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The built environment provides an excellent setting for interdisciplinary research on the dynamics of microbial communities. The system is simplified compared to many natural settings, and to some extent the entire environment can be manipulated, from architectural design, to materials use, air flow, human traffic, and capacity to disrupt microbial communities through cleaning. Here we provide an overview of the ecology of the microbiome in the built environment. We address niche space and refugia, population and community (metagenomic) dynamics, spatial ecology within a building, including the major microbial transmission mechanisms, as well as evolution. We also address the landscape ecology connecting microbiomes between physically separated buildings. At each stage we pay particular attention to the actual and potential interface between disciplines, such as ecology, epidemiology, materials science, and human social behavior. We end by identifying some opportunities for future interdisciplinary research on the microbiome of the built environment., Comment: 23 pages

Investigations of infectious disease outbreaks often focus on identifying place- and context-dependent factors responsible for emergence and spread, resulting in phenomenological narratives ill-suited to developing generalizable predictive and preventive measures. We contend that case-control hypothesis testing is a more powerful framework for epidemiological investigation. The approach, widely used in medical research, involves identifying counterfactuals, with case-control comparisons drawn to test hypotheses about the conditions that manifest outbreaks. Here we outline the merits of applying a case-control framework as epidemiological study design. We first describe a framework for iterative multidisciplinary interrogation to discover minimally sufficient sets of factors that can lead to disease outbreaks. We then lay out how case-control comparisons can respectively center on pathogen(s), factor(s), or landscape(s) with vignettes focusing on pathogen transmission. Finally, we consider how adopting case-control approaches can promote evidence-based decision making for responding to and preventing outbreaks.

This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match between simulations and observations. Imperfect match between simulations and observations can be more pronounced when there are many summary statistics, a phenomenon coined as the curse of dimensionality. Because of this imperfect match, credibility intervals obtained with regression approaches can be inflated compared to true credibility intervals. The chapter presents the main concepts underlying regression adjustment. A theorem that compares theoretical properties of posterior distributions obtained with and without regression adjustment is presented. Last, a practical application of regression adjustment in population genetics shows that regression adjustment shrinks posterior distributions compared to rejection approaches, which is a solution to avoid inflated credibility intervals., Comment: Book chapter, published in Handbook of Approximate Bayesian Computation 2018

Approximate Bayesian computation is a statistical framework that uses numerical simulations to calibrate and compare models. Instead of computing likelihood functions, Approximate Bayesian computation relies on numerical simulations, which makes it applicable to complex models in ecology and evolution. As usual for statistical modeling, evaluating goodness-of-fit is a fundamental step for Approximate Bayesian Computation. Here, we introduce a goodness-of-fit approach based on hypothesis-testing. We introduce two test statistics based on the mean distance between numerical summaries of the data and simulated ones. One test statistic relies on summaries simulated with the prior predictive distribution whereas the other one relies on simulations from the posterior predictive distribution. For different coalescent models, we find that the statistics are well calibrated, meaning that the type I error can be controlled. However, the statistical power of the two statistics is extremely variable across models ranging from 20% to 100%. The difference of power between the two statistics is negligible in models of demographic inference but substantial in an additional and purely statistical example. When analyzing resequencing data to evaluate models of human demography, the two statistics confirm that an out-of-Africa bottleneck cannot be rejected for Asiatic and European data. We also consider two speciation models in the context of a butterfly species complex. One goodness-of-fit statistic indicates a poor fit for both models, and the numerical summaries causing the poor fit were identified using posterior predictive checks. Statistical tests for goodness-of-fit should foster evaluation of model fit in Approximate Bayesian Computation. The test statistic based on simulations from the prior predictive distribution is implemented in the gfit function of the R abc package.

To characterize natural selection, various analytical methods for detecting candidate genomic regions have been developed. We propose to perform genome-wide scans of natural selection using principal component analysis. We show that the common Fst index of genetic differentiation between populations can be viewed as a proportion of variance explained by the principal components. Considering the correlations between genetic variants and each principal component provides a conceptual framework to detect genetic variants involved in local adaptation without any prior definition of populations. To validate the PCA-based approach, we consider the 1000 Genomes data (phase 1) after removal of recently admixed individuals resulting in 850 individuals coming from Africa, Asia, and Europe. The number of genetic variants is of the order of 36 millions obtained with a low-coverage sequencing depth (3X). The correlations between genetic variation and each principal component provide well-known targets for positive selection (EDAR, SLC24A5, SLC45A2, DARC), and also new candidate genes (APPBPP2, TP1A1, RTTN, KCNMA, MYO5C) and non-coding RNAs. In addition to identifying genes involved in biological adaptation, we identify two biological pathways involved in polygenic adaptation that are related to the innate immune system (beta defensins) and to lipid metabolism (fatty acid omega oxidation). An additional analysis of European data shows that a genome scan based on PCA retrieves classical examples of local adaptation even when there are no well-defined populations. PCA-based statistics, implemented in the PCAdapt R package and the PCAdapt open-source software, retrieve well-known signals of human adaptation, which is encouraging for future whole-genome sequencing project, especially when defining populations is difficult.

Patterns of isolation-by-distance arise when population differentiation increases with increasing geographic distances. Patterns of isolation-by-distance are usually caused by local spatial dispersal, which explains why differences of allele frequencies between populations accumulate with distance. However, spatial variations of demographic parameters such as migration rate or population density can generate non-stationary patterns of isolation-by-distance where the rate at which genetic differentiation accumulates varies across space. To characterize non-stationary patterns of isolation-by-distance, we infer local genetic differentiation based on Bayesian kriging. Local genetic differentiation for a sampled population is defined as the average genetic differentiation between the sampled population and fictive neighboring populations. To avoid defining populations in advance, the method can also be applied at the scale of individuals making it relevant for landscape genetics. Inference of local genetic differentiation relies on a matrix of pairwise similarity or dissimilarity between populations or individuals such as matrices of FST between pairs of populations. Simulation studies show that maps of local genetic differentiation can reveal barriers to gene flow but also other patterns such as continuous variations of gene flow across habitat. The potential of the method is illustrated with 2 data sets: genome-wide SNP data for human Swedish populations and AFLP markers for alpine plant species. The software LocalDiff implementing the method is available at http://membres-timc.imag.fr/Michael.Blum/LocalDiff.html, Comment: In press, Evolution 2014

Many recent statistical applications involve inference under complex models, where it is computationally prohibitive to calculate likelihoods but possible to simulate data. Approximate Bayesian Computation (ABC) is devoted to these complex models because it bypasses evaluations of the likelihood function using comparisons between observed and simulated summary statistics. We introduce the R abc package that implements several ABC algorithms for performing parameter estimation and model selection. In particular, the recently developed non-linear heteroscedastic regression methods for ABC are implemented. The abc package also includes a cross-validation tool for measuring the accuracy of ABC estimates, and to calculate the misclassification probabilities when performing model selection. The main functions are accompanied by appropriate summary and plotting tools. Considering an example of demographic inference with population genetics data, we show the potential of the R package. R is already widely used in bioinformatics and several fields of biology. The R abc package will make the ABC algorithms available to the large number of R users. abc is a freely available R package under the GPL license, and it can be downloaded at http://cran.r-project.org/web/packages/abc/index.html.

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s_obs from the data and simulating summary statistics for different values of the parameter theta. The posterior distribution is then approximated by an estimator of the conditional density g(theta|s_obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment and of the transformations of the summary statistics. Supplemental materials containing the details of the proofs are available online.

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%.

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool of analysis is a coupling argument with another well-known index called the Sackin statistic. Asymptotics for the mean, variance and covariance of these two statistics are obtained, as well as their limiting joint distribution for large phylogenies. Under the Yule model, the limiting distribution arises as a solution of a functional fixed point equation. Under the uniform model, the limiting distribution is the Airy distribution. The cornerstone of this study is the fact that the probabilistic models for phylogenetic trees are strongly related to the random permutation and the Catalan models for binary search trees., Comment: Published at http://dx.doi.org/10.1214/105051606000000547 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)