitudinal data is proposed. It takes into account regression structures on the mean and the variance‐covariance matrix of normal observations. The approach is based on the modeling strategy suggested by Pourahmadi (1999, Biometrika 86, 667–690). After revising this methodology, we present the Bayesian approach used to fit the models, based on a generalization of the Metropolis‐Hastings algorithm of Cepeda and Gamerman (2000, Brazilian Journal of Probability and Statistics, 14 , 207–221). The approach is used to the study of growth and development of a group of deaf children. The paper is concluded with a few proposed extensions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian Weighing of Electron Cryo-Microscopy Data for Integrative Structural Modeling

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Hierarchical Bayesian Modeling of Pharmacophores in Bioinformatics

Summary One of the key ingredients in drug discovery is the derivation of conceptual templates called pharmacophores. A pharmacophore model characterizes the physicochemical properties common to all active molecules, called ligands, bound to a particular protein receptor, together with their relative spatial arrangement. Motivated by this important application, we develop a Bayesian hierarchical model for the derivation of pharmacophore templates from multiple configurations of point sets, partially labeled by the atom type of each point. The model is implemented through a multistage template hunting algorithm that produces a series of templates that capture the geometrical relationship of atoms matched across multiple configurations. Chemical information is incorporated by distinguishing between atoms of different elements, whereby different elements are less likely to be matched than atoms of the same element. We illustrate our method through examples of deriving templates from sets of ligands that all bind structurally related protein active sites and show that the model is able to retrieve the key pharmacophore features in two test cases.     

Digital PCR Modeling for Maximal Sensitivity,Dynamic Range and Measurement Precision

The great promise of digital PCR is the potential for unparalleled precision enabling accurate measurements for genetic quantification. A challenge associated with digital PCR experiments, when testing unknown samples, is to perform experiments at dilutions allowing the detection of one or more targets of interest at a desired level of precision. While theory states that optimal precision (P_o) is achieved by targeting ~1.59 mean copies per partition (λ), and that dynamic range (R) includes the space spanning one positive (λ_L) to one negative (λ_U) result from the total number of partitions (n), these results are tempered for the practitioner seeking to construct digital PCR experiments in the laboratory. A mathematical framework is presented elucidating the relationships between precision, dynamic range, number of partitions, interrogated volume, and sensitivity in digital PCR. The impact that false reaction calls and volumetric variation have on sensitivity and precision is next considered. The resultant effects on sensitivity and precision are established via Monte Carlo simulations reflecting the real-world likelihood of encountering such scenarios in the laboratory. The simulations provide insight to the practitioner on how to adapt experimental loading concentrations to counteract any one of these conditions. The framework is augmented with a method of extending the dynamic range of digital PCR, with and without increasing n, via the use of dilutions. An example experiment demonstrating the capabilities of the framework is presented enabling detection across 3.33 logs of starting copy concentration.     

Bayesian Partitioning for Modeling and Mapping Spatial Case–Control Data

Summary Methods for modeling and mapping spatial variation in disease risk continue to motivate much research. In particular, spatial analyses provide a useful tool for exploring geographical heterogeneity in health outcomes, and consequently can yield clues as to disease etiology, direct public health management, and generate research hypotheses. This article presents a Bayesian partitioning approach for the analysis of individual level geo‐referenced health data. The model makes few assumptions about the underlying form of the risk surface, is data adaptive, and allows for the inclusion of known determinants of disease. The methodology is used to model spatial variation in neonatal mortality in Porto Alegre, Brazil.     

Bayesian Hierarchical Modeling and Selection of Differentially Expressed Genes for the EST Data

Summary Expressed sequence tag (EST) sequencing is a one‐pass sequencing reading of cloned cDNAs derived from a certain tissue. The frequency of unique tags among different unbiased cDNA libraries is used to infer the relative expression level of each tag. In this article, we propose a hierarchical multinomial model with a nonlinear Dirichlet prior for the EST data with multiple libraries and multiple types of tissues. A novel hierarchical prior is developed and the properties of the proposed prior are examined. An efficient Markov chain Monte Carlo algorithm is developed for carrying out the posterior computation. We also propose a new selection criterion for detecting which genes are differentially expressed between two tissue types. Our new method with the new gene selection criterion is demonstrated via several simulations to have low false negative and false positive rates. A real EST data set is used to motivate and illustrate the proposed method.     

Modeling Historic Rangeland Management and Grazing Pressures in Landscapes of Settlement

Defining historic grazing pressures and rangeland management is vital if early landscape threshold crossing and long–term trajectories of landscape change are to be properly understood. In this paper we use a new environmental simulation model, Búmodel, to assess two contrasting historical grazing landscapes in Myvatnssveit Iceland for two key periods—the colonization period (ca. Landnám, a.d. 872–1000) and the early eighteenth century a.d. Results suggest that there were spatial and temporal variations in productivity and grazing pressure within and between historic grazing areas and indicate that land degradation was not an inevitable consequence of the livestock grazing introduced with settlement. The results also demonstrate the significance of grazing and livestock management strategies in preventing overgrazing, particularly under cooler climatic conditions. The model enables detailed consideration of historic grazing management scenarios and their associated landscape pressures.     

Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions

Nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this article, the focus is on nonparametric estimation through a mixture of triangular distributions. The optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived. Although our approach is more widely applicable, we focus for simplicity on estimation of a monotone nondecreasing regression on [0, 1] with additive error, effectively approximating the function of interest by a function having a piecewise linear derivative. Computationally accessible methods of estimation are described through an amalgamation of existing Markov chain Monte Carlo algorithms. Simulations and examples illustrate the approach.     

Bayesian Modeling of Haplotype Effects in Multiparent Populations

A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus.     

Village Drift and Riverine Settlement: Modeling Akimel O'odham Land Use

Regular unscheduled movements of rancherías within a confined area or settlement district result in the phenomenon described as "village drift," a process whereby a settlement may change its location gradually by several kilometers over a period of years. This article presents a model of village drift based on data acquired from recent archaeological and geomorphological field studies and archival research on the Akimel O'odham, the Gila River Pima of south-central Arizona. The model provides an excellent example of human ecodynamics---an emerging landscape perspective that emphasizes the coevolution of humans and their ecosystem---with implications for understanding prehistoric and historic settlement in desert riverine environments.     

Bayesian Spatial Semi-Parametric Modeling of HIV Variation in Kenya

Spatial statistics has seen rapid application in many fields, especially epidemiology and public health. Many studies, nonetheless, make limited use of the geographical location information and also usually assume that the covariates, which are related to the response variable, have linear effects. We develop a Bayesian semi-parametric regression model for HIV prevalence data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (McMC). The model is applied to HIV prevalence data among men in Kenya, derived from the Kenya AIDS indicator survey, with n = 3,662. Past studies have concluded that HIV infection has a nonlinear association with age. In this study a smooth function based on penalized regression splines is used to estimate this nonlinear effect. Other covariates were assumed to have a linear effect. Spatial references to the counties were modeled as both structured and unstructured spatial effects. We observe that circumcision reduces the risk of HIV infection. The results also indicate that men in the urban areas were more likely to be infected by HIV as compared to their rural counterpart. Men with higher education had the lowest risk of HIV infection. A nonlinear relationship between HIV infection and age was established. Risk of HIV infection increases with age up to the age of 40 then declines with increase in age. Men who had STI in the last 12 months were more likely to be infected with HIV. Also men who had ever used a condom were found to have higher likelihood to be infected by HIV. A significant spatial variation of HIV infection in Kenya was also established. The study shows the practicality and flexibility of Bayesian semi-parametric regression model in analyzing epidemiological data.     

Bioclimatic Modeling of Southern African Bioregions and Biomes Using Bayesian Networks

This study uses Bayesian networks (BNs) to simulate the spatial distribution of southern African biomes and bioregions using bioclimatic variables. Two Tree-Augmented Naïve (TAN) BN models were parameterized from 23 bioclimatic variables using the expectation-maximization (EM) algorithm. Using sensitivity analyses, the relative influence of each variable was determined using the mutual information from which six bioclimatic variables were selected for the final models. Precipitation of the warmest quarter and extra-terrestrial solar radiation was found to be the most influential variables on both bioregion and biome distributions. Isothermality was the least influential bioclimatic variable at both bioregion and biome levels. Overall correspondence was very high at 93.8 and 87.1% for biomes and bioregions, respectively, whereas classification errors were obtained in transition areas indicating the uncertainties associated with vegetation mapping around margins. The findings indicate that southern African bioregions and biomes can be classified and mapped according to key bioclimatic variables. Spatio-temporal, in particular, monthly and quarterly variations in both precipitation and temperature are found to be ecologically significant in determining the spatial distribution of biomes and bioregions. The findings also reflect the hierarchical relationship of biomes and bioregions as a function of local bioclimatic gradients and interactions. The results indicate the ecological significance of bioclimatic conditions in ecosystem science and offer the opportunity to utilize the models for predicting future responses and sensitivities to climatic changes.     

Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.