# Discriminant Canonical Analysis of the Contribution of Spanish and Arabian Purebred Horses to the Genetic Diversity and Population Structure of Hispano-Arabian Horses

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Registries and Software Tool

#### 2.2. Genealogical Information Evolution

_{b}is the total number of ancestors of the animal, b and g

_{ab}is the number of generations between b and its ancestor a [20]; and the pedigree information quality assessing the proportion of pedigree registered known parents, grandparents, great-grandparents, and great-great-grandparents. Generation intervals [21] and the mean age of parents when their offspring were born were calculated for the 4 gametic pathways: stallion to colt and stallion to filly and mare to colt and mare to filly, from every animal’s date of birth registry together with those of its parents’. The stallion/mare ratio was calculated considering the percentage of mares and stallions with breeding progeny and the number of breeding animals selected.

#### 2.3. Inbreeding, Coancestry, and Assortative Mating Degree

_{b}is the number of complete equivalent generations and F

_{b}is the inbreeding coefficient of the individual b. The individual rate of coancestry ($\overline{\Delta C}$) for the generation was computed following the methods in Cervantes et al. [25] through ${C}_{ba}=1-\sqrt[\frac{tb+ta}{2}]{1-{C}_{ba}}$, where t

_{b}and t

_{a}are the number of equivalent complete generations and C

_{ba}is the coancestry coefficient for the individuals b and a. The degree of assortative mating (non-random mating of individuals having more genetic or phenotypic traits in common than likely in random or disassortative mating), was computed following the methods of Caballero and Toro [26], through $\left(1-F\right)=\left(1-C\right)\left(1-\alpha \right)$ [27,28].

#### 2.4. Ancestral Contributions and Probabilities of Gene Origin

_{e}), was calculated using ${f}_{e}=\frac{1}{{{\displaystyle \sum}}_{k=1}^{f}{q}_{k}^{2}}$, where q

_{k}is the probability of gene origin of the k

^{th}founder and f is the real number of founders [29]. The effective number of ancestors (f

_{a}), was determined by ${f}_{a}=\frac{1}{{{\displaystyle \sum}}_{k=1}^{f}{p}_{k}^{2}}$ where p

_{k}is the marginal contribution of a k

^{th}ancestor [20]. The effective number of founder genomes (f

_{g}) was computed as the inverse of twice the average coancestry as reported in Caballero and Toro [26]. The expected marginal contribution of each major ancestor j was computed as Boichard, et al. [20] and the contributions to inbreeding of nodal common ancestors (inbreeding loops), were computed according to Colleau and Sargolzaei [30]. The mean effective population size ($\overline{{N}_{e}}$) [27] was calculated as $\overline{{N}_{e}}=\frac{1}{2\overline{\Delta IBD}}$. The number of equivalent subpopulations was computed according to Cervantes, et al. [31] using $S=\frac{\overline{{N}_{e}{C}_{i}}}{{N}_{e}{F}_{i}}$, where $\overline{{N}_{e}{C}_{i}}=\frac{1}{\left(2\overline{\Delta C}\right)}$, is the mean effective population size considering the coancestry coefficient [32] and $\overline{{N}_{e}{F}_{i}}=\frac{1}{\left(2\overline{\Delta F}\right)}$, considering the inbreeding coefficient. Genetic diversity (GD) was calculated using $GD=1-\frac{1}{2{f}_{g}}$. GD lost in the population since the founder generation was estimated using $1-GD$. GD loss derived from the unequal contribution of founders was estimated as Caballero and Toro [26] using $1-G{D}^{*}$, where $G{D}^{*}=1-\frac{1}{2{f}_{e}}$. The difference between GD and GD* indicates the GD loss owed to genetic drift accumulated since the foundation of the population [29], and the effective number of non-founders (N

_{ef}) was computed using ${N}_{ef}=\frac{1}{\frac{1}{{f}_{ge}}-\frac{1}{{f}_{e}}}$ considering the formula proposed by Caballero and Toro [26]. CFC version 1.0. was used to perform the analysis of ancestral contributions and probabilities of gene origin [33].

#### 2.5. Canonical Discriminant Analysis (CDA)

#### 2.5.1. Multicollinearity Preliminary Testing

^{2}). A recommended maximum VIF value of 5 [43] and even 4 [44] can be found in the literature. VIF was computed using the Linear routine of the Regression package of the software SPSS, version 25.0 [40].

#### 2.5.2. Canonical Correlation Dimension Determination

#### 2.5.3. Canonical Discriminant Analysis Efficiency

^{2}. When significance is below 0.05, the corresponding function can be concluded to explain group adscription well [49].

#### 2.5.4. Canonical Discriminant Analysis Model Reliability

#### 2.5.5. Variable Dimensionality Reduction

#### 2.5.6. Canonical Coefficients and Loading Interpretation and Spatial Representation

^{−1}the inverse of the covariance matrix of measured variable x and $\overline{{Y}_{i}}$ and $\overline{{Y}_{j}}$ are the means of variable x in the ith and jth populations, respectively. The Mahalanobis squared distance, defined as the square of the distance between centroids, was used to determine the existence of significant differences in the values for genetic diversity parameters across the three breeds [55]. Additionally, to confirm such differences, Nei’s minimum genetic distances [56] among the individuals of the breeds were computed. Dendrograms for PRá, PRE, and Há breeds were constructed using the construct Unweighted Pair-Group Method using Arithmetic averages (UPGMA) Tree task from the Phylogeny procedure of MEGA X 10.0.5.

#### 2.5.7. Discriminant Function Cross-Validation

^{2}/N(K − 1)

^{2}with one degree of freedom at a significance of 0.01. Under this assumption, when Press’ Q exceeds the critical value of χ

^{2}= 6.63, cross-validated classification can be regarded as significantly better than chance.

## 3. Results

#### 3.1. Genealogical Information Evolution

#### 3.2. Inbreeding, Coancestry/Kinship and Degree of Non-Random Mating

#### 3.3. Ancestral Contributions and Probabilities of Gene Origin

_{g}) in the historical PRá, PRE, and Há horse breeds was 11.02, 7.90, and 7.61, respectively. Current f

_{g}was 7.45, 13.47, and 13.94 for PRá, PRE, and Há horse breeds, respectively.

#### 3.4. Genetic Relationships between Breeds

_{IT}) was 0.03 for the historical population and 0.04 for the currently living population when breed was chosen as the subdivision criteria. The inbreeding coefficient relative to the subpopulation (F

_{IS}) varied from 0.02 for the historical population to 0.01 for the current population (Supplementary Table S4). The correlation between random gametes drawn from the subpopulation relative to the total population (F

_{ST}) was 0.01 for the historical population and 0.03 for the currently living population.

#### 3.5. Variable Dimensionality Reduction

#### 3.6. Canonical Discriminant Analysis

#### 3.6.1. Canonical Discriminant Analysis Model Reliability

^{2}) and variance inflation factor (VIF) were analyzed to identify those variables that were responsible for multicollinearity between variables. VIF estimation suggested the parameters of inbreeding (F, %) and equivalent generations (VIF > 4) should not be considered in the analyses. After the removal of these variance explanatory redundant variables, the results for tolerance and VIF can be observed in Table 8.

#### 3.6.2. Canonical Coefficients and Loading Interpretation and Spatial Representation

#### 3.6.3. Discriminant Function Cross-Validation

^{2}critical value for one degree of freedom at a 95% confidence level (p < 0.01), predictions were significantly better than chance. Hence, there is a correct classification rate of at least 50% [64].

## 4. Discussion

_{ef}) for PRá, PRE, and Há horse breed were 10, 11.40, and 23.57, respectively. These values support those reported in the literature [26,93], even more so when these values are evaluated in the context of the inbreeding levels presented for the three horse breeds discussed. In line with these results, we may determine that relative founder contributions may tend to stabilize after a short number of generations, which has been described in Thoroughbred horses [94]. Either the population is closed or remains open, as is the case of the Há horse breed [17,92].

_{e}), where N

_{e}is the effective population size.

_{e}is complex, but certain criterion must be considered to permit a correct interpretation of this parameter. For instance, the sex ratio must be equal and individuals must randomly mate. A number of additional “ideal” characteristics could be stated. In practice, N

_{e}is always smaller than the actual number of breeding individuals. Thus, N

_{e}must equal at least 50 if our aim is to keep inbreeding rate below 1%. Still, even if inbreeding rate is 1%, the loss of genetic diversity is appreciable after a few generations, and a gradual erosion of genetic variation cannot be avoided. Eventually, the population will become virtually homozygous, the time depending on N

_{e}. Consequently, 1% criterion must be viewed as short-term criterion. A population with an effective size of 50 will lose about a quarter of its genetic diversity after 20–30 generations, and along with this, much of its capacity to adapt to changing conditions [97].

_{e}must be increased. FAO/UNEP [95] suggests that G must approximately equal to N

_{e}, G being the number of generations the population is likely to retain its fitness at a relatively high level. Still, to conserve short-term fitness, or to maintain short-term fitness in captive populations other criteria must be accounted for, given effective population size is considerably affected by unbalanced sex ratios, population size evolution, by a non-random distribution of progeny among families, and other characteristics of the breeding systems implemented.

_{e}and f

_{a}could be used to assess the occurrence of changes in genetic drift and recent bottlenecks in a population, which are corroborated if (f

_{e}/f

_{a})>1, respectively. In our study, f

_{e}and f

_{a}were 2.35, 1.54, and 1.48, respectively, for each of the horse breeds considered (PRá, PRE, and Há). This finding is indicative of the fact that genetic drift may not have been stable in the three horse breeds studied, with a progressive loss of founder representation, which had previously been reported in the literature [93,101]. Despite these values for f

_{e}/f

_{a}, our study confirms that an increasing trend has been described by GCI over time. Hence, the fact that founder representation is being progressively gained, not only in the Há horse breed, but also in its two ancestor breeds, may derive from the attempts of breeders and breeding associations to plan matings, trying to compensate for the aforementioned loss of founder representation.

## 5. Conclusions

## Supplementary Materials

_{IS}(inbreeding coefficient relative to the subpopulation), F

_{ST}(Correlation between random gametes drawn from the subpopulation relative to the total population) and F

_{IT}(Inbreeding coefficient relative to the total population).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Shrestha, J. Conserving domestic animal diversity among composite populations. Small Rumin. Res.
**2005**, 56, 3–20. [Google Scholar] [CrossRef] - Gour, D.S.; Malik, G.; Ahlawat, S.; Pandey, A.; Sharma, R.; Gupta, N.; Gupta, S.; Bisen, P.; Kumar, D. Analysis of genetic structure of Jamunapari goats by microsatellite markers. Small Rumin. Res.
**2006**, 66, 140–149. [Google Scholar] [CrossRef] - Roux, I. Le Cheval Barbe. Destrier de l’antique Libye et de la Conquête Musulmane. Sa Descendance et son Expansion en Amérique, son Harnachement; Jean Maisonneuve: Paris, France, 1987; p. 173. [Google Scholar]
- De Andrade, R. Alrededor del Caballo Español; Sociedade Astória, Limitada: Lisboa, Portugal, 1954; p. 867. [Google Scholar]
- Espeso del Pozo, G. Los caballos eumétricos de España destinados a la exportación. Ganad. Rev. Nac. Sind. Vert. Ganad.
**1950**, 81, 149–152. [Google Scholar] - Lloyd, A.S.; Martin, J.E.; Bornett-Gauci, H.L.I.; Wilkinson, R.G. Horse personality: Variation between breeds. Appl. Anim. Behav. Sci.
**2008**, 112, 369–383. [Google Scholar] [CrossRef] - Rodríguez Gallardo, P.P.; Aguilar Sánchez, P.; Vega-Pla, J.L.; De Andrés Cara, D.F. Blood group and protein polymorphism gene frequencies for the Andalusian horse breed. A comparison with four American horse breeds. Arch. Zootec.
**1992**, 41, 433–442. [Google Scholar] - Ouragh, L.; Mériaux, J.C.; Braun, J.P. Genetic blood markers in Arabian, Barb and Arab-Barb horses in Morocco. Anim. Genet.
**1994**, 25, 45–47. [Google Scholar] [CrossRef] - Bowling, A.T.; Clark, R.S. Blood group and protein polymorphism gene frequencies for seven breeds of horses in the United States. Anim. Blood Groups Biochem. Genet.
**1985**, 16, 93–108. [Google Scholar] [CrossRef] - Álvarez de Morales, C. Un Tratado Granadino de Hipiatría; Universidad de Granada: Granada, Spain, 1987; pp. 305–312. [Google Scholar]
- Al-‘Awwām, I. Kitāb al-Filāḥa (Libro de Agricultura). Preliminary Study and Notes; Ministerio de Agricultura, Pesca y Alimentación, Ministerio de Asuntos Exteriores: Madrid, Spain, 1802. [Google Scholar]
- Pleguezuelo, J.A. El Caballo Español e Hispano-árabe en la Historia y en los Manuscritos de Al-Ándalus; Editorial Almuzara: Palma del Río, Córdoba, Spain, 2006. [Google Scholar]
- Provençal, E.L.; Al-Himyari, A.A.A. La Péninsule Ibérique au Moyen Age: D’après le Kitab ar-Rawd al-Mi’tar fi Habar al-Aktar d’Ibn’Abd al-Mun’im al-Himyari; E.J. Brill: Leiden, The Netherlands, 1938. [Google Scholar]
- Herrera García, M.; López Rodríguez, J.M. The special protection horse breeds: The Marismeña horse breed, The Andalusian ass breed and the Hispano-Arabe horse. In Andalusian Livestock Heritage, 2: Livestock Breeds from Andalusia [Spain]; Serrano, E.R., Córdoba, M.V., Eds.; Junta de Andalucía: Sevilla, Spain, 2007; pp. 511–558. [Google Scholar]
- Gómez, M.; León, J.; Delgado, J. Demographic analysis of the equine breed Spanish-Arabic. Arch. Zootec.
**2011**, 60, 341–344. [Google Scholar] [CrossRef][Green Version] - Navas, F.J.; Jordana, J.; León, J.M.; Barba, C.; Delgado, J.V. A model to infer the demographic structure evolution of endangered donkey populations. Animal
**2017**, 11, 2129–2138. [Google Scholar] [CrossRef] - Cervantes, I.; Molina, A.; Goyache, F.; Gutiérrez, J.P.; Valera, M. Population history and genetic variability in the Spanish Arab Horse assessed via pedigree analysis. Livest. Sci.
**2008**, 113, 24–33. [Google Scholar] [CrossRef][Green Version] - Gutiérrez, J.P.; Marmi, J.; Goyache, F.; Jordana, J. Pedigree information reveals moderate to high levels of inbreeding and a weak population structure in the endangered Catalonian donkey breed. J. Anim. Breed. Genet.
**2005**, 122, 378–386. [Google Scholar] [CrossRef] [PubMed][Green Version] - Maignel, L.; Boichard, D.; Verrier, E. Genetic variability of French dairy breeds estimated from pedigree information. Interbull Bull.
**1996**, 14, 49–54. [Google Scholar] - Boichard, D.; Maignel, L.; Verrier, E. The value of using probabilities of gene origin to measure genetic variability in a population. Genet. Sel. Evol.
**1997**, 29, 5–23. [Google Scholar] [CrossRef] - James, J.W. A note on selection differential and generation length when generations overlap. Anim. Sci.
**1977**, 24, 109–112. [Google Scholar] [CrossRef] - Meuwissen, T.H.E.; Luo, Z. Computing inbreeding coefficients in large populations. Genet. Sel. Evol.
**1992**, 24, 305–313. [Google Scholar] [CrossRef] - Leroy, G.; Mary-Huard, T.; Verrier, E.; Danvy, S.; Charvolin, E.; Danchin-Burge, C. Methods to estimate effective population size using pedigree data: Examples in dog, sheep, cattle and horse. Genet. Sel. Evol.
**2013**, 45, 1–10. [Google Scholar] [CrossRef][Green Version] - Gutiérrez, J.P.; Cervantes, I.; Goyache, F. Improving the estimation of realized effective population sizes in farm animals. J. Anim. Breed. Genet.
**2009**, 126, 327–332. [Google Scholar] [CrossRef] [PubMed] - Cervantes, I.; Goyache, F.; Molina, A.; Valera, M.; Gutierrez, J.P. Estimation of effective population size from the rate of coancestry in pedigreed populations. J. Anim. Breed. Genet.
**2011**, 128, 56–63. [Google Scholar] [CrossRef] - Caballero, A.; Toro, M.A. Interrelations between effective population size and other pedigree tools for the management of conserved populations. Genet. Res.
**2000**, 75, 331–343. [Google Scholar] [CrossRef] - Wright, S. Evolution and the Genetics of Populations. Theory of Gene Frequencies; University of Chicago Press: Chicago, IL, USA, 1969. [Google Scholar]
- Jiang, Y.; Bolnick, D.I.; Kirkpatrick, M. Assortative Mating in Animals. Am. Nat.
**2013**, 181, E125–E138. [Google Scholar] [CrossRef][Green Version] - Lacy, R.C. Analysis of founder representation in pedigrees: Founder equivalents and founder genome equivalents. Zoo Biol.
**1989**, 8, 111–123. [Google Scholar] [CrossRef] - Colleau, J.J.; Sargolzaei, M. A proximal decomposition of inbreeding, coancestry and contributions. Genet. Res.
**2008**, 90, 191–198. [Google Scholar] [CrossRef] - Cervantes, I.; Goyache, F.; Molina, A.; Valera, M.; Gutiérrez, J.P. Application of individual increase in inbreeding to estimate realized effective sizes from real pedigrees. J. Anim. Breed. Genet.
**2008**, 125, 301–310. [Google Scholar] [CrossRef] [PubMed][Green Version] - De La Rosa, A.M.; Cervantes, I.; Gutiérrez, J. Equivalent effective population size mating as a useful tool in the genetic management of the Ibicenco rabbit breed (Conill Pages d’Eivissa). Czech J. Anim. Sci.
**2016**, 61, 108–116. [Google Scholar] [CrossRef] - Sargolzaei, M.; Iwaisaki, H.; Colleau, J. CFC: A tool for monitoring genetic diversity. In Proceedings of the 8th World Congress on Genetics Applied to Livestock Production, Belo Horizonte, Brazil, 13–18 August 2006. [Google Scholar]
- Sánchez, A.; López, L. Clasificación y ordenación de la vegetación del norte de la Sierra Nevada, a lo largo de un gradiente altitudinal. An. Inst. Biol. Univ. Nac. Autón. Méx. Ser. Bot.
**2003**, 74, 47–71. [Google Scholar] - Cuadras, C.M.; Augé, J. A continuous general multivariate distribution and its properties. Commun. Stat. Theory Methods
**1981**, 10, 339–353. [Google Scholar] [CrossRef] - Cuadras, C.M. Métodos de Análisis Multivariante; CMC Editions Barcelona: Barcelona, Spain, 1981. [Google Scholar]
- Johnson, R.A.; Wichern, D.W. Applied Multivariate Statistical Analysis; Prentice Hall Inc.: Englewood Cliffs, NJ, USA, 1982. [Google Scholar]
- Roemisch, U.; Jaeger, H.; Mateev, P. Stepwise Regularized Discriminant Analysis for Determining the Origin of Authentic Wines from different Vintages. In Proceedings of the 5th Conference of Eastern Mediterranean Region- International Biometric Society, Istanbul, Turkey, 10–14 May 2009. [Google Scholar]
- Tai, F.; Pan, W. Incorporating prior knowledge of gene functional groups into regularized discriminant analysis of microarray data. Bioinformatics
**2007**, 23, 3170–3177. [Google Scholar] [CrossRef][Green Version] - IBM SPSS Statistics for Windows, 25.0; IBM Corp: Armonk, NY, USA, 2017.
- Poulsen, J.; French, A. Discriminant function analysis. In Biology 710—Advanced Biometry; San Francisco State University: San Francisco, CA, USA, 2008. [Google Scholar]
- Addinsoft XLSTAT; Pearson Edition: Paris, France, 2014.
- Rogerson, P.A. Data Reduction: Factor Analysis and Cluster Analysis; Sage: London, UK, 2001; pp. 192–197. [Google Scholar]
- Pan, Y.; Jackson, R.T. Ethnic difference in the relationship between acute inflammation and serum ferritin in US adult males. Epidemiol. Infect.
**2008**, 136, 421–431. [Google Scholar] [CrossRef] - Tabachnick, B.; Fidell, L. Using Multivariate Statistics; Harper Collins: New York, NY, USA, 1996. [Google Scholar]
- Sherry, A.; Henson, R.K. Conducting and interpreting canonical correlation analysis in personality research: A user-friendly primer. J. Pers. Assess.
**2005**, 84, 37–48. [Google Scholar] [CrossRef][Green Version] - Thompson, B. Canonical Correlation Analysis: Uses and Interpretation; Sage: London, UK, 1984. [Google Scholar]
- Financial & Programming. Canonical Correlation. 2005. Available online: https://rabbitshin.tistory.com/112 (accessed on 8 December 2020).
- OriginLab Corporation. Interpreting Results of Discriminant Analysis. In Multivariate Analysis; OriginLab: Northampton, MA, USA, 2019. [Google Scholar]
- Hahs-Vaughn, D.L. Applied Multivariate Statistical Concepts; Routledge & CRC Press: Abingdon, UK, 2016. [Google Scholar]
- Tabachnick, B.G.; Fidell, L.S. Principal components and factor analysis. In Using Multivariate Statistics; Harper Collins: New York, NY, USA, 2001; pp. 582–633. [Google Scholar]
- Pillai, K. Some new test criteria in multivariate analysis. Ann. Math. Stat.
**1955**, 26, 117–121. [Google Scholar] [CrossRef] - IBM Corp. Technote 1479621. Available online: http://www-01.ibm.com/support/docview.wss?uid=swg21475033 (accessed on 8 December 2020).
- Manly, B.F.J. Multivariate Statistical Methods: A Primer; Chapman and Hall: London, UK, 1986; p. 159. [Google Scholar]
- Silva, A.P.d.; Imhoff, S.; Giarola, N.F.B.; Tormena, C.A. Análisis multivariado y univariado en la discriminación de sistemas de uso de suelos del centro de Santa Fe. Edafología
**2001**, 8, 21–34. [Google Scholar] - Nei, M. Molecular Evolutionary Genetics; Columbia University Press: New York, NY, USA, 1987. [Google Scholar]
- Ramayah, T.; Ahmad, N.H.; Halim, H.A.; Zainal, S.R.M.; Lo, M.-C. Discriminant analysis: An illustrated example. Afr. J. Bus. Manag.
**2010**, 4, 1654–1667. [Google Scholar] - Schneider, J. Cross validation. A Locally Weighted Learning Tutorial Using Vizier. Tech. Report, CMU-RI-TR-00–18; Robotics Institute, Carnegie Mellon University: Pittsburgh, PA, USA, 1997. [Google Scholar]
- Friel, C.M. Notes on Discriminat Analysis; Sam Houston State University: Huntsville, TX, USA, 2002. [Google Scholar]
- Palomo, A.G. Fin de una crisis de caballo. In National Edition of 27 Novemeber, 2015; El País: Málaga, Spain, 2015. [Google Scholar]
- Fernandez de Castillejo, A. La cría de caballos de raza repunta tras una dura crisis. In Ganadería; Diario de Sevilla: Seville, Spain, 2016. [Google Scholar]
- Sakthivel, M.; Balasubramanyam, D.; Kumarasamy, P.; Raja, A.; Anilkumar, R.; Gopi, H.; Devaki, A. Genetic structure of a small closed population of the New Zealand white rabbit through pedigree analyses. World Rabbit Sci.
**2018**, 26, 101–112. [Google Scholar] [CrossRef] - Beuchat, C. COI FAQS: Understanding the Coefficient of Inbreeding. Available online: www.instituteofcaninebiology.org/blog/coi-faqs-understanding-the-coefficient-of-inbreeding (accessed on 28 December 2020).
- Chan, Y. Biostatistics 303. Discriminant analysis. Singap. Med. J.
**2005**, 46, 54. [Google Scholar] - Canon, J.; Checa, M.; Carleos, C.; Vega-Pla, J.; Vallejo, M.; Dunner, S. The genetic structure of Spanish Celtic horse breeds inferred from microsatellite data. Anim. Genet.
**2000**, 31, 39–48. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pablo Gómez, M.; Landi, V.; Martínez, A.M.; Gómez Carpio, M.; Nogales Baena, S.; Delgado Bermejo, J.V.; Oom, M.d.M.; Luis, C.; Ouragh, L.; Vega-Pla, J.L. Genetic diversity of the semi-feral Marismeño horse breed assessed with microsatellites. Ital. J. Anim. Sci.
**2017**, 16, 14–21. [Google Scholar] [CrossRef][Green Version] - Aparicio Sánchez, G. Zootecnia Especial. Etnología Compendiada; Facultad de Veterinaria: Córdoba, Spain, 1960. [Google Scholar]
- Jónsson, M. The expulsión of the Moriscos from Spain in 1609–1614: The destruction of an Islamic periphery. J. Glob. Hist.
**2007**, 2, 195. [Google Scholar] [CrossRef] - Valera, M.; Molina, A.; Gutiérrez, J.P.; Gómez, J.; Goyache, F. Pedigree analysis in the Andalusian horse: Population structure, genetic variability and influence of the Carthusian strain. Livest. Prod. Sci.
**2005**, 95, 57–66. [Google Scholar] [CrossRef][Green Version] - Cervantes, I.; Gutiérrez, J.; Molina, A.; Goyache, F.; Valera, M. Genealogical analyses in open populations: The case of three Arab-derived Spanish horse breeds. J. Anim. Breed. Genet.
**2009**, 126, 335–347. [Google Scholar] [CrossRef] - Vallecillo, A.; Pérez-Marín, C.; Henríquez, O.; Delgado, J.; Cabello, A. Potencial de la transferencia embrionaria para la conservación del caballo de raza hispano-árabe. Arch. Zootec.
**2007**, 56, 581–585. [Google Scholar] - Giontella, A.; Pieramati, C.; Silvestrelli, M.; Sarti, F. Analysis of founders and performance test effects on an autochthonous horse population through pedigree analysis: Structure, genetic variability and inbreeding. Animal
**2019**, 13, 15. [Google Scholar] [CrossRef] - Duru, S. Pedigree analysis of the Turkish Arab horse population: Structure, inbreeding and genetic variability. Animal
**2017**, 11, 1449. [Google Scholar] [CrossRef] [PubMed] - Mancin, E.; Ablondi, M.; Mantovani, R.; Pigozzi, G.; Sabbioni, A.; Sartori, C. Genetic Variability in the Italian Heavy Draught Horse from Pedigree Data and Genomic Information. Animals
**2020**, 10, 1310. [Google Scholar] [CrossRef] [PubMed] - Todd, E.T.; Ho, S.Y.W.; Thomson, P.C.; Ang, R.A.; Velie, B.D.; Hamilton, N.A. Founder-specific inbreeding depression affects racing performance in Thoroughbred horses. Sci. Rep.
**2018**, 8, 6167. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gregory, K.; Cundiff, L.V.; Koch, R.M. Composite Breeds-What Does the Research Tell Us? In Proceedings of the The Range Beef Cow Symposium XIII, Cheyenne, WY, USA, 6–8 December 1993. [Google Scholar]
- Santana, M., Jr.; Oliveira, P.S.; Eler, J.P.; Gutiérrez, J.; Ferraz, J.B.S. Pedigree analysis and inbreeding depression on growth traits in Brazilian Marchigiana and Bonsmara breeds. J. Anim. Sci.
**2012**, 90, 99–108. [Google Scholar] [CrossRef] - Parland, S.M.; Kearney, J.F.; Rath, M.; Berry, D.P. Inbreeding Effects on Milk Production, Calving Performance, Fertility, and Conformation in Irish Holstein-Friesians. J. Dairy Sci.
**2007**, 90, 4411–4419. [Google Scholar] [CrossRef] - Norén, K.; Godoy, E.; Dalén, L.; Meijer, T.; Angerbjörn, A. Inbreeding depression in a critically endangered carnivore. Mol. Ecol.
**2016**, 25, 3309–3318. [Google Scholar] [CrossRef] - Navas González, F.J.; Jordana Vidal, J.; León Jurado, J.M.; McLean, A.K.; Delgado Bermejo, J.V. Nonparametric analysis of noncognitive determinants of response type, intensity, mood, and learning in donkeys (Equus asinus). J. Vet. Behav.
**2020**, 40, 21–35. [Google Scholar] [CrossRef] - Bittles, A.H.; Black, M.L. Evolution in health and medicine Sackler colloquium: Consanguinity, human evolution, and complex diseases. Proc. Natl. Acad. Sci. USA
**2010**, 107, 1779–1786. [Google Scholar] [CrossRef][Green Version] - Alderson, G. A system to maximize the maintenance of genetic variability in small populations. In Genetic Conservation of Domestic Livestock II; Alderson, L., Bodo, I., Eds.; CABI: Wallingford, UK; pp. 18–29.
- IDAD: Initiative for Domestic Animal Diversity. Secondary Guidelines for Development of National Farm Animal Genetic Resources Management Plans: Management of Small Populations at Risk; FAO: Rome, Italy, 1998. [Google Scholar]
- Fernández, J.; Villanueva, B.; Pong-Wong, R.; Toro, M.Á. Efficiency of the Use of Pedigree and Molecular Marker Information in Conservation Programs. Genetics
**2005**, 170, 1313–1321. [Google Scholar] [CrossRef][Green Version] - Fernández, J.; Toro, M.; Caballero, A. Management of subdivided populations in conservation programs: Development of a novel dynamic system. Genetics
**2008**, 179, 683–692. [Google Scholar] [CrossRef] [PubMed][Green Version] - Oldenbroek, K. Utilisation and Conservation of Farm Animal Genetic Resources; Wageningen Academic Publishers: Wageningen, The Netherlands, 2007. [Google Scholar]
- Villanueva, B.; Pong-Wong, R.; Woolliams, J.; Avendaño, S. Managing genetic resources in selected and conserved populations. BSAS Occas. Publ.
**2004**, 113–132. [Google Scholar] [CrossRef] - Weigel, K. Controlling inbreeding in modern breeding programs. J. Dairy Sci.
**2001**, 84, E177–E184. [Google Scholar] [CrossRef] - Ablondi, M.; Vasini, M.; Beretti, V.; Superchi, P.; Sabbioni, A. Exploring genetic diversity in an Italian horse native breed to develop strategies for preservation and management. J. Anim. Breed. Genet.
**2018**, 135, 450–459. [Google Scholar] [CrossRef] - Goyache, F.; Fernández, I.; Álvarez, I.; Gutiérrez, J.; Royo, L. Pedigree analysis of the Asturcón pony in a partially open situation of its studbook. In Proceedings of the XI Jornadas sobre Producción Animal, Zaragoza, Spain, 11–12 May 2005; pp. 108–110. [Google Scholar]
- McManus, C.; Santos, S.A.; Dallago, B.S.L.; Paiva, S.R.; Martins, R.F.S.; Braccini Neto, J.; Marques, P.R.; Abreu, U.G.P.d. Evaluation of conservation program for the Pantaneiro horse in Brazil. Rev. Bras. Zootec.
**2013**, 42, 404–413. [Google Scholar] [CrossRef][Green Version] - Perdomo-González, D.I.; Sánchez-Guerrero, M.J.; Molina, A.; Valera, M. Genetic Structure Analysis of the Pura Raza Español Horse Population through Partial Inbreeding Coefficient Estimation. Animals
**2020**, 10, 1360. [Google Scholar] [CrossRef] - McPhee, H.C.; Wright, S. Mendelian analysis of the pure breeds of livestock: III. The shorthorns. J. Hered.
**1925**, 16, 205–215. [Google Scholar] [CrossRef] - Cunningham, E.; Dooley, J.; Splan, R.; Bradley, D. Microsatellite diversity, pedigree relatedness and the contributions of founder lineages to thoroughbred horses. Anim. Genet.
**2001**, 32, 360–364. [Google Scholar] [CrossRef] - FAO/UNEP. Conservation of the Genetic Resources of Fish: Problems and Recommendations. Report of the Expert Consultation on the Genetic Resources of Fish; FAO: Rome, Italy, 1980; p. 43. [Google Scholar]
- Franklin, I.; Soulé, M.; Wilcox, B. Conservation Biology: An Evolutionary-ecological Perspective; Sinauer Associates: Sunderland, MA, USA, 1980. [Google Scholar]
- Hoffmann, I. Climate change and the characterization, breeding and conservation of animal genetic resources. Anim. Genet.
**2010**, 41, 32–46. [Google Scholar] [CrossRef] - Leroy, G.; Gicquel, E.; Boettcher, P.; Besbes, B.; Furre, S.; Fernandez, J.; Danchin-Burge, C.; Alnahhas, N.; Baumung, R. Coancestry rate’s estimate of effective population size for genetic variability monitoring. Conserv. Genet. Resour.
**2020**, 12, 275–283. [Google Scholar] [CrossRef][Green Version] - Gutiérrez, J.P.; Cervantes, I.; Molina, A.; Valera, M.; Goyache, F. Individual increase in inbreeding allows estimating effective sizes from pedigrees. Genet. Sel. Evol.
**2008**, 40, 359–378. [Google Scholar] [CrossRef] [PubMed] - Malhado, C.H.M.; Ferraz, P.; Ramos, A.; Carneir, P.; Aragao, E.; s Barbosa, A.; Carrillo, J. Inbreeding, Average Relatedness Coefficient and Effective Population Size in Jaffarabadi Buffaloes Raised in Brazil. Buffalo Bull.
**2013**, 32, 641–645. [Google Scholar] - Sørensen, A.C.; Sørensen, M.K.; Berg, P. Inbreeding in Danish dairy cattle breeds. J. Dairy Sci.
**2005**, 88, 1865–1872. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Historical birth number evolution in Hispano-Arabian (Há), Spanish (PRE) and Arabian (PRá) Purebred Horses from 1900 to 2019.

**Figure 2.**Evolution of pedigree completeness index (PCI), inbreeding (F), coancestry (C) and population size (n) in Spanish (PRE) and Arabian (PRá) Purebred and Hispano-Arabian (Há) horses until the 21st generation.

**Figure 3.**Cladogram constructed from Nei’s Distances between Arabian purebred (PRá), Spanish purebred (PRE), and Hispano-Arabian (Há) horse breeds.

**Figure 5.**Territorial map depicting the results of the canonical discriminant analysis on the individuals comprising the Arabian purebred (PRá), Spanish purebred (PRE) and Hispano-Arabian (Há) horse breeds.

**Table 1.**Statistics summary of the analysis of the pedigree, maximum number of traced generations, pedigree completeness (1st, 2nd, 3rd, 4th and 5th generation), number of maximum generations, number of complete generations and number of equivalent generations in the studied population sets for Arabian Purebred (PRá), Spanish Purebred (PRE) and Hispano-Arabian (Há) horse breeds.

Population Set | Historical (n = 207,100) | Current (n = 164,941) | |||||
---|---|---|---|---|---|---|---|

Parameter | PRá | PRE | Há | PRá | PRE | Há | |

Population size | 23,293 | 172,797 | 11,010 | 13,576 | 141,357 | 9997 | |

Maximum number of traced generations, n | 18 | 20 | 21 | 18 | 20 | 21 | |

Pedigree completeness level at 1st generation, (Known parents) | 92.08 | 99.77 | 96.4 | 98.89 | 99.99 | 96.46 | |

Pedigree completeness level at 2nd generation, (Known grandparents) | 85.33 | 98.61 | 83.71 | 94.70 | 99.86 | 85.26 | |

Pedigree completeness level at 3rd generation, (Known great grandparents) | 78.51 | 95.77 | 76.34 | 90.38 | 99.65 | 78.84 | |

Pedigree completeness level at 4th generation, (Known great great grandparents) | 71.07 | 94.99 | 64.13 | 85.21 | 98.80 | 66.38 | |

Pedigree completeness level at 5th generation, (Known great great great grandparents) | 64.57 | 91.93 | 58.01 | 83.29 | 96.81 | 58.55 | |

Number of maximum generations (mean ± SD) | 10.27 ± 4.89 | 14.28 ± 2.65 | 12.15 ± 5.75 | 12.86 ± 3.14 | 15.08 ± 1.38 | 12.54 ± 5.54 | |

Number of complete generations (mean ± SD) | 3.35 ± 1.89 | 4.59 ± 1.20 | 2.96 ± 1.78 | 4.03 ± 1.68 | 4.86 ± 0.95 | 3.04 ± 1.78 | |

Number of equivalent generations (mean ± SD) | 5.76 ± 2.78 | 8.36 ± 1.61 | 6.15 ± 3.04 | 7.11 ± 1.99 | 8.85 ± 0.83 | 6.34 ± 2.96 |

**Table 2.**Summary of the statistics derived from pedigree analysis including maximum progeny per stallion and mare, mean age of stallions and mares in reproduction and foals of stallions and mares selected for breeding in the historical (n = 207,100) and current (n = 164,941) Arabian Purebred (PRá), Spanish Purebred (PRE) and Hispano-Arabian (Há) horse breed populations.

Populational Sets | Historical | Current | |||||
---|---|---|---|---|---|---|---|

Parameters | PRá | PRE | Há | PRá | PRE | Há | |

Males% | 47.84 | 48.27 | 38.76 | 48.84 | 48.95 | 40.32 | |

Mean number of foals per stallion, (mean ± SD) | 8.18 ± 10.31 | 13.67 ± 10.38 | 17.99 ± 103.01 | 7.08 ± 11.04 | 11.77 ± 18.50 | 11.42 ± 20.51 | |

Maximum foal number per stallion, n | 215 | 1804 | 1659 | 140 | 366 | 219 | |

Average age of stallions in reproduction, years (mean ± SD) | 22.14 ± 4.99 | 23.87 ± 4.99 | 18.21 ± 4.99 | 23.32 ± 5.81 | 25.31 ± 5.82 | 17.66 ± 5.74 | |

Females% | 52.16 | 51.73 | 61.24 | 51.16 | 51.05 | 59.68 | |

Mean number of foals per mare, (mean ± SD) | 3.54 ± 3.10 | 4.28 ± 3.40 | 2.73 ± 2.44 | 3.13 ± 2.55 | 3.68 ± 2.73 | 2.45 ± 2.21 | |

Maximum foal number per mare, n | 20 | 24 | 17 | 18 | 16 | 17 | |

Average age of mares in reproduction, years (mean ± SD) | 23.01 ± 4.84 | 23.73 ± 4.97 | 21.65 ± 4.80 | 24.55 ± 5.09 | 24.17 ± 5.09 | 20.50 ± 4.03 | |

Male/Female Ratio | 0.92/1 | 0.96/1 | 0.93/1 | 0.96/1 | 0.63/1 | 0.68/1 | |

Progeny from stallions selected for breeding, % | 91.77 | 99.20 | 92.66 | 97.92 | 99.93 | 80.94 | |

Progeny from mares selected for breeding, % | 92.02 | 48.27 | 94.20 | 98.85 | 49.74 | 94.08 |

**Table 3.**Generation intervals (years) for the four gametic routes in the Spanish Purebred (PRE), Arabian Purebred (PRá) and Hispano-Arabian (Há) breeds.

Parameter | Gametic Route | Stallion to Colt | Mare to Colt | Stallion to Filly | Mare to Filly | Total | |
---|---|---|---|---|---|---|---|

Population Set | |||||||

PRá | N | 2524 | 2480 | 5606 | 5579 | 16,189 | |

Mean | 13.03 | 12.94 | 13.14 | 12.23 | 12.78 | ||

SD | 12.58 | 14.69 | 13.13 | 13.12 | 13.30 | ||

PRE | N | 12,681 | 12,619 | 40,297 | 40,217 | 105,814 | |

Mean | 10.58 | 9.68 | 10.67 | 9.56 | 10.12 | ||

SD | 6.82 | 5.48 | 6.87 | 5.95 | 6.40 | ||

Há | N | 275 | 274 | 1643 | 1643 | 3835 | |

Mean | 14.81 | 14.44 | 27.94 | 28.43 | 26.24 | ||

SD | 16.88 | 17.14 | 23.96 | 24.49 | 23.80 |

**Table 4.**Statistics of pedigree analysis: inbreeding (F), average individual increase in inbreeding (ΔF, %), maximum coefficient of inbreeding (%), inbred and highly inbred animals (%), average coancestry (C, %), average relatedness (ΔR, %), non-random mating rate (α), and genetic conservation index (GCI).

Populational Sets | Historical (n = 207,100) | Current (n = 164,941) | |||||
---|---|---|---|---|---|---|---|

Parameters | PRá | PRE | Há | PRá | PRE | Há | |

Inbreeding (F, %) | 6.79 | 8.42 | 2.85 | 8.44 | 8.50 | 2.89 | |

Average individual increase in inbreeding (ΔF, %) | 1.02 | 1.03 | 0.95 | 1.14 | 1.02 | 0.94 | |

Maximum coefficient of inbreeding (%) | 43.03 | 55.04 | 49.61 | 43.03 | 55.04 | 49.61 | |

Inbred animals (%) | 71.96 | 33.48 | 43.11 | 39.84 | 24.94 | 5.18 | |

Highly inbred animals (%) | 48.08 | 26.04 | 40.34 | 30.55 | 19.41 | 4.60 | |

Average kinship or coancestry (C, %) | 0.60 | 5.57 | 2.06 | 0.72 | 5.62 | 2.13 | |

Average relatedness (ΔR, %) | 1.21 | 11.13 | 4.12 | 1.42 | 11.25 | 4.25 | |

Non-random mating rate (α) | 0.06 | 0.03 | 0.01 | 0.08 | 0.03 | 0.01 | |

Genetic Conservation index (GCI) | 9.65 | 9.34 | 9.11 | 11.50 | 9.74 | 9.38 |

**Table 5.**Measures of genetic variability and analysis of gene origin, effective number of non-founders (N

_{ef}), number of founder equivalents (f

_{e}), effective number of ancestors (f

_{a}) of Arabian purebred (PRá), Spanish purebred (PRE) and Hispano-Arabian (Há) horse breeds.

Parameter | PRá | PRE | Há | |||
---|---|---|---|---|---|---|

Historic | Current | Historic | Current | Historic | Current | |

Historical population | 23,293 | 13,586 | 172,797 | 141,358 | 11,010 | 9997 |

Base population (one or more unknown parents) | 1975 | 199 | 1110 | 33 | 406 | 362 |

Actual base population (one unknown parent = half founder) | 257 | 68 | 483 | 15 | 19 | 15 |

Number of founders, n | 1718 | 131 | 625 | 18 | 387 | 347 |

Number of ancestors, n | 56 | 958 | 379 | 192 | 876 | 847 |

Effective number of non-founders (N_{ef}) | 14.73 | 10.00 | 12.06 | 11.40 | 24.99 | 23.57 |

Number of founder equivalents (f_{e}) | 43.76 | 37.67 | 20.63 | 21.49 | 29.23 | 34.11 |

Effective number of ancestors (f_{a}) | 22 | 16 | 14 | 14 | 22 | 23 |

Founder genome equivalents (f_{g}) | 11.02 | 7.90 | 7.61 | 7.45 | 13.47 | 13.94 |

f_{a}/f_{e} ratio | 0.50 | 0.42 | 0.68 | 0.65 | 0.75 | 0.67 |

f_{g/}f_{e} ratio | 0.25 | 0.21 | 0.37 | 0.35 | 0.46 | 0.41 |

**Table 6.**Summary of the results of Pillai’s Trace of Equality of Covariance Matrices of Canonical Discriminant Functions.

Pillai’s Trace Criterion | 0.951 |

F | 675,108.085 |

Hypothesis df | 6 |

Error df | 207,094 |

Sig. | 0.001 |

Test of Function(s) | Wilks’ Lambda | Chi-Square | df | Sig. |
---|---|---|---|---|

1 through 2 | 0.181 | 354,364.706 | 12 | 0.001 |

2 | 0.944 | 11,883.207 | 5 | 0.001 |

Parameters/Statistics | Tolerance (1 − R^{2}) | VIF |
---|---|---|

Genetic Conservation Index | 0.449 | 2.225 |

Coancestry, % | 0.593 | 1.688 |

Non-random mating degree (α) | 0.900 | 1.112 |

Number of Maximum Generations, n | 0.362 | 2.761 |

Number of Complete Generations, n | 0.353 | 2.835 |

Offspring number, n | 0.988 | 1.012 |

**Table 9.**Canonical variate pairs (discriminant functions) found in canonical discriminant analysis for genetic diversity parameters.

Function | 1 | 2 |
---|---|---|

Eigenvalue | 4.227 | 0.059 |

Variance (proportion of discriminating ability), % | 98.6 | 1.4 |

Canonical Correlation | 0.899 | 0.236 |

Rc-Squared, Squared canonical correlation (shared variance), % | 80.8 | 5.6 |

**Table 10.**Results for the tests of equality of group means to test for differences across breeds once redundant variables have been removed.

Rank of Variables | Wilk’s Lambda | df1 | df2 | df3 | Exact F | df1 | df2 | Sig. | Rank |
---|---|---|---|---|---|---|---|---|---|

Offspring number, n | 0.181 | 6 | 2 | 207,097 | 46,688.827 | 12 | 414,184 | 0.000 | 1 |

Average relatedness (AR), % | 0.181 | 5 | 2 | 207,097 | 56,013.680 | 10 | 414,186 | 0.000 | 2 |

Non-random mating degree, α | 0.190 | 4 | 2 | 207,097 | 67,054.671 | 8 | 414,188 | 0.000 | 3 |

Number of Maximum Generations, n | 0.200 | 3 | 2 | 207,097 | 85,176.481 | 6 | 414,190 | 0.000 | 4 |

Number of Complete Generations, n | 0.213 | 2 | 2 | 207,097 | 120,731.985 | 4 | 414,192 | 0.000 | 5 |

Genetic Conservation Index | 0.235 | 1 | 2 | 207,097 | 337,293.642 | 2 | 207,097 | 0.000 | 6 |

Items | Function | |
---|---|---|

F1 | F2 | |

Average relatedness (AR), % | 1.083 | 0.071 |

Genetic Conservation Index (GCI) | −0.368 | 0.227 |

Non-random mating degree, α | −0.257 | 0.513 |

Number of Maximum Generations, n | 0.475 | −0.899 |

Number of Complete Generations, n | −0.380 | 0.887 |

Offspring number, n | 0.008 | 0.062 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Marín Navas, C.; Delgado Bermejo, J.V.; McLean, A.K.; León Jurado, J.M.; Rodriguez de la Borbolla y Ruiberriz de Torres, A.; Navas González, F.J. Discriminant Canonical Analysis of the Contribution of Spanish and Arabian Purebred Horses to the Genetic Diversity and Population Structure of Hispano-Arabian Horses. *Animals* **2021**, *11*, 269.
https://doi.org/10.3390/ani11020269

**AMA Style**

Marín Navas C, Delgado Bermejo JV, McLean AK, León Jurado JM, Rodriguez de la Borbolla y Ruiberriz de Torres A, Navas González FJ. Discriminant Canonical Analysis of the Contribution of Spanish and Arabian Purebred Horses to the Genetic Diversity and Population Structure of Hispano-Arabian Horses. *Animals*. 2021; 11(2):269.
https://doi.org/10.3390/ani11020269

**Chicago/Turabian Style**

Marín Navas, Carmen, Juan Vicente Delgado Bermejo, Amy Katherine McLean, José Manuel León Jurado, Antonio Rodriguez de la Borbolla y Ruiberriz de Torres, and Francisco Javier Navas González. 2021. "Discriminant Canonical Analysis of the Contribution of Spanish and Arabian Purebred Horses to the Genetic Diversity and Population Structure of Hispano-Arabian Horses" *Animals* 11, no. 2: 269.
https://doi.org/10.3390/ani11020269