In horses, CA is a neurologic disease that develops almost exclusively in Arabians.1–4 Foals affected with the disease may appear clinically normal at birth; signs of disease generally develop between 6 weeks and 4 months of age but occasionally later. Clinical signs include ataxia, intention head tremor, exaggerated action of the forelimbs, a wide-based stance, and a lack of menace response.2–4 Affected horses often startle easily, fall, and may be unable to rise from a recumbent position.5
The pathological features of CA include postnatal degeneration of the Purkinje cells and associated neurons from the granular layer of the cerebellum, which results in disorganization of the molecular and granular layers.3,6 The remaining Purkinje cells are small and shrunken, with abnormal morphological characteristics.1,2 The death of Purkinje cells appears to be due to a failure of these cells to migrate correctly through the cerebellum during development. Recent research findings implicate an apoptosis mechanism in the loss of Purkinje cells.6
Although CA itself is not fatal, the general lack of balance equilibrium and hyperreactivity of affected horses poses a danger to the horses and handlers. Horses with CA are most often euthanized or, in some circumstances, maintained as pasture pets because they are never sufficiently coordinated to be ridden safely and do not generally make good breeding candidates. Diagnosis of the disease is almost always made following the recognition of clinical signs by an attending veterinarian. Definitive diagnosis can only be made after death via histologic examination of cerebellar tissue.
Cerebellar abiotrophy was first described in the veterinary medical literature in the late 1960s.1 Early publications were limited to case reports2–4 involving Arabians that had neurologic signs for which there was subsequent histologic confirmation of the disease. Examination of the affected foals' pedigrees, lack of environmental causes, and the fact that the disease was virtually restricted to the Arabian breed suggested a genetic basis for the condition.2–4 Although a recessive mode of inheritance has been suggested, the rarity of confirmed cases made it impossible to determine the mode of inheritance with any statistical support.3,4
Development of CA is a source of concern for breeders of Arabians. Currently, it appears that < 1% of Arabians are affected with the disease at birth but the incidence of affected foals seems to be increasing. For example, with regard to affected foals, we were informed of 5 born in 2008 but 14 born in 2009. Because of underreporting or misdiagnosis, available data may not reflect the actual incidence of the disease. The cost of a CA-affected foal in terms of lost revenue can be considerable, as many of these foals come from valuable breeding stock. Establishing the mode of inheritance of the disease will help breeders make informed decisions about the animals selected for mating to reduce the risk of producing a CA-affected foal. The purpose of the study reported here was to determine the mode of inheritance for CA among Arabians via complex segregation analysis of the phenotypic data (segregating for the disease) from familial horses.
Materials and Methods
Animals—A total of 804 horses were used in the study. Horses segregating for the disease were identified on the basis of samples (from affected horses and their sires, dams, and other related unaffected siblings) submitted for a linkage mapping study of CA.7 Family groups were identified from these samples and expanded via additional searches to include mares involved in other matings of the stallions and the offspring of those matings. Of the 804 horses, there were 29 Arabians (15 males and 14 females) for which a diagnosis of CA had been made. The affected horses were born between 2000 and 2008, with 1 mare born in 1987. Twenty-four of these horses were purebred Arabians, 4 were three-quarters Arabian-one-quarter pony crosses, and 1 was a three-quarters Arabian-one-quarter Saddlebred cross. Of the 29 horses, all had clinical signs of CA; 25 were euthanized at the request of the owners after the appearance of signs of CA. For 8 of the euthanized horses, the diagnosis was confirmed after death via histologic examination of cerebellar tissue; for the other 21 CA-affected horses, CA was diagnosed by attending veterinarians on the basis of clinical signs consistent with the disease. Horses were euthanized by licensed veterinarians either at the University of California-Davis School of Veterinary Medicine or at other facilities. Histologic examination of cerebellar tissues was performed by the Department of Pathology at the university.
Most horses (n = 755) belonged to 1 of 4 paternal families in which the founding sire had produced affected and unaffected foals. Twelve CA-affected foals were produced from matings of the 4 stallions with 12 mares. Hair root or whole blood samples obtained from the 12 affected foals in this group as well as from the 4 sires and 12 dams and similar samples from an additional 26 unaffected offspring produced from matings of the 4 stallions with those same 12 mares that had been submitted to the University of California-Davis Veterinary Genetics Laboratory by the owners of the stallions for use in a linkage mapping study. The 4 stallions that founded these 4 families shared a common ancestor within 9 generations on the paternal and maternal sides of the pedigrees of the affected foals. Through a search of breeding records of the Arabian Horse Association, an additional 351 foals (160 males and 191 females) produced from matings of the 4 stallions with 340 other mares that were unaffected were identified. These foals were born during the same period in which the CA-affected foals were produced (2000 to 2007) and were therefore at least 2 years of age at the time of the study. Because the owners of the 4 stallions contacted us to report the birth of the first affected foal and because the signs of CA are typically noticeable, these additional 351 foals were presumed to be unaffected. Also, because the signs of the disease almost always cause an animal to be unfit for breeding, the additional 340 dams were also presumed to be unaffected.
A fifth paternal family (a Veterinary Genetics Laboratory herd generated at the University of California-Davis) comprised 19 animals (1 stallion, 5 mares, and 13 offspring). All horses were examined by veterinarians from the School of Veterinary Medicine. The horses used for breeding in this family were donated to the university by the owners, and no pedigree information was available for them. Therefore, it is unknown whether the Arabian-pony crosses generated by this family shared common ancestry with the other affected foals. However, among these 19 horses, 7 (3 mares and 4 of their offspring) were affected with CA.
The remaining 40 horses consisted of smaller family groups and comprised 7 unaffected stallions, 12 unaffected dams, 10 affected offspring, and 12 unaffected offspring. The affected foals produced by these matings, including an Arabian-Saddlebred cross, also shared the same common ancestors on maternal and paternal sides of the pedigrees of affected foals produced by the 4 paternal half-sibling families.
Complex segregation analysis—The possibility that CA in Arabians is influenced by the action of a segregating locus of large effect can be examined statistically. Briefly, this technique, called complex segregation analysis, is intended to integrate Mendelian transmission genetics and models of penetrance with the patterns of covariance expected in polygenic inheritance. A more complete description of complex segregation analysis has been published.8 An outline of the criteria that must be satisfied before acceptance of the single major locus model is available.9 Adherence to these criteria reduces the number of false-positive results. Evaluation of the models necessary for complex segregation analysis was conducted by use of a computer software package.10,a
The goal of this strategy was to simultaneously estimate the posterior density for a polygenic contribution to disease along with the contributions of a putative Mendelian locus. Specifically, for this mixed-inheritance model, the strategy allowed the evaluation of a polygenic variance component, the additive and dominance contributions of a single locus (the parameters −a, d, and a for the putative major locus genotypes AA, AB, and BB, respectively), and the frequency of allele A of the putative major locus (defined as p). Given a scoring of binary phenotypes, where normal is 1 and affected is 0, the B allele represents the putative disease-enhancing allele. The softwarea used models the unobservable scale of this threshold trait such that the residual variance (ie, σe2) is fixed at 1.0.
Creation of a Gibbs sample requires several key assumptions about the behavior of the unknown parameters. Although a variety of models can be considered, all are some variant of the following: sex as a fixed effect with a flat (ie, uniform) prior density and the polygenic variance component with a flat prior density as well as flat prior densities for the additive, dominance, and allele frequency parameters. A Gibbs sample of 9,000 was generated, beginning with the creation of 350,000 samples, a burn-in (ie, how long to run the chain before keeping samples) of 50,000, and a sampling rate of every 100th Gibbs value. This process was repeated 2 additional times to create 3 replicate chains. The post-Gibbs analysis was implemented with statistical software packages.11,b,c Convergence of the Gibbs sampling process was performed by contrasting sample means from the first 10% of the sample with the last 50% of the sample.12 Also, from the 9,000 Gibbs samples, the mean, SD, median, and upper and lower limits of a 95% HDR were computed for each of the unknown parameters by use of software.d
Results
The pedigree of horses used in the present study consisted of 804 animals, 29 of which were listed as affected with CA. Inbreeding coefficients were calculated for 16 CA-affected horses and compared with a group of 16 horses from the general Arabian population. The mean inbreeding coefficient was 0.0871 for both groups, suggesting that all Arabians are inbred to the same degree and that CA-affected horses are not more inbred than are unaffected horses. Of the 29 horses affected with CA, 15 were male and 14 were female. The categorical model used for this dichotomous trait, as part of the complex segregation analysis in a threshold model, can be used to evaluate the difference between the risk of disease for males and the risk of disease for females. On this unobservable scale, the mean difference of the male effect minus the female effect was 0.18, with an SD of 0.29 (estimated 95% HDR, −0.35 to 0.77). A 95% HDR that spans the value of 0 indicates that sex of the offspring did not have a significant effect on the inheritance of CA. An X-linked mode of inheritance for CA was therefore excluded.
Results of the complex segregation analysis of the binary measure of CA were summarized (Table 1). Although a variety of genetic models were evaluated, for brevity, only those results where the putative major locus was thought to act in a recessive fashion (ie, horses homozygous for the CA allele [referred to as allele B] have an increased risk of disease, compared with those heterozygous for the CA allele) are reported. With the assumption that the alleles were transmitted in the usual Mendelian fashion, there was strong evidence for the presence of a major locus influencing expression of CA. Specifically, the 95% HDR region for the additive effect (0.71 to 3.23) of this putative locus did not overlap 0, nor did the variance attributed to this potential locus (0.50 to 5.29). Additional models of inheritance, in which the putative major locus was assumed to act in a dominant fashion and in which a and d were allowed to be estimated by the data (complete model), were created (Table 2). In contrast to the recessive model, the 95% HDR for the variance and a and d values in these scenarios spanned 0; therefore, the models were not significant.
Mixed-inheritance model parameters for CA in Arabians, determined from a data set obtained from 804 horses that included 29 CA-affected animals.*
| Model (type of transmission) | Variable | Polygenic variance | Locus variance | Additive effect (a) | τAA† | τAB | τBB | Allele frequency (q) |
|---|---|---|---|---|---|---|---|---|
| Recessive | Mean | 1.82 | 2.34 | 1.83 | 1 | 0.50 | 0 | 0.20 |
| major | Median | 1.74 | 1.94 | 1.70 | — | — | — | 0.16 |
| (Mendelian) | SD | 1.09 | 1.50 | 0.78 | — | — | — | 0.14 |
| Effective sample size | 5,618 | 5,833 | 4,856 | — | — | — | 4,886 | |
| Convergence score‡ (Pvalue) | −0.61 (0.54) | 0.24 (0.81) | 1.45 (0.15) | — | — | — | 1.36 (0.17) | |
| 95% HDR | 0.01 to 3.72 | 0.50 to 5.29 | 0.71 to 3.23 | — | — | — | 0.01 to 0.48 | |
| Recessive | Mean | 2.33 | 1.89 | 1.50 | 0.94 | 0.35 | 0.14 | 0.16 |
| major | Median | 2.41 | 1.56 | 1.46 | 0.94 | 0.34 | 0.12 | 0.16 |
| (non-Mendelian) | SD | 1.05 | 1.18 | 0.39 | 0.04 | 0.17 | 0.11 | 0.03 |
| Effective sample size of Gibbs sampling | 5,027 | 4,726 | 4,669 | 3,784 | 3,106 | 3,869 | 4,861 | |
| Convergence score‡ (Pvalue) | 1.66 (0.10) | −1.52 (0.13) | −1.28 (0.20) | 1.01 (0.31) | −0.39 (0.70) | −0.17 (0.86) | 1.01 (0.32) | |
| 95% HDR | 0.42 to 3.99 | 0.47 to 4.41 | 0.81 to 2.28 | 0.78 to 1.00 | 0.36 to 0.67 | 0.00 to 0.34 | 0.09 to 0.22 |
Estimates are taken from a Gibbs sample of 9,000 values.
Mendelian transmission parameter; the probability of transmitting an A allele. For Mendelian transmission, these values are fixed as 1.0, 0.50, and 0.0 for putative major genotypes AA, AB, and BB, respectively, with BB being affected. Non-Mendelian transmission implies estimation of these values from the data.
Convergence score is the Gibbs sample convergence statistic.
— = Not applicable.
Mixed-inheritance model parameters for CA in Arabians, determined from a data set obtained from 804 horses that included 29 CA-affected animals.*
| Model (type of transmission) | Variable | Polygenic variance | Locus variance | Additive Effect (a) | Dominance effect (d) | Allele frequency (p) |
|---|---|---|---|---|---|---|
| Dominant major locus (Mendelian) | Mean | 0.83 | 0.50 | 0.63 | — | 0.44 |
| SD | 0.91 | 0.94 | 0.55 | — | 0.27 | |
| 95% HDR | 0.00 to 2.99 | 0.00 to 2.23 | 0.00 to 1.72 | — | 0.00 to 0.93 | |
| Complete major locus (Mendelian) | Mean | 0.93 | 0.50 | 0.65 | −0.04 | 0.49 |
| SD | 0.95 | 0.64 | 0.51 | 1.08 | 0.29 | |
| 95% HDR | 0.00 to 3.09 | 0.00 to 1.74 | 0.00 to 1.65 | −2.10 to 2.10 | 0.05 to 1.00 |
See Table 1 for key.
With the assumption of the locus to be transmitted in a non-Mendelian fashion, the data analysis established that this trait is influenced by a single locus with a large effect (Table 1). Fitting a model of non-Mendelian inheritance is one of the requirements of complex segregation analysis,9 and this is done to decrease the probability of a false-positive declaration of the presence of a major locus. Specifically, we fit the data to a non-Mendelian model to determine whether the estimated transmission probabilities were significantly different from the expected 1, 0.5, and 0 for transmission of one of the alleles of the putative major locus. The 95% HDR for the transmission probabilities indicated that the estimates were within the expected Mendelian values and were simultaneously distinct from each other. For example, the expected transmission probability for the putative heterozygote should be 0.5, and the 95% HDR for our estimated transmission probability was between 0.36 and 0.67, an interval that overlaps 0.5 but does not overlap the transmission probabilities of the other genotypic classes.
Discussion
The objective of the present study was to use statistical analysis to elucidate the most likely mode of inheritance for CA in Arabians. The finding that the 95% HDR region for the additive effect of the putative locus and the variance attributed to it did not overlap 0 provided strong evidence that CA is influenced by a single locus with large effect. Additionally, the transmission probabilities that would be expected if CA were caused by a single recessive locus were within the range delineated by the 95% HDR for predicted transmission probabilities and did not overlap with each other. Analysis of the data revealed that sex did not have a role in the inheritance of CA. Together, these results provide statistical evidence that CA in Arabians is caused by a single, autosomal recessive locus. To our knowledge, this represents the first statistical analysis of the mode of inheritance of CA in Arabians.
The frequency of the putative recessive allele (q) was determined to be 0.16 in the data set in the present study. It is important to note that this allele frequency was specific to these families of horses and is not necessarily representative of the Arabian breed as a whole. The Arabian breed has been subject to population substructuring that has led to the selective breeding of animals within particular bloodlines, and matings are more common between horses that have ancestors within these subpopulations. For example, Arabians of Egyptian bloodlines are more often mated to each other than to Arabians of Polish or Spanish bloodlines. Therefore, the frequency of the putative CA allele could differ among these groups as certain horses are more prevalent in certain subpopulation pedigrees than others. However, the CA-affected horses used for this research project represented a variety of these bloodlines and were not specific to 1 group of Arabians, which suggests that either the mutation causative of CA developed prior to the geographic segregation of the breed or that particular horses carrying the mutation have been used for breeding within many of these various bloodlines.
The earliest birth year of a CA-affected foal among the horses that were not part of the Veterinary Genetics Laboratory herd (which was specifically bred for CA) was 2000. Since that time, > 76,000 Arabians have been registered with the Arabian Horse Association. Therefore, CA appears to be relatively rare in the breed, although misdiagnosis or nondiagnosis of the disease is likely because of an inability to conclusively identify the disease before death. Estimation of the carrier frequency of the CA allele in Arabians is therefore difficult to determine because of the low frequency of reported affected foals and the fact that the disease is likely more prevalent in certain bloodlines within the breed. The carrier frequency in the data set used in the present study was 26.9%, but this value cannot be extrapolated to the entire Arabian population. The popularity of a particular breed of horse as breeding animals, especially stallions, can vary widely between subpopulations, leading to differences in allele frequencies between groups. The high frequency of inbreeding in particular subpopulations or families can also lead to an increase in the frequency of an allele and therefore the number of carriers of that allele.
The results of the present study have provided breeders of Arabians with a means to estimate the risk of producing a foal affected with CA from a given mating. An autosomal recessive mode of inheritance can now be applied to matings between horses known to have produced affected offspring. A CA carrier will pass on the defective allele to 50% of its offspring; therefore, there is a 50% chance that a mating involving an unaffected horse that has produced CA-affected offspring will result in a carrier foal. With 2 known carriers of the disease, a carrier foal will be produced from 50% of matings and a CA-affected foal will be produced from 25% of the matings. Breeders can therefore make informed choices about selection of mating pairs and can avoid matings between horses known to have produced CA-affected foals. Removing carrier horses from the breeding population can reduce the frequency of CA in the Arabian breed; however, such horses could have other desirable traits that would also be removed from the gene pool. Without a diagnostic test for CA, complete elimination of the disease is difficult because carriers can pass the CA allele in an undetected manner through many generations before producing an affected foal.
Results of the present study have also provided the foundation for identifying the gene and mutation that cause CA. A known mode of inheritance for the disease will allow linkage mapping of the trait within the families included in data set used in the present study. Identification of the causative mutation of CA may lead to the development of a specific diagnostic genetic test for accurate identification of carrier horses in the Arabian breed.
ABBREVIATIONS
| CA | Cerebellar abiotrophy |
| HDR | Highest density region |
iBay, version 1.33, Janss Biostatistics, Leiden, Netherlands.
coda: output analysis and diagnostics for MCMC, R, version 0.13–4, R Foundation for Statistical Computing, Vienna, Austria. Available at: www.r-project.org/. Accessed May 1, 2008.
R, version 0.13–4, R Foundation for Statistical Computing, Vienna, Austria. Available at: www.r-project.org/. Accessed May 1, 2008.
hdrcde: highest density regions and conditional density estimation, package for R, version 2.09, Monash University, Melbourne, VIC, Australia. Available at: www.robhyndman.info/Rlibrary/hdrcde. Accessed Nov 1, 2009.
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