The Weight of Genetic Drift: A Pedigree-Based Evaluation of the Breton Horse Population in Brazil

The genetic diversity of Breton horses in Brazil is a critical concern, mainly due to the small population size and low number of births per year. Given that the inbreeding was overlooked by breeders for multiple generations, we estimated the genetic diversity of this population utilizing pedigree-based measures of population diversity. A total of 1394 six-generation pedigrees representing the full population of registered Breton horses in Brazil defined a total population (TP, N = 2679), with horses born between 2000 and 2022, reproductively active and alive, as reported by the breed association, representing the reference population (RP, N = 731). Using the R package PurgeR, we estimated inbreeding coefficient (Fped), maternal inbreeding coefficient (Fda m), paternal inbreeding coefficient (Fsire), individual reproductive values, number of equivalents to complete generations (t), and unbiased ancestral inbreeding coefficient (Fa). We established the equivalent complete generations (ECG), effective population size (Ne), total number of founders (Nf), effective number of founders (Nfe), total number of ancestors (Na), effective number of ancestors (Nae), founder genomes (Ng), and the inbreeding coefficient estimated with effective population size (Ne) and generation numbers (t) (FNe:t), as well as Nfe/Nae and Nfe/Ng ratios for the RP. The RP inbreeding levels have stabilized, although they are still significantly rising by generation (t), and the Nfe/Ng ratio strongly suggests genetic drift. Pedigree-based analysis demonstrates that only five stallions have sired 52.83% of the RP individuals, which along with the Nae value of 36.73 implies that the observed inbreeding can be arising from patrilines. Our results suggest that observed inbreeding is due to Popular Sire Effect, highlighting the importance of monitoring breeding schemes and genetic diversity to maintain health.


Introduction
Originally from the Brittany and Loire Atlantique regions of France, the Brazilian population of Breton draft horses (Equus caballus) is based on fewer than 180 individuals.Te base population results from importations of animals and genetic material spanning from 1925 to early 2010's [1].Due to the small number of founder individuals, a small population size of 1420 horses, and fewer than sixty-fve births per year from 2004 to 2011 (personal communication, Brazilian Association of Breton Horse Breeders-BABHB), the current status of the Breton breed in Brazil is concerning.Te deleterious potential of inbreeding and loss of genetic diversity presents a challenge to the health and overall breed maintenance in Brazil [2,3].
A previous inbreeding estimation of the Breton horse in Brazil evaluating the maternal lineages through mitochondrial DNA (mtDNA) resulted in average genomic-based (F st ) inbreeding estimates of 0.17, yet this approach presents limitations given the solely maternal perspective of mtDNA, especially if the inbreeding is mainly of paternal origin [4].Pedigree analysis can be utilized as a low-cost, accessible tool when compared to genomic-based studies [5] to estimate measures of genetic diversity, inbreeding, diferences in estimated and efective population, as well as signs of founder efect [2,5].Pedigree analysis successfully predicted inbreeding and its associations with health and ftness parameters such as fertility and growth in dogs, laboratory mice, sheep, and other animals [2,3,5,6].Pedigree-based evaluation was also efectively used in the Brazilian Sport Horse (BH) to measure genetic diversity [7,8].Furthermore, pedigree analysis can serve as baseline for future genomicbased assessments, providing approximations of parameters supporting evaluations of genetic diversity [3].
To assess inbreeding and other population diversity measurements, we performed a pedigree-based analysis of 1,394 individuals registered with BABHB, representing the complete Breton horse population in Brazil, through 6generation pedigrees.We evaluated the resulting inbreeding coefcient (F ped ) in the total and reproductively active or reference population, the estimated and efective number of founders and ancestors, and signs of founder efect.

Ethics Statement.
Institutional Care and Use Committee (IACUC) ethical approval was not required as this research utilized nonidentifable computational pedigree data collected voluntarily and provided by the Brazilian Association of Breton Horse Breeders.

Animals.
One thousand, three hundred and ninety-four individuals and their respective pedigrees representing the registered population of Breton horses registered in Brazil and containing up to the sixth generation of ancestors were provided by BABHB and utilized in this study.Tis data was manually entered in a Microsoft Excel spreadsheet following the recommended guidelines by the purgeR package [9], resulting in 2679 total entries representing each individual and respective ancestors noted in the pedigrees.
We further divided the population in total (TP) and reference (RP) population, with the reference constituted of reproductively active, alive individuals as reported by the breed association, born from the year 2000 to 2022 (N � 731 horses), and the total population representing all individuals observed in the pedigrees provided by BABHB including horses ancestral to the reference population (N � 2679, or 1948 horses added to the RP).Te RP represents the currently active Breton population.

Pedigree Analysis.
Te R package purgeR [9] was applied to the dataset using RStudio [10] to obtain measurements of inbreeding and population diversity as inbreeding coefcient (F ped ), maternal inbreeding coefcient (F da m ), paternal inbreeding coefcient (F sire ), individual reproductive values, number of equivalents to complete generations (t), and unbiased ancestral inbreeding coefcient (Fa) (Sup.Table 1).Using these results, we established for the RP: equivalent complete generations (ECG), efective population size (Ne), total number of founders (Nf ), efective number of founders (Nfe), total number of ancestors (Na), efective number of ancestors (Nae), founder genomes (Ng), and the inbreeding coefcient estimated with efective population size (Ne) and generation numbers (t) (referred to here as F Net ), following published guidelines [9].We further compared Nfe/Nae and Nfe/Ng ratios to evaluate founder efects in this population [5].Statistical analysis was performed using JMP Pro 16 (SAS Institute, Inc., Cary, NC).Year born and F ped for both TP and RP were evaluated for normality using the Anderson-Darling test.Standard Least Squares was used to assess linear association of F ped to year of birth and generation (t) for the TP and RP.Results were considered statistically signifcant at p ≤ 0.05.

Results and Discussion
While average F ped inbreeding coefcients signifcantly increase by birth year in the TP (F(1,2588) � 261.77, p � 3.65 × 10 -56 ), there is no association observed in the RP, where F pe d seems to have stabilized (F(1,729) � 0.001, p � 0.97) (Figure 1).Still, in the RP, the F pe d signifcantly increases by generation (t) (F(1,729) � 65.78, p � 2.13 × 10 -15 ), suggesting that inbreeding levels may be rising with each generation.Te F ped superfcial stabilization in recent years is possibly due to a lower overall number of reproductively active animals or refecting the increasing use of imported semen and embryos from 2006 to 2015, slowing down the rise in inbreeding [1].Supporting the introduction of new genetics through imported germline, we observe a small decrease in the average F ped of individuals born from 2016 to 2022 (N � 127, mean � 0.030, standard deviation/SD ± 0.034).A similar efect was observed in the BH population, where recent introduction of imported individuals in the breeding program has decreased the overall F ped [8].Furthermore, despite the RP efective population size (Ne) of 83.86 animals (SD ± 3.56) (Table 1) being lower than values observed in other Brazilian breeds [8,11], the genetic diversity of the Breton horse in Brazil has not reached levels considered critical (Ne ≤ 50) [12,13].Tus, the observed RP F ped stabilization is likely a product of artifcial insemination and embryo transfer technologies utilized in the breeding program and the relatively low number of reproductive active animals.Still, preventative measures focusing on increasing genetic diversity are necessary to avoid reaching critical effective levels for this population, especially since there are no set limits for the number of annual ofspring of a stallion [1].
Although mtDNA analysis of Brazilian Breton horses does not suggest a high F st (17.68%) for the population when compared to other Brazilian equid populations, mtDNA is limited to maternal lines [4].Our RP results demonstrated an average maternal inbreeding coefcient (F da m ) ranging from 0% to 26.51% (mean � 2.71%, SD ± 3.60%) while the paternal inbreeding coefcients (F sire ) range from 0% to 13.49% (mean � 1.80%, SD ± 1.87%), suggesting that higher inbreeding values arise from the maternal lines (Table 1).Still, pedigree analysis showed that of 729 stallions represented in the RP, just fve (0.68%) have sired over half or 52.83% of the RP individuals.Te most prolifc sire was born in 1982 and had 54 ofspring, a substantial number when compared to the most prolifc dam which had only 12 ofspring in her lifetime.Furthermore, individual #1205 of the RP demonstrated a reproductive value of 0.0020, the highest in our analysis, and sired 44 ofspring in the RP population (Sup.Table 1).Even with modern equine reproductive technologies, males have a higher likelihood of genetic propagation than females, given the feasibility of germplasm collection, storage, and utilization [23].In  Veterinary Medicine International addition, the resulting Nae value of 36.73 also indicates an overuse of some individuals [14].Likewise, the loss of genetic diversity noted in the Turkish Arab horse and BH is implied as caused by the restricted number of stallions used for breeding [8,15].Although the pedigree-based F da m is higher than the F sire , increasing inbreeding levels in the Brazilian population of Breton horses can be patriline associated, which may have stemmed from the overuse of specifc sires during the history of the breed, an efect commonly known as "Popular Sire Efect" [24], and the selection of their ofspring.Te Popular Sire Efect and its consequences are demonstrated by the Y chromosome loss of diversity through the domestication selection bias for stallions during modern human breeding practices [22].Further evaluations of the Y chromosome diversity in this population of horses can provide support for improved breeding practices and patriline diversifcation.
Te RP pedigree analysis demonstrated inbreeding coefcients (F ped ) between 0.0 and 0.29 (mean � 0.036, SD ± 0.0399) and accounting for efective population size (Ne) and generation number (t), a mean inbreeding coefcient (F Ne: t ) of 5.31% (Table 1).While the RP mean is higher than observations in Brazilian autochthonous breeds such as the BH (0.033) [8], Mangalarga Marchador (0.011) [11], and Crioulo (0.0088) [18], other foreign breeds have noted higher F such as the Turkish Arab horse (0.046) [15], Mallorquí (0.047) [25], yet not higher than the F Ne:t of 5.31%, except for observations in the Lusitano horse (0.1134) [19].Te variance between the noted F ped values can be due to reproductive population diversity, breeding practices or pedigree completeness.A limitation of the pedigree analysis is the lack of information on complete generations (e.g., missing or unknown ancestors), as evidenced by the observed F ped values of 0.00.While the RP population has a mean Equivalent Complete Generations (ECG) of 7.05 (SD ± 0.89), representing the pedigree completeness of this group [14], 1002 ancestral individuals (51.44%) have a F ped of 0.00, likely due to the lack of pedigree ancestor information.Furthermore, comparisons between genomic and pedigree-based inbreeding in Arabian [26] and Mangalarga [27] horses found moderate to low correlation between genomic (F st ) and pedigree-based (F ped ) inbreeding coefcients.Terefore, the RP F ped mean of 3.6% (SD ± 3.99%) may be underestimated in our population, and the F Ne:t may represent the mean inbreeding in this population more accurately.Te observed F ped of 0% can be an artifact of limiting the pedigree entries to Brazilian-registered horses only or due to the lack of records for the early Breton populations.Tus, pedigree-based inbreeding coefcients may be a good baseline tool for analyzing inbreeding yet presents limitations in precisely measuring the genomic diversity at both individual and population levels.
Due to the suggested genetic drift that occurred in the population of Breton horses in Brazil, their management could beneft from increasing diversity through the introduction of new, genetically diverse individuals, especially regarding male lines.Since pedigree analysis is sensitive to the incomplete written records observed in real populations [14], and given the discrepancy between the F ped results and previously reported F mtDNA [4] for the Breton breed, further evaluations using nuclear genomic approaches are recommended to obtain more precise population inbreeding levels.

Conclusion
Our investigation highlighted the signifcant efects of genetic drift over many generations.Using pedigree data from the complete population of registered individuals, we noted that the RP inbreeding coefcient has apparently stabilized, although the inbreeding is rising by generation.Tis can be due to modern management practices not limiting progeny by individual males and the smaller infuence of imported germplasm, an essential aspect in maintaining the genetic diversity of this geographically isolated population.We reiterate the importance of managing horse populations using genetic-based methodologies to avoid inbreeding depression and the loss of genetic diversity.Furthermore, the breed association can utilize current pedigree records to establish mating strategies with the goal of increasing the population genetic diversity.Results from pedigree and further genomic analysis can support improved genotypebased selection to maintain genetic diversity and expand the understanding of genetic drift impacts in domestic, smallpopulation equine breeds such as the Breton horse in Brazil.Further studies assessing the genomic inbreeding and diversity of Y chromosome are recommended.

Table 1 :
Inbreeding and populational parameters of the Breton horse reference population (RP) resulting from purgeR pedigree analysis.
(-) Tere is no standard deviation (SD) and/or mean and CI for this data.