Sire evaluation is a cornerstone of genetic improvement programs in livestock production systems. By identifying and selecting genetically superior males, producers can enhance economically important traits across subsequent generations, including growth rate, fertility, milk yield, carcass quality and disease resistance (
Henderson, 1984;
VanRaden, 2008). Sire evaluation refers to the process of selecting breeding bulls for future use in genetic improvement programs, based on the performance records of their progeny and related animals (
Henderson, 1973). Sire evaluation offers greater advantages over dam evaluation due to the feasibility of more intense sSelection in males, the ease of disseminating superior germplasm and the potential for early selection using genetic markers
(Penagaricano et al., 2012).
Sire evaluation is widely used dairy cattle improvement. The primary goal of dairy cattle breeding programs is to identify and select individuals with the highest breeding values to become parents of the next generation. Among these, the breeding value of dairy sires plays a crucial role in determining their genetic impact on the population. Consequently, a key focus of such improvement programs is the identification of sires with superior genetic potential. Several methods have been developed and compared for estimating the breeding value of sires, including approaches based on simple averages, daughter-dam comparisons, herd-mate comparisons and daughter contemporary herd comparisons, both with and without adjustments for the number of daughters per sire
(Bajetha et al., 2015). Accurate sire evaluation relies on the integration of quantitative genetics, statistical modelling and increasingly, genomic tools that together refine estimates of breeding values (EBVs) or genomic estimated breeding values (GEBVs). A reliable sire evaluation method is characterized by low within-sire or error variance, ensuring greater accuracy in estimating genetic merit (
Dongre and Gandhi, 2014).
The evaluation of a sire’s genetic merit has been a critical component of animal breeding since ancient times. In modern dairy cattle improvement programs, the prediction of breeding values plays a central role in enhancing economically important traits. The most economic traits, such as milk yield, fertility and longevity, are polygenic in nature, improving these traits requires reliable genetic evaluation methods
(Lodhi et al., 2016). Among the available techniques, bull progeny testing remains one of the most dependable approaches, as it provides a more accurate estimate of a sire’s genetic potential compared to evaluations based solely on the performance of female ancestors or relatives. Consequently, precise, unbiased and efficient evaluation methods are crucial for ranking sires and selecting those with the highest genetic merit.
As the livestock industry continues to evolve, continuous refinement of sire evaluation techniques remains essential to meet the growing demands for productivity, efficiency and sustainability. Therefore, this review aims to provide a comprehensive overview of the methodologies, advancements and challenges associated with sire evaluation.
Method of sire evaluatoon
Various methods have been employed for the evaluation of dairy sires, with the most commonly used approaches including simple daughter averages, contemporary comparisons, least squares techniques and best linear unbiased prediction (BLUP).
Norton’s index
Norton’s Index, proposed by Norton in 1953, was one of the earliest systematic methods used for the genetic evaluation of dairy sires based on the performance of their daughters. The index aimed to reduce bias in sire evaluation that arises due to differences in the genetic potential of dams to which sires are mated. It does so by adjusting the average performance of daughters for the production level of their dams using the regression of daughter records on dam records. This adjustment helped correct for environmental and maternal influences, ensuring a more accurate estimate of a sire’s true genetic merit. Specifically, it addressed the issue where sires might be non-randomly mated to superior or inferior dams, which could otherwise lead to misleading comparisons. Although relatively simple, Norton’s Index laid the groundwork for more advanced techniques such as the contemporary comparison method, least squares Means and ultimately, best linear unbiased prediction (BLUP), which is now the gold standard in genetic evaluation. The methodology was built on the foundational concepts of regression and genetic correlation, as described in the quantitative genetics literature (
Norton, 1953;
Lush, 1945;
Falconer and Mackay, 1996). The continued evolution of genetic evaluation methods, including the replacement of Norton’s Index with more robust mixed model methodologies, reflects the increasing emphasis on precision and the handling of complex data structures in modern animal breeding (
Mrode, 2014).
Rice index
Rice Index, proposed by
Rice (1944), is one of the foundational methods developed for the early evaluation of dairy sires using progeny performance data. This index estimates the genetic merit of a sire by taking the average performance of his daughters and adjusting it using a selection index approach, which incorporates the heritability of the trait and the number of progeny records available. The key contribution of the Rice Index was its attempt to increase the accuracy of sire evaluation by weighting daughter performance according to the amount of information available, thus acknowledging that sires with more progeny provide more reliable estimates of genetic potential. Unlike simple daughter averages, the rice index also aimed to account for random variation in performance, which could otherwise mislead selection decisions. Though the method is considered outdated today, it played a crucial role in transitioning from raw averages to statistical evaluations in animal breeding. It served as a precursor to more sophisticated methods like least squares and BLUP (Best Linear Unbiased Prediction), which now dominate genetic evaluations (
Rice, 1944;
Lush, 1945;
Mrode, 2014).
Tomar index
The tomar Index was introduced as an improvement over earlier sire evaluation methods by incorporating more refined corrections for non-genetic factors. This index adjusts the average performance of daughters not only for the production level of the dams but also for the period-to-period variation in environmental conditions, as well as the number of progeny per sire. The Tomar Index considers that sires might be evaluated over multiple time periods and under varying management conditions, which can bias daughter performance data. To correct for such disparities, the index applies statistical adjustments that better isolate the genetic contribution of the sire. This makes it more accurate than simpler indices like those proposed by Rice or Norton. The tomar index represents a transitional methodology between early selection indices and the more complex models such as BLUP, which later became standard in sire evaluation. While its practical use has diminished with the advent of mixed model approaches, it contributed significantly to the conceptual development of modern genetic evaluation systems by addressing limitations of data heterogeneity and sampling error (
Lush, 1945;
Mrode, 2014).
Simple daughter average index
The simplest way to evaluate a bull is by his daughter’s production alone. The fault with this method is that it does not consider the probable contributions of the dam. It would be all right if all the bulls were bred to average group of cows. This index when used for ranking sires would be subject to bias if the levels of production of dams allotted to different sires were unequal (
Tomar, 2004). This index assumes that the phenotypic expression of a trait in daughters is a direct reflection of the sire’s genetic contribution. However, it does not adjust for environmental or non-genetic factors such as herd management, dam performance or period effects, making it highly susceptible to bias. Because sires are often mated to dams of varying genetic and environmental backgrounds, the unadjusted averages may misrepresent the true breeding value of the sire. Despite these limitations, the simple daughter average index laid the foundation for more sophisticated genetic evaluation methods and was widely used before the development of statistical corrections and mixed model approaches (
Lush, 1945;
Shanks, 1986).
Equi parent index
It is widely known as Yaap’s index or intermediate Index. This index is based on the principle that the two parents contribute equally to the genetic make-up of the progeny. This index overestimates the breeding value of a sire mated to set of dams inferior on the average and underestimates if dams happen to be superior on the average to the general level of herd. This index is also known as Mount Hope Index because it was first used at mount hope farm in 1928. This index is based on the assumption that the dams and daughters are raised under similar conditions so that the daughter dam difference reflects the sire effect otherwise it will reflect management practices in the herd (
Tomar, 2004).
Corrected daughter average index
This index adjusts the average performance of daughters by accounting for the varying production levels of dams sired by different bulls, using the regression of daughters’ records on those of their dams (
Tomar, 2004). The corrected daughter average index was developed to overcome the major limitation of the simple daughter average index by accounting for the influence of non-genetic factors on the performance of daughters. In this method, daughter records are statistically adjusted for environmental effects such as herd, year, season, parity and management practices, before calculating the sire’s average. By doing so, this index provides a more accurate and fair comparison among sires, especially when they are used across diverse production environments. The development of this method served as a foundation for later, more refined methods like contemporary comparison and best linear unbiased prediction (
Harvey, 1987;
Lush, 1945).
Contemporary daughter average index
The contemporary daughter average index represents an important advancement in sire evaluation by introducing comparisons within contemporary groups that is, daughters of different sires raised under similar environmental and management conditions. This index improves upon earlier methods by reducing bias caused by environmental variation and non-random mating. Instead of evaluating a sire solely based on the average performance of his daughters, this index compares each daughter’s performance relative to her contemporaries, thus accounting for factors like herd, year and season that might influence productivity. This adjustment ensures that the sire’s breeding value reflects his true genetic merit rather than environmental advantages or disadvantages. While the CDA Index does not completely eliminate all sources of bias such as the genetic potential of dams, it significantly increases the accuracy and fairness of sire comparisons.
(Swiger et al., 1964; Lush, 1945;
Mrode, 2014). CDA is particularly valuable in large-scale breeding programs where multiple sires are used across common management groups.
Corrected contemporary daughter average index
It is an enhanced version of the Contemporary Daughter Average Index, designed to further refine sire evaluation by correcting daughter performance not only for environmental effects but also for dam’s production level and other non-genetic influences (period to period variations). It is known as dairy Search Index. In the year 1965, Sunderasan and co-workers proposed the following index. The CCDA Index addresses this by applying statistical corrections, often through regression techniques, to adjust daughter records based on the production level of their dams. This method significantly increases the reliability of sire evaluations by reducing the impact of selective mating and environmental heterogeneity. As a result, it provides a more equitable estimate of the true genetic merit of sires, particularly in field progeny testing programs (
Tomar, 1971;
Lush, 1945;
Mrode, 2014).
Least squares method (LSM)
This method was introduced by
Harvey, 1960. The least-squares principle aims to reduce the error variance by adjusting the data to account for various non-genetic influences such as season, parity, herd, or management conditions (
Tomar, 2004). The principle of Least Squares Method (LSM) is based on minimizing the squared differences between the observed values and the estimated values of the dependent variable. The major limitation of the Least Squares Method (LSM) is its high sensitivity to outliers or extreme values. This occurs because squaring the differences amplifies their size, leading to a greater impact from unusually large deviations
(Talokar et al., 2023). By adjusting for fixed effects, LSM offer a more accurate comparison among genetic groups, such as sires or breeds. They are frequently used in sire evaluation, breed performance comparisons and genotype-environment interaction studies. The use of LSM has been enhanced by statistical software that allows for complex modeling, making it a standard tool in both experimental and observational studies (
Harvey, 1990;
Littell et al., 2006; Mrode, 2014).
Best linear unbiased prediction (BLUP)
When the performance records are used as clues in selection index, it is automatically assumed that the records have been adjusted previously for all known sources of environmental bias using adjustment factors. This method was proposed by Henderson and co-workers in the year 1975 which is considered as the most efficient method of sire evaluation. The basic steps involved in BLUP estimates are as an expression (model) that describes an individual’s performances in terms of all factors, that need to be taken into account
i.
e., herd-year-season (
Tomar, 2004).
Henderson (1949) introduced a method known as Best Linear Unbiased Prediction (BLUP), which allows for the simultaneous estimation of fixed effects and breeding values. This approach shares similar properties with the selection index method and simplifies to a selection index in cases where adjustments for environmental factors are not required. The key features of the BLUP (Best Linear Unbiased Prediction) method are as follows:
Best: It maximizes the correlation between the true and predicted breeding values or, equivalently, minimizes the prediction error variance.
Linear: The predicted breeding values are expressed as a linear function of the observed data.
Unbiased: It provides unbiased estimates of fixed effects and enables the estimation of true breeding values for random variables, such as a sire’s breeding value.
Prediction: It ensures accurate prediction of breeding values.
Due to its strong statistical advantages, BLUP has become a widely adopted method in genetic evaluation. It is commonly used to estimate sire breeding values based on progeny data, repeated performance records and across all sires within a pedigree. In recent years, its application has expanded significantly, supported by continuous advancements in computational capabilities. This progress has enabled the transition from simple sire models to more sophisticated approaches, including animal models, maternal models, multivariate analyses and random regression models (
Mrode, 2014).
Best linear unbiased Estimator (BLUE)
The best linear unbiased estimator (BLUE) is a fundamental concept in statistical estimation theory, particularly within the framework of linear models. It refers to an estimator that satisfies three key criteria: best, linear, unbiased and estimator.
Best: Among all linear and unbiased estimators, BLUE has the smallest variance, making it the most efficient and it provides minimum variance linear unbiased estimates (MVLUE).
Linear: The estimator is a linear function of the observed data.
Unbiased: The expectation of the estimator equals the true value of the parameter.
Estimator: The estimates of fixed effects.
The classical linear model assumptions must be satisfied the linearity in parameters, errors have zero mean, constant variance and no autocorrelation and the design matrix has full rank.
BLUE derives its foundation from the Gauss-markov Theorem, which states that under the assumptions of the classical linear regression model, the ordinary least squares (OLS) estimator is BLUE (
Searle, 1971;
Henderson, 1953;
Seber and Lee, 2003;
Christensen, 2002;
Gujarati, 2009).
In genetic evaluations, BLUE is often used to estimate fixed effects, whereas BLUP (Best Linear Unbiased Prediction) is applied for predicting random effects like breeding values.
Advancements in linear approaches to genetic evaluation of sires
REML
Restricted maximum likelihood (REML) is a widely used statistical method for estimating variance components in linear mixed models, particularly in the context of genetic evaluation. Introduced by
Patterson and Thompson (1971), REML overcomes the bias inherent in traditional maximum likelihood (ML) estimation by basing the likelihood function on a transformation of the data that removes the fixed effects, thus focusing solely on the random components. This makes REML especially suitable for animal breeding studies, where separating genetic (random) from environmental (fixed) influences is crucial. Unlike ML, which tends to underestimate variance components due to fixed effect overfitting, REML provides unbiased and consistent estimates, making it more reliable for use in the estimation of breeding values. REML has become the backbone of modern genetic evaluation software such as ASReml, WOMBAT and BLUPF90, which implement mixed model equations for complex traits under field conditions. In livestock breeding, REML is extensively applied in animal models, sire models and maternal effect models, allowing researchers to improve the genetic gain while maintaining statistical rigor and accuracy (
Patterson and Thompson, 1971;
Mrode, 2014;
Meyer, 2007;
Gilmour et al., 2015).
DFREML
DFREML is a computational algorithm developed for estimating variance components in linear mixed models using the REML approach without relying on the analytical derivatives of the likelihood function. Introduced by
Meyer (1989), DFREML became popular in animal breeding due to its ability to efficiently estimate co-variance components even in complex and unbalanced datasets, such as those encountered in field progeny testing. The method is especially useful in genetic evaluation of livestock, where data often include repeated records, missing values or multiple traits. DFREML iteratively searches for parameter estimates that maximize the residual likelihood, using numerical optimization techniques. It has been widely used for estimating genetic parameters in cattle, sheep and other livestock species, particularly when standard derivative-based REML algorithms are not feasible. In the Indian context, DFREML has been found highly effective in sire evaluation of indigenous breeds like Red Sindhi, Frieswal and Sahiwal, providing more accurate and efficient estimates compared to other methods like BLUP, SRLS and LSM
(Kumar et al., 2003; Gaur et al., 2010). The method laid the foundation for more advanced mixed model software such as WOMBAT, which inherited many of DFREML’s features while improving computational speed and flexibility.
Indian researchers have reported that the DFREML method proved to be the most efficient and accurate approach for sire evaluation in Red Sindhi and Frieswal cattle, based on both actual and predicted first lactation 305-day milk yield. Based on their findings, it was recommended that DFREML should be the preferred method for sire evaluation in Sahiwal cattle, followed in order of effectiveness by best lllinear unbiased prediction, simplified regressed least squares and least squares means methods
(Mallick et al., 2018 and
Rajeev et al., 2021).
AI-REML
The AI-REML (Average Information Restricted Maximum Likelihood) algorithm is a quasi-Newton optimization technique that utilizes the first derivatives of the likelihood function, while substituting the second derivatives with the average of the observed and expected information matrices. This approach significantly enhances computational efficiency compared to derivative-free methods, making AI-REML particularly advantageous for large-scale and complex genetic evaluations (
Meyer, 1997). This significantly reduces computa- tional time while maintaining accuracy and stability, making it highly suitable for large and complex datasets often encountered in animal breeding. AI-REML has become a core algorithm in software like ASReml and BLUPF90, which are extensively used in sire evaluation programs. FORTRAN- based programs for implementing the AI-REML algorithm have been developed and datasets involving various sires have been analyzed to evaluate the algorithm’s relative computational performance
(Talokar et al., 2023).
Software and tools for sire evaluation
The advancement of statistical methods for sire evaluation has been complemented by the development of specialized software tools that facilitate large-scale data handling and complex genetic analyses. Among the most widely used is ASReml, a powerful software for fitting linear mixed models, including BLUP, REML and multivariate models, which is especially suited for animal breeding data
(Gilmour et al., 2015). WOMBAT, an open-source software, is another popular tool for estimating (co)variance components and predicting breeding values using restricted maximum likelihood (REML) under mixed models (
Meyer, 2007). For large-scale national or field-based genetic evaluations, the BLUPF90 family of programs (including REMLF90, AIREMLF90 and GIBBSF90) has become a standard due to its flexibility in handling various model structures, including genomic data and single-step GBLUP
(Misztal et al., 2002). Additionally, DMU software developed by the Danish Institute of Agricultural Sciences is widely used for genetic evaluation using multivariate animal models and random regression models (
Madsen and Jensen, 2013). Apart from these, general-purpose statistical environments like R and SAS also offer packages and procedures (
e.
g., lme4, nlme, MIXED) to fit mixed models, making them suitable for preliminary sire evaluation studies. The choice of software often depends on the size of the dataset, model complexity and availability of pedigree and genomic information. These tools have revolutionized the precision and efficiency of genetic evaluations, playing a crucial role in modern sire selection and breeding programs.
Future directions of sire evaluation methods in India
The future of sire evaluation methods in India is poised to advance significantly with the integration of genomics, big data analytics and artificial intelligence. While traditional approaches like BLUP and least squares continue to play an essential role, the incorporation of genomic selection (
e.
g., GBLUP and single-step GBLUP) is expected to revolutionize the accuracy and speed of sire evaluations by capturing within-family genetic variation
(Mishra et al., 2021). With the growing availability of SNP genotyping platforms and initiatives like the National Dairy Genomic Center, genomic data can now complement conventional performance and pedigree records, especially in indigenous breeds. Furthermore, the digitization of farm records and implementation of on-field progeny testing through national programs such as Rashtriya Gokul Mission and National Dairy Plan are contributing to more robust data pipelines for evaluation. The use of AI-based models and machine learning algorithms may offer dynamic predictions of breeding values using multi-source, real-time data. Future efforts should also focus on developing breed-specific evaluation models, improving data recording infrastructure and enhancing farmer participation to ensure wide-scale applicability. Collaborative efforts between ICAR institutes, state universities and private breeding organizations will be key to building scalable and accurate sire evaluation systems tailored for India’s diverse cattle and buffalo genetic resources.
