Missing genotype imputation in non‐model species using self‐organizing maps

Abstract

Current methodologies of genome‐wide single‐nucleotide polymorphism (SNP) genotyping produce large amounts of missing data that may affect statistical inference and bias the outcome of experiments. Genotype imputation is routinely used in well‐studied species to buffer the impact in downstream analysis, and several algorithms are available to fill in missing genotypes. The lack of reference haplotype panels precludes the use of these methods in genomic studies on non‐model organisms. As an alternative, machine learning algorithms are employed to explore the genotype data and to estimate the missing genotypes. Here, we propose an imputation method based on self‐organizing maps (SOM), a widely used neural networks formed by spatially distributed neurons that cluster similar inputs into close neurons. The method explores genotype datasets to select SNP loci to build binary vectors from the genotypes, and initializes and trains neural networks for each query missing SNP genotype. The SOM‐derived clustering is then used to impute the best genotype. To automate the imputation process, we have implemented gtimputation, an open‐source application programmed in Python3 and with a user‐friendly GUI to facilitate the whole process. The method performance was validated by comparing its accuracy, precision and sensitivity on several benchmark genotype datasets with other available imputation algorithms. Our approach produced highly accurate and precise genotype imputations even for SNPs with alleles at low frequency and outperformed other algorithms, especially for datasets from mixed populations with unrelated individuals.

Short abstract

see also the Perspective by Katia Bougiouri

1. INTRODUCTION

Fractional genome sequencing strategies are routinely employed to simultaneously detect and genotype thousands of genome‐wide single‐nucleotide polymorphisms (SNP) in model and non‐model species. One of the most popular among these reduced genome representation methods is the restriction site‐associated DNA sequencing (RADseq), which is based on the digestion of genomic DNA with a restriction enzyme (Baird et al., 2008; Davey & Blaxter, 2010; Miller et al., 2007). This genotyping methodology, and modified versions of it, such as genotyping by sequencing (GBS) (Elshire et al., 2011), and double‐digested restriction site‐associated DNA sequencing (ddRADseq) (Peterson et al., 2012), are suitable for studies that require large number of markers, such as genome‐wide association analysis (GWAS), genetic map construction, quantitative trait loci (QTL) screening, genomic selection, phylogenetics, and analysis of population structure and genetic variation (Kumar et al., 2012).

One of the caveats of these methodologies of reduced representation genome approaches is that they produce large amounts of missing data that may impact statistical inference and introduce bias in the outcome of experiments (Andrews et al., 2016). Missing data may occur due to: (1) unequal depth coverage that impedes mapping to the genome of fragments with low depth; (2) mutation in one of the restriction sites that prevents fragment amplification; or (3) the complete depletion of the genomic region of interest, and can be derived either from technical errors or from the intrinsic nature of the set of samples considered in the experiment (Guillardín‐Calvo et al., 2019; Mastretta‐Yanes et al., 2015; O'Leary et al., 2018).

Consistent sets of SNPs minimizing the proportion of missing data are required in order to avoid incorrect biological conclusions (Pompanon et al., 2005). Producing robust SNP sets from next‐generation sequencing (NGS)‐based genotyping experiments is not a straightforward task and largely depends on the aim of the study, the genomic determinants of the focal species/populations and on the sequencing conditions, such as the sequencing depth coverage or technical errors produced in the laboratory (Pavan et al., 2020). High‐quality SNP sets can be achieved after the initial variant calling using two complementary procedures: (1) filtering of variants and/or individuals with high proportions of missing data (Carson et al., 2014; O'Rawe et al., 2013) or by (2) imputation methods (Browning, 2008). Filtering strategies usually consist on supervised procedures to exclude low‐quality variants that fall into the extremes of SNP quality control variables such as call rate, Hardy–Weinberg equilibrium, minor allele frequency (MAF) or missing proportion (MSP) (Pongpanich et al., 2010). SNP filtering is always advisable to a certain degree, as it does not only apply to remove missing data, but also to exclude incorrectly called variants. However, while there are some general rules to perform SNP filtering, its implementation may sometimes remove relevant information from the variant calling file (VCF). For instance, in low‐quality sequencing experiments, or when multiple species are considered, too few high‐quality SNP will be kept in the final set if the filtering procedure is too restrictive, cancelling out the power of reduced genome representation methods (Roshyara et al., 2014).

The other common strategy to improve the resolution of SNP sets is missing data imputation, an issue that has long been approached in the literature (Li et al., 2009; Das et al., 2016). Missing genotype imputation is commonly used in several applications of genomics and population genetics, such as GWAS (Browning, 2008), where researchers analyse the genetic variations across a large population to identify associations between genetic markers and particular traits. Additionally, population genetics studies, such as inferring population history or demographic events, often require imputation of missing genotype data to accurately reconstruct the genetic landscape and evolutionary dynamics of different populations (Fu, 2014). In general, missing data imputation is approached using model‐based methods, such as maximum likelihood using the expectation–maximization (EM) algorithm and multiple imputation techniques (Little & Rubin, 2002; Schafer, 1997). In the GBS context, imputation is the process of inferring untyped polymorphic markers (usually only SNPs) in a genotyped population. Imputation strategies are important when using GBS for genomic predictions and many imputation methods have been developed. Typically, genotype imputation methods are based on haplotype‐clustering algorithms using EM (Scheet & Stephens, 2006) and hidden Markov models (Marchini et al., 2007). Several applications including these types of algorithms are available, such as fastphase (Scheet & Stephens, 2006), BEAGLE (Browning & Browning, 2007), IMPUTE2 (Howie et al., 2009), mach (Li et al., 2010), HiFi (Li et al., 2015) or PHG (Long et al., 2022). These methods are very accurate for widely studied model species that count with reference haplotype panels or have so densely typed SNPs that allow robust inference of haplotype phasing, but may be less efficient when there are no reference haplotype panels or when the focal population presents strong underlying genetic structure (Marchini et al., 2006).

Machine learning algorithms can also be applied to imputation of missing data in many study fields (Stekhoven & Bühlmann, 2012; Troyanskaya et al., 2001), including NGS‐based genotyping (Monaco et al., 2021). In a supervised mode, these algorithms (e.g. random forest, Schwarz et al., 2009) require haplotype panels or phasing of genotypic data. As unsupervised methods, however, other machine learning algorithms, such as k‐nearest neighbours (KNN) (Money et al., 2015), impute missing genotypes without requiring external information to the dataset. These machine learning methods produce overall acceptable imputations when missing genotypes are distributed at random in the focal dataset. In some cases, these methods employ different encoding types for unordered markers and exploit internal ‘hidden’ structures of data, such as linkage disequilibrium (LD) correlations, read counts or identity by descent or kinship matrices to weight or optimize the imputation algorithms (Money et al., 2017).

In the present manuscript, we report the development of an unsupervised machine learning algorithm based on Kohonen's self‐organizing maps (SOM) (Kohonen, 2001). Kohonen's SOM are a kind of neural network that performs unsupervised data clustering and visualization that have been applied to explore partially observed data and to infer missing values in incomplete environmental samples (Folguera et al., 2015), hydro‐meteorological time series (Nkiaka et al., 2016) and soil properties (Rivas‐Tabares et al., 2020). SOM have been also applied to cluster genomic sequences (Delgado et al., 2015), to explore genome‐wide expressional patterns (Nikoghosyan et al., 2022) or to infer protein macro‐molecular conformations generated by molecular dynamics simulations (Mallet et al., 2021). In the context of missing genotype imputation, our method explores the underlying structure of SNP VCFs and produces accurate results without requiring haplotype panels. We show that SOM‐based imputation in non‐model organisms outperforms other popular machine learning methods, presenting comparable results to those of methods based on haplotype clustering, and even improving them in datasets that include mixed populations with unrelated individuals.

2. MATERIALS AND METHODS

We have implemented a method to apply SOM to missing genotype imputation in gtimputation, an open‐source user‐friendly software package programmed in Python3 (https://www.python.org/). Briefly, complete genotypes are clustered in a neural network and then queries with missing data are assigned to the best‐matching neuron. Imputation is then performed according to user‐defined criteria (Figure 1). The program runs in any computer with an OS supporting Python3: Linux/Unix, Windows or Mac OS X. gtimputation is publicly available along with its manual from either a GitHub (https://github.com/GGFHF/gtImputation/) or a zenodo software repository (Mora‐Márquez et al., 2023), and is distributed under GNU general public licence Version 3. The application provides a user‐friendly front end to facilitate the imputation process using standard VCF files or genotype tables containing missing data as input.

FIGURE 1.

Overview of the self‐organizing map (SOM)‐based imputation method implemented in gtimputation showing the training and query phases.

2.1. SOM algorithm rationale

Based on natural visual systems, SOM (Kohonen, 1982a, 1982b) are neural networks formed by spatially distributed neurons that map similar inputs into close neurons. SOM are commonly used for data clustering and representation of a high dimensional dataset into a lower‐dimensional space, while preserving the topological structure of the data. SOM perform an unsupervised clustering process that spatially organizes (typically in two dimensions) the patterns found in a dataset considering only their homology, without knowing the class to which they belong. The algorithm is able to conduct exploratory data analysis and visualization without the need for calibration or classification of the information to be processed.

SOM, like most artificial neural networks, operate in two phases: training and mapping. The training phase uses an input dataset (the ‘input space’) to generate a lower‐dimensional representation of the input data (the ‘map space’). As expected, SOM are able to discern among data with similar properties, which are consequently clustered in different regions of the extended network. For each input, the neuron of the SOM with the smallest distance (the Best Matching Unit [BMU]) is selected. Using a neighbourhood function centred on this BMU (σ) that shrinks gradually as the data are shown, the weights, the so‐called codebooks, of the neighbour neurons are updated. After convergence, the weights of the neurons reflect a particular feature of the input data. During the subsequent mapping phase, additional (new) input data are exposed to the neural network and assigned to their corresponding BMUs. In so doing, this algorithm generates a mapping between data and the SOM neurons. This property enables the imputation of the missing SNP genotypes by defining completion rules based on the BMU element properties.

2.2. SOM‐based genotype imputation

The SOM imputation performed by gtimputation consists of six stages (Figure 2): (1) whole dataset exploration and pre‐processing of the data; (2) selection of SNPs for each query missing SNP genotype to build the training sets; (3) SOM initialization; (4) training; (5) assignment to the BMU; and (6) imputation of the best genotype to each query missing SNP genotype.

FIGURE 2.

Overview of self‐organizing map (SOM) initialization, training and missing data imputation in gtimputation. G₁₇ is the individual with the query missing single‐nucleotide polymorphism (SNP) genotype (N). A rectangular 3 × 3 design is presented in this example. Five SNPs with the highest LD r _ij ² were selected to generate the vectors of the training set with the rest of SNP genotypes. The length of the translated numeric vectors is 5 SNPs × 10 possible genotypes and equals the length of the numeric vectors of each neuron. The initial weights of the neuron k,l ( W _kl ) are randomly assigned from the PCA of the full training set vectors with the function pca_weights_init() of the minisom package. The weights of the neuron in the position k,l ( W' _kl ) are updated after each iteration in the training process following an asymptotic decay function that shrinks the initially set lr and σ parameters, and a Gaussian neighbourhood function. The correspondence of each genotype of the input set to its Best Matching Unit (BMU) is calculated according to the minimum Euclidean distance ${\delta }_{\mathit{Gi}-\mathit{kl}}$ scored for each genotype using the weights of each neuron in the last iteration (W″ _kl ). The query vector for G₁₇ is assigned to a BMU and the most frequent genotype (MF), as in this example, or the genotype of the individual with the closest kinship among all the genotypes in the BMU is imputed to the query missing genotype.

2.2.1. Exploration and pre‐processing of the whole dataset

Pre‐processing of the whole dataset containing the samples and SNP information is a common stage that is run only once before starting the SOM and imputation procedures for each query missing genotype. A VCF or a genotype table are initially parsed (Box S1) and a genotype SQLite database is created (Box S2). The genotype SQLite database also includes estimators of the LD between each pair of SNPs (${r_{\mathit{ij}}}^2$) according to the version for unphased genotypes by Ragsdale and Gravel (2020) (Equation 1) that was derived from classical formulas by Hill (1974) and Lewontin (1988), and of the sample unbiased kinships over loci ($r_{\mathit{ij}}^u$) according to Goudet et al. (2018) (Equation 2):

$${r_{\mathit{ij}}}^2=\frac{{\widehat{D_{\mathit{ij}}}}^2}{p_1{q}_1{p}_2{q}_2},$$ (1)

where $\widehat{D_{\mathit{ij}}}$ is the unbiased estimator for the covariance of alleles of two SNP i and j co‐occurring on a haplotype, p ₁ and q ₁ are the frequencies of the reference alleles in the population for SNP i and j, respectively, and p ₂ and q ₂ are the frequencies of the alternative alleles in the population for SNPs i and j, respectively.

$$r_{\mathit{kk}\prime }^u=\frac{1}{L}\sum _{l=1}^L\frac{\left(X_{\mathit{kl}}-2{\tilde{p}}_l\right)\left(X_{k\prime l}-2{\tilde{p}}_l\right)}{2{\tilde{p}}_l\left(1-{\tilde{p}}_l\right)},$$ (2)

where $r_{\mathit{kk}\prime }^u$ is the unbiased kinship estimate between individuals k and k′, l = 1, …, L are the SNP loci in the genotype file, ${\tilde{p}}_l$ are the sample allele frequencies for the reference allele at locus l, and $X_{\mathit{kl}}$ and $X_{k\prime l}$ are the dosages of the reference allele, at locus l for individual k and k′, respectively. LD and kinship estimators will be further used to configure the training set for the SOM of each missing genotype and to perform the final imputation step.

2.2.2. SNP selection to configure the training sets

The user defines the number of SNPs with the highest LD to be considered by SOM for each missing genotype, among those exceeding a user‐defined threshold of LD squared correlation estimator (mr ²).

To adjust to the traditional SOM, which works with a continuous numerical input space and Euclidean distances, genotypic data need to be converted to numerical vectors (Figure 3). For the case of a bi‐allelic SNP, a vector of genotypes representing all the possible states in a VCF can be easily defined by using the IUPAC nucleotide codes (Delgado et al., 2015): {A (A/A), C (C/C), G (G/G), T (T/T), R (A/G), K (G/T), M (A/C), S (G/C), W (A/T), Y (C/T)}. This vector does not consider InDel or multi‐allelic loci. In order to work with nucleotide sequences, gtimputation converts these codes to numerical values using an array of 10 positions such that the first position corresponds to the character ‘A’, the second to the character ‘C’ and so on up to the tenth position, which corresponds to the character ‘Y’. Each coded genotype assigns a ‘1’ to the element of the array corresponding to its character and ‘0’ to the rest. In the case of missing data, all the elements of the array have a value of ‘0’.

FIGURE 3.

Schematic representation of single‐nucleotide polymorphism (SNP) selection for the query missing SNP genotype (N) and translation of the genotype sequences to binary vectors to train the self‐organizing map (SOM). In this example, five SNPs are selected for SOM training. Notice that SNPs do not necessarily have to be in adjacent positions, but are selected according to a minimum linkage disequilibrium (LD) threshold mr ² or by a maximum number of SNPs with the highest LD ${r_{\mathit{ij}}}^2$. Genotypes are labelled according to the IUPAC nucleotide codes.

2.2.3. SOM initialization

The SOM objects to impute missing genotypes are created using minisom 2.3.0 software (Vettigli, 2018) (Box S3). The initial attributes of the SOM can be defined by setting the following minisom input parameters: (1) x and y dimensions of the rectangular SOM; (2) spread of the neighbourhood function (σ), which needs to be adequate to the dimensions of the map; (3) initial learning rate (lr); (4) maximum number of iterations for the training (n). Each neuron k,l of the SOM will receive a vector of the same length of the translated numeric vector sequences with randomly distributed weights at each element of the vector (W _kl ). These weights are initially obtained from a PCA of the full training set vectors with the function pca_weights_init() of the minisom package.

2.2.4. SOM training

Once the initial SOM is created, the numeric vectors of each sample (G _i ) are iteratively assigned to specific neurons based on the Euclidean distance (${\delta }_{\mathit{Gi}-\mathit{kl}}$) between G _i and the weighted vectors of each neuron W _kl (Equation 3).

$${\delta }_{\mathit{Gi}-\mathit{kl}}=\sqrt{\sum _x{\left(G_{\mathit{ix}}-W_{\mathit{klx}}\right)}^2},$$ (3)

where x is the index of the vector components (x = 10 × the number of selected SNPs).

At each iteration, the neuron vector weights (W _kl ) within the BMU neighbourhood are re‐calculated according to equation (Equation 4):

$$W_{\mathit{kl}}\left(t+1\right)=W_{\mathit{kl}}\left(t\right)+h\left(t\right)\left(G_i-W_{\mathit{kl}}\left(t\right)\right).$$ (4)

The term h(t) is a Gaussian neighbourhood core function calculated as in (Equation 5):

$$h\left(t\right)=\mathit{lr}\left(t\right)e^{-\frac{{d_{\mathit{kl}}}^2}{2\sigma {\left(t\right)}^2}},$$ (5)

where lr(t) is the learning rate at time t, σ(t) is the spread of the neighbourhood function at time t, and d _kl is the Euclidean distance between the positions of the BMU and the k,l neurons. Considering lr and σ as the initial values, and T as half the maximum number of iterations (T = n/2), lr(t) and σ(t) decrease monotonously towards 0 following (Equation 6) and (Equation 7), respectively.

$$\mathit{lr}\left(t\right)=\frac{\mathit{lr}}{\left(\frac{t+1}{T}\right)},$$ (6)

$$\sigma \left(t\right)=\frac{\sigma }{\left(\frac{t+1}{T}\right)}.$$ (7)

2.2.5. Imputation of the missing genotype

The correspondence of each genotype to a neuron is calculated according to the minimum ${\delta }_{\mathit{Gi}-\mathit{kl}}$ scored for each genotype using the weights of each neuron in the last iteration (W″ _kl ) as in Equation 3. The query genotype sequence associated with the missing data is assigned to a BMU calculated in the same way. A SNP genotype is finally imputed to the missing data considering the samples mapped into the BMU. In gtimputation, this imputation step can be performed in either two ways (1) by imputing the most frequent (MF) SNP genotype of all the samples in the same neuron (MF) or (2) by imputing the SNP genotype of the sample with the closest kinship found in that neuron (CK).

2.3. Validation of SOM‐based genotyped imputation

In order to validate the SOM imputation algorithm and compare its performance with other available methods, we used a series of five real genotype benchmark datasets without missing data from Mus musculus (Shi & Peng, 2021) and Mediterranean Quercus (López de Heredia et al., 2020). The tested datasets differed in sample size, number of SNPs, relatedness between samples (estimated as the average matching for all pairs of distinct individuals for a sample of n individuals (M _s) following Goudet et al., 2018), mean expected heterozygosity (H _e), inbreeding coefficient (F) and global linkage disequilibrium (global LD) (Table 1). Dataset 1 consisted of mice SNPs from Chr1 in 1940 moderately related individuals (M _s ≈ 0.5) (mr‐Mice1940). Dataset 2 consisted of two SNP datasets (mr‐Mice98 and mr‐QS98) of 98 samples and c. 730 SNPs each picked up from Mice1940 and from a larger dataset of Q. suber (López de Heredia et al., 2020), respectively, using vcftools (Danecek et al., 2011). Dataset 3 was obtained from the same Quercus study and consisted of three SNP sets of adults from Q. suber (mr‐QS), Q. ilex (mr‐QI) and their hybrids Q. ilex × suber (mr‐HY). These datasets varied in the number of sampled individuals (adults), which were moderately related between them within each file (M _s ≈ 0.5), and also in the number of SNPs. Dataset 4 consisted of three genotype files that included SNPs for half‐siblings of Q. suber (hr‐QS07), Q. ilex (hr‐QI96) and their hybrids (hr‐HY20), therefore showing high relatedness between individuals at each genotype file (0.75 < M _s < 0.968). While QS and QI samples from Datasets 3 and 4 had similar H _e, F and global‐LD values, HY samples presented significantly higher H _e and smaller negative inbreeding coefficient, suggesting populations with higher proportions of heterozygotes. Dataset 5 consisted of 197 samples and 400 SNPs from two different species (Q. suber and Q. ilex) in the same data file (2SP‐QSQI). As a result of mixing SNPs and individuals from two species, this dataset presented high global LD and high positive inbreeding coefficient.

TABLE 1.

Description of the main characteristics of the original genotype files in the genomic datasets used to validate gtimputation performance.

Dataset	Genotype file	N ind	N SNPs	M s a	H e (SD) b	F (SD) c	Global LD (SD) d
Dataset 1	mr‐Mice1940	1940	729	0.500	0.377 (0.084)	0.025 (0.193)	0.010 (0.029)
Dataset 2	mr‐Mice98	98	729	0.554	0.358 (0.106)	−0.051 (0.236)	0.017 (0.034)
	mr‐QS98	98	723	0.520	0.292 (0.028)	−0.030 (0.053)	0.004 (0.012)
Dataset 3	mr‐QS	98	1717	0.520	0.296 (0.025)	−0.038 (0.045)	0.004 (0.012)
	mr‐QI	99	2078	0.500	0.251 (0.076)	−0.101 (0.095)	0.011 (0.025)
	mr‐HY	22	4804	0.516	0.570 (0.048)	−0.426 (0.090)	0.005 (0.011)
Dataset 4	hr‐QS07	94	1453	0.968	0.326 (0.021)	−0.119 (0.036)	0.003 (0.010)
	hr‐QI96	93	2090	0.751	0.268 (0.032)	−0.167 (0.037)	0.005 (0.019)
	hr‐HY20	30	4424	0.903	0.453 (0.105)	−0.250 (0.135)	0.008 (0.018)
Dataset 5	2SP‐QSQI	197	400	0.503	0.217 (0.068)	0.431 (0.093)	0.251 (0.281)

^a M _s is the average matching for all pairs of distinct individuals for a sample of n individuals (Goudet et al., 2018).

^b H _e mean expected heterozygosity across loci.

^c F is the inbreeding coefficient.

^d Global LD is the mean of the LD r ² scored for all the SNP comparisons as in Equation 1 (Ragsdale & Gravel, 2020). Standard deviation for H _e, F and Global LD among brackets.

In all cases, missing data were generated directly on the genotype file, simulating non‐systematic laboratory errors from reduced genome representation sequencing methods using NGShelper (Mora‐Márquez et al., 2021). Rather than producing missing values at random, we produced files with varying values of probability of a locus having missing data (mdp = 0.1, 0.2 and 0.3) and of maximum percentage of individuals with missing data at each locus (mpiwmd = 10, 20 and 30%), to obtain more realistic missing error distributions. The genotype files with missing data were prompted to seven methods representing different statistical approaches to the imputation problem in non‐model species without reference haplotype panels: (1) the SOM‐based imputation algorithms (gtimputation); (2) a naïve imputation of the MF value in the dataset (naive); (3) an imputation based on inverse non‐linear principal component analysis (Scholz et al., 2005) as implemented in the pcamethods Bioconductor package (Stacklies et al., 2007) (nlpca); (4) an imputation based on the random forest algorithm implemented in the R package missforest (Stekhoven & Bühlmann, 2012); (5) the LD KNN imputation method (Money et al., 2015) implemented in the software tassel (Bradbury et al., 2007) (tassel‐ld‐knn); (6) a haplotype phasing, clustering and imputation method estimating clustering parameters with the EM algorithm using the version of fastphase (Scheet & Stephens, 2006) that does not consider haplotype reference panels; and (7) a reference panel free haplotype phasing and imputation algorithm based on Monte Carlo Markov Chains (MCMC) implemented in mach (Li et al., 2010).

In each dataset, we systematically tested the impact of several parameter combinations relevant to each imputation method, aiming to allow a robust comparison of the algorithm performance (Table 2). All the gtimputation runs consisted of 1000 iterations and an initial learning rate of lr = 0.5, while we modified the x and y dimensions of the rectangular SOM space, the spread of the neighbourhood function (σ), the minimum squared correlation (mr ²) and the maximum number of SNP per vector (snp). Thus, we could generalize default values for these parameters that could be applied with optimal results in a wide range of situations. We performed several runs of the LD K‐NN method in tassel using the Euclidean distance and modifying the number of nearest neighbours (nn) and the number of sites in high LD to be used in imputation (hld) (Table 2). The maximum distance between sites to find LD was set to the default value (10,000,000). fastphase was run using default parameters: 20 random starts of the EM algorithm (‐T), 25 iterations of the EM algorithm (‐C) and 50 haplotypes sampled for the posterior distribution (‐H). Five principal components and 300 iteration steps were used to run nlpca. missforest was run with a maximum number of 10 iterations and growing 100 trees in each forest.

TABLE 2.

Parameter combinations for the algorithms tested in the study.

Parameters	gtImputation	Tassel‐LD‐KNN	MissForest	nlPCA	FastPhase	MaCH
phasing	No	No	No	No	Yes	Yes
gim	(MF, CK)	–	–	–	EM	MF
iterations	162	12	10	300	25	50
dim	(3 × 3, 4 × 4, 5 × 5)	–	–	–	–
σ	(0.5, 1, 2)	–	–	–	–
mr2/hld	(0.001, 0.1, 0.2)	(15, 20, 30, 40)	–	–	–
snps/nn	(5, 10, 15)	(5, 10, 15)	–	–	–
‐T	–	–	–	–	20
‐C	–	–	–	–	25
‐H	–	–	–	–	50
PCs	–	–	–	5	–
trees	–	–	100	–	–
states						200

Note: Phasing: haplotype phasing required to run imputation. gim: genotype imputation in gtimputation as the most frequent SNP genotype of all the samples in the same neuron (MF), or as the SNP genotype of the sample with the closest kinship found in that neuron (CK). Expectation–maximization (EM) algorithm in fastphase. The most frequent genotype in the phased haplotype panel in mach (MF). iterations: number of times run for each algorithm. dim: x and y dimensions of the rectangular SOM (gtimputation). σ: initial spread of the neighbourhood function. mr2/hld: minimum LD squared correlation estimator (r ²) threshold between SNPs/number of sites in high LD to use in imputation. snps/nn: maximum number of SNPs for each vector in gtimputation/number of nearest neighbours in tassel‐ld‐knn. ‐T: number of random starts of the EM algorithm in fastphase. ‐H: number of haplotypes sampled for the posterior distribution in fastphase. PCs: Number of principal components in nlpca. trees: Number of growing trees in the random forest (missforest). states: number of haplotypes to be considered when updating each individual (mach).

The comparison of the original genotype files without missing data and the imputed files for each method and parameter combination allowed the construction of multiclass confusion matrices including the scoring of the true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) for each element of the SOM vector. Using this information, we were able to assess the relative efficiency of the different imputation methods by computing the multiclass metrics depicted by Sokolova and Lapalme (2009). The average accuracy (Equation 8) is an estimator of the average per‐class efficiency.

$$\text{Average accuracy}=\frac{\sum _{i=1}^l\frac{{\mathrm{TP}}_i+{\mathrm{TN}}_i}{{\mathrm{TP}}_i+{\mathrm{FN}}_i+{\mathrm{FP}}_i+{\mathrm{TN}}_i}}{l}$$ (8)

The macro average precision (Equation 9) reflects the agreement of the real with the imputed genotypes for each class of the data, the macro average recall (Equation 10) measures the model's ability to predict the correct imputation, and the macro F1‐score (Equation 11) is the harmonic mean of precision and recall, and offers a more balanced summary of the imputation performance. Since we are working with unbalanced datasets, where all classes are equally important and the macro average treats all classes equally, macro estimators for these parameters may be the most suitable metrics to assess the performance of the imputation methods (De Diego et al., 2022).

$${\text{Precision}}_M=\frac{\sum _{i=1}^l\frac{{\mathrm{TP}}_i}{{\mathrm{TP}}_i+{\mathrm{FP}}_i}}{l}$$ (9)

$${\text{Recall}}_M=\frac{\sum _{i=1}^l\frac{{\mathrm{TP}}_i}{{\mathrm{TP}}_i+{\mathrm{FN}}_i}}{l}$$ (10)

$$F1-{\text{score}}_{\mathrm{M}}=\frac{\left({\mathrm{\beta }}^2+1\right){\text{Precision}}_{\mathrm{M}}{\text{Recall}}_{\mathrm{M}}}{{\mathrm{\beta }}^2{\text{Precision}}_{\mathrm{M}}+{\text{Recall}}_{\mathrm{M}}}$$ (11)

To compare the performance between methods, we considered the best imputation runs corresponding to the different missing data levels obtained for each algorithm and dataset in terms of maximum accuracy, precision and recall. Furthermore, we explored the most accurate parameter combination of gtimputation for each dataset in order to suggest default parameters for the different characteristics of the populations to populations to be imputed (degree of relatedness, heterozygosity and inbreeding coefficient and global LD). In addition to global imputation statistics, we also calculated the percentage of correctly imputed genotypes in a selection of 195 SNPs with MAF <0.02 from mr‐QS, mr‐QI, hr‐QS and hr‐QI genotype files.

2.4. Runtimes of SOM‐based genotyped imputation

The computation runtimes of all methods were calculated on a VMware virtual machine with Ubuntu 22.04, 8 GB of RAM and 300 GB of disc size on a host computer with a processor Intel(R) Core™ i9‐11950H of 2.60 GHz. For SOM‐based genotyped imputation, we estimated separately the runtimes of the database building step and of the building and imputation runs for each genotype file in the datasets with the maximum level of missing data (mdp = 0.3 and mpiwmd = 30).

3. RESULTS

After 16,380 imputation runs (1638 per genotype file), gtimputation has achieved overall good imputation results for all the datasets evaluated and for all the tested missing data conditions (Table S1). Considering only the best imputations for all datasets and missing data conditions, we observed differences between algorithms in terms of accuracy (>0.97), precision (median_all >0.8), recall (median_all >0.8) and F1‐score (median_all >0.8) (Figure 4; Table S2).

FIGURE 4.

Boxplot comparison of the best average accuracy (a), macro‐precision (b), macro‐recall (c) and macro‐F1‐score (d) computed as in (Equations (8), (9), (10), (11)) values obtained across all datasets for the algorithms used for genotype imputation. The differences between gtimputation and tassel‐ld‐knn accuracy, precision and F1‐score were slight but significant, according to a one‐way ANOVA for those metrics. The differences between gtimputation‐fastphase, missforest‐tassel‐ld‐knn and fastphase‐mach were non‐significant for any of the parameters considered. n.s. non‐significant; * 0.1; ** 0.05; *** 0.001.

For all the metrics, gtimputation outperformed naive, nlpca, missforest and tassel‐ld‐knn; it produced similar values to those of fastphase and mach, but with less variance in accuracy, pointing to less dependence on the dataset structure for gtimputation (Figure 4). The differences between gtimputation and tassel‐ld‐knn were slight but significant in terms of accuracy, precision and F1‐score, according to a one‐way ANOVA for those metrics that were non‐significant for the comparison gtimputation versus fastphase.

A more detailed analysis of the algorithm performance by dataset provided additional evidence of the good performance of gtimputation for the different missing data conditions. For Dataset 1, consisting in SNPs from a single chromosome in 1940 individuals, accuracy and F1‐score of gtimputation, tassel‐LD‐KNN, missforest, fastphase and mach were above 0.99, much better in all cases than for nlpca and naive imputations (Figure 5a,b). Regarding Dataset 2, the best algorithms for mr‐Mice98 were fastphase and mach, closely followed by gtimputation, tassel‐ld‐knn and missforest for all the missing data conditions. All the algorithms imputed less accurately than for mr‐Mice1940 (Figure 5c,d). For the other genotype file from Dataset2, mr‐QS98, both accuracy and F1‐score were dependent on the missing data conditions at the same time they offered worse accuracy and F1‐score than mr‐Mice98 (Figure 5e,f). In this case, fastphase and gtimputation were the best imputation algorithms, closely followed by mach, tassel‐ld‐knn and missforest, and much better than nlpca and naive imputations.

FIGURE 5.

Comparison of the best average accuracy and macro‐F1‐score computed as in (Equations 8 and 9) for Dataset 1 and Dataset 2 with all the algorithms under several missing data conditions. naive: crosses, orange; nlpca: blades, ochre; missforest: asterisks, green; tassel‐ld‐knn: squares, turquoise; gtimputation: circles, blue; fastphase: solid up‐pointing triangles, purple; mach: empty down‐pointing triangles, pink. (a, b) mr‐Mice1940; (c, d) mr‐Mice98; (e, f) mr‐QS98.

The ranking of algorithm performance obtained for Datasets 1 and 2 was confirmed for Dataset 3 (Figure 6). The good performance of fastphase, mach and gtimputation was overall very consistent for any missing data level. However, the magnitude of the difference in the accuracy and especially in the F1‐score between algorithms diverged depending on the genotype file we considered in the dataset, being less for mr‐QS (Figure 6a,b) and mr‐QI (Figure 6c,d) than for mr‐HY (Figure 6e,f). In this latter genotype file, fastphase and mach were significantly better than the rest of algorithms. Moreover, mr‐QS presented slightly better results with all algorithms for accuracy and F1‐score than the subset mr‐QS98, which had the same number of individuals but only 50% of SNPs.

FIGURE 6.

Comparison of the best average accuracy and macro‐F1‐score computed as in (Equations 8 and 9) for Dataset 3 with all the algorithms under several missing data conditions. naive: crosses, orange; nlpca: blades, ochre; missforest: asterisks, green; tassel‐ld‐knn: squares, turquoise; gtimputation: circles, blue; fastphase: solid up‐pointing triangles, purple; mach: empty down‐pointing triangles, pink. (a, b) mr‐QS; (c, d) mr‐QI; (e, f) mr‐HY.

Overall, better performance was achieved for Dataset 4 (highly related individuals) than for Dataset 3 (less related individuals) with all the imputation methods. While the ranking of imputation algorithms was the same as for Dataset 3, with fastphase, gtimputation and mach as the top imputation methods, the difference in accuracy was smaller for Dataset 4 than for Dataset 3, with gtimputation even outperforming fastphase and mach for several missing data conditions (Figure 7). Again, the underlying structure of the population seems to have an effect in the magnitude of the metrics, so there were differences between accuracy and F1‐score of hr‐QS07 (Figure 7a,b), hr‐QI96 (Figure 7c,d) and hr‐HY20 (Figure 7e,f), yielding the best imputation for the latter.

FIGURE 7.

Comparison of the best average accuracy and maro‐F1‐score computed as in (Equations 8 and 9) for Dataset 4 and Dataset5 with all the algorithms under several missing data conditions. naive: crosses, orange; nlpca: blades, ochre; missforest: asterisks, green; tassel‐ld‐knn: squares, turquoise; gtimputation: circles, blue; fastphase: solid up‐pointing triangles, purple; mach: empty down‐pointing triangles, pink. (a, b) hr‐QS07; (c, d) hr‐QI96; (e, f) hr‐HY20; (g, h) 2SP‐QSQI.

For Dataset 5, which mixed samples from two different species, gtimputation, mach and missforest were the best imputation algorithms and clearly outperformed fastphase, which was worse than tassel‐ld‐knn and even nlpca. (Figure 7g,h).

Consistently with the global imputation results, the most efficient algorithms imputing SNPs with low MAF (<0.02) were fastphase, gtimputation and mach (Table 3). Particularly, gtimputation performed much better than the other algorithms in this respect in the genotype file showing the highest global LD (i.e. mr‐QI).

TABLE 3.

Percentage of correctly imputed SNPs by all algorithms considering only those SNPs with MAF <0.02 from four genotype files.

Algorithm	Mr‐QS (%)	Mr‐QI (%)	Hr‐QI (%)	Hr‐QS (%)	All (%)
01‐naive	36.8	51.2	27.1	33.3	40.0
02‐nlpca	36.8	61.6	35.6	33.3	47.2
03‐missforest	36.8	55.8	27.1	33.3	42.1
04‐tassel‐ld‐knn	36.8	51.2	32.2	33.3	41.5
05‐gtimputation	47.4	81.4	37.3	58.3	60.0
06‐fastphase	63.2	72.1	52.5	66.7	64.1
07‐mach	52.6	67.4	47.5	58.3	57.9

A closer exploration of the impact of the SNP selection and SOM initial parameters in the outcome of the imputation procedure did not show an apparent correlation between them. Actually, for each dataset, and even each genotype file from the same dataset, the best imputation metrics were achieved using different parameter combinations (Figure 8).

FIGURE 8.

Percentage of self‐organizing map (SOM) parameters that produced the best results in accuracy for each genotype file in the Datasets. (a) SOM rectangular size; (b) spread of the neighbourhood function (σ); (c) minimum linkage disequilibrium (LD) squared correlation estimator (mr ²); (d) maximum number of single‐nucleotide polymorphisms (SNPs) to build each SOM vector; (e) imputation criterion: CK closest kinship, MF most frequent.

Regarding the parameters involved in the SNP selection step, genotype imputation for populations with highly related individuals (Dataset 4) and with SNPs from the same chromosome (mr‐Mice1940 and mr‐Mice98) was better when using a minimum LD squared correlation estimator between SNPs of mr ² = 0.001 (Figure 8a). Conversely, for moderately related individuals, the best genotype imputation was achieved using mr ² = 0.1 (Dataset 3, mr‐QS98), and for the two‐species case (Figure 8a). When considering the maximum number of SNPs to construct the SOM vectors, the best imputation was achieved for snps = 5, except for mr‐QI (Dataset 3) and 2SP‐QSQI (Dataset 5), where the best imputations were obtained either using snps = 5, 10 or 15, and for hr‐HY20 (Dataset4), for which better results were obtained using vectors with higher snps values (Figure 8b).

In the same way, specific SOM initial parameters for each dataset need to be defined in order to obtain the best imputation results. While small SOM rectangular size of 3 × 3 cells produced good imputations for populations with moderately related individuals from Dataset 2 (mr‐QS98), for Dataset 3 and for the hybrid population from Dataset 4 (hr‐HY20), larger SOM are required to get the best imputations for Dataset 1 and the other populations from Dataset 4 (hr‐QS07 and hr‐QI96) (Figure 8c). For most populations, σ = 1 produces the best imputation, although in some cases, such as Dataset 1, mr‐HY (Dataset3) and Dataset 5 σ = 0.5 does also produce the best genotype imputations (Figure 8d).

For Dataset 1 and the subset mr‐Mice98 (Dataset 2), which included SNPs from a single chromosome, the most accurate imputations were obtained by imputing the genotype of the CK rather than the MF genotype. For the other datasets, the best imputations were achieved either using CK or MF (Figure 8e).

Finally, our approach proved to be very efficient in terms of computation times (Table 4), especially if compared with the other best algorithms fastphase and mach. The most limiting step in the process was the genotype database building, which was very quick for genotype files with a low number of individuals, but that took several minutes for Dataset 1 that included 1940 samples. Once the genotype database was constructed, it took a few seconds to run the SOM building and imputation steps in all cases.

TABLE 4.

Runtimes (s) of the tested imputation algorithms for all the genotype files in the datasets with the maximum level of missing data (mdp = 0.3, mpiwmd = 30%).

Dataset	Genotype file	gtImputation	Naive	nlPCA	MissForest	tassel‐ld‐knn a	FastPhase	MaCH
Dataset 1	mr‐Mice1940	1305.8 + 30.4	1.0	673.8	13.0	<10.0	5361.0	5799.1
Dataset 2	mr‐Mice98	10.9 + 6.9	<1.0	36.8	27.7	<5.0	302.6	272.2
	mr‐QS98	10.7 + 4.4	<1.0	39.9	19.5	<5.0	184.5	273.4
Dataset 3	mr‐QS	59.7 + 13.3	1.0	82.2	116.4	<5.0	550.2	641.8
	mr‐QI	84.8 + 17.2	1.0	108.0	111.6	<5.0	733.0	795.0
	mr‐HY	185.8 + 32.7	1.0	57.7	79.8	<5.0	400.1	20.4
Dataset 4	hr‐QS07	39.7 + 10.0	1.0	67.8	78.6	<5.0	444.0	488.5
	hr‐QI96	82.5 + 14.8	<1.0	99.0	168.6	<5.0	658.7	708.1
	hr‐HY20	211.1 + 42.7	1.0	70.8	138.0	<5.0	497.2	48.9
Dataset 5	2SP‐QSQI	11.1 + 4.9	<1.0	42.8	39.94	<5.0	211.3	328.3

Note: All runtimes were calculated on a VMware virtual machine with Ubuntu 22.04, 8 GB of RAM and 300 GB of disc size on a host computer with an Intel(R) Core™ i9‐11950H processor of 2.60 GHz. gtimputation runtimes include separate estimation of the database building step and the SOM building and imputation steps. For the other algorithms, runtimes do not include estimations for input file preparation and output reconstruction, which for most algorithms required additional time‐consuming bioinformatics operations.

^a tassel‐ld‐knn imputation is run through a GUI and it does not produce a time‐log and runtimes were estimated.

4. DISCUSSION

4.1. gtimputation efficiency and comparison to other methods

The SOM‐based genotype imputation procedure we have designed and implemented in gtimputation has proven to allow very efficient, quick and robust missing data imputation in a wide variety of case studies resulting from fractional genome sequencing methodologies in non‐model species, such as GWAS or when inferring population history or demographic events genetics. When compared to other similar imputation methods that do not rely on the previous existence of haplotype panels, gtimputation is accurate and precise, and provides overall good results irrespective of the dataset and missing data conditions. Moreover, gtimputation is particularly efficient imputing SNPs with low MAF, equalling or even outperforming phasing‐based algorithms in genotype files with high global LD. While fastphase and mach produced significantly better results than gtimputation for the datasets with a smaller number of individuals, fastphase showed the second worst results in the genotype file that combined samples from two species. Indeed, it has been reported that fastphase is a very reliable imputation technique for datasets that allow robust haplotype inference, which is the case on a per‐marker basis with denser SNP files, irrespective of the number of samples (Browning & Browning, 2011), or in the case of strongly related samples (Marchini et al., 2006). However, our results suggest that this approach is not advisable when there is a strong underlying genetic structure in the studied population (e.g. when there are two or more divergent genetic pools). For such cases, typical in many population genetics or phylogeographic analysis, unsupervised machine learning algorithms produced much better results than fastphase, with gtimputation showing comparable results to the MCMC phasing‐based method mach. Apparently, phasing is more robust in mach than in fastphase in these situations.

As was expected, gtimputation is much more precise and accurate than naively imputing missing data as the MF genotype for each SNP in the population. gtimputation does also outperform other unsupervised machine learning methods, such as tassel‐ld‐knn or the random forest imputation implemented in missforest, and especially the non‐linear PCA‐based imputation method, for the majority of datasets and missing data conditions. The strength of the significant improvement obtained by gtimputation over other similar methods stems on an efficient initial exploration of the underlying structure of the whole genotype dataset. Indeed, running a modified version of gtimputation that built SOM vectors by selecting those SNPs with the lowest LD (instead of the highest) produced similar outcome than for naive imputation (data not shown). Therefore, building databases for inter‐individual kinship and pairwise LD estimation is crucial to correctly configure the SNP vectors that will sustain the neuron weights at the SOM initialization step and a precise and accurate imputation of each missing genotype query in the dataset. A correct treatment of LD between SNPs is particularly relevant for SNPs with low MAF, which is probably the most challenging imputation case (Aleknonytė‐Resch et al., 2021). In these cases, both gtimputation and phasing‐based algorithms have shown to perform much better than the other methods.

Our method is not very different in this respect to other methods that have previously explored the relationships between samples and SNPs in the datasets. Actually, tassel‐ld‐knn, also designed for unordered SNPs, performs a similar initial exploration of the dataset using only the l SNPs most correlated with the SNP to be imputed to determine the nearest neighbour and the weightings to be used when imputing (Money et al., 2015). However, while this fast method is based on similar premises to gtimputation, it has shown to be globally less accurate, particularly for SNPs with low MAF. Along with LD between SNPs and kinship between individuals, further versions of tassel‐ld‐knn have also considered other features inherent to the SNP calling procedure on NGS data, such as read count information (i.e. the DP field in the VCF files) to improve imputation (Money et al., 2017). In the present study, we assumed that the input genotype files were filtered by individual read depth to keep only robust SNPs before imputing missing data, so as to enable a proper comparison of methods.

Other more sophisticated and far more complex deep learning methods, such as deep learning autoencoders (Islam et al., 2021) and recurrent or convolutional neural networks (Chen & Shi, 2019; Shi & Peng, 2021), are starting to be tested in non‐model organisms. In any case, improvement in the accuracy, precision and recall of all these methodologies would require testing with a robust and complete benchmark dataset collection.

4.2. Considerations regarding input data

There are some inherent properties of the specific case study related to the population structure that, along with other potential sources of missing data produced in the laboratory (Mastretta‐Yanes et al., 2015), will cause a non‐random distribution of missing data that should be considered to achieve optimal imputations (Wang & Qiang, 2021). Among others, missing genotype imputation should consider the population structure of the genotyped individuals, the extent of recombination in the dataset, the distribution of the allele frequencies or the heterozygosity level presented by the focal population (Alipour et al., 2019; Long et al., 2022). To test the performance of gtimputation, we utilized datasets with varying population structure in terms of sample size, number of SNPs, relatedness between samples, mean expected heterozygosity (H _e), inbreeding coefficient (F) and global LD to further mimic the way the most frequent types of missing data are produced in the laboratory. Doing so, we were able to obtain more reliable results than other comparative studies that employed datasets with missing data simply distributed at random (Shi & Peng, 2021). Actually, we observed significant differences in imputation accuracy between datasets differing not only in the level of LD shown by the SNPs, but also in the heterozygosity and inbreeding levels. With some exceptions, the percentage and distribution of missing data in the datasets affected the accuracy imputation in a very similar way for all algorithms.

From our results, we can extract several conclusions that may apply not only to gtimputation but also to other imputation methods. SOM vector construction and fastphase/mach haplotype phasing will be better for datasets that contain strongly linked SNPs, such as those belonging to the same chromosome, scaffold or contig, thus producing very good imputations. The sensitivity of imputation algorithms to highly heterozygous populations has been previously reported (Swarts et al., 2014). In our case, the imputation provided by unsupervised machine learning algorithms for datasets with high mean expected heterozygosity is significantly worse than fastphase and mach imputation. Conversely, for mixed datasets with low heterozygosity and high positive inbreeding coefficient, unsupervised machine algorithms have produced more accurate imputation than fastphase, with gtimputation getting comparable results to mach. While the decrease in imputation accuracy of haplotype phasing‐based methods was already reported by Marchini et al. (2006), the good performance of unsupervised machine learning algorithms in the two‐species dataset could be partially due to the effect of the high positive inbreeding coefficient or by the high global‐LD parameter scored for this dataset.

Another expected trend, observed in the results, is that gtimputation accuracy decreases with the number of samples and the number of SNPs in the genotype file. Currently, gtimputation can process any VCF or genotype table with bi‐allelic SNPs irrespective of the laboratory procedure or software employed to produce the files. GBS experiments produce thousands of SNPs, which are usually filtered according to different criteria defined by the researcher (missing data thresholds, MAF, depth coverage, H‐W equilibrium, etc.), producing much smaller datasets that may range from hundreds to several thousand SNPs. Considering that gtimputation is very accurate for the tested missing data conditions, it can be employed with high confidence to relax the missing data filtration threshold, thus recovering around 30% more SNPs from the sequencing experiment. Moreover, the good performance of the method imputing SNPs with low MAF could also be used to be less restrictive in MAF filtering. For large datasets with many samples and several thousand SNPs, it must be stressed out that SOM computation times will scale to hours, particularly at the genotype database building stage, but still remaining in reasonable times.

4.3. Parameter tuning

It has been suggested for several data types that, providing the adequate parameters, SOM may produce better classification than other methods, such as K‐means (Bação et al., 2005) and KNN (Suchenwirth et al., 2014). gtimputation parameters should be selected according to the inherent properties of the focal dataset to get optimal results, because SOM is highly sensitive to the choice of initial values (Cottrell et al., 2001). Actually, there is no general proof of the convergence of the classic unsupervised SOM algorithm, which is not straightforward (Fort & Pagès, 1995). However, some recommendations for parameter tuning arise from our study.

Building vectors of highly related SNPs to produce optimal SOM seems to largely improve the outcome of the imputation. For datasets with individuals without strong familiar structures, we suggest using a 0.1 mr ² threshold in order to include less SNP genotypes in the SOM vectors. For datasets of high mean kinship values or when the SNPs are located in the same chromosome, we suggest using a more relaxed mr ² threshold of 0.001, to take advantage of more SNP genotypes. In most cases, the best results can be obtained using vectors of 5 SNPs, except for the case of highly heterozygous small populations, where vectors of 10 SNP genotypes produce better imputations. Regarding the size of the map and considering all the possible genotypes for a specific SNP, rectangular maps of 3 × 3 and 4 × 4 are recommended for datasets with moderate and high relatedness between individuals, respectively. Larger maps are expected to produce worse results because higher variability in the quantization error is observed for big maps (De Bodt et al., 2002). On the contrary, the selection of the initial σ parameter is not straightforward, since the best results were obtained with values of 0.5 and 1. While this parameter needs to be adequate to the dimensions of the map, we observed no clear relationship between the selected sizes and the tested σ values, at the same time convergence was achieved for any value we tested. Therefore, in order to provide unique default values, and after an examination of the complete set of simulations (Table S1), we recommend to run gtimputation with the default values of 3 × 3 SOM size, σ = 1, mr ² = 0.001 and snps = 5 in order to produce precise and accurate imputations for most datasets.

5. CONCLUSIONS

gtimputation has revealed as a fast and powerful methodology, applicable to imputation of missing data in genotype files. The advantage of using this method relies on its simplicity and on the easy comprehension of the data it provides. In addition, SOM are very suitable for the missing genotype problem because they can handle a variety of categorization issues while simultaneously producing a practical summary of the data that enables further imputation. In the present manuscript, we have demonstrated that SOM‐based imputation implemented in gtimputation is comparable to haplotype clustering‐based algorithms for datasets with diverse population structures and distribution of the errors, even outperforming some of them when there is strong underlying population structure. gtimputation is also more accurate and precise than other similar unsupervised machine learning algorithms in most situations. Moreover, this open‐source Python3 application has a GUI that makes the handling and visualization of the missing data imputed easy. However, there is still room for improvement the capabilities of SOM‐based imputation. Further optimization of the SOM imputation method by coupling with pre‐filtering methods, optimization of the variant calling procedure or by considering alternatives to the Euclidean Distance or additional exploration of the non‐random distribution of missing data could improve the SOM imputation efficiency.

AUTHOR CONTRIBUTIONS

ULH, AS, JCN and FMM conceived the ideas. FMM programmed the scripts and ran the simulations. ULH, AS, JCN and FMM analysed and interpreted the results. FMM and ULH wrote the paper. All authors commented on and approved the final version of the manuscript.

CONFLICT OF INTEREST STATEMENT

The authors declare that they have no conflict of interest.

Supporting information

Table S1

Table S2

Box S1

Box S2

Box S3

Mora‐Márquez, F. , Nuño, J. C. , Soto, Á. , & López de Heredia, U. (2025). Missing genotype imputation in non‐model species using self‐organizing maps. Molecular Ecology Resources, 25, e13992. 10.1111/1755-0998.13992

DATA AVAILABILITY STATEMENT

gtimputation along with its manual and the data that support the findings are available from the software repositories GitHub (https://github.com/GGFHF/gtImputation/) and zenodo (Mora‐Márquez et al., 2023). Additional supporting information may be found online in the Supporting Information section.