White-naped mangabeys’ viable insurance population within European Zoo Network

The success and viability of an ex-situ conservation program lie in the establishment and potential maintenance of a demographically and genetically viable insurance population. Such population reserve may support reintroduction and reinforcement activities of wild populations. White-naped mangabeys are endangered restricted-range African primates which have experienced a dramatic population decrease in their natural habitats over the last few decades. Since 2001, some European zoos singularly monitor an ex-situ population aiming to seek the recovery of the current wild population. The aim of the present paper is to evaluate the genetic status and population demographics of European zoo-captive white-naped mangabeys based on pedigree data. The captive population is gradually growing and preserves specific reproductive and demographic parameters linked to the species. The intensive management program that is implemented has brought about the minimization of inbreeding and average relatedness levels, thus maintaining high levels of genetic diversity despite the existence of fragmented populations. This finding suggests white-naped mangabey ex-situ preservation actions may be a good example of multifaceted conservation throughout studbook management which could be used as a model for other ex-situ live-animal populations.

www.nature.com/scientificreports/ The maximum progeny per male and female decreased almost linearly in the current population. However, the mean (± SD) progeny per male was 1.57 ± 4.17 in the historic population and 2.07 ± 4.19 in the current population; 1.68 ± 3.02 and 1.92 ± 2.78 in the historic and current population, respectively, for females. The female/ male ratio is increased in the current population (1.22/1) in respect of the historic population (0.90/1). The percentage of males with progeny selected for breeding, that is all males whose offspring has acted as a breeding male or female, was 45.62% and 84.10% in the historic and current population, respectively; 41.34% and 75.73% for females, all females whose offspring has acted as a breeding female or male ( Table 1). The average generation interval and the mean age of parents at offspring's birth and dispersion statistics (SD and SEM) are presented in Table 2, respectively.

Identity by descent estimators and degree of non-random mating. Although mean (± SD)
inbreeding is low (3.19% ± 0.07% in the historic population and 1.64% ± 0.05%) in the current population), highly inbred animals are present in each population set (12.75% and 4.16% of the animals in the historic and current population, respectively).  www.nature.com/scientificreports/ The percentage of inbred animals was 23.15% and 17.5%; the average (± SD) coancestry was 4.21% ± 2.00% and 4.18% ± 2.00%; and the degree of non-random mating presented mean values of − 0.02 ± 0.07 and − 0.03 ± 0.05, for the two population sets, respectively. The highest values for these three parameters were 0.25 (25%) for different ages between 1985 and 2018, 0.0914 (9.14%) for coancestry in 1997 and 0.225 for non-random mating degree in 1999.
Registered values for mean (± SD) Genetic Conservation Index (GCI) were of 2.84 ± 1.48 and 3.52 ± 1.52 for the historic and current population, respectively. The summary of identity by descent estimators, non-random mating degree and genetic conservation index parameters is presented in Table 3.
The evolution of the non-random mating degree (α), inbreeding rate (F), average relatedness (ΔR), and Genetic Conservation Index (GCI) of the European captive white-naped mangabey from 1951 to 2019 is represented in Fig. 3. Regression equations for the prediction of the evolution of average inbreeding (F) and average relatedness (ΔR) up to 15 generations are shown in Fig. 4. Linear, logarithmic and polynomic functions were tested seeking the best fitting models to describe the trends presented by each parameter. The polynomic function was selected upon considering the functions reporting the highest value for the determination coefficient (R 2 ) 39 .
Probabilities of gene origin, ancestral contributions and genetic diversity. The results for the analysis of the gene origin probabilities, ancestral contributions and genetic diversity, are shown in Table 4.  www.nature.com/scientificreports/ Considering the marginal genetic contribution, the genetic constitution of a single ancestor (identification code: 33) explained 16.99% of the total genetic pool within the population (91.62%), 1.69% of the total inbreeding coefficient (3.09%) and 1.68% of the total coancestry (3.93%). The 10 ancestors with higher marginal genetic contributions were responsible for the total inbreeding and 3.72% of the total coancestry in the population.
The mean (± SD) effective population size calculated by the individual inbreeding rate was 47.33 ± 21.04 in the reference population, whereas the mean (± SD) effective population size based on the individual coancestry rate (N e C i ) was 17.76 ± 1.59. The number of equivalent subpopulations (± SD) was 0.37 ± 0.17.
Herd relationships and breeding strategy. The mean (± SD) number of animals per zoo was 8.51 ± 10.26, ranging from 1 to 40. Related to Wright's F statistics, the inbreeding coefficient relative to the total population 40 was − 0.01, the inbreeding coefficient relative to the subpopulation 41 was − 0.16 and the correlation between randomly drawn gametes from the subpopulation relative to the total population (F ST ) was 0.13 (Table 5). There were considered a total of 561 Nei's genetic distance between the 35 zoos. The average (± SD) Nei's genetic distance was 0.253 ± 0.126. The mean (± SD) coancestry within subpopulations was 0.16 ± 0.02 (16.00% ± 2.00%) and the mean inbreeding was 0.032 ± 0.02 (3.20% ± 2.00%). In the metapopulation, the mean (± SD) coancestry and self-coancestry were 0.04 ± 0.02 and 0.52, respectively.
Zoo structure assessment revealed none of the zoos could be considered the population nucleus neither totally isolated. The number of zoos that used foreign father was 19, whereas 17 used own fathers and 14 used both foreign and own fathers. In total, 28 pairs of zoos showed the greatest Nei's genetic distance (50%) among them. The minimum Nei's genetic distance was 0.0619 (6.19%) and was shared between one pair of zoos (Supplementary Table S1). A cladogram representing all the relationships between the 34 zoos is shown in Fig. 5. www.nature.com/scientificreports/ to 6ª generation, and their prediction from 7ª to 15ª generation. Provided we measured the variability of timeseries data, we relied on the standard error of the mean (SEM) rather than the standard deviation (SD), as it removes variability imposed by the trend in the data, which the SD does not. www.nature.com/scientificreports/

Discussion
Conservation measurements implemented in captive European white-naped mangabeys have focused on maintaining a healthy ex-situ population mimicking the natural framework of the species. The captive population has maintained high genetic diversity and minimized inbreeding levels since 1951 (see Fig. 3). Two of the highest annual birth rates were experienced in 2016 and 2018 (see Fig. 2) 4 . The minimum number of animals born per year (≤ 4) describes a cyclical trend which lasts approximately 20 years, a period after which white-naped mangabeys naturally display signs of reproductive senescence 42 .
The demographic evolution of captive population is parallel to the improvement of the risk situation faced by white-naped mangabeys wild populations, which promoted the reclassification of the species by The Red List of IUCN to the lower threat category of "Endangered" in 2015. The inclusion of twenty-one new institutions reinforced EAZA's network and brought about the addition of new founders (twenty-eight unrelated, wild-born individuals) and genealogy-known individuals to the ex-situ population since 2012 19 . The progressive increase in pedigree knowledge up to 90% at first generation occurred in the context of the scarcely available data from other threatened species held at offsite emplacements for similar conservation purposes (for instance, 27%-35% known pedigree for sable antelope 32,43 and 70.9% for African Penguin 44 ).
This lack of information occurs even if institutions make every effort to implement the most efficient standardized methods. Pedigrees can remain problematic due to multiple reasons, including difficulties associated with discerning parentage with herd or flock breeding 22,23 , low generation depth 24 , unknown founder relationships 25 , and human error 21 , among others 45 .
As a result, the analysis of incomplete pedigree records may lead to biased calculations of demographic and genetic parameters, even if self-sustainability could be expected from most managed populations 46 . For instance, 78% of bird and 52% of mammal captive populations registered in EAZA's studbooks 47 , have pedigree completeness index levels below 85% and 58% fail to achieve the target conditions for sustainability (effective population size, growth rates, sex ratio and similar life-time family sizes across zoos) 46 .
The pedigree completeness levels in our study provide the first evidence of the success of white-naped mangabey ex-situ programme, which in turn enhances the possibilities for protection and recovery at medium and long-term, as long as genealogical recording and intensive management husbandry practices continue 19 .
The captive population constitutes itself a short-term backup reserve if the imminent extinction of wild populations occurred. In fact, it is the intensive management implemented, which aims at preserving the demographic and biologic structure of white-naped mangabeys wild counterparts, which potentializes the breeding capacities of the individuals to effectively retain high levels of genetic diversity. Maximum progeny per male and female were higher in the historic population. However, this could be ascribed to the fact that in the origin of the captive population, the main objective was to ensure a number of animals which may permit the captive population's long-term viability 48 .
High mean progeny per male and female in current population denote the balance of the differential contribution of individuals to reproduction may have effectively contributed to the maintenance of genetic diversity 49 . This was supported by the negative values of F IS (Table 5), suggesting breeding policies implemented may enable maximizing the likelihood of unrelated matings pairs 50 .
Mean age of animals at breeding (Table 1) and mean age of parents at the birth of their offspring selected for breeding ( Table 2) were lower in the current population. This may be indicative of the attempts to maximize reproductive potential promoting maternal reproductive skills and interactions during high fertility periods 42 . In these regards, feeding and handling in early growth stages, first parturition and lactation must be appropriate to ensure reproductive success is not affected 51 .
Prolonging generational intervals can effectively increase the number of animals selected for breeding, progressively increasing effective population sizes and, therefore, generating a proportional reduction in inbreeding 52 , which maximizes the preservation of genetic diversity. To increase selection pressure, older animals with more progeny registries may be required, which may extend generation intervals. Shortening generation intervals may imply younger animals with fewer progeny registries may be considered, which may decrease selection pressure. This negative correlation could be compensated as young animals often present a greater genetic value provided they are the result from maximized genealogical diversity practices 53 . By contrast, reduced generation www.nature.com/scientificreports/ intervals may imply a larger number of animals reach sexual maturity age (set around 6 years old) earlier, with the consequent increase in birth number and population growth rate. Additionally, the balance between such strategies may lead to the success of the breeding programme, as suggested by the relatively low negative values of F IS , which may be indicative of the promotion of breeding policies that consider unrelated animals at a rate at which the population does not excessively depart from Hardy-Weinberg equilibrium.
Mean generation intervals were higher for the current sire-daughter and dam-daughter pathways, which could be explained by a sex-ratio which favours females (Table 1), a common demographic feature to wild populations of the genus Cercocebus 54 which could be ascribed to the philopatric nature of primate females.
This biological condition provides primates with an important functional role for ecosystem health and wellbeing which simultaneously enables the survival and success of offspring to breed 55 . Additionally, in Old World monkeys (Family Cercopithecidae), milk amount and quality may be influenced by offspring sex, to the detriment of baby females 56,57 , which determines a lower growth rate in their early stages and a delay in the mean age of prepuberal females in reproduction. www.nature.com/scientificreports/ Parents' mean age at their offspring's birth was slightly lower than generation intervals ( Table 2), suggesting selection of breeding animals whose offspring may potentially breed is performed slightly later than the moment when their first offspring is born. This way, data and reproductive records (health status, sexual cyclicity and maternal skills) may adjust to life expectancy (males: 26.7 years; females: 34.7 years 58 ) and maximum periods of fertility (males: 19 years; females: 15 years 19 ) of captive individuals.
Historical and current percentages of females with progeny selected for breeding were lower than those of males (also slightly older). This suggests breeding selection policies pay a greater attention to males [either phenotypically (for instance, considering their behaviour, adaptability to environment or resistance to stress 58 ), functionally (reproductive effectiveness) or conservationally (higher levels of genetic diversity and reduced inbreeding)] as suggested for other species 59 . This policies simulate the sexual dispersion of this species, in which the males constitute the migratory sex 60 .
The implementation of a EEP since 2000 significantly contributed to inbreeding and average relatedness reduction 19 . However, levels above 1% and highly inbred animals can be found in the captive population (Table 3), suggesting matings between closely-related animals may still occur. Although inbred individuals could be outcrossed with unrelated individuals from the wild 61 , obtaining new founders from wild populations is difficult, provided these populations currently describe a decreasing trend.
Inbreeding has remained below coancestry levels, suggesting matings among closely-related individuals were unintentionally performed 62 . The different subpopulations are substantially separated, making it difficult to involve different genetic resources. This is consistent with the degree of non-random mating (α) and F IS values, which suggested higher rates of random matings among closely-related individuals may occur, which is common in small-sized populations which develop in limited spaces.
Current ΔF slightly exceeds the recommended maximum of 1%, level below which the fitness of a population steadily decreases [63][64][65] . Hence, effective population size may still not reach the recommended threshold to maintain genetic variability (≥ 50 individuals). However, the trends described for the historical evolution of ΔF report promising outcomes, as there has been a decrease of around 4 points, which may imply genetic variability may be recovering acceptable levels. As Lee and Wilcken 66 stated, a population of any size can be sustainable if a supplementing source population can effectively suit the required harvest of new individuals and cooperation across institutions is well-established. The incorporation of Accra's Zoo (within the species geographical range) in 2010, meant an invaluable source for genetically unrelated wild-born animals which may prevent genetic erosion.
The number of equivalent subpopulations below 1 revealed a high level of population structuration. According to Fernández, et al. 67 , population subdivision may be beneficial, provided the extinction risk derived from compromising events such as accidents or health-related factors, may only cause the disappearance of population sections. Furthermore, genetic diversity may reach its highest levels when populations subdivide into as many separate groups as possible. Still, caution should be taken, provided the benefits of subdivision may be counteracted by the negative effects derived from the reduction in effective size and increase in inbreeding.
Although population structure can greatly affect ΔF, it hardly affects coancestry increase, hence N e C i may more accurately estimate effective population size than N e F i 68 . Hence, progressively adding individuals through the participation of new institutions may be beneficial to maintain a high degree of genetic diversity for as long as possible 19 . Simultaneously, the proportion of translocated males is higher than that of females. This practice may be an additional attempt to simulate the male sexual dispersion of the species 60 , an implicit evolutionary strategy for the prevention of inbreeding increase [69][70][71] .
Values of f e (15.41) and f a /f e (0.71) may suggest the frequent use of a small number of animals for breeding may lead to the loss of genetic variability, which may be supported by the low number of ancestors (5) which explains 50% of population's gene pool. Still, founders' genotypes are represented in the current population. The unequal contribution of founders may be confirmed by the values of f g (11.85) and f a /f e (0.71) as one of the main causes for the current genetic diversity loss. The difference between f e and f a suggests bottlenecks, although not sharply, may have reduced population's genetic variability. The lower the f e /f a is, the greater impact bottlenecks have on the population.
These bottlenecks may be associated to a progressive increase in the occurrence of abnormalities and susceptibility to disease or stressful environmental situations. Such an increased susceptibility may derive from the increase in the incidence of deleterious recessive mutations, which may potentially lead populations to extinction 72 . Mutations that are only mildly deleterious are difficult to eliminate and are the principle cause of inbreeding depression 73 . Furthermore, even if lethal and semi-lethal mutations disappear rapidly due to inbreeding, the large costs of this process may affect population viability 73 .
For instance, infant mortality levels of in white-naped mangabeys in captivity of 37.2% with most deaths occurring within the first two months of life 58 , could potentially be ascribed to increased inbreeding levels (around 25%) in primate captive populations among other factors 74 . However, theoretically, species that are naturally inbred to some degree in the wild, should potentially show less of a deleterious effect when subjected to inbreeding in captivity, which may somehow explain the low representativity of the loss of genetic diversity derived from the occurrence of bottlenecks and genetic drift in the population under study (0.97%) 74 .
Additionally, the difference between f g and f a (11) would suggest the effects of genetic drift on genetic diversity may have been compensated by the higher value of f g . The difference between f g and the number of founders (f) (29) may be indicative of the loss of founder's offspring, inbreeding increase at founder stages, or a combination of both causes 19,75 . This could be justified by the absence of an intensive population breeding programme until 2000 when the EEP 76 of this species was set 19 . Nevertheless, according to genetic theory, twenty unrelated individuals may be enough to retain 97.5% of the wild gene diversity within the founder population 72 .
Long generation intervals found in primates may permit genetically self-sustainability with few founders. In fact, this specific ex-situ programme may have effectively captured at least 90% of wild gene diversity for 100 years since the captive population was established, as most of the EEPs and ESBs within EAZA institutions 77  www.nature.com/scientificreports/ with levels of genetic diversity (95.78%) in the captive population progressively increasing since 2012 (93%) 19 .
Considering that intensive management for this captive population is relatively recent, the maintenance of such high genetic diversity levels may depend on multiple simultaneous factors. For instance, not enough generations may have passed since the decrease in the effectives comprising the wild population pushed the species to its current endangered situation. Hence, generation number in captivity may not be enough to verify the magnitude of genetic variability reduction 8,78 . However, in the absence of conservation efforts, a substantial loss could be confirmed in the near future for these primates. For instance, as reported by Jara et al. 19 , the number of founder genome equivalents was half the number of founders in captive white-naped mangabeys in 2016, which was indicative of either lost descendants of the original founders or that the original founders were inbred, or a combination of these factors.
In this context, the lower difference between founder genome equivalent and number of founders in the present study confirms special efforts may be being made on the preservation of descendants from the founder population, as if the cause for such differences may have been the fact that founder animals were inbred, these values may have remained somehow stable. This supports the fact that the founder population of captive whitenaped mangabeys may have been highly genetically diverse and may have included individuals from a wide range of geographic origins hence, the variability to be expected from wild populations' sub-structuration may be well represented 79 as described for other captive populations of critically endangered species 80 .
Genetic diversity may be the basis for individuals' resilience to the factors that extensively threat their wild populations and the adverse effects of adaptation to captive breeding 81 . In this context, research seeking to understand viability and resilience mechanisms in captive populations may bring about the development of tools which may enable to evaluate genetic diversity levels indirectly. This in turn may help to fulfill conservation purposes more efficiently and practically, as the more diverse populations are, the more capable to adapt to captivity environments they will be as well.
In this sense, a recent population viability analysis simulating different scenarios combining deterministic and stochastic factors and their potential impact on the viability of wild isolated populations of white-naped mangabey has suggested high levels of genetic diversity may be generally maintained under all assumptions (> 90%) 82 . Hence, the subdivided populations could contribute to the conservation of genetic diversity, as shown in wild fragmented populations of other nonhuman primates [83][84][85] .
The minimum Nei's genetic distance between institution pairs, effective population size and Wright's F statistics confirmed a certain subdivision degree. A single institution (26) is at the top of the relationship cladogram (Fig. 5). This may base on the private character of the institution and on the frequent translocation of the offspring born to other zoos, while no genetic material is received (from live animals or assisted reproduction).
Reproductive policies normally consider a small number of ancestors as the basis for subsequent generations, which indirectly replicates the natural isolation patterns found for fragmented wild animal populations 86 . Table 5 suggests the breeding strategy should aim at mating animals keeping relationship coefficients (R) below 10% to maintain the inbreeding below 1%, which may increase effective population size up to a minimum of 50 to counteract the risk of extinction. Breeding animal selection should consider conservation criteria such as mean kinship rankings (average relatedness value of an animal towards the current population) to reduce inbreeding and genetic variability loss 87 .
Bearing this in mind, current pairing/transfer criteria focuses on ranking animals in the population considering their individual inbreeding coefficients (F) and genetic conservation index (GCI). GCI 88 measures the proportion of genes of founder animal i in the pedigree of each particular individual in the population. GCI is a measure of the representativity of founding population in the individuals, and acts as a measure of genetic diversity in the range of the genetic pool of the base population. The highest score in the rank was given to the model obtaining the most desirable value for each particular criterion. For instance, those individuals presenting the lowest inbreeding coefficients may be ranked higher, while those animals presenting the highest genetic conservation indexes will be ranked higher as well. Then, the rest of positions in the rank were determined in ascending or ascending order from the most desirable values to the lowest desirable ones, which are ranked with the value of 1.
Afterwards, as aforementioned inbreeding and GCI differ in terms of which their most desirable values are and what their magnitude is, a combined selection index (ICO) is developed following the premises in Van Vleck 89 to summarize the position in the rank for each of the two parameters. The combined index used (ICO) was as follows; where W 1 is the weight for inbreeding coefficient, W 2 for GCI rank position. All criteria are given the same relevance in the ICO, hence, no coefficient was used, that is the proportion of 1:1 is followed. As a result, the animals presenting greater ICO values are the ones presenting the highest levels of genetic diversity from the pool of the founding population and having those founding genes from the least related animals. Conclusively, the individual values for ICO and mean kinship rankings between pairs of individuals are considered to determine which the most appropriate pairing/transfer candidates are.
This use of mean kinship, inbreeding and GCI values for best guiding of animal pairing is proposed to be more attainable in zoo-kept intensive-managed populations than in other large housing facilities where social structure and therefore mate choices cannot be accurately handled 4 . Such condition may translate into a more successful genetic and demographic intensive management of biodiversity conservation 43 . Comparing genetic diversity and structure between captive and wild populations using genomic markers would help to determine www.nature.com/scientificreports/ the magnitude of the potentially occurring bias when using information from pedigrees and which of these two alternatives may eventually more effective 26,90 .

Methods
White-naped mangabey breeding-management programme in captivity. Barcelona Zoo coordinates the European Studbook (ESB) for the white-naped mangabey. This population breeding/management programme registers the information in respect birth place, birth and death dates, average kinship (average relatedness between an individual to all others in the population, including itself) and transfers of the individuals that are housed in EAZA-member institutions.
Through the compilation of this information, a demographic and genetic assessment is regularly performed to effectively manage the general status of the population. If derived results indicate a non-self-sustaining population at a given time, more intensive management (i.e. increasing the rate of exchange of individuals between zoos and planning matings carefully considering their diversity, inbreeding levels and relatedness) are proposed for the ongoing population viability 19 .
Transfer decisions are based on internal criteria such as lack of space for more individuals in a particular location for welfare issues, existing heavy disputes among congeners sharing resources, desired phenotypic traits and/or low reproduction performance within a captive herd.
Concerning exchanging rates, sixty-eight males and fifty-seven females have been subjected to translocation activities for improved pairing since 1994. In fifty-five cases, this genetic exchange has been made through assisted reproduction techniques by expert veterinarians instead of removing the animals from their living emplacement for mating attending to animal welfare-related logistic and biological constraints (transport and potential destabilization of social hierarchy in acceptor herd).
Data registries and software tools. The historical population comprises 298 animals (157 males and 141 females) born between January 1951 and January 2019. The current population comprised 120 white-naped mangabeys (54 males and 66 females) which were born between September 1987 and January 2019 and are alive. Only thirty-three animals (11%) were wild-born.
Thirty-four European Association of Zoos and Aquaria's member zoos houses white-naped mangabeys and compiles genealogical information for the commitment of this species conservation program's goals 19 (Fig. 1). The studbook was provided by the white-naped mangabey EEP coordinator. The registries consist of the individual name and identification code, sire code, dam code, sex, birthdate (to know the temporal evolution or tendency of some parameters), birthplace (captive-born or wild-born) and status (death or alive).
The demographic and genetic parameters of variability were evaluated using the ENDOG software (v 4.8) 91 . The analysis of the probabilities of genetic origin and ancestral contributions was carried out with the CFC software 92 , on all the data sets. Dendroscope 3 software 93 was used for the graphical representation of the dendrogram based on Nei's genetic distance between subpopulations.

New-born annual increase and pedigree completeness index.
New-born annual median number, maximum and mean number of offspring per sire and dam were calculated. Pedigree completeness index (PCI), which summarizes the percentage of known ancestors of each ascending generation, was evaluated as in Navas et al. 62 computing the maximum number of traced generations; the number of complete traced generations; the number of complete equivalent generations (all known ancestors); and the quality of the genealogical information of the pedigree were determined after the calculation of the proportion of known parents through to greatgreat-great-great-grandparents (first to fifth generation inclusive).
Breeding animals, generation interval and mean age of parents at offspring's birth. Generation intervals were computed as the mean age of parents at the birthdate of their offspring selected for breeding 94 and the mean age of parents at offspring's birth (selected for breeding or not), were calculated for each of the four gametic pathways: sire to son, sire to daughter, dam to son and dam to daughter. These parameters were obtained from the birthdate for every animal together with those of its parents. Female/male ratio was considered the relationship between total number of females and males in historical and current populations.
Identity by descent estimators and degree of non-random mating. Individual inbreeding (F) was computed according to Luo 95 . The average relatedness (ΔR) of each individual or the probability that an allele randomly selected within the population belongs to a given animal, was obtained as proposed by Gutiérrez et al. 91 . The individual rate of inbreeding ( �F) for the number of complete equivalent generations was computed according to Gutiérrez et al. 96 . The individual rate of coancestry ( �C) for the number of complete equivalent generations was computed as suggested by Cervantes et al. 97 . Mean inbreeding (F) per generation and average relatedness (ΔR) were used to issue regression equations fitting lineal, logarithmic and polynomic functions to predict for the evolution of inbreeding and relatedness up to fifteen generations onwards. Non-random mating (α) was calculated as described by Caballero and Toro 98 . Genetic Conservation Index (GCI) or the effective number of founder ancestors of each pedigree, was estimated as proposed by Alderson 88 . Probabilities of gene origin, ancestral contributions and genetic diversity. The effective number of founders (f e ) or founders equally contributing that are expected to generate the same genetic diversity that in the studied population, was computed as; www.nature.com/scientificreports/ where q k is the probability of gene origin of the founder and f the real number of founders 75 . The minimum number of ancestors (f a ), founders or not, necessary to explain the entire genetic constitution of the population, was determined as; where p k is the marginal contribution of an ancestor k, which means the contribution not explained yet by the rest of ancestors 99 . Both parameters (f e and f a ) can be used to summarise the loss of genetic variability because of the non-proportional breeding animals' contribution 100 .
The effective number of founder genomes (f g ) or the number of equally contributing founders without founder alleles loss that are expected to generate the same genetic diversity than in reference population (both parents known), was obtained by calculating the inverse of twice the average coancestry 98 .
The expected marginal contribution of each major ancestor j (the largest genetic contributing founders or not) was computed as the expected genetic contribution independently of the rest of ancestors' contribution 99 .
The contributions to inbreeding of nodal common ancestors (highest marginal genetic contributions) that form inbreeding loops, were obtained according to Colleau and Sargolzaei 101 . An inbreeding loop exists when the ancestor of an individual is that by both maternal and paternal pathway. Mean effective population sizes ( N e ) 102 , was calculated as; The number of equivalent subpopulations 103 was assessed as the relationship between N e Ci = 1 (2�C) or the mean effective population size considering the coancestry coefficient and N e Fi = 1 (2�F) that is the mean effective population size considering the inbreeding coefficient. Genetic diversity (GD) was calculated as 75,104 ; The GD loss (GDL) in the population since the founder generation was estimated as 1 − GD . Considering the different possible causes of this loss, GDL derived from the unequal contribution of founders was calculated as; The difference between GD and GD* is referred to genetic drift accumulated since the foundation of the population 75 .
The effective number of non-founders (N ef ) was calculated as proposed by Caballero and Toro 98 to describe the relationship between the effective number of founders and the number of equivalent genomes of founders.
Zoo relationships and breeding strategy. The relationships between zoos were evaluated using Wright's F statistics and Nei's genetic distance. The Wright's F statistics 105 for each subpopulation (35) were calculated according to Caballero and Toro 106 . Wright's F statistics allow pairwise comparisons among subpopulations or populations but those pairwise "distances" take account only of the data for the two populations concerned, not all the data simultaneously. Still this provides relevant information in the context of pedigree evaluation as the differences between both parameters may account for the estimation bias that may occur. For this reason and to quantify the degree to which populations differs from the entire pool of data using distance measures that make biological assumptions, Nei's distances were used as well. Nei's genetic distance 69 between subpopulations i and j was computed as; where Cij is the average pairwise coancestry between individuals of the subpopulations i and j, including all Ni × Nj pairs. Cii and Cij are the average pairwise within subpopulations i and j, to assess interzoo relationships.
Afterward, a simulation was made to determine the maximum limit of relatedness coefficient existing in the population between mated animals to determine which matings maintained ( F ) in a generation equal or below 1%.
These levels of individual increase in inbreeding correspond to N e = 50. Below these levels fitness of a population noteworthily decreases 107 . Relatedness coefficient (ΔR) can be defined as the probability that two individuals share an allele because of common ancestry. Relatedness coefficient (ΔR) of a pair of mating animals is the potential inbreeding coefficient of their potential offspring. This parameter ranges from 0 (unrelated) to www.nature.com/scientificreports/ 1 (clones or identical twins). This definition excludes alleles that are shared because of belonging to the same species or population. Five mating groups were considered for the simulation. The average relatedness coefficient between mated animals was kept below 0.00%, 5.00%, 10.00%, 15.00% and 20.00% (greatest feasible limit considering all possible mating among all 120 alive animals). The inbreeding coefficient of the offspring for each mating was estimated as one-half of the parental relationship coefficient. The inbreeding rate 96 was calculated by averaging the individual inbreeding increase through; where t i is the number of complete equivalent generations 108 and F i the inbreeding coefficient of the individual i.
For each group, 17 random matings were selected, basing on the number of births in the last natural complete year (2018: 17 births) and on the assumption of one baby per female 42 using SPSS Inc. 109 . Thirty replicates were evaluated within each group to calculate the average effective population size (N e ) as described by Gutiérrez et al. 96 .

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. www.nature.com/scientificreports/