Genetic Diversity and Trends of Ancestral and New Inbreeding in German Sheep Breeds by Pedigree Data

Simple Summary Sheep breeding is a long-standing tradition throughout Germany. Due to breeding in marginal and harsh sites, sheep developed into a large number of unique breeds adapted to many different ecosystems. In this work, we study demographic measures of genetic diversity and inbreeding trends in 35 sheep breeds using the national database of herdbook breeders in Germany. This database is a valuable resource to manage and monitor diversity in breeding populations. The loss of genetic diversity was found in all breeds studied, mainly due to genetic drift rather than unequal use of founders. The analysis of pedigree data from more than 1.4 million sheep revealed an overall measure of inbreeding of F = 0.031, an individual rate of inbreeding of ΔFi = 0.0074, and a realized effective population size of Ne = 91.4 with 25–75% quartiles of 0.019–0.040, 0.0040–0.0086, and 57.9–125.3, respectively. Trends in individual inbreeding were significantly positive in meat and mountain sheep, but trends in the individual rate of inbreeding were only slightly positive. Country sheep showed significantly negative trends in the rate of individual inbreeding. Ancestral inbreeding had increasing trends in all sheep breeds. Our results demonstrate the efficiency of genetic diversity management and should help to conserve endangered breeds and maintain high genetic diversity in breeds used for wool, meat, and milk production. Abstract In Germany, many autochthonous sheep breeds have developed, adapted to mountain, heath, moorland, or other marginal sites, but breeds imported from other countries have also contributed to the domestic breeds, particularly improving wool and meat quality. Selective breeding and the intense use of rams may risk losing genetic diversity and increasing rates of inbreeding. On the other hand, breeds with a low number of founder animals and only regional popularity may not leave their endangered status, as the number of breeders interested in the breed is limited. The objective of the present study was to determine demographic measures of genetic diversity and recent as well as ancestral trends of inbreeding in all autochthonous German sheep breeds and sheep of all breeding directions, including wool, meat, and milk. We used pedigree data from 1,435,562 sheep of 35 different breeds and a reference population of 981,093 sheep, born from 2010 to 2020. The mean number of equivalent generations, founders, effective founders, effective ancestors, and effective founder genomes were 5.77, 1669, 123.2, 63.5, and 33.0, respectively. Genetic drift accounted for 69% of the loss of genetic diversity, while loss due to unequal founder contributions was 31%. The mean inbreeding coefficient, individual rate of inbreeding (∆Fi), and realized effective population size across breeds were 0.031, 0.0074, and 91.4, respectively, with a significantly decreasing trend in ∆Fi in 11/35 breeds. New inbreeding, according to Kalinowski, contributed to 71.8% of individual inbreeding, but ancestral inbreeding coefficients showed an increasing trend in all breeds. In conclusion, in our study, all but one of the mountain-stone sheep breeds and the country sheep breed Wald were the most vulnerable populations, with Ne < 50. The next most endangered breeds are exotic, country, and heath breeds, with average Ne of 66, 83, and 89, respectively. The wool, meat, and milk breeds showed the highest genetic diversity, with average Ne of 158, 120, and 111, respectively. The results of our study should help strengthen conservation program efforts for the most endangered sheep breeds and maintain a high genetic diversity in all sheep breeds.


Introduction
Sheep are one of the oldest domestic animal species in the world, and were bred long ago for their robustness, frugality, and adaptability to climatic conditions and a changing food supply. The most important breeding characteristics were milk, wool, and meat. Breeding has resulted in a very wide variety of breeds, especially in Europe, with varying degrees of adaptation to landscape and climatic conditions [1,2]. Intensive production, improvement in autochthonous breeds with other foreign and more productive breeds, and increased commercial demands, particularly since the last 50-70 years, have contributed significantly to the threats facing European sheep breeds [3].
However, due to the production system and the associated selection pressure, many of these breeding successes correlate with a decrease in the biodiversity of animal genetic resources, especially in the livestock sector, including the sheep sector [1,4]. The genetic diversity of a population is represented as a collection of alleles and genotypes. It is expressed among individuals and populations in different phenotypes, physiologies, and behaviors [5,6]. Knowledge of the pedigree can be used to monitor changes in genetic diversity under constant selection pressure [6,7]. Even if breeds are not yet endangered, it is important to analyze them when herdbook numbers are already decreasing in order to preserve remaining genetic resources, since small populations in particular harbor an increased risk of inbreeding and loss of genetic variability [8]. Maintaining genetic diversity among breeding animals in closed and small populations is very important because of the accelerated depletion of allelic distinctiveness and heterozygosity. Genetic selection and drift in small populations leads to adverse consequences, such as reduced vigor or production in animals with increased homozygosity and loss of allelic diversity [9]. For example, in a study on the inbreeding estimation in the small population of Basco-Béarnaise sheep, inbreeding depression was shown to have a significant effect on sperm motility [10].
Selective breeding is expected to reduce the fitness of animal populations through its negative effects on genetic diversity, especially in small, closed populations. The reduction in fitness caused by intensive selection for production traits is more pronounced in random mating systems due to more frequent mating between close relatives [11,12]. Today's partly highly specialized sheep breeds are the product of a long selective breeding history and, therefore, differ breed-specifically to a greater or lesser extent in their characteristics and properties. They are grouped into economic and land breeds and can be further differentiated into meat, merino, milk, country, and hair sheep, depending on their main breeding aim or a specific objective, with only one exception. Merinos are also bred for meat production. Breeding for specific traits enforces unequal founder contributions and loss of founder genomes, leading to a reduction in genetic variability, as shown in the Swedish Gute [2], Nellore [6], Valachian [7], Xalda [13], Santa Inês [14], Zandi [15], and Afshari [16] breeds. In order to conserve the remaining animal genetic resources, they must first be documented and assessed from a population genetics perspective [1].
The development of sound genetic conservation strategies for livestock species requires, as a first step, the monitoring of existing genetic diversity within and between breeds. The availability of sufficient genetic variation in a given population provides the basis for sustained genetic improvement in economically important traits and facilitates adaptation to changing environmental conditions [17,18]. In this work, pedigree data of 35 sheep breeds bred in Germany were analyzed. Among the breeds studied, autochthonous breeds of all breeding directions (merino, meat, country, and milk) in Germany were represented. The pedigree data for our analyses were provided by vit/Verden (Vereinigte Informationssysteme Tierhaltung w.V., Verden, Germany), the information service provider for animal husbandry and breeding in Germany.

Materials and Methods
For our analysis, we used the pedigree data of 1,435,562 sheep from 35 different sheep breeds. The reference population were sheep born between 2010 and 2020 and included 981,093 animals (Table 1). Pedigree data were extracted from serv.it OviCap by Vit/Verden, Germany. The OviCap database has been managed by vit/Verden since 2007 and has been available to all sheep breeders since 2013 as an internet-based platform for viewing performance data, as well as for their own work with data from the herdbook and national evaluations of breeding values. All pedigree entries are checked for consistency during data entry and errors must be corrected before the data are accepted. Breeders can use pedigree data from OviCap to avoid inbreeding in the next generation of lambs when planning future mating. In addition, breeders can obtain information on male founders and their contribution to the animals of the current and next generation. Estimates of demographic measures of genetic diversity were obtained for the respective reference populations of each breed using the PEDIG software [19]. Data editing and calculation of individual rates of inbreeding and realized effective population sizes were performed using SAS, version 9.4 (Statistical Analysis System, Cary, NC, USA, 2022).
In brief, we calculated the number of equivalent complete generations (GE) to determine the degree of completeness of the pedigrees in the total dataset [20] as well as the generation intervals (GI) for sires and dams [21]. The demographic measures of genetic diversity estimated included number of founders (f ), number of effective founders (f e ), effective number of founder genomes (f g ), effective number of ancestors (f a ), and the ratios f e /f, f a /f e and f g /f e [22,23] based on following formulas: with f = number of founders, a = number of ancestors, q k = probability of gene origin of the individual ancestor (k), and r k = expected proportion of founder alleles that have been kept within the descendant population, marginal genetic contribution of an individual ancestor (q j ). In addition, we derived the amount of genetic diversity (GD) resulting from unequal contribution of founders and genetic drift [18,24] as follows: The amount of genetic diversity (GD*) due to an unequal contribution of founders was: The loss of genetic diversity resulting from unequal contribution of founders is given by 1 − GD* and from genetic drift by GD* − GD. The relative amounts of these losses of genetic diversity can be calculated as proportions of the sum of 1 − GD* and GD* − GD.
We estimated individual inbreeding coefficients (F) according to Meuwissen and Luo [25] using PEDIG [19], the genedrop method (F gd ), ancestral inbreeding coefficients according to Ballou [26] (F a_Bal ), ancestral (F a_Kal ) and new (F New ) inbreeding coefficients according to Kalinowski et al. [27], and ancestral history coefficients (AHC) defined by Baumung et al. [28] using GRAIN, version 2.2 [28,29]. In the data analysis of the reference population, we distinguished estimates for F for all animals and only for inbred animals (F inbred ).
We calculated the degree of deviation of random mating from Hardy-Weinberg proportions as the indicator of genetic substructure by comparing the average coancestry within the parental population (Φ) with the average coefficient of inbreeding according to Meuwissen and Luo [25] in the reference population as follows [30]: The individual rate of inbreeding (∆F i ) was adjusted to GE according to Gutiérrez et al. [31] and calculated as follows: The realized effective population size (N e ) was derived from the mean ∆F i (∆Fi) of the reference population [32]: The unbalanced use of male and female breeding animals is expressed by the effective number of sires (NeffS) and dams (NeffD): where s i (or d i ) is the relative frequency of use of the sire or dam i among all sires (or dams) in the reference population [33].
The distributions of the demographic parameters f e , f g , f a , and their ratios, losses due to unequal contributions of founders and genetic drift, and number and effective number of dams and sires are presented for the 35 breeds using boxplots. The boxplots show, in addition to the median, the lower and upper quartiles, as well as the upper and lower whisker, each marking 1.5 times the interquartile range. In order to differentiate the 35 different breeds, we have chosen bee swarm models for the plots.
We calculated all different inbreeding coefficients' means by breed and birth year to analyze trends in these parameters over time. The model applied included breed as a fixed effect and a linear regression coefficient within breed on birth year encoded 1 (=2010) to 11 (=2020). Pearson correlation coefficients among the different coefficients of inbreeding were calculated using SAS. In addition, we calculated Pearson correlation coefficients for individual and ancestral inbreeding coefficients between offspring and parents, as well as between both parents, using SAS.

Results
The number of animals in the pedigrees and the reference population as well as GE, GI, number of founders, effective number of founders, effective number of founder genomes, and effective number of ancestors for each of the 35 sheep breeds are shown in Table 1 All ratios of fe/f, fa/fe, and fg/fe, were less than 1, which is indicative of bottlenecks, drift, and unequal use of founders in all breeds ( Figure 1, Table S1). Ratios of fe/f ranged from 0.03 (Dorper) to 0.296 (Swifter). Outside the first and third quartiles from 0.06 to 0.14 were 18/35 breeds. Ratios of fa/fe ranged from 0.28 (German Mutton Merino) to 0.95 (Baraka). Within first and third quartiles (0.47-0.63) were 16/35 breeds. The ratios of fg/fe had the lowest value in German Mutton Merino with 0.13 and the highest in Baraka with 0.60, and 17/35 breeds were within the quartiles (0.22-0.39).
In addition, we calculated how many ancestors explained 30/50/70/90/95% of the genetic diversity in the different sheep breeds (Table S1). The mean number of ancestors explaining 30% of the gene pool of the 35 sheep breeds was 8.74. Suffolk had the highest number of ancestors with 33 explaining 30% of the gene pool, whereas Alpine Steinschaf and Black Mountain had the lowest value with only 2 ancestors. The mean number of ancestors explaining 50% of the gene pool was 23.94 on average, with ranges between 5 (SBS) and 96 (SUF). The highest number of ancestors explaining 90% of the population diversity reached 1000 ancestors in German Mutton Merino, but the lowest in Black Mountain with 48 ancestors. The average number of ancestors explaining 30%, 50%, 70%, and 90% of the population diversity across all breeds was 8.74, 23.94, 62.77, and 273.89, respectively.
The mean loss of genetic diversity due to unequal founder contributions (1-GD*) was 0.0066 on average across all breeds ( Figure 2, Table S2). The first and third quartile ranged from 0.0032 to 0.009 and included 17/35 breeds. Outliers were the breeds AST and SBS, with estimates of 0.0207 and 0.0196, respectively. Suffolk had the lowest estimate for the loss of genetic diversity due to unequal founder contributions with 0.001. All ratios of f e /f, f a /f e , and f g /f e , were less than 1, which is indicative of bottlenecks, drift, and unequal use of founders in all breeds ( Figure 1, Table S1). Ratios of f e /f ranged from 0.03 (Dorper) to 0.296 (Swifter). Outside the first and third quartiles from 0.06 to 0.14 were 18/35 breeds. Ratios of f a /f e ranged from 0.28 (German Mutton Merino) to 0.95 (Baraka). Within first and third quartiles (0.47-0.63) were 16/35 breeds. The ratios of f g /f e had the lowest value in German Mutton Merino with 0.13 and the highest in Baraka with 0.60, and 17/35 breeds were within the quartiles (0.22-0.39).
In addition, we calculated how many ancestors explained 30/50/70/90/95% of the genetic diversity in the different sheep breeds (Table S1). The mean number of ancestors explaining 30% of the gene pool of the 35 sheep breeds was 8.74. Suffolk had the highest number of ancestors with 33 explaining 30% of the gene pool, whereas Alpine Steinschaf and Black Mountain had the lowest value with only 2 ancestors. The mean number of ancestors explaining 50% of the gene pool was 23.94 on average, with ranges between 5 (SBS) and 96 (SUF). The highest number of ancestors explaining 90% of the population diversity reached 1000 ancestors in German Mutton Merino, but the lowest in Black Mountain with 48 ancestors. The average number of ancestors explaining 30%, 50%, 70%, and 90% of the population diversity across all breeds was 8.74, 23.94, 62.77, and 273.89, respectively.
The mean loss of genetic diversity due to unequal founder contributions (1 − GD*) was 0.0066 on average across all breeds ( Figure 2, Table S2). The first and third quartile ranged from 0.0032 to 0.009 and included 17/35 breeds. Outliers were the breeds AST and SBS, with estimates of 0.0207 and 0.0196, respectively. Suffolk had the lowest estimate for the loss of genetic diversity due to unequal founder contributions with 0.001. The mean loss of genetic diversity due to genetic drift (GD*−GD) was 0.0141 and ranged from 0.0029 (SUF) to 0.036 (WGH) among all breeds. The lower quartile was at 0.0095 and the upper quartile at 0.0176, including 17/35 breeds. The loss of genetic diversity caused by genetic drift was, across breeds, on average, higher, as opposed to losses due to unequal founder contributions. Relative loss of genetic diversity resulting from genetic drift reached 69.4% on average for all breeds, whereas unequal contributions of founders were responsible for a relative loss of 30.6% of the genetic diversity (Table 2).  The mean loss of genetic diversity due to genetic drift (GD* − GD) was 0.0141 and ranged from 0.0029 (SUF) to 0.036 (WGH) among all breeds. The lower quartile was at 0.0095 and the upper quartile at 0.0176, including 17/35 breeds. The loss of genetic diversity caused by genetic drift was, across breeds, on average, higher, as opposed to losses due to unequal founder contributions. Relative loss of genetic diversity resulting from genetic drift reached 69.4% on average for all breeds, whereas unequal contributions of founders were responsible for a relative loss of 30.6% of the genetic diversity (Table 2). The different measures of inbreeding are shown in Table 3 and               New inbreeding, according to Kalinowski [27], is higher than ancestral inbreeding F a_Kal . The mean F a_New was 0.022, and its range across breeds was between 0.008 (CHA) and 0.046 (WAD). The mean F a_Kal 0.009 ranged from 0 (BDC, CHA) to 0.033 (WAD). Ancestral inbreeding coefficients AHC and F a_Bal were higher than classical inbreeding coefficient F. AHC, with an average of 0.09, ranged from 0.005 (CHA) to 0.261 (OUS). The mean F a_Bal was 0.082, with the minimum value of 0.005 (CHA) and the maximum of 0.19 (OUS).
Trends over birth years by breed are shown for F in all and inbred animals, as well as proportion of inbred animals, in Figure S3. Figure S4  We assigned the breeds to their breeding directions and tested whether significant differences could be found in demographic measures of genetic diversity and inbreeding coefficients (Tables S5 and S6). Merino, meat, and milk breeds had the largest f, f e , f g , and f a , the lowest losses due to drift and unequal contributions from founders, the lowest value for α, the lowest individual rate of inbreeding, and the largest N e . In contrast, mountain-stone sheep showed the lowest f, f e , f g , and f a , the highest losses due to unequal contributions from founders, the highest individual rate of inbreeding, the lowest N e , and the lowest effective number of sires and dams.
On average, per breed and birth year, 1522.61 dams and 1289.25 effective number of dams were present ( Figure 6). More than half of the breeds (n = 18/35) were within the first and third quartile of the boxplot, and three breeds were outliers (MLS, SKF, and MFS). The maximum effective number of dams was found in German Merino, German Blackhead Mutton, and German Mutton Merino with 6870.4, 4229.4, and 3949.2 animals, respectively. The lowest effective number of dams, with 83.7, was seen in the Black Mountain (Table S7).  (Table S7).  (Table S8).  (Table S8). Pearson correlation coefficients across breeds among the different inbreeding coefficients and proportion of inbred animals were highly positive ( Table 4). The individual rate of inbreeding was strongly positively correlated with loss due to unequal use of founders. Ancestral inbreeding coefficients Fa_Bal and AHC had correlations with ΔFi close to zero.  With a larger number of founders (f), effective number of founders (fe), effective number of founder genomes (fg), and effective number of ancestors (fa) per breed, inbreeding coefficients, individual rates of inbreeding, Fa_Kal, and Fa_New significantly decrease (Table  5). A large effective number of sires is highly positively correlated with f, fe, fg, and fa. Similar correlations were obtained for effective number of dams with the exception of fg. The relative loss of genetic diversity due to drift was significantly positively correlated with f Pearson correlation coefficients across breeds among the different inbreeding coefficients and proportion of inbred animals were highly positive ( Table 4). The individual rate of inbreeding was strongly positively correlated with loss due to unequal use of founders. Ancestral inbreeding coefficients F a_Bal and AHC had correlations with ∆F i close to zero.  With a larger number of founders (f ), effective number of founders (f e ), effective number of founder genomes (f g ), and effective number of ancestors (f a ) per breed, inbreeding coefficients, individual rates of inbreeding, F a_Kal , and F a_New significantly decrease (Table 5). A large effective number of sires is highly positively correlated with f, f e , f g , and f a . Similar correlations were obtained for effective number of dams with the exception of f g . The relative loss of genetic diversity due to drift was significantly positively correlated with f and f e . The decline in f g correlated more strongly with the increasing loss of drift-related diversity than with unequal contributions from founders. Table 5. Correlation coefficients across breeds between inbreeding coefficients for all (F), inbred animals (F inbred ), proportion of inbred animals (Inbred), individual rate of inbreeding (∆F i ), realized effective population size (N e ), inbreeding coefficients according to Ballou (F a_Bal ), Kalinowski (F a_Kal , F a_New ) and Baumung (AHC), relative (%) and absolute losses due to genetic drift (Loss drift ), and unequal founder contributions (Loss founder ), effective number of sires (NeffS) and dams (NeffD) with number of founders (f ), effective number of founders (f e ), effective number of founder genomes (f g ), and effective number of ancestors (f a ). p-values < 0.05 are marked (*).

Parameter
f

Discussion
The aim of this study was to assess genetic diversity and inbreeding trends comprising all autochthonous German sheep breeds and sheep of all breeding directions including wool, meat, and milk. There is a great interest in genetic diversity studies in domestic animals, with special focus on ruminants [34]. The present study also aims to demonstrate the efficiency of breed conservation programs underway in Germany.
Completeness and depth of pedigree data is crucial for the estimation of pedigreebased measures of genetic diversity and inbreeding. All but two autochthonous and all but two imported breeds reached >3.5 equivalent generations. Equivalent generations >4 and >5 had 27/35 and 23/35 breeds, respectively. Similar to the Santa Inês sheep (2.26) [14] and the Kermani sheep (2.22) [35], the breeds Baraka (2.55), Charollais (3.08), and Lacaune (3.09) showed pedigrees with the lowest depth. Summarizing previous reports (Table S9), equivalent generations were 5.42 on average, 24/33 with >4, and 17/33 with >5 equivalent generations, and in the present study, with an average of 5.77 equivalent generations in the same range. Because of the importance of pedigree completeness and quality, equivalent generations should be four and larger [36,37]. Six breeds (BLS, MLS, OMS, SKF, WBS, and WHH) reached equivalent generations near 8 or even >8, which is similar to the summary of previous reports on Bleu du Maine [38], Lacaune Confederation, Lacaune Ovitest [39], German Whitehead Mutton [8], Romanov in vivo [38], and Belgium Milk Sheep [40]. Breeds imported a few decades ago such as BDC, CHA, LAC, IDF, and SWS do not have deep pedigrees due to their short breeding history in Germany. NOL was developed in recent years as hair sheep in Germany and has, therefore, only a short history as its own officially recognized breed. The mountain sheep GBS and SBS are color variants arisen from WBS and have been recognized as independent breeds with their own herdbook only in the last few decades.
In agreement with previous reports (Table S9), ratios of f e /f, f g /f e , and f a /f e < 1 indicate the loss of genetic diversity since the founder generation. All breeds had ratios <1, and f e /f was, on average, the smallest ratio in all breeds, while f a /f e was the largest. A similar distribution was also found in French sheep breeds [38], Afshari [16], Nellore [6], Iran-Black [41], and Iranian Baluchi [42], but not in Zandi [15], Kermani [35], Iranian Lori-Bakhtiari [43], and Swedish Gute [2]. The unequal use of founders and the presence of genetic drift, indicated by f e /f <1, was more obvious in merino (0.042) and heath sheep (0.069) than in milk (0.175), exotic (0.166), and mountain-stone (0.123) sheep breeds. In exotic and mountain-stone sheep, f e /f may be related with shorter historical pedigree records and, therefore, overestimated [44]. The lowest f e /f estimates in previous reports were 0.09 in Roussin de la Hague, Charmoise [38], Bharat Merino [45], and Iran-Black [41]. In contrast to previous reports, we found f e /f <0.09 in 17/35 breeds. One possible explanation for this result is that in the OviCap database, important founders could be traced back over 15 generations, in some cases even more. Relative loss of genetic diversity due to drift was much more important in all breeds, with the exception of GBS and NOL. In these breeds, losses due to unequal founder contributions were larger compared to losses due to genetic drift.
The merino breed MFS, the heath breed GGH, and the milk breed OMS showed the largest drift-related losses in our study, with f g /f e ratios of 0.131, 0.165, and 0.166, respectively. The French breeds Roussin de la Hague (0.14), Romanov (0.15), and Charmoise (0.17) had similarly low f g /f e ratios and, thus, high losses of founder genomes [38]. Severe bottlenecks may be assumed in 9/35 breeds with f a /f e below the first quartile (0.472). All breeding directions were represented among these breeds with f a /f e <0.472. The merino breed MFS had the lowest f a /f e ratio of 0.281, followed by the exotic breed ZWS (0.381) and the heath breed GGH (0.383). In Valachian sheep, an even lower f a /f e ratio of 0.25 [7] was reported, while German Whitehead Mutton [8] and Charmoise [38] reached estimates of 0.36 and 0.37.
If there is evidence of genetic bottlenecks, as was the case in our study for all breeds studied, the effective number of sires and dams should be reviewed. The numbers of effective sires and dams estimated for each breed and birth year strongly correlated with the number of founders, effective number of founders, founder genomes and ancestors, and the ratios f e /f, f g /f e , and f a /f e , as well as the individual rate of inbreeding and realized effective population size. Particularly, breeds with small population sizes have to control the number of progeny per sire in order to avoid popular sire effects with negative consequences of an increase in individual rate of inbreeding and decrease in realized effective population size. De Vries showed with a simulation study that it is essential to have a low ram-to-ewe ratio to maintain genetic diversity [46]. Furthermore, most of the rams used for breeding are still young, about 2 years old, and are replaced only to a very limited extent. Windig investigated different mating schemes for this purpose and proved that in all of the different schemes, ∆F i decreased and, thus, inbreeding rates could be restricted by means of targeted mating [47]. Ghafouri-Kesbi also recommends a scheme to keep the inbreeding rate low with targeted mating and further points out the importance of sufficiently high generation intervals [16].
We found no evidence of line breeding or a significant increase in inbreeding in offspring of already inbred parents, as correlations of individual and ancestral inbreeding measures between parents were very close to zero for most breeds (Tables S10 and S11). In addition, the correlations of F New of the animal with the measures of ancestral inbreeding between the dam and sire were close to zero, indicating that new inbreeding in the offspring was not associated with ancestral inbreeding in the parents.
The negative trends in effective number of sires for merinos, meat, and heath breeds were due to decreasing population size across birth years, with the exception of MLW. For this breed, decreasing population size was not responsible for the decreasing effective number of sires with birth years. For the exotic breeds, the positive trends are related with increasing population size, but for the mountain-stone and country sheep, the positive trends are equally associated with improved management of breed diversity and increasing population size. For COF, the main factor appears to be improved breed management. This was demonstrated by a model extended by a linear regression of population size per birth year within breed.
The realized effective population size plays an important role in breed conservation and assessing the endangerment status of breeds (Table S12). We derived N e from the individual rate of inbreeding (∆F i ) to obtain estimates independent of the number of generations recorded in the pedigree data. Both parameters varied in a wide range, similar to previous studies, and showed similar distributions (Table S9).
In the present study, the parameters most strongly correlated with ∆F i across breeds were f a /f e (0.623), f g /f e (0.667), f e (−0.531), and loss of genetic diversity due to unequal contributions of founders (0.799). New inbreeding (F a_New ) had a higher impact on ∆F i (0.755) and N e (−0.756) than the classical inbreeding coefficient (0.649, −0.699), because F a_New had a higher relative contribution to inbreeding. Inverse relationships across breeds were found between N e and f a /f e (−0.590), f g /f e (−0.529), f e (0.652), f (0.687), and unequal founder contributions (−0.716). In previous reports, we found strong correlations between ∆F i and f e /f a (0.873), f g /f e (0.747), and f g /f a (0.632), and between N e and f g /f e (−0.668) and f g /f a (−0.549). In the across-breed comparisons of the present study, loss of genetic diversity due to unequal contribution of founders was found to be the most important factor leading to increasing individual rates of inbreeding and smaller realized effective population sizes. The greatest influence on the loss of genetic diversity due to unequal contributions from founders was the effective number of sires and dams. Data from the across-breed comparisons showed that high effective numbers of dams and high numbers of founders, and high effective numbers of sires and high effective numbers of founders were mutually dependent. Our data suggest that breeding organizations and breeders should be concerned with keeping the number of breeding dams and sires high and using dams and sires as equally as possible in breeding programs.
Breeds with N e values in the critical ranges of 50-100 are considered endangered. In the present study, 15/35 breeds and 5/35 breeds were below a N e of 100 and a N e of 50, respectively. The latter five breeds would reach an estimated increase in inbreeding of 25.89% (GBS), 23.06% (SBS), 19.10% (AST), 17.11% (WAD), and 15.95% (NOL) in 50 years and, thus, be above the critical threshold of a 5% increase in inbreeding in 50 years [48]. The trends in ∆F i were significantly decreasing in GBS, NOL, and WAD and, therefore, we may expect a lower increase in inbreeding rates for these breeds than calculated from the present breed averages. In the breed AST, a slightly negative trend for rate of inbreeding was observed, but for the breed SBS, a slightly increasing trend was observed, which may lead to a lower-than-expected increase in inbreeding in AST, but a higher-than-expected increase in inbreeding in SBS. Only 7/35 (MLS, MFS, MLW, SKF, TEX, RHO, and GGH) and 24/35 breeds are expected not to miss the threshold of 5% and 10% increase in inbreeding in 50 years.
The breeds classified as threatened according to N e < 100 can be grouped into imported and autochthonous breeds (Table S12). While breeds such as Ile-de-France, Dorper, and Zwartbles were imported from France, South Africa, and The Netherlands for meat production, autochthonous breeds including country (BRI, COF, LES, RPL, and WAD), all mountain-stone (e.g., AST, GBS, and SBS), and heath breeds (SKU, WGH, and WHH) were bred in marginal sites under harsh climatic conditions. Since these breeds are adapted to these specific ecosystems, they gained little to no recognition in other regions. In addition, these breeds had mostly fewer foundation animals. Despite these limitations, these autochthonous breeds can be conserved through appropriate breeding management, which is supported via the OviCap database. In addition, the use of marginal landscapes in breeding sheep will increase in the future to save natural areas, and this could create demand for sheep suitable for marginal and harsh ecosystems.
Negative effects of inbreeding are assumed to be mainly caused by recent inbreeding than by ancestral inbreeding, as the frequency of deleterious alleles is expected to decrease over the time through selection [29]. Trends in ancestral inbreeding were positive in all breeds, but on average across all breeds, new inbreeding was attributable to 76.9% of individual inbreeding. Among the breeds with N e < 50, F a_New is responsible for 72.7% of individual inbreeding on average, while in the mountain-stone breed AST and country breed WAD, which belong to breeds with N e < 50, F a_New is only responsible for less than 60% of individual inbreeding. In the breeds with N e > 100, the proportion of F a_New to individual inbreeding reaches 85.9% on average. In summary, the ancestral and new inbreeding coefficients by Kalinowski [27] differ significantly among breeds and breeding directions, and, therefore, may have different impacts on the future development of ∆F i and N e . In particular, in breeds with N e > 100, F a_New has to be regarded in planning future mating, as well as loss of genetic diversity due to unequal contributions of founders and effective number of dams and sires. Among breeding directions, heath sheep had the lowest proportion of F a_New in individual inbreeding, while milk sheep had the highest proportion of F a_New in individual inbreeding. As the proportion of F a_New in individual inbreeding decreases, the loss of genetic diversity due to drift becomes more important for maintaining genetic variability, and, thus, the effective number of founder genomes.

Conclusions
The present study shows the development of demographic measures of genetic diversity and trends of inbreeding for autochthonous sheep breeds and breeds for wool, meat, and milk production in Germany. The across-breed analysis revealed losses of genetic diversity, mainly due to unequal contributions of founders in the past. This parameter had the largest impact in all 35 breeds on new inbreeding (F a_New ), and new inbreeding was much more important for individual rates of inbreeding and realized effective population sizes compared to ancestral inbreeding and the classical inbreeding coefficient. Trends for individual rates of inbreeding were negative in 11 of the 35 breeds analyzed, which may demonstrate the efficiency of maintaining breed diversity. However, the large differences in population structure and breeding history in the different breeds makes it necessary to consider the trends for new and ancestral inbreeding and their impact on breed conservation. In addition, we demonstrated significant differences between the different breeding directions. Mountain-stone sheep breeds had the lowest average Ne value with <50, the lowest number of founders and founder genomes, a relatively high coancestry coefficient on average, positive trends for ancestral inbreeding (F a_Kal ), but negative trends for new inbreeding (F a_New ) and an increasing trend in population sizes and number of effective sires. On the contrary, merino breeds had an average N e > 150 and an expected increase in inbreeding <5% within 50 years, but a negative trend for population sizes and number of effective sires. Annual analyses of demographic data and their trends can be made available through the OviCap national database. This should help to critically review genetic diversity conservation efforts and focus on the most endangered breeds. Along with these analyses, breed associations and breeders can be informed on unequal use of founders and which founder lines are highly threatened and need special consideration in the breeding program. The results of the present study should strengthen the efforts for maintaining the genetic diversity of sheep breeds with a focus on the different ecosystems in Germany.

Supplementary Materials:
The following supporting information can be downloaded at: https://www. mdpi.com/article/10.3390/ani13040623/s1, Figure S1. Number of animals in the reference population (N Ref ) and the number of equivalent generations (EqG) for the birth years 2010 to 2020 for each of the 35 sheep breeds in Germany. Figure S2. Degree of deviation of random mating from Hardy-Weinberg proportion (α) and average coancestry within the parental population (Φ) for the reference populations including birth years 2010-2020 in each of the 35 sheep breeds. Figure S3. Inbreeding coefficients for all (F) and only inbred animals (F inbred ), as well the proportion of inbred animals for the birth years 2010 to 2020 for each of the 35 sheep breeds in Germany. Figure S4. Individual rate of inbreeding (∆F i ) and realized effective population size (N e ) for the birth years 2010 to 2020 for each of the 35 sheep breeds in Germany. Figure S5. Ancestral inbreeding coefficients according to Baumung (AHC), Ballou (F a_Bal ), and Kalinowski (F a_Kal ), and the new inbreeding coefficient according to Kalinowski (F a_New ) for the birth years 2010 to 2020 for each of the 35 sheep breeds in Germany. Table S1. Pedigree analysis for measures of genetic diversity for 35 sheep breeds in Germany and ancestors explaining 30/50/70/90/95% of the gene pool (30%, 50%, 70%, 90%, 95%). Table S2. Amount of genetic diversity accounting for the loss of genetic diversity resulting from genetic drift (GD) or unequal contribution of founders (GD*), losses due to drift in % (Loss drift ), and losses due to unequal contributions of founders in % (Loss founder ) as relative effects for each of the 35 sheep breeds. Table S3. Linear regression coefficients of the inbreeding coefficient for all (F), inbred animals (F inbred ), individual rate of inbreeding (∆F i ), realized effective population size (N e ), effective number of sires and dams (effective sires, effective dams), and effective number of sires and dams corrected for yearly trend of population size (effective sires corrected, effective dams corrected) within breed on birth year with their p-values testing difference to zero for each of the 35 sheep breeds. Table S4. Linear regression coefficients of the inbreeding coefficients according to Ballou (F a_Bal ), Kalinowski (F a_Kal , F a_New ), and Baumung (AHC), within breed on birth year with their p-values testing difference to zero for each of the 35 sheep breeds. Table S5. Least-Square (LS) means for the size of the reference population, genealogical estimators number of founders (f ), effective number of founders (f e ), effective number of founder genomes (f g ), effective number of ancestors (f a ), and the ratios f e /f, f a /f e , f g /f e , losses due to drift and unequal contributions from founders, inbreeding coefficient (F), individual rate of inbreeding (∆F i ), realized effective population size (N e ), expected ∆F i in 50 years, degree of deviation (α) of random mating from Hardy-Weinberg proportions, number of progeny per sire and year, effective number of sires and dams by breeding direction groups with their standard errors, and p-values for differences among LS-means. Table S6. Least-Square (LS) means for the ancestral inbreeding coefficient according to Ballou (F a_Bal ) and Baumung (AHC), and new inbreeding coefficient according to Kalinowski (F a_New ) and its proportion of inbreeding by breeding direction groups with their standard errors, and p-values for differences among LS-means. Table S7. Number of dams (No_dams) and effective number of dams (Effective_dams) for each birth year from 2010 to 2020 with their standard deviations (SD) for each of the 35 sheep breeds. Table S8. Number of sires (No_sires) and effective number of sires (Effective_sires) for each birth year from 2010 to 2020 with their standard deviation (SD) for each of the 35 sheep breeds. Table S9. Overview on previous studies analyzing genetic diversity in sheep breeds using pedigree data. Table S10. Correlations of measures of inbreeding in animals with inbreeding measures of their sires and dams for each of the 35 sheep breeds. Table S11. Correlations of measures of inbreeding among sires and dams for each of the 35 sheep breeds. Table S12. Autochthonous and imported sheep breeds in Germany with their risk levels, sustainable developmental goal (SDG) risk status, and their local endangerment status.  Data Availability Statement: Restrictions apply to the availability of these data. Data were obtained from vit/Verden and are available on reasonable request from the authors with the permission of the German sheep breeding associations.