## Detecting environmental selection using SNP data

Compiled by Rachael Dudaniec, Macquarie University, 23 January 2020

### Table of contents

- Part 1.0 Load and examine genetic data, plot and correlate environmental variables
- Part 2.0 Differentiation-based outlier detection with pcadapt and OutFLANK
- Part 3.0 Multivariate EAA with redundancy analysis (RDA)
- Part 4.0 Univariate EAA with latent factor mixed models (LFMM)

### Introduction

**Practical learning goals**

- Learn code for running a variety of popular differentiation-based and environmental association analyses (EAA)
- Modify the code to apply different parameter sets and evaluate how different settings impact outlier detection
- Plot and interpret results of different test
- Compare results across tests and determine reasons for differences across methods

**Recommendations**

- Work together with your neighbor(s) (i.e. try out different parameter sets)
- Please ask if you have questions!

**The dataset**

The data for the practical come from:

Dudaniec RY, Yong CJ, Lancaster LT, Svensson EI, Hansson B (2018) Signatures of local adaptation along environmental gradients in a range-expanding damselfly (*Ischnura elegans*). Molecular Ecology. 27(11): 2576-2593

Code for this practical have been adapted from:

- Dudaniec RY, Yong CJ, Lancaster LT, Svensson EI, Hansson B (2018) Signatures of local adaptation along environmental gradients in a range-expanding damselfly (Ischnura elegans). Molecular Ecology. 27(11): 2576-2593
- Forester BR, Lasky JR, Wagner HH, Urban DL (2018) Comparing methods for detecting multilocus adaptation with multivariate genotype-environment associations. Molecular Ecology 27, 2215-2233
- Some of the code and annotations for this practical are adapted from:

Forester et al. online tutorial and Brenna Forester: Practical 2 of the Workshop on Ecological and Evolutionary Genomics 2019, Sydney, Australia.

### Part 1.0: The Data

The data are from adult damselflies of Ischnura elegans, collected in southern Sweden. This damselfly is undergoing a poleward range shift under climate change. Here we are interested to know how environmental selection are operating on the species during range expansion.

**The genetic data (“SNPdata.txt”):**

- Contain 13,612 SNPs, from RAD sequencing, filtered as described in Dudaniec et al. (2018), with a MAF = 0.05 and mean 15x depth of coverage.
- Contain 426 individuals collected from 25 sites (10-20 per site), sampled following a temperature gradient, with latitudinal replicates from south to north.
- Are not at equilibrium (i.e. not at migration-selection balance), genetic structure is evident with 4 main genetic clusters identified in Dudaniec et al. (2018), but with moderate gene flow between clusters that increases towards the range limit.

**The environmental data (“envDat.env”):**

- Consist of 5 environmental variables important for the ecology and survival of I. elegans: Mean Annual Temperature, Mean Annual Precipitation, Maximum Mean Summer Temperature, Wind Speed, and % Tree Cover.
- Are extracted from the WorldClim (BioClim) database and from the Global Land Cover Facility
- Are at 1km resolution (raster cell size)
- The distribution of environmental values is generally correlated with latitude, and the range expansion axis.

`Part1_TheData.R`

### Part 2.0: Differentiation-based outlier detection

Differentiation-based outlier detection is most useful for detecting loci of large effect, or those with large differences in allele frequencies between locations. The approach does not examine environmental selection, and detects outliers using genetic data only.

Here we will run two methods of differentiation-based outlier detection, OutFLANK (Whitlock and Lotterhos 2015) and pcadapt (Luu et al. 2017). We will compare the output from each program, with different parameters. Some points about these differing approaches:

- pcadapt is based on Principal Component Analysis to detect outliers where each SNP is regressed against each principal component, with outliers extracted using z-scores.
- OutFlank calculates a normal distribution of Fst values from all SNPs and detects outliers using left and right-tail trim fractions.
- pcadapt is not impacted by admixture as it does not require ‘populations’ to be defined – OutFlank requires individuals to be grouped into genetic clusters or populations.
- The
**genomic inflation factor (GIF)**is used in pcadapt to correct for inflation of the test score at each locus, which occurs when population structure or other confounding factors are not appropriately accounted for. See François et al. (2016), Mol Ecol. - Both methods apply a False Discovery Rate (FDR) that the user decides, which is a cut-off applied to identify outliers with a given number of expected false positives.

`Part2_Outliers.R`

**Table 1:** Fill in your outlier results using different OutFlank parameters. You may wish to divide the tests with your neighbour(s) and fill in the table. *K* is set to 25, the number of sites. Note that `$dfInferred`

is produced in `head(OFoutput,5)`

, and is the inferred degrees of freedom for the chi-square distribution of neutral FST (from which outliers are detected).

q-threshold (FDR rate) | L + R Trim Fraction? | Number of outliers? | $dfinferred |
---|---|---|---|

0.10 | 0.10 | ? | ? |

0.10 | 0.05 | ? | ? |

0.10 | 0.01 | ? | ? |

0.05 | 0.10 | ? | ? |

0.05 | 0.05 | ? | ? |

0.05 | 0.01 | ? | ? |

0.01 | 0.10 | ? | ? |

0.01 | 0.05 | ? | ? |

0.01 | 0.01 | ? | ? |

Remember: The Genomic Inflation Factor (GIF) expresses the deviation of the distribution of the observed test statistic from the distribution of the expected test statistic, i.e. inflation of scores. GIF is used to recalibrate P-values to control FDR.

**Table 2:** Fill in your results using different pcadapt parameters (FDR, *K*). For *K*, compare *K* = 2 and *K* = 4. You may wish to divide tests with your neighbour(s) and fill in the table. Note: Keep the modified GIF the same across tests to enable meaningful comparisons.

K (FDR rate) |
FDR (qval) | Modified GIF | Number of outliers pcadapt? |
---|---|---|---|

2 | 0.10 | 1.10 | ? |

2 | 0.05 | 1.10 | ? |

2 | 0.01 | 1.10 | ? |

4 | 0.10 | 1.10 | ? |

4 | 0.05 | 1.10 | ? |

4 | 0.01 | 1.10 | ? |

*K* and FDR?) and across the two detection methods (pcadapt vs OutFLANK)?

### Part 3.0: Multivariate Environmental Association Analysis

Multivariate EAAs are a powerful complement to univariate detection approaches. RDA is a multivariate ordination technique that analyzes matrices of loci and environmental predictors simultaneously. Some points about RDA:

- It determines how groups of loci covary in response to the multivariate environment, as opposed to univariate approaches that apply multiple tests per locus. This makes it more useful for detecting weaker, polygenic signatures of adaptation.
- RDA performs multivariate linear regression on genetic and environmental data, producing a matrix of fitted values. Then PCA of the fitted values is used to produce canonical axes, which are linear combinations of the environmental predictors.
- RDA doesn’t require corrections for multiple tests because it analyzes all genomic and environmental data simultaneously. However, post processing includes checking and modification of the GIF and p-value distribution, with application of the FDR threshold.

Though we do not cover it here, see Partial Redundancy Analysis (pRDA), which is a good complement to RDA that integrates effects of geographic distance on gene x environment correlations (e.g. Vollis et al. 2004).

`Part3_MultivariateEAA.R`

Here we run an RDA with our environmental variables and examine the data in two different ways. Firstly (1) we use an FDR approach based on Mahalanobis distance calculation and apply the modified GIFs to examine outlier numbers. Secondly (2) we use the standard deviation p-value ‘cut-off’ method of Forester et al. (SD Approach) which does not depend on the assumptions of a ‘flat’ p-value distribution required for reliable FDR application.

**Table 3** Fill in your results using different RDA parameters (i.e. FDR, GIF) when retaining all 4 PC axes. You may wish to divide tests with your neighbour(s) and fill in the table together. Note: Keep the modified GIF the same (e.g. 1.0) across tests to enable meaningful comparisons.

PC axes retained | FDR (qvalue) cut-off | Original GIF | Number of outliers | Modified GIF | Number of outliers |
---|---|---|---|---|---|

4 | 0.10 | ? | ? | 1.1 | ? |

4 | 0.05 | ? | ? | 1.1 | ? |

4 | 0.01 | ? | ? | 1.1 | ? |

### Part Part 4.0: Univariate EAA: Latent Factor Mixed Models

LFMM is a regression model that includes unobserved variables (latent factors) that correct the model for confounding effects. The latent factors are estimated simultaneously with the environmental and response variables, which can help improve power when environment and demography are correlated.

The previous version of LFMM (v1.5, implemented in the LEA package) uses an MCMC algorithm to identify GEAs while correcting for confounding factors. MCMC made it (very!) time-intensive for large data sets. LFMM v.2 (Caye et al. (2019)) computes LFMMs for GEA using a least-squares estimation method that is substantially faster than v1.5.

`Part4_UnivariateEAA.R`

**Table 4.** Complete the table for the first variable “Max Temp”, applying modified vs. original GIF

K | FDR (qval) | Adjusted/modified GIF | Number of outliers | Unadjusted, original GIF | Number of outliers |
---|---|---|---|---|---|

4 | 0.01 | ? | ? | ? | ? |

4 | 0.001 | ? | ? | ? | ? |

4 | 0.0001 | ? | ? | ? | ? |

Optional |
|||||

5 | 0.01 | ? | ? | ? | ? |

5 | 0.001 | ? | ? | ? | ? |

5 | 0.0001 | ? | ? | ? | ? |

*K* have on outlier detection? What effect does increasing FDR have on outlier detection?

*The following questions and tasks are optional:*

**Table 5.** Modify the R script to test for the different variables (see code annotations). Complete the table below for the rest of the environmental variables in the LFMM, with *K*=4, and FDR = 0.0001, applying the modified GIF only (you may insert result for Max Temp from Table 4).

K=4 |
FDR (qval) | Adjusted/modified GIF | Number of outliers |
---|---|---|---|

Max Temp | 0.0001 | ? | ? |

Precipitation | 0.0001 | ? | ? |

Tree Cover | 0.0001 | ? | ? |

Wind Speed | 0.0001 | ? | ? |

There is no agreement among statisticians on multiple test corrections for this case: we are testing e.g. 13612 SNPs and 4 predictors = 54,448 tests, with each SNP tested 4 times. But we are not making a correction for that. This may be problematic but there doesn’t appear to be a right answer.

One solution is to run a PCA on the predictors and only run tests on the first one (or two, or three) PCs…this will minimize the number of tests, while maintaining the information in our set of predictors. However, __PCs should also be biologically meaningful__, and using this approach may depend on the objectives of your study.

**General things to consider in Environmental Association Analyses:**

- How do you want to handle multiple environmental predictors (lfmm only)?
- How sensitive are the results to your choice of K (lfmm only)?
- How much do you want to adjust the p-value distribution (a.k.a adjust the GIF)?
- How sensitive are the results to different cutoff thresholds/values of K?
- How sensitive are the results to the MAF filter applied to your data?
- How sensitive are the results to missing data, other technical errors?