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At the present, with the fast development of genotyping, we have access to genomic data that we can use with different statistical and computational approaches, for example, to accelerate genetic gains and to select outstanding genotypes as parents for commercial release. Genomic data is also useful to assess genetic variability and diversity in the context of breeding programs or other research studies.

Most of the genomic data used for breeding comes from single nucleotide polymorphism (SNP). Typically, we see this data as a matrix containing several individuals, often thousands, genotyped for a number of SNPs (i.e., nucleotide readings AA, AC, TT, etc.). Depending on the quality and characteristics of this data, we can use it for different analytical purposes. 

In this blog, we will describe some of the uses of this SNP data. We will focus mainly on the available number of SNPs (i.e., markers) and what analyses these enable. Note, the classification of low-, medium- and high-density panels is somewhat arbitrary but it’s what’s often used in plant breeding.

Low-density (LD) panels

Let’s start with what is known as low-density (LD) panels. These typically contain fewer than 200 SNPs, and are the cheapest option you can have (often just a couple of US dollars per sample). With this small number of SNP markers, their main use is for quality assurance (QA) and quality control (QC). That is, they can be used for:

• Verification of Crosses. If parents are genotyped, then it is possible to check that the correct crosses were performed.
• Parentage Reconstruction. If parents are genotyped, it is possible to reconstruct the full pedigree of a group of offspring. 
• Marker Assisted Selection. If a preliminary group of markers were identified to be associated with one or more QTLs of interest, these can easily be incorporated into the panel and used to discriminate genotypes.
• Population Assignment. A group of markers can be used to assign individuals to different populations (e.g., origins).
• Assign Sex. Depending on the dynamics of the organism, sometimes it is possible to identify one or more markers that can be used to assign sex to the individuals before they mature.

Other uses are possible but they can be limited. For example, we could identify sibships on some individuals (e.g., full-sibs), and it may be possible to calculate some population statistics of genetic diversity. However, these uses can yield high levels of uncertainty.

An important aspect of LD panels it that they often have markers for verification, and in addition some markers will be missing due to genotyping issues. Hence, their effective size will be lower than their nominal size. Another important consideration is that often these commercial panels are constructed for general use; hence, they may not exactly be based on the population of interest. This will lead to some fixated (MAF = 0%) or almost fixated (MAF < 2%) markers that have little or no contribution to the above uses. 

However, despite the above shortcomings, LD panels constitute a very good and cheap alternative for some small programs to start considering genomic tools in their breeding; and for example, verifying crosses is a critical step!

Medium-density (MD) panels

The medium-density (MD) panels are defined very differently depending on the field. Here, we will consider the plant breeding definition of between 2,000 to 10,000 SNPs (i.e., 2K to 10K). In animal breeding, MD panels will be at least 5 times larger. This larger number of SNPs offers more opportunities, but the cost of an MD panel is several times greater than an LD panel. This increased cost often limits, for most breeding programs, the number of individuals to be genotyped. However, they offer more genomic analysis opportunities. In addition to the uses for LD panels mentioned above, for MD panels we also have:

• Genomic Relationship Matrix Estimation. It is now possible to estimate with reasonable accuracy the relatedness between any pair of individuals. And these matrices can be used for many other objectives.
• Genomic Prediction Models. MD panels allows us to fit genomic prediction (GP) models. However, these tend to be on the low level of accuracy, but still sufficient and useful for operational use.
• Marker Imputation. Missing marker data, if complemented with individuals genotyped using a high-density (HD) panel, can be imputed successfully, and that data can be used for other purposes, like genomic prediction.  
• Genetic Linkage Maps. This large number of markers allows for the construction of reliable linkage (or genetic) maps with plenty of other uses, such as imputation.
• QTL Analysis. This MD panel has a reasonable number of markers to perform QTL analysis, for example on recombinant inbred lines (RIL) populations. 
• Diversity Studies. It is easier to perform several genomic studies that deal with diversity, as it is now possible to follow over generations, for example, inbreeding, effective population size, etc.

In addition, MD panels can also include several markers previously detected for use in Marker Assisted Selection (MAS) or for sex determination. Given the larger number of SNPs, the presence of verification, missing or fixed markers is of less concern, but should be kept under control in order to maximize the usefulness of the panel. Good or poor selection of SNP markers can make a large difference on the life of the panel and the accuracy of the GP models. Hence, it is recommend to ensure markers are well selected for the construction of these panels.

At the present, MD panels should be the panel of choice for most breeding operations. These panels will ensure that the collected data is reasonably good for use in the future, especially as technology and prices will change, justifying the genotyping investment in the long term. In addition, these represent the best panels for breeding programs to start applying (and playing) with more sophisticated genomic tools, such as genomic prediction with GBLUP and/or Bayes B.

High-density (HD) panels

Finally, we have the high-density (HD) panels with more than 20,000 SNPs (20K). But again, this is relative. Most HD panels for plants and aquatic species are in the range of 30K to 70K, but in some species the size considered is in excess of 700K (as in dairy) or even in the millions (as in humans). The cost of an HD panel varies greatly with the number of SNPs considered, the technology used, and number of individuals to genotype. The uses that these panels provide, in addition to all the previous uses for LD and MD panels, are:

• High Accuracy Genomic Prediction Models. We expect greater accuracy from these panels, possible with a long useful life not requiring tuning over time, and little or no imputation required. 
• Genome-wide Association Studies (GWAS). This is the key data for the discovery of markers under GWAS studies, where it will be more likely to find a marker positioned directly on a coding area within a functional gene.

These HD panels often are very redundant in their information. Hence, they tend to present a good portion of fixed alleles, and missing data that rules many markers out. However, they are still sufficiently large enough to provide all required above mentioned uses. It is also possible that these panels can be used by a combination of programs or research groups, allowing: 1) pooling of resources, 2) price negotiation, and 3) sharing of genomic information. This is commonly seen in some genomic consortiums. In addition, these HD panels, if originally constructed using a diverse base population, might not require much future revisions.

Another important aspect of HD panels is that they constitute the raw information for imputation in MD panels (and, although only remotely possible, in LD panels) and they will be the ones that in the future will link the array of available panels used in a breeding program (including, LD, MD or from different groups). Hence, HD panels allow us to connect different sources of genomic data.

Final Comments

One important note is in relation to the number of markers required for genomic selection (GS). We recommend at least an MD panel is used for this, with no fewer than 2K useful (post-filtering) SNPs. It is interesting to note that some studies have reported that dropping the number of SNPs to 1K or fewer results in a considerable loss of accuracy of the GP models. And, also, often more than 10K SNPs does not yield considerably better accuracies than 5K SNPs. In addition, some studies have successfully focused on 2-3K SNP panels supported with imputation from an HD panel, with an interesting increase in accuracy. Hence, there are plenty of options to exploit MD panels.

Another aspect is in relation to maximizing the accuracy of GP models. Of course, the more informative SNPs available the better! But there are many other aspects that affect, in good or bad ways, the success of a genomic model. For example, the level of relatedness between the training and evaluation populations, linkage-disequilibrium, genetic architecture of the traits, and of course heritability of the traits of interest. All of these elements may eventually tilt the decision from one type of panel to another.

Another difficulty that can arise is the detection of markers associated with some traits that are present in the population at very low rates, such as the case of ‘standing genetic variation’. This implies that it is difficult to find these markers on most panels as they will tend to be dropped early. Therefore, specific or very large HD panels might be needed in these cases.

Finally, as mentioned before, the use of LD or MD panels requires a careful pre-selection of markers to make the most of these panels. If this is done poorly, or for another population (e.g., using an available panel developed for another breeding group), then the benefits of the corresponding panels will possibly be greatly reduced. This also implies that, particularly for the LD panel, the set of markers in use has to be constantly reviewed as the population changes over time or new markers from MAS or sex determination are discovered.

In this blog, we have pointed out a few of the uses and benefits of each of the different panels. As the cost and offering of these panels changes constantly, we suspect that at some point we will be able to afford HD panels for a few cents (or pennies)! But before we get there, we need to make the most of our current resources, and gathering the right data for the right analysis is critical.

About the author

Dr. Salvador Gezan is a statistician/quantitative geneticist with more than 20 years’ experience in breeding, statistical analysis and genetic improvement consulting. He currently works as a Statistical Consultant at VSN International, UK. Dr. Gezan started his career at Rothamsted Research as a biometrician, where he worked with Genstat and ASReml statistical software. Over the last 15 years he has taught ASReml workshops for companies and university researchers around the world. 

Dr. Gezan has worked on agronomy, aquaculture, forestry, entomology, medical, biological modelling, and with many commercial breeding programs, applying traditional and molecular statistical tools. His research has led to more than 100 peer reviewed publications, and he is one of the co-authors of the textbook Statistical Methods in Biology: Design and Analysis of Experiments and Regression.

ASReml caters for a wide range of linear mixed models. Some models are quite complex involving hundreds of diverse variance components, each model has its own characteristics and some involve special ‘tricks’ in their specification. In addition, some datasets are quite large with millions of fixed and random effects, requiring the use of efficient computational tools, such as those exploiting sparsity. In the following sections, I describe some of these challenges and provide some details to consider.

Processing time

Gilmour (2019, DOI: 10.1111/jbg.12398) describes the process of fitting linear mixed models as implemented in ASReml. That paper highlights the principle of minimising the computation by the use of sparsity, an important requirement for fast processing. A second requirement is the efficiency of numerical calculations and this has been significantly enhanced in ASReml 4.2 (build ng, May 2022) in particular by rearranging the computation. Consequently, this build of stand-alone ASReml is up to 100 times faster than ASReml 4.1 (available in 2019).

An appropriate model

There are some widely used, well founded mixed models such as the animal model, the sire model, maternal model, spatial analysis as well as basic regression, factorial and (in)complete block analyses. These become the building blocks for multi-trait and multi-environment analyses. Each data set has its own characteristics and these should always be recognised. For example, litters in extensively grazed sheep are not biologically equivalent to litters in intensively housed pigs! Potential issues include the distribution of the data (binary, normal, skewed), variance heterogeneity, outliers and missing values. In addition, there is the issue of the purpose of the analysis: to select individuals for breeding, test a treatment hypothesis, estimate heritability, understand genetic and phenotypic correlations. All of these affect the type and structure of the model fitted.

Incremental complexity

It is important to perform univariate/single site analyses first before considering multi-variate/multi-environment analyses since the latter will fail to estimate covariance if the former fail to establish there is variance. In a recent case a user wanted to fit a trivariate animal model with repeated records. The trivariate analysis failed. The model involved additive genetic effects (animal effects estimated with a numerator relationship matrix), permanent environment (PE) effects (uncorrelated animal effects), fixed contemporary group effects and correlated residuals. However, for the second trait, there was no PE variance and for the third trait, there were no repeat observations although the data was set up with the animal effect repeated. Consequently, with no ‘residual’ (sampling) variance, univariate analysis of the third trait failed. After modifying the data file so that the third trait only appeared once for each animal, the trivariate analysis was performed with 3 variances and covariances at the genetic level, 2 variances and a covariance at the animal level (1 and 3) and 2 variances and a covariance at the sampling level (1 and 2). 

Big Data

Many datasets are quite big and consequently models become quite large. The issue then becomes one of sparsity. With field trials, a spatial analysis based on an autoregressive correlation of plots within rows and within columns has become common because it accommodates most field correlation patterns well and is sparse in that only immediate neighbours are connected in the inverse residual variance matrix. Similarly, very large data sets can be analysed using the numerator relationship matrix to define genetic links because the inverse is sparse with links between parents and their offspring and between parents with common offspring. This sparsity is exploited successfully by ASReml.

Similarly, if we want a covariance matrix across many traits/environments, it is likely to be over parameterised. The Factor Analytic variance structure allows the matrix to be estimated with reduced parameterization (in the spirit of principal components) and has been formulated to fit more sparsely as loadings plus specific variances. This formulation also helps avoid getting negative definite covariance matrices.

Processing efficiency

In specifying a model in ASReml, the terms are organised in 3 groups.  The first group is for small fixed factors for which the order of fitting is important because of the desire to perform significance testing using Wald F statistics. The equations for these are likely to be relatively dense, especially after adjusting for the other terms in the model, but there are typically less than 1000 of them. The second group is for random factors; a variance structure is declared for each. The third group is for large fixed effects (no variance structure). After forming the mixed model equations, ASReml reorders the equations in the last 2 groups to retain as much sparsity as possible. More sparsity means less computation (fewer elements of the sparse inverse to compute). Generally, this reordering has no impact on the answers (effects estimated) unless the fixed model is over-parameterised in which case different equations may be declared singular.

More recent developments in ASReml include storing and processing the sparse matrices more efficiently and changing the order of computation to reduce reading and writing to memory. It can also successfully access more RAM, allowing even larger models to be fitted.

User support

ASReml is designed to cater for a wide range of linear mixed models, being extensively used in plant and animal breeding, forestry and for analysis of human epidemiological data. That breadth of coverage is sometimes daunting to new users as most options are only relevant to particular situations. VSNi is committed to helping new and experienced users identify the most appropriate model for their data although VSNi does not provide an analysis service as such; but the developers of ASReml have broad experience as biometricians/statisticians. 

Final words

The linear mixed model, as implemented in ASReml, has allowed immense advances in global food productivity and health (plant, animal and human) via quantitative and marker-based genetics over the last 25 years.

About the author

Arthur Gilmour obtained his BSc Agr from Sydney University majoring in Biometry in 1970 with a NSW Government traineeship. He served as a biometrician until his retirement from NSW Agriculture as a Principal Research Scientist in 2009. The generalized linear mixed model has been the major research interest of Dr Gilmour, motivated by problems arising in research data generated by agricultural scientists. From the outset, he was involved in software development to meet the current statistical analysis needs of his clients and colleagues. He obtained his PhD in animal breeding from Massey University in 1983 during which time he came into contact with Robin Thompson. This led to an ongoing collaboration also with Brian Cullis, resulting in the development of ASReml in 1996.

When choosing which error bar to plot, keep the following in mind: the SD is a descriptive statistic that informs us about the variability of our data. Thus, you should use the SD as your error bar when you want to describe how spread-out the values in your dataset are.

On the other hand, the SEM is associated with inferential statistics.  It reflects the uncertainty in the mean and depends on the sample size. Thus, you should use the SEM as your error bar when making inferences (i.e., drawing conclusions) about the population mean.

Example

Imagine we are interested in estimating grain yield per plant on our farm. We randomly select a sample of n plants, and for each, measure its yield . 

Now, imagine that we repeat this random sampling process several times (for arguments sake, another 3 times).  From each of our random samples (a, b, c, d), we can estimate the mean grain yield per plant () This estimate of mean yield will vary between the samples. The SEM estimates this variability. The lower the SEM, the more precise our estimate of the population mean is. Conversely, the SD is a measure of the spread or variability of the data.