Technical Note: Software for Calculation of the Inverse Numerator Relationship Matrix

Software was developed to compute the non-zero elements of the inverse of the numerator relationship matrix used in estimation of (co)variances and breeding values. The program was written to be flexible with regard to format of the input pedigree file and integration with existing software packages for genetic evaluation. The program was further designed to be highly portable, with a minimum of compiler dependence, and to use dynamic rather than static memory allocation. Real time required to read and sort input pedigrees containing 5,000 to 100,000 animals with varying levels of inbreeding and to compute the non-zero elements of the matrix was < 9.5 min and increased as the numbers of animals in the pedigree file increased beyond 20,000 animals. Increased numbers of inbred animals in large (≥20,000 animals) pedigrees increased the time required to complete computations. Although a combination of alphanumeric animal identification codes were allowed, the time required to initially read pedigrees and, therefore, total run time was significantly decreased (P < 0.001) for large pedigrees when identification codes were strictly numeric for all animals.     

Effects of incomplete pedigree on genetic management of the Dutch Landrace goat

Genetic diversity in the Dutch Landrace goat was investigated based on information from the pedigree with about 6500 animals. Annual inbreeding rate after 1985 was below 0.5% and after 1987 close to 0%. However, pedigree information was incomplete, and 350 animals had unknown parents, while for the majority the real parents must have been in the pedigree. To determine the influence of unknown parents, 20 new pedigrees were created by random assignment of animals, alive at the time of birth, as parents to individuals with unknown parents. Only 12 founders remained for these pedigrees, and inbreeding levels varied considerably between these 20 pedigrees. However, inbreeding rates were remarkably constant. They increased to about 0.2%, indicating that the population is not endangered by inbreeding. The optimal contribution theory was used to evaluate possibilities of decreasing the average relationship in the population and thus to increase the genetic diversity of the breed. Optimal contribution decreased the average relationship in the population whether randomly assigned parents were used or not. However, individuals selected as parents for the resampled pedigrees differed from the original pedigree, and only a few animals were selected for all pedigrees. Candidates for inclusion in the genebank were also selected using optimal contribution. Adding animals to the genebank increased the conserved genetic diversity substantially, but as the lists differed between the analysed pedigrees it was not clear which animals were best added to the genebank.     

Efficient computation of genotype probabilities for loci with many alleles: II. Iterative method for large, complex pedigrees

An algorithm for computing genotype probabilities for marker loci with many alleles in large, complex pedigrees with missing marker data is presented. The algorithm can also be used to calculate grandparental origin probabilities, which summarize the segregation pattern and are useful for mapping quantitative trait loci. The algorithm is iterative and is based on peeling on alleles instead of the traditional peeling on genotypes. This makes the algorithm more computationally efficient for loci with many alleles. The algorithm is approximate in pedigrees that contain loops, including loops generated by full sibs. The algorithm has no restrictions on pedigree structure or missing marker phenotypes, although together those factors affect the degree of approximation. In livestock pedigrees with dense marker data, the degree of approximation may be minimal. The algorithm can be used with an incomplete penetrance model for marker loci. Thus, it takes into account the possibility of marker scoring errors and helps to identify them. The algorithm provides a computationally feasible method to analyze genetic marker data in large, complex livestock pedigrees.     

Application of individual increase in inbreeding to estimate realized effective sizes from real pedigrees

The objective of this study was to test the performance of a recently proposed methodology for the estimation of realized effective size (N(e)) based on individual increase in inbreeding (DeltaF(i)) on several real pedigrees: (a) an experimental mice population; (b) a closed pedigree of fighting bulls; (c) the Spanish Purebred (SPB, Andalusian) horse pedigree; (d) the Carthusian strain of SPB pedigree; (e) the Spanish Arab horse pedigree; and (f) the Spanish Anglo-Arab horse pedigree. Several reference subpopulations were defined on the basis of generation length in order to consider only animals in the last generation, to assess the influence of the pedigree content on the estimates of N(e). The estimates of realized N(e) computed from DeltaF(i) (Ne) tended to be higher than those obtained from regression on equivalent generations. The new parameter Ne remained approximately stable when pedigree depth achieved about five equivalent generations. Estimates of take into account the genetic history of the populations, the size of their founder population, and the mating policy or bottlenecks caused by poor use of reproducing individuals. The usefulness of the realized N(e) computed from individual increase in inbreeding in real pedigrees is also discussed.     

Different methods of selecting animals for genotyping to maximize the amount of genetic information known in the population

It is possible to predict genotypes of some individuals based on genotypes of relatives. Different methods of sampling individuals to be genotyped from populations were evaluated using simulation. Simulated pedigrees included 5,000 animals and were assigned genotypes based on assumed allelic frequencies for a SNP (favorable/unfavorable) of 0.3/0.7, 0.5/0.5, and 0.8/0.2. A field data pedigree (29,101 animals) and a research pedigree (8,688 animals) were used to test selected methods using simulated genotypes with allelic frequencies of 0.3/0.7 and 0.5/0.5. For the simulated pedigrees, known and unknown allelic frequencies were assumed. The methods used included random sampling, selection of males, and selection of both sexes based on the diagonal element of the inverse of the relationship matrix (A(-1)) and absorption of either the A or A(-1) matrix. For random sampling, scenarios included selection of 5 and 15% of the animals, and all other methods presented concentrated on the selection of 5% of the animals for genotyping. The methods were evaluated based on the percentage of alleles correctly assigned after peeling (AK(P)), the probability of assigning true alleles (AK(G)), and the average probability of correctly assigning the true genotype. As expected, random sampling was the least desirable method. The most desirable method in the simulated pedigrees was selecting both males and females based on their diagonal element of A(-1). Increases in AK(P) and AK(G) ranged from 26.58 to 29.11% and 2.76 to 6.08%, respectively, when males and females (equal to 5% of all animals) were selected based on their diagonal element of A(-1) compared with selecting 15% of the animals at random. In the case of a real beef cattle pedigree, selection of males only or males and females yielded similar results and both selection methods were superior to random selection.     

Inheritance of pancreatic acinar atrophy in German Shepherd Dogs

OBJECTIVE: To assess the heritability of pancreatic acinar atrophy (PAA) in German Shepherd Dogs (GSDs) in the United States. ANIMALS: 135 GSDs belonging to 2 multigenerational pedigrees. PROCEDURE: Two multigenerational pedigrees of GSDs with family members with PAA were identified. The clinical history of each GSD enrolled in the study was recorded, and serum samples for canine trypsin-like immunoreactivity (cTLI) analysis were collected from 102 dogs. Dogs with a serum cTLI concentration < or = 2.0 microg/L were considered to have exocrine pancreatic insufficiency (EPI) and were assumed to have PAA. RESULTS: Pedigree I consisted of 59 dogs and pedigree II of 76 dogs. Serum cTLI concentrations were measured in 48 dogs from pedigree I and 54 dogs from pedigree II. A total of 19 dogs (14.1%) were determined to have EPI, 9 in pedigree I (15.3%) and 10 in pedigree II (13.6%). Of the 19 dogs with EPI, 8 were male and 11 were female. CONCLUSIONS AND CLINICAL RELEVANCE: Evaluation of data by complex segregation analysis is strongly suggestive of an autosomal recessive mode of inheritance for EPI in GSDs in the United States.     

Effects of errors in pedigree on three methods of estimating breeding value for litter size, backfat and average daily gain in swine

Estimated breeding value (EBV) was calculated based on either individual phenotype (SP), an index of individual phenotype and full- and half-sib family averages (SI) or Best Linear Unbiased Prediction (BLUP). Calculations were done with correct data or data with 5, 10, 15 or 20% of the records per generation containing pedigree errors. Traits considered were litter size (LS), backfat (BF) and average daily gain (ADG). When data were correct, BLUP resulted in an advantage in expected genetic gain over SP of 22, 7.2 or 30.8% for LS, BF and ADG, respectively, and over SI of 9.6, 3.8 or 21.4%. When sire and dam pedigrees were incorrect for 20% of the pigs each generation, genetic gain using SI was reduced by 7, 2.5 or 6.5% and genetic gain using BLUP was reduced by 9.3, 3.2 or 12.4% for LS, BF and ADG, respectively. With 20% of the pedigrees in error, the advantages in genetic gain of using BLUP over SP, the method unaffected by errors in pedigree, were 10.5, 3.8 and 14.6% for LS, BF and ADG, respectively. These results suggest that, although BLUP is affected to a greater degree by pedigree errors than SP or SI, selection of swine using BLUP still would improve response to selection over the use of SP or SI.     

Variance of actual inbreeding derived from the number and variance of chromosome segment

The inbreeding coefficient (F) is used as a central parameter inferring a proportion of alleles identical by descent within an individual and by genetic variability within a population. The actual inbreeding coefficient varies around a central value, the inbreeding coefficient. C ockerham and W eir (1983) derived the method for computing the variance of inbreeding while reviewing several other methods. The variance of inbreeding in their report was considered to be of two components: one within population and the other between population of varied pedigrees. If pedigree is fixed, F is easily computed for an individual by the standard method (F alconer 1989). For domestic animals, pedigree information is usually available because it is requisite for a programme of genetic improvement. In this study, the variance of inbreeding coefficient was derived for an individual with a pedigree having a single path to a foundation animal.     

Thoroughbred racehorse mitochondrial DNA demonstrates closer than expected links between maternal genetic history and pedigree records

The potential future earnings and therefore value of Thoroughbred foals untested in the racing arena are calculated based on the performance of their forebears. Thus, lineage is of key importance. However, previous research indicates that maternally inherited mitochondrial DNA (mtDNA) does not correspond to maternal lineage according to recorded pedigree, casting doubt on the voracity of historic pedigrees. We analysed mtDNA of 296 Thoroughbred horses from 33 maternal lineages and identified an interesting trend. Subsequent to the founding of the Thoroughbred breed in the 16th century, well‐populated maternal lineages were divided into sub‐lineages. Only six in 10 of the Thoroughbreds sampled shared mitochondrial haplotype with other members of their maternal lineage, despite having a common maternal ancestor according to pedigree records. However, nine in 10 Thoroughbreds from the 103 sub‐lineages sampled shared mtDNA with horses of their maternal pedigree sub‐lineage. Thus, Thoroughbred maternal sub‐lineage pedigree represents a more accurate breeding record than previously thought. Errors in pedigrees must have occurred largely, though, not exclusively, at sub‐lineage foundation events, probably due to incomplete understanding of modes of inheritance in the past, where maternal sub‐lineages were founded from individuals, related, but not by female descent.     

Genetic evaluation using parentage information from genetic markers

Genetic evaluation relies on pedigree information to account for the trait information on individuals and their relatives. Recording pedigrees may place unfavorable restrictions on the management of breeding populations, such as the use of single-sire mating groups and the observation of parturition. The use of DNA marker information is an alternative method to identify parents, but it is difficult to assign the parents unambiguously for all progeny in extensively farmed livestock without the use of very many markers. We present methods that use DNA information on parentage within a genetic evaluation system that allow for genotyping errors and for the parentage information to be incomplete, with probabilities assigned to possible parent pairs (i.e., fractional parentage assignment). Two of these methods use a computing strategy that circumvents the high memory requirements associated with the application of previous methods designed for use with fractional parentage assignment. This strategy has an additional advantage of allowing the same statistical models to be used in the evaluation as with recorded pedigrees. The use of DNA marker-based parentage for genetic evaluation is associated with lower genetic gain (at the same survival levels) than by using the true pedigree. This decrease in gain depends on a number of factors, including trait heritability and the DNA markers used. The methods we have described show how DNA marker information could be used to replace traditional pedigree recording.     

Microsatellite analysis in a population of Baudet du Poitou donkeys

A population of Baudet du Poitou donkeys was genetically characterized using microsatellites. The results were used to verify the pedigrees and to estimate the genetic variability. It could be confirmed that a equine parentage test kit works well for donkeys and that by using 13 microsatellites more than 99% of wrong pedigree informations would be detected. The genetic variability was comparable to a representative group of Baudet du Poitou donkeys in France.     

A retrospective study on the prevalence of primary cataracts in two pedigrees from the German population of English Cocker Spaniels

Objective  Two pedigrees from the German English Cocker Spaniel population are presented to illustrate the familial occurrence of primary cataract (CAT) in single- and multicolored English Cocker Spaniels. The aim was to characterize similarities and differences in the prevalence and formation of CAT in these separately bred color variants of English Cocker Spaniels.
Materials  The study was based on the veterinary records for presumed inherited eye diseases of 1232 English Cocker Spaniels which were provided by the German panel of the European Eye Scheme for diagnosis of inherited eye diseases in animals (DOK, < http://www.dok-vet.de >). Data included information on 615 single-colored and 617 multicolored English Cocker Spaniels.
Results  CAT was diagnosed in 92 (14.96%) of the single-colored and 34 (5.51%) of the multicolored English Cocker Spaniels. The pedigree of the single-colored English Cocker Spaniels included 40 ophthalmologically examined dogs with 18 unaffected and 22 affected dogs. The pedigree of the multicolored English Cocker Spaniels contained 16 ophthalmologically examined dogs with 11 unaffected and five affected dogs.
Conclusions  In both color variants of the English Cocker Spaniels different forms of primary CAT with respect to location within the lens occurred among close relatives. Appearance of CAT was very heterogeneous without obvious sex differences. The sample pedigrees do not support the assumption of familial segregation of specific forms of primary CAT in English Cocker Spaniels.     

How the Orthopedic Foundation for Animals (OFA) is tackling inherited disorders in the USA: using hip and elbow dysplasia as examples

The Orthopedic Foundation for Animals (OFA) maintains an on-line health pedigree database for inherited disorders of animals. With the American Kennel Club Canine Health Foundation, the OFA maintains the Canine Health Information Center (CHIC) for parent breed clubs to identify breed-specific required health tests. Analysis of the results of OFA evaluations in the hip and elbow registries show that selection based on phenotype improves conformation. Disorders with complex inheritance respond best to selection based on depth (ancestors) and breadth (siblings) of pedigree health test results. This information can be derived from vertical pedigrees generated on the OFA website.     

Experiences with pedigree control for Swiss dog breeds]

Each year approximately 13,000 new pedigrees for puppies are issued by the Swiss Kennel Club Except for a few cases there are no regulations to verify the paternities independently. This report describes the practical procedure for disputed paternities and summarizes the results from 35 cases which were resolved during the last three years. Most cases relate to unwanted or wanted double matings. Generally the owner of the bitch can not state the sire. For roughly half of the cases where a sire was given as the parent the information was disproven by the genetic analysis in the laboratory. These experiences confirm the need for a better pedigree control in Swiss dog breeds. Breeding without correct pedigree control is restricted to animal keeping.     

Efficient computation of genotype probabilities for loci with many alleles: I. Allelic peeling

Genetic marker data are likely to be obtained from a relatively small proportion of the individuals in many livestock populations. Information from genetic markers can be extrapolated to related individuals without marker data by computing genotype probabilities using an algorithm referred to as peeling. However, genetic markers may have many alleles and the number of computations in traditional peeling algorithms is proportional to the number of alleles raised to the sixth or eighth power, depending on pedigree structure. An alternative algorithm for computing genotype probabilities of marker loci with many alleles in large, nonlooped pedigrees with incomplete marker data is presented. The algorithm is based on recursive computations depending on alleles instead of genotypes, as in traditional peeling algorithms. The number of computations in the allelic peeling algorithm presented here is proportional to the square of the number of alleles, which makes this algorithm more computationally efficient than traditional peeling for loci with many alleles. Memory requirements are roughly proportional to the number of individuals in the pedigree and the number of alleles. The recursive allelic peeling algorithm cannot be applied to pedigrees that include full sibs or loops. However, it is a preliminary step toward a more complex and encompassing iterative approach to be described in a companion paper.     

Inheritance of hypoadrenocorticism in bearded collies

OBJECTIVE: To assess heritability and mode of inheritance for hypoadrenocorticism in Bearded Collies. ANIMALS: 635 Bearded Collies. PROCEDURES: Dogs were classified as affected by hypoadrenocorticism or unaffected. Phenotypic and pedigree data were analyzed. Heritability was estimated by use of Bayesian statistical methods. Regressive logistic models for complex segregation analyses were used to characterize mode of inheritance. RESULTS: Hypoadrenocorticism was diagnosed in 60 (9.4%) dogs. Heritability of hypoadrenocorticism was estimated to be 0.76 with both sexes affected with equal probability. Evaluation of the pedigrees did not support a Mendelian autosomal dominant mode of inheritance. Evidence from the complex segregation analysis for a single locus of large effect on hypoadrenocorticism was not convincing. CONCLUSIONS AND CLINICAL RELEVANCE: Hypoadrenocorticism in Bearded Collies is highly heritable. Although a precise genetic mechanism responsible for inheritance of the disorder remains undetermined, breeding decisions must include consideration of the genetic likelihood of passing on this deleterious disorder to offspring of affected dams and sires.     

Hereditary parakeratosis in shorthorn beef calves

Parakeratosis was diagnosed in 9 Shorthorn beef calves over a 4-year period. When pedigrees of these calves were analyzed, familial associations were strong. Thirty-six coefficients of relationship among all possible combinations of the 9 affected calves ranged from 0.5 to 39.8% and averaged 15.6%. All affected calves were descendants of bull A. Of 9 affected calves, 6 had bull A in their paternal and maternal pedigrees. The 3 remaining affected calves had bull A in their sire's pedigree and were born to 2 full-sib dams. Seemingly, parakeratosis in this Shorthorn herd was hereditary with the mode of inheritance being that of a simple autosomal recessive.     

Simple and rapid inversion of additive relationship matrices incorporating parental uncertainty.

Animals bred in pastoral systems are often part of multiple-sire groups, introducing uncertainty into pedigrees. Genetic evaluation of sires and dams in such instances is complicated by the uncertainty of parenthood. This article defines a simple and rapid algorithm to compute the inverse of a numerator relationship matrix under uncertain parenthood. The algorithm can accommodate inbreeding and uncertainty of parenthood on both paternal and maternal sides of the pedigree.     

Differences between genomic‐based and pedigree‐based relationships in a chicken population,as a function of quality control and pedigree links among individuals

This work studied differences between expected (calculated from pedigree) and realized (genomic, from markers) relationships in a real population, the influence of quality control on these differences, and their fit to current theory. Data included 4940 pure line chickens across five generations genotyped for 57 636 SNP. Pedigrees (5762 animals) were available for the five generations, pedigree starting on the first one. Three levels of quality control were used. With no quality control, mean difference between realized and expected relationships for different type of relationships was ≤ 0.04 with standard deviation ≤ 0.10. With strong quality control (call rate ≥ 0.9, parent‐progeny conflicts, minor allele frequency and use of only autosomal chromosomes), these numbers reduced to ≤ 0.02 and ≤ 0.04, respectively. While the maximum difference was 1.02 with the complete data, it was only 0.18 with the latest three generations of genotypes (but including all pedigrees). Variation of expected minus realized relationships agreed with theoretical developments and suggests an effective number of loci of 70 for this population. When the pedigree is complete and as deep as the genotypes, the standard deviation of difference between the expected and realized relationships is around 0.04, all categories confounded. Standard deviation of differences larger than 0.10 suggests bad quality control, mistakes in pedigree recording or genotype labelling, or insufficient depth of pedigree.