Module one: Optimization and determination of relevance of descriptors and analysis of the phenotypic and genotypic diversity of genebanks.

As stated before, genebanks are not only responsible for collecting and maintaining germplasm collections, but also for documenting and characterizing the collections in order to enhance their use. In many cases, genebanks not only register basic passport data for each accession, but also collect a series of trait data (i.e., morpho-agronomic data) in multiple sites or years to describe the accessions. An accurate evaluation of morpho-agronomic traits is labor-intensive and, in numerous cases, these valuable data are not further used for measuring the genetic diversity of the collection or for breeding purposes. In other cases, genebanks also collect molecular marker data, which may provide valuable and complementary information. A comprehensive analysis of the genetic diversity held in a genebank could offer useful information for breeders. For example, deciphering patterns of genetic structure and linkage disequilibrium, with selected descriptors and molecular marker data, is key when carrying out robust Genome-Wide Association Studies (GWAS) and in the identification of Quantitative Trait Loci (QTL) that can be used in Marker Assisted Selection (MAS). Also, genetic diversity analyses are necessary to establish core collections, which minimize the number of accessions that breeders need to screen for useful traits. For all these reasons, this module implements methods based on machine learning or on traditional approaches with the aim to assist genebank curators in the analysis of phenotypic and molecular marker data.

1. a. Submodule one: Descriptor optimization and analysis of phenotypic diversity of genebanks

The aim of this submodule is twofold: to select the phenotypic descriptors that are most useful in classifying a sample of genebank accessions into taxonomic groups or intraspecific groups predefined by the user, and to explore the diversity of a group of germplasm accessions with a set of phenotypic descriptors.

As mentioned above, genebanks not only register for each accession basic passport data, but may also collect characterization and evaluation descriptors which, along with passport data, are usually registered according to international standards (i.e., crop descriptors [20]). Crop descriptors can serve as a starting point to collect data that can be used in this submodule. These descriptors include characterization (e.g., botanical characteristics) and evaluation descriptors (e.g., yield, reaction to biotic or abiotic stress), which may differ in the way they are registered across multiple experiments or the degree in which they are affected by the environment. Usually, evaluation descriptors are highly influenced by the environment, so users should determine the quality of these data beforehand. For doing so, users should consider the methods used, experimental designs, statistical analyses applied, replicated trials performed over different years or locations, and the site and site environment descriptors that were registered. All these data will be useful to interpret the results coming from trials where evaluation descriptors were recorded. If this is the case, users should apply methods to analyze and validate these data to produce ready-to-use data, as done elsewhere [12].

The working example of this submodule analyzes a database that contains conventional morpho-agronomic traits (descriptors), and seed nutritional and biochemical traits, evaluated in a group of 1440 accessions, from the CIAT’s core collection of domesticated common bean (Phaseolus vulgaris L.). For this example, the domesticated accessions were classified into landraces of Mesoamerican, Andean or Colombian origin, according to their phaseolin type [21,22]. Andean landraces show phaseolins T, H, C, PA, CA, and TO, Mesoamerican landraces contain phaseolins S, M, Sb and Sd, and Colombian landraces show phaseolins B and CH. The database is organized in columns, with the ID of the accessions in the first column, followed by 44 descriptors. The descriptors include morphological traits from flower, seed, stem, and leaf, two phenological traits (Days to Flowering (DAF) and Days to Physiological Maturity (DAM), growth habit, phaseolin type, amylase inhibitor type, and nutritional compounds in the seed (concentration of micro and macronutrients and protein content). Additional descriptors are country of origin, municipality, and collection site. The database can be found at https://github.com/agrocompuepidemlab/GermVersity/releases/tag/v1.0.0. If users wish to reproduce the analyses with our example data, we advise them not to modify the additional descriptors because these are necessary for the biological interpretation of results.

The selection of descriptors was carried out using a machine learning approach [9] implemented in the package randomForest in R. The pipeline was as follows. Initially, Random Forests (RF) were used to perform accession classification based on phenotypic descriptors and Out Of Bag (OOB) accuracy of accession classification was calculated. For this, 70% of the data were used for training, and the remaining 30% for testing. The value of the Minimum Depth Distribution (MDD) and its relationship to the number of trees determined the selection of phenotypic descriptors of importance in the classification of accessions. Lower MDD values suggest more important traits in the classification. Furthermore, the confusion matrix enables the classification of accessions to be visualized. The confusion matrix can be examined in two ways: (i) the ability to distinguish between unrelated accessions and (ii) the sensitivity to detect phenotypic similarities across accessions of the same cluster [23].

Subsequently, with the descriptors selected in the previous stage, a multi-step approach was applied to a group of common bean accessions from CIAT’s core collection, with the aim of exploring their phenotypic diversity. For this, the number of phenotypic groups (K) was initially defined from a set of 26 clustering indices that support group selection by K-means. In our working example, the selected number of groups (K) was four, without limiting the clustering optimization for other case studies. For comparison purposes, users can visualize the clustering pattern of the accessions for two different K values. Finally, a principal component analysis was applied to display the relationships between each variable and the selected groups, as well as a hierarchical clustering analysis that allows the phenotypic similarity among groups of accessions to be visualized.

1. b. Submodule two: analysis of the genetic stratification of a sample of germplasm accessions with SNP markers

The aim of this submodule is to define the genetic structure of a sample of genebank accessions and calculate basic genetic diversity statistics. For the analyses of genetic data, the user must input a matrix of SNP data in VCF format. A VCF file can be built from sequencing data in fastq format, such as those derived from Illumina or other sequencing platforms, and a reference genome sequence. There are various tutorials available on how to obtain analysis-ready VCF files, to which the readers are referred (https://sourceforge.net/projects/ngsep/files/training/ManualNGSEP_v4.0.3.pdf/download). The SNP matrix should be previously filtered to minimize missing data (a maximum of 10%−20% missing data is recommended) and SNPs with rare variants [for example, a MAF (Minor Allele Frequency) of 5%]. The SNP file available for this demo (in VCF format) consists of 482 accessions of wild and domesticated Lima bean (Phaseolus lunatus L.) genotyped at 12,398 SNP loci with the reduced genomic scanning technique known as GBS (Genotyping-By-Sequencing) [24], using the restriction enzyme ApeKI. This VCF file has already been published, analyzed, and discussed elsewhere as source data [25].

For these samples there is associated metadata relevant to the analysis of genetic diversity, such as the biological status (wild or domesticated), country of origin and genepool for each accession. Previous studies have indicated that in this species there are four genepools for the wild accessions: two Mesoamerican (wild_MI, wild_MII) and two Andean (wild_AI, wild_AII); and two additional genepools for the domesticated accessions: Mesoamerican (DOM_MI) and Andean (Dom_AI) [25,26]. These two domesticated genepools originated from two independent domestication processes, one in Mesoamerica from the genepool MI in central-western Mexico, and the other from the wild genepool AI in the Andes of Ecuador-northern Peru. In this submodule we used this Lima bean dataset to show how to carry out analyses of genetic diversity to classify wild and domesticated accessions into genetic clusters using SNP data, and how to calculate basic diversity indexes for the observed genetic clusters. The VCF file and associated metadata can be found at https://github.com/agrocompuepidemlab/GermVersity/releases/tag/v1.0.0. Below we describe the process step-by-step.

The first step is to import the SNP matrix as a VCF file and the associated metadata in a text file. The latter is a tab-delimited text file with one row per accession, the first column with the taxa ID and the associated metadata in different columns. In the text file used for the working example, the second column is the biological status (wild or domesticated), the third column is the country of origin, and the fourth column is the genepool. From this last column, an object called “genepool” is created (this object is used in later analyses). When using his/her own dataset, the user can a priori define in the column called “genepool” the population to which each individual belongs. Accessions or individuals can be grouped according to the research questions and comparisons as required. If the population is not known, the analyses described below can help the user to define the population structure and optimum clustering. Then, the VCF file is converted (with the function vcfR2genind of the vcfR library) into a genind object (used by the package adegenet and other packages), indicating that the population assigned to each individual or accession is stored in the object “genepool”.

In the first analysis, the submodule calculates an Euclidean distance matrix between individuals on the basis of the observed allele frequencies among individuals. This distance is not a genetic distance per se (i.e., s.s.) but a geometric distance since it does not assume any evolutionary model of molecular evolution. The function nj of the ape package [27] is used to build a tree topology using this distance matrix and the neighbor-joining algorithm [28]. The submodule also calculates a dendrogram, with bootstrap support of groups, from a genlight object. For this, a distance matrix is calculated, based on the proportion of loci that are different among individuals, and the UPGMA (Unweighted Pair Group Method with Arithmetic mean) algorithm is applied. The number of bootstrap replicates is set to 1,000. For this analysis, GermVersity applies the aboot function of the poppr package.

Sometimes the genetic unit of interest is the population and not the individual. For this reason, we implemented the construction of a genetic distance matrix among populations (or genepools) and the derived tree topology. Unlike geometric distances, genetic distances are based on a specific evolutionary model. Genetic distances can be seen as summary statistics because they take the whole dataset (for example, data from SNP loci) and summarize the genetic differentiation between samples (individuals or populations) in a value. One of the most used genetic distances is Nei’s [29], which measures the genetic distance among populations on the basis of their genetic identity, namely the proportion of alleles that are shared between pairs of populations. To calculate Nei’s genetic distances among populations we need to add the strata to the genind object (in this case based on the genepool) to define the populations. Then the sub-module uses this distance matrix to build a UPGMA tree and a neighbor-joining topology, applying 1,000 bootstrap permutations to get statistical support of the groups in the topologies. These analyses use the aboot function of the poppr package.

This submodule further explores the genetic structure of the sample with a Principal Component Analysis (PCA). PCA is a multivariate technique that summarizes the information provided by the genetic markers (in this case SNPs) into a few sets of components. The submodule applies PCA to a genlight object with the function glPca of the package adegenet. To identify genetic clusters, this submodule implements another multivariate approach known as Discriminant Analysis of Principal Components (DAPC) [30]. This approach is convenient when the interest is in describing the diversity among groups of individuals rather than within groups. This approach maximizes discriminant functions that better describe the differences among groups, while minimizing the differences within groups. However, to find the discriminant functions, the groups need to be known a priori, and in many cases this information is missing. To address this issue, the function find.clusters of the adegenet package is run to optimize the number of clusters by means of a PCA and the K-means algorithm. Then, it runs the function dapc to establish the relationships among clusters. In this submodule, the membership probabilities of each individual to each of K populations are calculated on the basis of the retained discriminant functions with the function compoplot.dapc.

After classifying the individuals into clusters or populations, the submodule calculates basic diversity indexes, first for the whole sample and per locus, and then for each cluster. For the analysis of the whole sample, it uses the function summary of the adegenet package to estimate the number of alleles per locus (NA), observed heterozygosity per locus (H_O) and expected heterozygosity (H_E) per locus. For SNP markers, NA might not be very useful because these loci are expected to be biallelic in populations (according to the infinite site mutational model). H_O is the proportion of heterozygous individuals that are observed in a locus. H_E is the heterozygosity expected to be observed in a locus assuming that the population (in this case the whole sample) is in Hardy-Weinberg Equilibrium (HWE) [31] at that particular locus. A significant difference among H_O and H_E means that the locus is not in HWE. Additionally, the submodule applies Bartlett tests to assess whether H_E is different from H_O. As the number of loci, and therefore the number of multiple tests, increases, it is advised to correct the p-values for multiple comparisons (for example with the Bonferroni correction).

GermVersity also estimates genetic diversity indexes for each cluster. This is useful in finding out which cluster is the most or least diverse. To do this, it uses the function basic.stats of the program hierfstat to estimate observed heterozygosity (H_O), mean gene diversities (H_S) within populations, and the fixation index F_IS. As stated before, a significant difference among H_O and H_S means that the population is not in HWE. As different populations may not be in HWE for various reasons, little comparison of diversity among populations can be made on the basis of H_O. For this reason, H_S is preferred for the comparison of the genetic diversity between populations, as with Hs all populations are assumed to be in HWE. The fixation index F_IS measures the deviation to the assumption of HWE in the populations.

In order to determine how genetically divergent the populations are, GermVersity calculates the fixation index F_ST, which measures the difference between H_S and the total genetic diversity expected in the whole population (H_T). The higher the difference between H_T and H_S, the higher the fixation index F_ST, and therefore the higher the divergence among the populations. GermVersity utilizes the function wc of the program hierfstat to calculate F_ST (global and pairwise) according to Weir and Cockerham [32].

Module two: Spatial analysis and current and potential distribution of germplasm based on Ecological Niche Model (ENM) approach.

Ecological Niche Modeling (ENM), and Spatial Distribution Modeling (SDM), revolutionized the identification and use of novel genetic resources by analyzing the spatial distribution of wild and landrace germplasm accessions. Utilizing geographic and environmental data, ENM predicts where specific genetic resources can be found, assisting their targeted collection and conservation. This method not only supports conservation efforts but also bolsters pre-breeding programs by pinpointing ecological niches of accessions, thus helping breeders select parental lines. By integrating ENM, the GermVersity platform enhances genetic resource management, providing a detailed framework for conserving and utilizing genetic diversity. ENM’s strategic application improves the resilience and productivity of crops, contributing to sustainable agricultural development amidst environmental shifts. Among the many methodologies used for SDM, two widely implemented advanced machine learning techniques are Generalized Linear Modeling (GLM) and Maximum Entropy Modeling (MaxEnt). The GLM approach analyzes the relationship between the presence of species and environmental factors, identifying key areas for the conservation and use of genetic resources, while MaxEnt assumes that the most probable distribution of a species is the one that maximizes entropy, given the existing information on its presence and the environmental characteristics of those locations, and is particularly useful when absence data are scarce. Both methods are fundamental in informing decisions in pre-breeding and conservation programs, thanks to their ability to handle diverse variables and generate accurate predictive models.

The aim of this module is to explore ENM and SDM. The paradigm of SDM is used for wild and landrace accessions of germplasm collections. For SDM, two types of data are required: accurate georeferencing data of each accession and the environmental layers (rasters). The georeferencing data is a list in excel format with the column names: ‘Species’, ‘Longitude’, and ‘Latitude’. The format for geographical coordinates supported by GermVersity is decimal degrees. Users have two options for using the layer data. One is to use the 19 bioclimatic variables from WorldClim (https://www.worldclim.org/) directly from the repository at approximately 2.5 minutes (17.2 km²) resolution [33]. The other is to upload their own layers. A description of the 19 bioclimatic variables can be found at https://www.worldclim.org/data/bioclim.html. To streamline the acquisition of the environmental layers required for model execution, an update was implemented utilizing the geodata library, in conjunction with other tools such as the terra package. This integration was necessary due to recent updates in the ENMevaluate package, which now operates exclusively with spatial objects defined by the terra framework. This modification ensures compatibility across modules and facilitates a more efficient and reproducible modeling workflow.

GermVersity automatically downloads the different layers in raster format based on the coordinate of latitude and longitude at the collection points of accessions. As a first approximation we recommend directly using environmental layers in WorldClim (19 bioclimatic variables). However, we encourage users to implement their own environmental layers at a resolution greater than 30 seconds (approximately 1 km²) for improved precision in the output of spatial distribution modeling. It is advisable to carry out an a priori analysis of data curation, correlation, Variance Inflation Factor (VIF), or to use other analytical methods to reduce redundancy and pseudo-replication among environmental variables, with tools outside GermVersity such as those implemented in the program Capfitogen3 (http://www.capfitogen.net/en/). Also, we suggest using inferred environmental indices for specific abiotic stresses rather than just using raw environmental variables, as implemented in ENVIREM (ENVIronmental Rasters for Ecological Modeling) resources (https://envirem.github.io/) [34]. The tutorial data for this module was based on Garcia et al. [25] and consists of the same accessions of Lima bean used in module one, submodule two. The original data of this module can be found at https://github.com/agrocompuepidemlab/GermVersity/releases/tag/v1.0.0.

This module offers two approaches for SDM, a classical Generalized Linear Model (GLM) function [35] and another algorithm using the popular Maximum Entropy (MaxEnt) method [36]. The GLM algorithm is implemented based on the R library Caret (Classification and Regression Training), widely used in data science. The first step is to extract the point values of the presence data from the user’s own environmental layers, or from those downloaded from WorldClim. Subsequently, a cleaning of missing values and selection of unique values by point of presence are performed. In parallel, pseudo-absences are captured with the function raster::sampleRandom(), avoiding sampling the same cell more than once. Next, presence and absence data are merged, having previously confirmed that both classes are balanced. Then the module proceeds to divide the data into training and testing sets at 80% and 20%, respectively. The resampling method chosen for class modeling is cross-validation with repetitions, for which 5 folds and 3 repetitions are fixed. Cross-validation with repetitions is a model evaluation technique that involves dividing data into groups (folds) to train and test the model multiple times in an iterative manner, repeating the process with different partitions to obtain a more accurate estimate of the model’s performance. By redoing the cross-validation several times and averaging the results, variability is reduced, and a more reliable evaluation of the model’s predictive ability is achieved. Subsequently, the training is carried out with the function caret::train() and the GLM algorithm modeling implemented in the stats::glm() protocol. The calculation of the accuracy of the model is made on the testing dataset to ultimately estimate the error of the model.

On the other hand, the MaxEnt is carried out by the R function MaxNet (https://github.com/mrmaxent/maxnet). The optimization of spatial distribution modeling via maximum entropy is implemented based on the R-package ENMeval 2−0 [37]. Firstly, the user selects the number of background points as input in the function ENMevaluate. Spatial cross-validation with four folds is implemented as a resampling method to measure the performance of different predictive models. The predictive models are generated by combinations of various transformations (L = linear, Q = quadratic, H = hinge, P = product and T = threshold) of the original predictor variables (‘feature classes’). Then, the corrected Akaike Information Criterion (AICc) [38] is used as a reference metric to select the best performing model.

Finally, the prediction of spatial distribution is executed using the raster:predict() function for GLM and MaxEnt. For both methods, projections are transformed into dataframe format through the sp::SpatialPixelsDataFrame() function and visualized with high-quality graphics via the R ggplot library.

The ENM or SDM analytical pipelines are by definition more complex and rigorous than what is presented in this module, which includes multiple processes of basic elements for the correct use of these algorithms and its numerous applications [39,40]. For instance, in this exploratory approach, the optimization automations were configured with specific values and ranges for parameters of both GLM and MaxEnt. Examples include the number of background points, the number of repetitions and folds in cross-validation, feature classes, and the regularization multiplier. For this reason, we highly recommend that users of this module consult different protocols for the correct and responsible use of these approaches [41,42].

Module three: Genome-environment association tests.

Genome-Wide Association Study (GWAS) is a key technique in genetics that enables the identification of genetic variants associated with specific biological traits. In the context of genebanks, these studies are highly useful for allele mining. Firstly, GWAS facilitates the identification of genes of interest for crop breeding. These genes may become valuable tools for genetic enhancement, enabling the selection of superior varieties. Moreover, GWAS helps characterize genetic diversity in genebanks, providing essential information for the conservation of genetic resources and the selection of parental lines in breeding programs. Secondly, GWAS helps unravel the underlying genetic architecture of complex traits, namely those influenced by multiple genes and the environment. By identifying the genome regions and genes involved in the variation of these traits, a deeper understanding is gained, which can be applied to design more effective strategies for genetic breeding.

In some cases, the interest lies in understanding how populations have adapted to local environmental conditions. Identifying the genes that underlie adaptation processes relevant for crop breeding, e.g., tolerance to drought, can be very useful in enhancing the value of germplasm collections. Genome-Environment Association (GEA) [43,44] among SNP markers and environmental variables or indices is an approach, based on the GWAS paradigm, that is implemented in this module. The utility of GEA studies lies in their ability to discern how environmental factors can modulate the influence of genes on the expression of complex traits.

Several analytical approaches have addressed the paradigm of GWAS analyses, the family of Mixed Linear Models (MLM) being one of the most commonly implemented tools in several species. Current MLM-based functions generally combine mixed linear models [45] with kinship and population structure as covariates to correct for false positives. However, new GWAS algorithms such as those implemented in GAPIT [46] and Latent Factor Mixed Model (LFMM) [47] have recently been developed in order to gain statistical power to assist in the detection of associated markers, to increase efficiency, and to decrease computational complexity [48].

1. a. Submodule one: GWAS of genetic and environmental variables with GAPIT

GAPIT is a genome association and prediction integrated tool freely available since 2011 [49] developed in the Zhiwu Zhang Laboratory (https://zzlab.net/GAPIT/) from Washington State University. Currently, Dr. Jiabo Wang is leading the newly-developed GAPIT version 3 that implements two new GWAS methods, FarmCPU [50] and BLINK [51]. These methods have shown to be more efficient in controlling false-positives due to confounding factors. In this submodule, the confounding effects of population structure are controlled by means of a PCA and a kinship matrix, both analyses based on genome-wide SNP markers. The novelty in both methods is in dividing the classic MLM algorithm into two parts that are used iteratively, a Random Effect Model (REM) and a Fixed Effect Model (FEM). BLINK replaces Restricted Maximum Likelihood (REML) in FarmCPU’s REM with Bayesian Information Criteria (BIC) in an FEM. López-Hernández & Cortés [52] explored the use of these tools to obtain GEAs in common bean using Genotyping-By-Sequencing (GBS) and customized environmental indices of heat stress.

For the GEA modeling, two types of data are required: the environmental data of each accession and the genomic data. The environmental data is a bio-variable or environmental index extracted from the specific collection site of each wild or landrace accession using georeferencing data. The environmental data can be provided as a list in excel format with the column names: ‘Taxa’, ‘Biovariable or Index 1’, ‘Biovariable or Index 2’… and ‘Biovariable or Index n’. The maximum number of environmental variables (columns) in the table are seven, apart from the ‘Taxa’ ID. The missing data is encoded as ‘NA’. The tutorial data for this submodule was based on accessions of wild Lima bean analyzed by García et al. [25] and the layers ‘bio1’ (average temperature), ‘bio12’ (average precipitation) and ‘bio3’ (isothermality) from the WorldClim platform, and the environmental indexes: ‘Annual PET’, ‘Aridity Index Thornthwaite’, ‘Climatic Moisture Index’ and ‘Continentality’ obtained from the ENVIREM resource.

For GAPIT, the genomic data is required in HapMap format (hmp.txt), initially used in the International HapMap Project. This format contains the genomic variation of SNP markers discovered and genotyped from Next Generation of Sequencing (NGS) methods such as GBS. A common format for GWAS analysis is the VCF format, which users can convert to hmp.txt format through popular resources such as the software Tassel 5.0 [53]. In this submodule, the genotypic data consists of 10,668 SNP loci, genotyped at 259 wild Lima bean accessions. MAF values are fixed at 5%. The environment and genomic data used in this module can be found at https://github.com/agrocompuepidemlab/GermVersity/releases/tag/v1.0.0.

The results generated by GAPIT are stored in the local folder ~ /GAPIT/. There are three tables for each variable of the phenotypic input and for each statistical approach (MLM. FarmCPU and BLINK) with information associated with: SNP identifier, chromosome, chromosome position, p value, MAF, r-square of model without SNP indexation, r-square of model per SNP, FDR-adjusted p-values and effect of the SNP. Also, for each trait, descriptive statistics as well as Manhattan and QQ-plots are provided. In addition, Manhattan and QQ-plots that show association results for all traits simultaneously are generated; therefore, we suggest the user input less than six variables at a time to be able to visualize these plots efficiently.

1. b. Submodule two: Latent Factor Mixed Model (LFMM) analysis

In this submodule, GermVersity implements a latent factor mixed model analysis (LFMM) to carry out GEA using. For this case study, we used the same genomic data as in submodule one, namely 259 accessions of wild Lima bean, that belong to four wild genepools (two Mesoamerican: MI and MII, and two Andean: AI and AII), and that have previously been genotyped at 10,668 SNP loci. Frichot et al. [54] implemented, in R’s LEA package, algorithms that combine linear regression with factor models to detect high correlations between allele frequencies, e.g., from SNP loci, and environmental variables of interest, while controlling for the confounding effects of population stratification, demography or other factors. In this approach, population structure is modeled using latent factors (K) (that can be set with the number of ancestral populations in the sample), while the environmental variables are considered fixed effects.

Here we describe the steps for LFMM analysis. For the LEA package, the user should provide a genotypic matrix of SNP data, that can be in VCF format, but without missing data. This file can be obtained by using imputation methods such as those implemented in programs such as Tassel. The VCF file is then converted to lfmm format with the function vcf2lfmm. Then, environmental data is uploaded as a text file. This file should contain one row for each individual and one column for each environmental variable. This file does not contain any columns with identifiers for the individuals; therefore, the order of the individuals should be the same as in the VCF file. In this submodule, the environmental data for the case study consists of the variable bio10 (average temperature of the warmest quarter) because previous analyses have indicated that this variable is important for the ecological adaptation of wild Lima bean (unpublished data). The environmental data were obtained from the WorldClim database using the geographic coordinates of the collection site of each accession. The next step is to decide on the number of K latent factors to model population structure. For this, the strategy outlined above, in submodule two of module one, can be used to define the number of K populations in the sample. Since modeling population structure is not a straightforward matter, it is recommended to run the LFMM analysis with a range of K values. For example, for the wild Lima bean dataset, previous results have shown that the number of genepools is four, and in this case, we run the LFMM analyses for values of K from 3 to 10. After analyzing the results, we have chosen K = 8 as the best K value to model population substructure; therefore, in this submodule we only show the results for K = 8.

To run the LFMM analysis, the function lfmm2 is first used to estimate the latent factors. This function returns an object that contains the following matrices: U, the estimated factors, and V, the loadings for all latent variables. Once the latent factors are estimated, association tests are performed with the function lfmm2.test, where population structure is accounted for, and p-values are adjusted by using genomic control. This function generates an object that contains the p-values of the association tests (one for each SNP locus), the scores of the Fisher’s tests, the effect size of the environmental variable on each SNP, and the genomic inflation factor (GIF).

After running the analyses for several values of K, the user should carefully inspect the results to decide whether confounding factors have been correctly controlled and choose the optimum value of K. For each K, the user can visualize the following: (a) the GIF, the best value of K should have a GIF value around 1, lower values are too conservative and higher values are too liberal; (b) a histogram of the p-values, the best value of K should show a flat histogram, with a peak around zero; and (c) a QQ-plot, the best value of K should have a QQ-plot where most of the observed p-values correspond to the expected p-values under the null hypothesis of no association, except for those p-values showing strong associations.

After the user has decided on the best value of K, candidate loci are identified. For this, a False Discovery Rate (FDR) control method is applied to convert p-values into q-values. Then, candidate loci under selection are identified according to an FDR threshold. In this example, a q-value < 0.1 is used as threshold. The last step is to combine the results of the association tests with the genomic positions of SNPs in a data frame. For this, the user should provide a text file with three columns, and the number of rows should equal the number of SNP loci analyzed. The first column, called “chrom”, is the chromosome number where each SNP is located; the second column, called “bp”, is the position of each SNP within the chromosome in base pairs (bp); and the third column, called “snp”, is the SNP ID. Finally, a Manhattan plot that shows the association results is built. The environment and genomic data used in this module can be found at https://github.com/agrocompuepidemlab/GermVersity/releases/tag/v1.0.0.