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Quasi Continuous Assignment

Abstract

Motivation: Large-scale genotype datasets can help track the dispersal patterns of epidemiological outbreaks and predict the geographic origins of individuals. Such genetically-based geographic assignments also show a range of possible applications in forensics for profiling both victims and criminals, and in wildlife management, where poaching hotspot areas can be located. They, however, require fast and accurate statistical methods to handle the growing amount of genetic information made available from genotype arrays and next-generation sequencing technologies.

Results: We introduce a novel statistical method for geopositioning individuals of unknown origin from genotypes. Our method is based on a geostatistical model trained with a dataset of georeferenced genotypes. Statistical inference under this model can be implemented within the theoretical framework of Integrated Nested Laplace Approximation, which represents one of the major recent breakthroughs in statistics, as it does not require Monte Carlo simulations. We compare the performance of our method and an alternative method for geospatial inference, SPA in a simulation framework. We highlight the accuracy and limits of continuous spatial assignment methods at various scales by analyzing genotype datasets from a diversity of species, including Florida Scrub-jay birds Aphelocoma coerulescens, Arabidopsis thaliana and humans, representing 41–197,146 SNPs. Our method appears to be best suited for the analysis of medium-sized datasets (a few tens of thousands of loci), such as reduced-representation sequencing data that become increasingly available in ecology.

Availability and implementation:http://www2.imm.dtu.dk/∼gigu/Spasiba/

Contact:gilles.b.guillot@gmail.com

Supplementary information:Supplementary data are available at Bioinformatics online.

1 Introduction

Inferring the geographic origin of living organisms from their genetic information is of great interest for many applications in biology. It can provide information about gene flow, migration patterns and connectivity in natural populations (Kremer et al., 2012; Schwartz et al., 2007; Waples and Gaggiotti, 2006) but can also help inform wildlife managers about illegal animal translocations and poaching hotspots (Manel et al., 2005; Ogden et al., 2009). As such, this information can complement the arsenal of DNA-based fraud detection methods, aiming at detecting derivatives of endangered and trade-restricted species (Coghlan et al., 2012). In addition, DNA-informed geospatial localization can reveal the geographic source of pathogens during epidemiological outbreaks (Sloan et al., 2009) or the geographic origin of plants and animals used in the industrial manufacture of food products (Lees, 2003). In forensics, DNA-informed geospatial localization can help profiling criminals and identifying the origin of unidentified bodies (Primorac and Schanfield, 2014). Here, we introduce Spatial Bayesian Inference (SPASIBA), a novel method for geospatial assignment. The premise of the SPASIBA method is that in most natural contexts, spatial patterns of allele frequencies are complex and are likely to be well captured by a geostatistical model such as the one implemented in the SCAT program (Wasser et al., 2004), but here, we leverage the power of a recent breakthrough statistical theory developed by (Rue et al. 2009) and (Lindgren et al. 2011). This allows us to make MCMC-free inference in only a fraction of the time required by SCAT.

2 Methods

We consider datasets consisting of a set of allelic counts at bi-allelic loci for a set of reference populations of known geographic locations. Individuals of unknown geographic origin are genotyped for the complete set of orthologous loci. Our method is tailored to geographically assign the latter individuals given the set of georeferenced genetic data (hereafter referred to as training data). We denote by fsl the frequency of a reference allele at locus l at geographic location s. We assume that the number of reference alleles is binomial with statistical independence across loci. This amounts to assuming that individuals located around location s form a population at Hardy–Weinberg equilibrium with linkage equilibrium across markers. Our model has therefore the same likelihood function as the one described by (Pritchard et al. 2000). We assume that spatial variation of allele frequencies can be described by a non-parametric surface in two dimensions. Following (Wasser et al. 2004), we model the spatial variation of by a set of spatially auto-correlated random variables with Gaussian distribution (a random field) denoted by ysl. We assume that fsl and ysl relate through a logistic function. We model the spatial auto-covariance of allele frequencies by imposing a parametric form to . We should stress that our method is designed to perform continuous assignment. Therefore, we cannot only rely on a covariance matrix, but need instead a covariance function, which models covariance variation in the continuous space. This model can be defined either in a flat geographic domain, using straightline distances (2D) or on the sphere using great circle distances (a sub-model referred to be low as 3D model, better appropriate to analyze worldwide datasets). Under our model, the covariance between allele frequencies at geographic locations s and decays with the geographic distance and therefore captures the form of population structure known as isolation-by-distance (Guillot et al., 2009). A key feature of our model is that it can be handled within the Integrated Nested Laplace Approximation (INLA) framework. The location of samples from unknown geographic origin is estimated following three steps. In the first step, we estimate the parameters of the covariance model from the set of georeferenced genetic data, which summarize information on the magnitude and the spatial scale of variation of allele frequencies. In the second step, we compute estimated geographic maps of allele frequencies for each locus using the parameters previously estimated. In the third step, we assign samples of unknown origin by maximizing the likelihood that a sample comes from a specific location over the study area (discretized over a fine grid). Our method is described in full detail in the Supporting material.

3 Results

In Supporting material, we assess the performance of our method and SPA (Yang et al., 2012), the most-commonly used method in geospatial assignment. We evaluated the accuracy of both methods using real and simulated datasets, spanning a range of possible applications in biology. The three application cases considered included organisms characterized by very diverse vagility and dispersal behaviors, spatial scales ranging from the regional to the continental scale and genotyping information ranging from 41 to 197 146 SNPs. Simulations were performed under a series of statistical models, selected to uncover different underlying biological processes. In most situations, our method was found to outperform SPA, showing assignment errors corresponding to only a fraction of those measured in SPA. The difference between both methods was most pronounced when a limited number of loci were considered.

4 Conclusion

The statistical model underlying our method is largely reminiscent of the SCAT program (Wasser et al., 2004, 2007). However, building on INLA instead of MCMC allowed us to significantly reduce computing times by typically several orders of magnitudes. In addition, our approach is free of MCMC convergence issues that can considerably increase the computation burden. In the Florida Scrub-jay dataset (1311 individuals, 41 SNPs), SPASIBA achieved a full analysis in ∼10 min using a single 3–GHz CPU. SCAT required about a week of computation, while SPA provided results within a few seconds. These computing times scale linearly with the number of loci. With such running times and the accuracy levels demonstrated above, SPASIBA appears appropriate for the routine analysis of SNP datasets consisting of a few tens of thousands of loci. In particular, it appears to be an ideal method for the analysis reduced-representation sequencing data that become increasingly available in ecology, including for non-model organisms (Davey et al., 2011).

Acknowledgements

Access to the POPRES dataset was granted by the Data Access Committee of the NCBI dbGaP Data Access request system at the National Institute of Health. We thank John W. Fitzpatrick, Reed Bowman, Aurelie Coulon, the Archbold Biological Station and the Cornell Lab of Ornithology for permission to use their extensive sample of georeferenced genetic data on Florida Scrub-jays.

Funding

The Danish e-Infrastructure for Computing, the working group on Computational Landscape Genomics at the National Institute for Mathematics and Biology Synthesis, a Marie-Curie Initial Training Network EUROTAST [Grant number FP7ITN-290344], the Danish Council for Independent Research, Natural Sciences, the Danish National Research Foundation [Grant number DNFR94] and Marie-Curie Actions [Career Integration Grant number FP7CIG-293845]. Florida Scrub-jays data were generated with support from the U.S. National Science Foundation [Grant number DEB-0316292].

Conflict of interest: none declared.

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© The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

QUASI-CONTINUOUS DYNAMIC TRAFFIC ASSIGNMENT MODEL

Several variants of combined dynamic travel models in discrete time with dynamic user equilibrium or system optimality as the assignment objective have been presented recently. This modeling approach is converted into quasi-continuous time, which enables two key model improvements: (a) traffic volumes are spread over time intervals in continuous time, allowing trips to be split among successive time intervals, and (b) the first-in first-out ordering of trips between all zone pairs is more precisely maintained. The means by which capacity losses are approximated on upstream links caused by spillback queueing from oversaturated links and accidents are also described. Trips are assumed to have scheduled departure times and variable arrival times, but notational variations allowing other model forms are briefly mentioned. Application of this model to a Denver-area network with comparison of results to observed speeds and volumes is described elsewhere.

  • Record URL:
  • Record URL:
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  • Supplemental Notes:
    • This paper appears in Transportation Research Record No. 1493, Travel Demand Forecasting, Travel Behavior Analysis, Time-Sensitive Transportation, and Traffic Assignment Methods. Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the Transportation Research Board of the National Academy of Sciences. Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved
  • Authors:
    • Janson, Bruce N
    • Robles, Juan
  • Publication Date: 1995

Language

Media Info

  • Features: Figures; References;
  • Pagination: p. 199-206
  • Monograph Title: Travel demand forecasting, travel behavior analysis, time-sensitive transportation, and traffic assignment methods
  • Serial:

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Filing Info

  • Accession Number: 00714872
  • Record Type: Publication
  • ISBN: 0309061709
  • Files: TRIS, TRB
  • Created Date: Dec 8 1995 12:00AM

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