## 1 Introduction  
In the last decade, the application of genomic evaluation in dairy cattle has been a crucial tool for the analysis and selection of suitable individuals thus ensuring better productivity. The technology has led to important changes in countries with dairy traditions, directly affecting the benefits of the world dairy industry [1]. Before the emergence of genomics, information to predict production and reproductive patterns was based on progeny selection tests that took long generation intervals [2]. Fortunately, the current trend is to perform evaluations based on genotyping of singlenucleotide polymorphisms (SNPs) which account for nearly 75% of reliability [3]. Nowadays, the number of dairy cows genotyped for heritable traits (e.g., productive, reproductive, fitness, and conformation) is increasing [1]. This is because genomic profiles have become more reliable for predictions [4; 5]. For these analyses, high-density SNP chips are used with one- or two-step frequentist and Bayesian methodologies [6]. The information generated can be used to build data banks and for the exchange of specific genotypes among countries interested in improving productive and reproductive herd traits, conforming, for instance, the inter-genomic database such as Interbull (Interbull Centre, Uppsala, Sweden) [3; 7; 8]. In the highly demanding dairy cattle industry, genetic improvement depended for decades on the use of pedigree and phenotype data to estimate breeding and production values [9]. However, at present, scarce knowledge is available about the genetic architecture of quantitative variation regarding features such as inbreeding and its influence on production and reproductive parameters [2; 5; 10]. Accordingly, the implementation of genomic evaluations can include more relevant parameters, such as inbreeding, with the potential of significantly affecting selection indices, with emphasis on milk production, milk characteristics, reproduction, conformation traits, and productive lifespan [11; 12]. Health parameters, selection for organic production, reduced waste, and gas emission are also currently considered traits of interest [13; 14]. Therefore, at present, it becomes necessary to add new parameters to genotype analyses to select animals with more accurate estimates of SNPs' effects that directly or indirectly affect profitability [15]. Consequently, routine genotyping of primiparous cows and the incorporation of new indices such as inbreeding can significantly aid in making better management decisions in herds [4; 16]. Genotyping is currently focusing on the selection of the female animals that should be kept in herds, increasing the information derived from estimates in young animals [7; 8]. Thus, future genomic evaluation algorithms will be based on one-step methodologies single-step Genomic Best Linear Unbiased Prediction (ssGBLUP) that will incorporate hundreds of thousands of cows with genotypes and trait records [17; 18] and that will gradually replace the pedigree relationship matrix with genomic relationships [2]. Inbreeding occurs when crossing genetically related animals because they share common ancestors [9]. Inbreeding in farm animals reduces genotypic variability by restricting heterozygosity [16; 19] with consequently an increase of deleterious recessive genes' frequency visible in a lower phenotypic variability [20]. Furthermore, inbreeding can lead to a reduction in genetic variability with possible harmful genetic and phenotypic effects [20]. Therefore, the study of inbreeding in dairy cattle is extremely important, particularly due to the widespread use of assisted reproductive technologies (ARTs) that produce high selection pressure and rapid genetic gain, resulting in thousands of offspring from a single parent [21]. A great effort has been made in the genotyping of dairy cattle of the Holstein breed, but in general, this task has been insufficient.