Testing for Associations between Loci and Environmental Gradients Using Latent Factor Mixed Models

Abstract

Adaptation to local environments often occurs through natural selection acting on a large number of loci, each having a weak phenotypic effect. One way to detect these loci is to identify genetic polymorphisms that exhibit high correlation with environmental variables used as proxies for ecological pressures. Here, we propose new algorithms based on population genetics, ecological modeling, and statistical learning techniques to screen genomes for signatures of local adaptation. Implemented in the computer program “latent factor mixed model” (LFMM), these algorithms employ an approach in which population structure is introduced using unobserved variables. These fast and computationally efficient algorithms detect correlations between environmental and genetic variation while simultaneously inferring background levels of population structure. Comparing these new algorithms with related methods provides evidence that LFMM can efficiently estimate random effects due to population history and isolation-by-distance patterns when computing gene-environment correlations, and decrease the number of false-positive associations in genome scans. We then apply these models to plant and human genetic data, identifying several genes with functions related to development that exhibit strong correlations with climatic gradients.

The challenge of separating signatures of local adaptation from those of isolation by distance and colonization history: The case of two white pines

“…Signatures of local adaptation to climate were investigated using two GEA methods that take into account neutral population structure: Bayenv2 (Coop et al., 2010; Gunther & Coop, 2013) and LFMM (Frichot et al., 2013). We first ran Bayenv2 using the entire SNP dataset and 100,000 Markov Chain Monte Carlo (MCMC) runs to estimate the covariance matrix (Figure S2, Appendix S2).…”

“…Loci showing signatures of selection are often detected by testing for atypically high or low among‐population genetic differentiation compared with the rest of the genome ( F ST outlier tests; Lewontin & Krakauer, 1973; Beaumont & Nichols, 1996; Beaumont & Balding, 2004; Foll & Gaggiotti, 2008; Excoffier, Hofer, & Foll, 2009), or by looking at correlations with environmental factors of interest after controlling for neutral population structure (genetic‐environment associations, GEA; Coop, Witonsky, Di Rienzo, & Pritchard, 2010; Frichot, Schoville, Bouchard, & François, 2013; Gunther & Coop, 2013). These methods show variable performances under different demographic scenarios (Excoffier et al., 2009; Frichot, Schoville, de Villemereuil, Gaggiotti, & François, 2015; Lotterhos & Whitlock, 2014, 2015; de Villemereuil, Frichot, Bazin, François, & Gaggiotti, 2014).…”

“…In addition, simulations showed that increasing the total number of sampled individuals increased the power of GEA and F ST outlier analyses (Lotterhos & Whitlock, 2015). Statistical methods that take into account uncertainty due to small population sample sizes (e.g., Coop et al., 2010; Foll & Gaggiotti, 2008; Frichot et al., 2013) are well suited for sampling schemes that aim to maximize environmental variation by including a large number of populations in order to improve our ability to detect signatures of local adaptation in natural populations.…”

Discovering variation of secondary metabolite diversity and its relationship with disease resistance inCornus floridaL.

“…We used genotype by sequencing (GBS; Peterson et al., 2012) of two Illumina Hiseq libraries, de novo assembly into 90‐bp GBS tags with STACKS (Catchen, Amores, Hohenlohe, Cresko, & Postlethwait, 2011), latent factor mixed modeling [a genotype–environment association (GEA) method; Frichot, Schoville, Bouchard, & François, 2013], and two F ST outlier methods (Excoffier, Hofer, & Foll, 2009; Foll & Gaggiotti, 2008) to classify putatively neutral SNPS and SNPs exhibiting varying support for being under selection (Pais et al., 2016). Putatively neutral reference SNPs were used to calculate marker‐based inbreeding coefficients ( F ; Keller, Visscher, & Goddard, 2011) and identity‐by‐state matrices using PLINK (Purcell et al., 2007).…”

Recent advances in conservation and population genomics data analysis

“…The reasons for the popularity of GEA analyses are practical: They require no phenotypic data or prior genomic resources, do not require experimental approaches (such as reciprocal transplants) to demonstrate local adaptation, and are often more powerful than differentiation‐based outlier detection methods (De Mita et al., 2013; de Villemereuil, Frichot, Bazin, François, & Gaggiotti, 2014; Forester, Lasky, Wagner, & Urban, 2018; Lotterhos & Whitlock, 2015). In particular, participants considered how and why detection rates differed between univariate and multivariate GEAs, exploring the use of latent factor mixed models (Frichot, Schoville, Bouchard, & Francois, 2013) and redundancy analysis (Forester, Jones, Joost, Landguth, & Lasky, 2016; Lasky et al., 2012), respectively. Recent work has shown that RDA is an effective means of detecting adaptive processes that result in weak, multilocus molecular signatures (Forester et al., 2018), providing a powerful tool for investigating the genetic basis of local adaptation and informing management actions to conserve evolutionary potential (Flanagan et al., 2017; Harrisson et al., 2014; Hoffmann et al., 2015).…”