The amount of genetic diversity in a finite biological population mostly depends on the interactions among evolutionary forces and the effective population size (Ne) as well as the time since population establishment. Because the Ne estimation helps to explore population demographic history, and allows one to predict the behavior of genetic diversity through time, Ne is a key parameter for the genetic management of small and isolated populations. Here, we explored an Ne-based approach using a bighorn sheep population on Tiburon Island, Mexico (TI) as a model. We estimated the current (Ncrnt) and ancestral stable (Nstbl) inbreeding effective population sizes as well as summary statistics to assess genetic diversity and the demographic scenarios that could explain such diversity. Then, we evaluated the feasibility of using TI as a source population for reintroduction programs. We also included data from other bighorn sheep and artiodactyl populations in the analysis to compare their inbreeding effective size estimates. The TI population showed high levels of genetic diversity with respect to other managed populations. However, our analysis suggested that TI has been under a genetic bottleneck, indicating that using individuals from this population as the only source for reintroduction could lead to a severe genetic diversity reduction. Analyses of the published data did not show a strict correlation between HE and Ncrnt estimates. Moreover, we detected that ancient anthropogenic and climatic pressures affected all studied populations. We conclude that the estimation of Ncrnt and Nstbl are informative genetic diversity estimators and should be used in addition to summary statistics for conservation and population management planning.
Citation: Gasca-Pineda J, Cassaigne I, Alonso RA, Eguiarte LE (2013) Effective Population Size, Genetic Variation, and Their Relevance for Conservation: The Bighorn Sheep in Tiburon Island and Comparisons with Managed Artiodactyls. PLoS ONE 8(10): e78120. doi:10.1371/journal.pone.0078120
Editor: William Barendse, CSIRO, Australia
Received: October 19, 2012; Accepted: September 18, 2013; Published: October 11, 2013
Copyright: © 2013 Gasca-Pineda et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This study was supported by a scholarship of the Consejo Nacional de Ciencia y Tecnología (CONACyT) to JGP (number 199870). The authors declare that the funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
It has been recognized that management strategies should consider non-genetic factors (e.g., demography) as well as genetic factors (e.g., genetic drift and inbreeding depression) [1,2]. Although it has been argued that non-genetic factors could be more relevant for conservation [3,4], it is accepted that minimizing the loss of genetic variation is a major goal for the management of small populations [1,5]. Actually, the amount of genetic diversity is considered a parameter for biological conservation [5–7]. In this context, a primary factor responsible for the rate of loss of genetic diversity as well as the rate of increase of inbreeding and genetic drift in a biological population is the effective population size (Ne) [6,8–10]. Therefore, the estimation of Ne has recently become a commonly used parameter in population genetics studies of endangered species [10–14]. Recent methods approximate past changes in Ne, allowing the inference of the population history by estimating changes in historical Ne [15–17]. This makes it feasible to distinguish between historical and recent human-influenced levels of genetic diversity [18,19]. Moreover, the estimation of Ne allows one to predict the behavior of genetic diversity under different demographic scenarios using computational simulations [15,18].
The effective population size (Ne) is defined as the size of a simple Wright-Fisher population that would have the same increase in homozygosity and the same random drift in allele frequencies as in the actual population considered [8,20–22]. Thus, the definition and estimation of Ne will depend on the feature or genetic property of interest, such as the loss of genetic diversity due to genetic drift or inbreeding . In conservation genetics studies, the most widely used definitions [13,15] are the variance effective population size NeV, which measures the variance of change in gene frequency through time due to genetic drift, and the inbreeding effective population size NeI, which is defined in terms of the probability that two individuals have the same parent (i.e., identical by descent) [14,22]. In other words, NeI measures the loss of expected heterozygosity due to relatedness . Based on these definitions, several methods for estimating Ne have been proposed [8,11–15,22,23]. Nonetheless, it is important to bear in mind that certain methods have particular assumptions or data requirements that could be applied to specific cases [8,12,15–17].
Tiburon Island Bighorn Sheep Population
The bighorn sheep (Ovis canadensis) population on Tiburon Island (TI) was founded in 1975 by a single introduction event of 16 individuals (14 ewes and 2 rams) from Punta Chueca Sonora, Mexico  (Figure 1). After this event, the population remained isolated [25–27], and in less than 20 years, the population increased to ~700 individuals [25,27]. This suggests that the TI population has not (at least not yet) shown issues associated with demographic trends, even it has been proposed that the island is near its carrying capacity .
Previous studies underlined the importance of retaining genetic diversity in bighorn sheep [28–31], especially when new populations are founded [28,29]. In general, it has been assumed that the number of founders determines the magnitude of the genetic diversity in captive populations [32–34], although there are some exceptions . This raises relevant questions. Did the founders used represent an "adequate" sampling of genetic diversity (i.e., no original genetic bottleneck)? What can the effects on genetic diversity be for using individuals from TI as the only source for founding new populations?
Hedrick et al.  conducted the first study that explored the genetic diversity and its impact on Ne in TI. They analyzed a limited number of samples (14 individuals, 10 microsatellite loci and 1 MHC locus) and found a lower effective number of founders than the actual number of individuals introduced (14 founders vs. 16 introduced). Recently, another study was published estimating the genetic diversity of the TI population , reporting HE, HO and F' statistics.
In this study, we explored an inbreeding effective population-size-based approach to assess the genetic diversity of the TI population, and the demographic scenarios that could explain such diversity, including its foundation and historical events. In addition, we estimated the possible outcome in terms of NeI and HE of using the TI population as a source of individuals for founding new populations. Finally, to compare our approach, we re-analyzed previously published microsatellite allelic data from seven O. canadensis populations and three other artiodactyl species.
The work met the Mexican legal requirements about animal welfare and field work, and was supervised and approved by Dirección General de Vida Silvestre (DGVS), Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT). The hair sampling was performed in accordance with the Mexican official standard NOM-062-ZOO-1999 (dealing with specific techniques for production, care, and use of laboratory animals). Because hair sampling is a non-invasive technique, it was not necessary to ask for the Institutional SICUAE (Subcomité Institucional para el Cuidado y Uso de Animales de Experimentación) approval.
The sampling in Tiburon Island was conducted under the Seri Government permission, as well as with permission of the owners of "Rincón de la Madera" and "La Mesa" UMAs (Unidad de Manejo para la Conservación de la Vida Silvestre; Management Unit for Wildlife Conservation). The special permit for sample collection was issued under Mexican law by DGVS and SEMARNAT.
Population sampling and DNA extraction
Tiburon Island is located in the Gulf of California near the coast of Sonora, Mexico (Figure 1). The island has an abundant, suitable habitat for bighorn sheep (Ovis canadensis), including mountain ranges and typical continental vegetation dominated by deciduous shrubs and succulent cacti [25,38]. Hair samples were collected from 63 animals captured along the different mountain ranges in Tiburon Island in 2007 (Figure 1). At the time of capture (October), ewes and rams were split and many different herds were found on the island; thus, the sampling was intended to include as many herds as possible. Hair samples were stored in paper envelopes at -80°C until used. DNA was extracted from 15–25 hairs per individual using a standard Chelex (Chelex 100, Bio-Rad) protocol [39,40].
Microsatellite genotyping and mitochondrial sequencing
To evaluate the nuclear genetic diversity, we used a set of 12 microsatellite loci isolated from Ovis aries or Bos taurus (Table S1). These markers had been reported as polymorphic and non-linked. Additionally, some of them had already been used in other genetic diversity studies on bighorn sheep populations [28,36,41]. The Polymerase Chain Reaction (PCR) conditions and primer sequences are reported in Table S1 and Protocols S1. In order to reduce possible genotyping errors, 30% of the sample was re-amplified at random for each locus. To detect possible bias due to stutter, allele dropout, and/or null alleles, we used the statistical tests implemented in Micro-checker version 2.2.3 . In addition, the mitochondrial control region was amplified using the primers previously reported by Boyce et al. . However, three internal primers were designed to obtain shorter fragments (primer sequences and conditions are reported in Protocols S1). Fragment assembly and nucleotide quality assessment were carried out with Consed version 1.9 [44,45]. The sequence alignment was done with ClustalX version 2.1 .
Population genetics analysis
To estimate the genetic diversity of the microsatellite data of the TI population, we calculated the expected heterozygosity (HE), observed heterozygosity (HO), and number of alleles (na), as well as its respective standard deviation (S.D.), using Arlequin version 3.5 . Tests for departures from Hardy-Weinberg expectations through the values of FIS statistic (fixation index, [48,49]) were carried out using the Genepop software, version 4.1 ; the significance of the estimated FIS value was calculated using the Fisher exact test with 10,000 dememorisation steps, 1,000 batches, and 5,000 iterations per batch. We also used Genepop to test for linkage disequilibrium for each pair of loci using the Fisher exact test with the same settings reported above. To detect within-island genetic structures, we used STRUCTURE version 2.3  with 500,000 MCMC iterations followed by a burning period of 250,000 steps. As the TI population was founded using individuals from the same location, the admixture model was implemented . The number of clusters (k) varied from 1 to 10 with 30 iterations for each one. Then, to obtain the most likely value of k, the Evanno et al.  method was applied using Structure Harvester . However, this method excludes the two extreme values of k (in this case, 1 and 10), so all LnP(D) values were plotted against k to visually inspect its behavior and choose the k value with higher likelihood and lower variance. The genetic diversity analysis of the mitochondrial sequences were carried out estimating the number of haplotypes, nucleotide diversity (π), and haplotype diversity using DnaSP version 5.10 .
Population size changes and inbreeding effective size (NeI) estimation
We used the method proposed by Beaumont  and Storz and Beaumont , which considers the inbreeding effective size definition (NeI) . This method explores hypotheses about the historical signal of demographic expansion or contraction in a closed population through coalescent simulations. Then, each hypothesis is evaluated and the parameters values are estimated via Bayesian inference. We chose this method because it does not require life history data and it only uses a single temporal sampling. Moreover, it allows variation on parameters from one locus to the next one (as different mutation rates), so it is suitable for multilocus microsatellite analyses. In addition, it has been used to estimate population size changes of several species, including lemurs  and martens . Finally, this method has demonstrated its robustness for detecting past population size changes . In order to detect signals of a genetic bottleneck, we used MSVAR version 0.4.1  to estimate the ratio of effective population size change r, defined as Ncrnt /Nstbl, where Ncrnt is the current inbreeding effective size and Nstbl is the ancestral stable inbreeding effective size (i.e., before effective population size change). The r ratio is expressed in log10. Thus, if r is negative, the population has declined; if r = 0, the population has remained stable; and if r is positive, expansion is indicated. MVSVAR version 0.4.1 also estimates θ defined as 2Ncrntμ, where μ is the mutation rate and tf is the time interval of the inbreeding effective population size change in generations scaled by Ncrnt. The software was run for 2x109 steps recording 20,000 points from the posterior distribution. The upper and lower bounds for the parameters θ, r, and tf were (-5, 2), (-5.5, 1.5), and (-1, 1), respectively. The limits for r comprised both population reduction and population expansion. If 95% of the High Density Interval (HDI) of the posterior distribution did not reach zero, we considered this as a signal of reduction on inbreeding effective population size. To quantify the time in years since the population size started to change (Tfa) and the ancestral stable and current inbreeding effective population sizes (hereafter Nstbl and Ncrnt), we used the software MSVAR version 1.3 . The number of steps and recorded points was the same as for MSVAR version 0.4.1, and the mean and variance for Nstbl, Ncrnt and Tfa were (4, 2.25), (4, 2.25), (5, 2.5). The generation time for each species was considered as the mean time for female sexual maturity; all values were taken from AnAge Database . For both programs, five independent runs were performed with different random seeds; for MSVAR 1.3, the mean and the variance for the initial values were varied for each parameter and for each run as recommended by the authors. To check Monte Carlo Markov Chain (MCMC) convergence, the Gelman-Rubin statistic  was used as suggested by the software authors, using the coda package  implemented in R version 2.12.1 . The last half of each run was combined to produce a 50,000-step output. The analyses of all posterior distributions were carried out using the packages locfit  and hdrcde . In order to avoid false population-collapse signals due to genetic structure , we analyzed the TI data considering the clustering results obtained with STRUCTURE. The value of each parameter (Nstbl, Ncrnt and Tfa) was reported as the mode of the posterior distribution, using the first and third quartiles as a measure of distribution dispersion.
To test for differences among populations in the Ncrnt and Nstbl estimates, we used the Robust Bayesian Estimate (RBE) . This approach allows a discrete decision about the null value (in this case, that the difference between two estimates is zero). It also provides an estimation of the differences among parameter values, expressed as the mean differences of the marginal posterior distributions including a 95% HDI (High Density Interval). This analysis was performed using the BEST package  implemented in R using the default settings.
TI population Approximate Bayesian Computation analysis and scenario simulations
It has been reported that MSVAR is not suitable for inferring very recent population size changes , as in the case of the TI foundation. In order to investigate the extent of this bottleneck, we performed an Approximate Bayesian Computation (ABC) analysis. The aim of the ABC analysis was to approximate the Ncrnt of the source population (in this case, the Sonora population) that could explain the actual genetic diversity observed in the TI population (Figure S1). We simulated demographic scenarios considering different bottleneck intensities. The actual date of TI foundation (32 years at the time of sampling) and the actual number of founders  were incorporated in the simulations.
The ABC analysis was performed using the DIY-ABC software, version 18.104.22.168 . The scenarios considered were the following: No bottleneck (Scenario A), with Sonora Ncrnt fixed at 271; reduced bottleneck (Scenario B), with Sonora Ncrnt=385; strong bottleneck (Scenario C) using Sonora Ncrnt=500; and severe bottleneck (Scenario D) at Sonora Ncrnt=918 (for details, see Figure S1). The parameters for the ABC analysis used were Tfa, Nstbl and Ncrnt estimates obtained from MSVAR. Additionally, we used the actual time of foundation (approximated at 15 generations ago) as well as the actual number of founders (16 individuals ) (Figure S1). The molecular markers simulated for the ABC analysis correspond to 12 autosomal microsatellite loci with a mean mutation rate (previously obtained with MSVAR) of 3.5x10-4 and a mean P coefficient of 0.22 (to avoid a strict stepwise mutation model). All loci had a 2 bp motif tandem repeat varying in range from of 20 to 40 bp in length. All summary statistics available were calculated and each scenario had 4 million simulations, from which 0.1% was used for parameter estimation. The scenario selection was carried out using the statistical tests implemented by the software.
In addition, to infer the possible impact on the genetic diversity using TI as a source of individuals for founding new populations, we simulated the possible outcome if new populations were founded from the TI population using 8, 16, 32 and 64 individuals (Figure S1). The simulations considered that founded populations had an instant growth to an Ncrnt equal to that estimated for TI. One thousand simulations were performed for each simulated population, and the analyses of the data sets were performed with Genepop using a Perl script (available upon request). The parameters recorded were HO, HE, and na. To evaluate the effects on Ncrnt on the simulated populations, one data set was selected at random and was analyzed using MSVAR version 1.3 using the settings reported above. All graphics and statistical analysis were performed with R.
Re-analyses of managed artiodactyl populations from previously published data
In order to compare the NeI-based approach with other populations and species, we re-analyzed seven populations of bighorn sheep (Table 1): four populations from Oregon, USA (HMO, LGO, SMO, JDO; for details see Table 1); one population from Nevada, USA (SRN) (Californian bighorn sheep, O.c. californiana); one population from New Mexico, USA (RRNM) (the desert sheep, O.c. mexicana); and one from Alberta, Canada (SRA) (the mountain sheep, O.c. canadensis) [29,30]. We also included data from three USA bison (Bison bison) populations : one population from Yellowstone National Park (YNP), founded with native members of the locality and from private herds; and one population each from Wind Cave National Park (WCNP) and Sully’s Hill National Game Preserve (SUH), mainly founded from private herds and zoos. We chose these bison populations because they have similar genetic diversity values and allele numbers but different population sizes, thus representing a good opportunity to investigate the relationship among HE, census size, and Ncrnt (Table 1). In order to compare species with different habitats and distribution, we included a population from another member of the Bovidae family, the Arabian oryx (Oryx leucoryx), from a protected area in Saudi Arabia  and from a captive population from China of the black muntjac (Muntiacus crinifrons) of the Cervidae  (Table 1). The Ncrnt estimation for all data sets was carried out with MSVAR using the scheme previously described for the TI population.
|Ovis canadensis mexicana||Tiburon Island, Sonora, México (TI)||63/12||650–700||Sixteen founders from a single source. Continuous population growth.||This work, 24|
|Ovis canadensis mexicana||Red Rock Refuge, New Mexico, USA (RRNM)||25/10||100–200||Captive herd derived from one source, San Andres Mt. Used as a translocation stock.||30|
|Ovis canadensis canadensis||Sheep River, Alberta, Canada (SRA)||55/10||Local population about 60–150||Historically large population, frequent contact with other herds. Past declines due epidemics.||30|
|Ovis canadensis californiana||Hart Mountain, Oregon, USA (HMO)||16/11||270||Twenty founders from a single source (Williams Lake), decline of the population. Isolation since establishment.||29|
|Ovis canadensis californiana||Leslie Gulch, Oregon, USA (LGO)||23/11||125||Seventeen founders from Hart Mt, posterior introduction of 72 individuals from Hart Mt or Steens Mt.||29|
|Ovis canadensis californiana||Steens Mountain, Oregon, USA (SMO)||18/11||185||Multiple releases from Hart Mt (152 in total), decline of the population.||29|
|Ovis canadensis californiana||John Day River, Oregon, USA (JDO)||19/11||310||Multiple introductions, most from Hart Mt (50 in total).||29|
|Ovis canadensis californiana||Santa Rosa Mountains, Nevada, USA (SRN)||31/11||295||Introductions from multiple sources (53 in total).||29|
|Bison bison||Sully’s Hill National Game Preserve, North Dakota, USA (SUH)||29/14*||35||Nineteen founders from five sources. Species under severe bottleneck.||69|
|Bison bison||Wind Cave National Park, South Dakota, USA (WCNP)||345/14*||350||Twenty founders from two sources (14 from a zoo and 6 from YNP).||69|
|Bison bison||Yellowstone National Park, Wyoming, USA (YNP)||505/14*||3,000||Fifty-one founders from three sources (30 indigenous, 21 from two private herds).||69|
|Oryx leucoryx||Mahazat As-Sayd Protected Area, Saudi Arabia (MNWSA)||24/7||200||Twenty-one samples taken from a protected area, founded from seven distinct groups. Three samples taken from a semi-captive population.||70|
|Muntiacus crinifrons||Hefei Wild Animal Park, China (HWCH)||14/11||45||Lower diversity than in the wild. Population founded from a single wild source.||71|
TI population genetic diversity and structure
We found 40 alleles for the 12 microsatellite loci analyzed. The number of alleles ranged from 2 to 7, with an average of 3.33 (S.D. 1.435) (details for each marker can be found in Tables S2 and S3). In general, the number of alleles per locus was lower than previously reported for O. canadensis [30,41] but higher than those reported by Hedrick et al.  for the same population (see Discussion). The Micro-checker analysis showed the presence of null alleles in locus OarFCB266. However, this locus was kept for future analysis because our simulations showed that a genetic bottleneck, like the one that occurred in the TI foundation, could generate an excess of homozygotes that could lead to a false null allele signal (see TI population ABC analysis section). The overall values of HE and HO were 0.501 (S.D. 0.155) and 0.472 (S.D. 0.159) (Table 2). There were notable differences among loci; for example, MAF48 showed HE=0.238 with 2 alleles, while BM848 had HE= 0.738 with 7 alleles (Table S2). Although positive and negative values of FIS were obtained at different loci (Table S2), only OarFCB266 (in accordance with the null alleles signal) and BM1818 had significant values (FIS=0.3629, p=0.011 and FIS=-0.0016, p=0.044, respectively). The overall locus analyses showed a slight, but significant, positive FIS value of 0.058, indicating a departure from H-W proportions for heterozygote deficit (p=0.008). Tests for linkage disequilibrium showed that 7 of 66 tests had a significant value (p < 0.05). It is worth mentioning that the loci used for this study are located on different chromosomes, except for OarFCB128 and BM2113, which are located in chromosome 2 (but have a distance > 250 cM). However, these loci did not show significant linkage values. We interpret this result as a signal of a population bottleneck, as linkage disequilibrium can be associated with population size reduction and genetic drift . The STRUCTURE analyses recorded the highest posterior probability at k=1; hence, the TI population was considered as a single population for the MSVAR runs.
|HE (S.D.)||na (S.D.)||r||Ncrnt (1st–3rd quartiles)||Nstbl (1st–3rd quartiles)||Tfa (1st–3rd quartiles)|
|O.c. mexicana||TI||0.501 (0.155)||3.33 (1.435)||-2.192||271 (145–436)||10,522 (6,237–20,941)||3,155 (1,517–6,123)|
|O.c. mexicana||RRNM||0.36 (0.268)||2.4 (0.843)||-2.817||191 (63–289)||12,148 (6,823–26,792)||3,211 (862–5,728)|
|O.c. canadensis||SRA||0.596 (0.153)||4.4 (1.173)||*||388 (158–585)||10,551 (6,339–17,906)||1,857 (723–3,457)|
|O.c. californiana||HMO||0.35 (0.262)||2.22 (1.09)||-2.774||62 (25–101)||56,865 (27,415–123,027)||2,951 (1,196–5,202)|
|O.c. californiana||LGO||0.34 (0.220)||2.33 (0.71)||-3.135||42 (15–72)||43,822 (21,379–86,497)||1,508 (564–2,756)|
|O.c. californiana||SMO||0. 32 (0.254)||2.22 (0.97)||-3.287||37 (12–62)||46,206 (24,099–93,111)||1,404 (500–2,518)|
|O.c. californiana||JDO||0.39 (0.232)||2.44 (0.88)||-2.892||57 (22–99)||39,210 (20,464–74,645)||1,938 (725–3,188)|
|O.c. californiana||SRN||0.57 (0.211)||3.78 (1.39)||-2.504||102 (34–179)||25,194 (14,622–44,055)||1,409 (478–2,477)|
|B. bison||SUH||0.604 (0.137)||4 (1.35)||*||45 (12–83)||17,853 (11,588–29,512)||440 (140–797)|
|B. bison||WCNP||0.650 (0.141)||4.92 (1.859)||-2.240||103 (33–162)||19,006 (11,885–30,690)||732 (264–1,229)|
|B. bison||YNP||0.619 (0.120)||4.17 (1.13)||*||220 (78–350)||24,980 (15,812–40,087)||1,803 (664–3,133)|
|O. leucoryx||MNWSA||0.565 (0.078)||3 (0.816)||-4.210||361 (163–587)||77,821 (24,889–242,103)||11,837 (3,606–24,266)|
|M. cinifrons||HWCH||0.675 (0.137)||5.3 (1.368)||*||487 (195–771)||77,357 (48,641–122,744)||1,508 (610–2,415)|
The TI population showed strong signals of a past genetic bottleneck, as the MSVAR r estimate was -2.192, while the estimates of the current (Ncrnt) and ancestral stables (Nstbl) were 271 (145–436, 1st–3rd quartiles) and 10,522 (6,237–20,941, 1st–3rd quartiles) individuals. Nevertheless, the date of the event of population decrease did not correspond to the TI foundation, as the Tfa estimate was 3,155 (1,517–6,123, 1st–3rd quartiles) years ago (Table 2).
Mitochondrial genetic diversity
We recovered the two TI haplotypes previously reported for the species in Genbank (Accession numbers: AY116621, AY116622). The haplotype AY116621 was predominant (present in 97% of the sample). There were 11 segregating sites, the haplotype diversity (H) was 0.125 (S.D. 0.055), and the nucleotide diversity (π) was 0.00249 (S.D. 0.0011).
TI population ABC analysis
The ABC analysis showed that Scenario C (Figure S1) had the highest probability, indicating that an Ncrnt of 500 individuals for the Sonora source population could explain the genetic diversity observed in the actual TI population. The analysis of the TI-simulated data sets showed an average value of HE=0.4897 (S.D. 0.0139) and na =3.639 (S.D. 0.3465), while the Sonora-simulated population had HE =0.5136 (S.D. 0.0128) and na of 4.168 (S.D. 0.317). In accordance with the real data set, we observed the presence of null alleles in a random sample of 100 simulations taken from the TI-simulated data (analyzed with Micro-checker). A g-test performed against a binomial distribution , based on 5% of the random variation, showed that the observed results departed from a stochastic process (p< 0.005). This finding suggests that the null allele signal observed in the OarFCB266 locus in the real TI population could be explained by a deficiency of heterozygotes on this locus. This deficiency could be caused by the population size reduction, due to the TI foundation, more than an artifact of the PCR amplification. As expected, the Sonora-simulated population showed higher diversity (t-test p=0.0002) than the TI-simulated population. In the hypothetical populations, we observed a steady decrease in HE and na as the number of founders was reduced (Figure 2A). This tendency can also be observed in the Ncrnt estimates (Figure 2B, Tables S4 and S5).
A) Plot of the loss of expected heterozygosity (HE) and mean number of alleles (Na) for the simulated scenarios. Number of founders correspond to population founded from TI-simulated population. Error bars correspond to standard error using the number of loci as sample size. B) Change in the inbreeding effective size (Ncrrnt) of TI- and Sonora-simulated populations, as well as for the new one founded from TI. Error bars represent first and third quartiles of the parameter distribution.
Current and ancestral stable inbreeding effective sizes and dates of size change of re-analyzed data sets
As shown in Table 2, all populations of bighorn sheep and other species showed signals of population decline. The MSVAR r estimate ranged from -2.24 for WCNP to -4.21 for MNWSA. We observed that the Gelman-Rubin statistic showed that some populations did not reach convergence (SRA, HWCH, YNP, and SUH). Nevertheless, as the 95% HDI of the Ncrnt and Nstbl posterior distributions did not overlap, we take this result as a significant signal of population size change.
The Ncrnt estimates exhibited differences among species and contrasting values within bighorn sheep and bison populations (Figure 3, Table 2). The Ncrnt obtained for bighorn sheep ranged from 37 (12–62, 1st–3rd quartiles) individuals for SMO to 388 (158–585, 1st–3rd quartiles) for SRA (Table 2). In the case of bison, the Ncrnt values were 45 (12–83, 1st–3rd quartiles), 103 (33–162, 1st–3rd quartiles), and 220 (78–350, 1st–3rd quartiles) for SUH, WCNP, and YNP, respectively. The Ncrnt estimates for the black muntjac (HWCH) were 487 (195–771, 1st–3rd quartiles) and 361 individuals (163–587, 1st–3rd quartiles) for the Arabian oryx (MNWSA). According to the Robust Bayesian Estimate (RBE) analysis, all paired comparisons of the Ncrnt estimates between populations showed significant differences (all comparisons are reported in Table S6).
Dots correspond to the modal value of parameter distributions obtained with MSVAR 1.3. Error bars represent the first and third quartiles.
The ancestral stable (Nstbl) estimates also had large ranges (Table 2, Figure 3). The O. canadensis populations exhibited values from 10,551 (6,339–17,906, 1st–3rd quartiles) for SRA to 56,865 (27,415–123,027, 1st–3rd quartiles) individuals for HMO. The SUH and WCNP bison populations showed 17,853 (11,588–29,512, 1st–3rd quartiles) and 19,006 (11,885–30,690, 1st–3rd quartiles) individuals, and the YNP population showed 24,980 (15,812–40,087, 1st–3rd quartiles) individuals. The estimates for MNWSA and HWCH were 77,821 (24,889–242,103, 1st–3rd quartiles) and 77,357 (48,641–122,744, 1st–3rd quartiles). All paired comparisons of Nstbl estimates and their significance are reported in Table S7.
The estimates of time of population size change (Tfa) are shown in Figure 3 and Table 2. The O. canadensis populations ranged from 1,404 years (500–2518, 1st–3rd quartiles) for SMO to 3,211 years (862–5,728, 1st–3rd quartiles) for RRNM. The bison SUH and WCNP populations showed recent Tfa values (440 years, 140–797, 1st–3rd quartiles and 732 years, 264–1,229, 1st–3rd quartiles), while YNP had 1,803 (664–3,133, 1st–3rd quartiles) years. HWCH showed a similar value to bighorn sheep populations (1,508 years, 610–2,415, 1st–3rd quartiles) while MNWSA was rather ancient (11,837 years, 3,606–24,266, 1st–3rd quartiles). Except for MNWSA, most of the Tfa results were similar and their interquartile intervals overlapped. Even more, some populations presented almost the same Tfa estimate (e.g., TI and RRNM, Table 2, Figure 4).
Solid line corresponds to Younger Dryas (11,000 years ago). The dashed line corresponds to late Holocene droughts (4,200 years ago), the dot-dash line corresponds to the first hunting pressures for bison (550 years ago) and the dotted line corresponds to the introduction of horses to North America (150 years ago). Dots correspond to the modal value of the parameter distribution obtained with MSVAR 1.3, and error bars correspond to first and third quartiles.
Genetic diversity and management of TI population
The HE estimated for TI was lower than the reported free-ranging or wild O. canadensis populations (e.g., SRA) but was higher than the estimates for other managed populations [29,30]. Our results differ from those of Hedrick et al. , as we find higher HE values (0.501 vs 0.420). However, this difference could be due to the difference in sample size that led to a sub-sampling of alleles and, therefore, a genetic diversity underestimation (we recovered one more allele on two of the same loci analyzed). Nevertheless, our analyses indicate that the TI population is not free from a genetic bottleneck. The simulations showed that TI suffered a bottleneck that reduced its Ncrnt to about half of the source population, and that the use of TI as a source for translocation of individuals could lead to a severe Ncrnt reduction, especially when a low number of founders are used. For example, using 16 founders the genetic diversity loss for HE was 3% and for Ncrnt was 25%; meanwhile, using 8 founders we observed a reduction of 8% in HE, and Ncrnt was reduced by about 82% (Figures 2A and 2B, Table S4). Considering our results, we do not recommend the use of the TI population as the only source for restocking other populations. Instead, we suggest the use of individuals from several sources in order to prevent the reduction of effective size and the consequent diminution of genetic variation [6,9,11,29,30,36].
So, what could explain the apparent success of the TI population and the relatively high levels of genetic diversity? It has been argued that the lack of predators, as well as the suitable habitat, promoted a steady growth of the population [25,74]. However, the demographic growth itself does not ensure the retention of genetic diversity. For example, a demographic increase with a continuous reduction in genetic diversity due to genetic drift and inbreeding was reported in mountain goats (Oreamnos americanus) . The authors stated that this could be a consequence of a small Ne caused by the mating system of the species and the isolation of the population . In the case of bighorn sheep, it has been reported that sexual segregation is strongly influenced by the presence of predators , and that in their absence, the herds can have a more homogeneous male-female proportion allowing ewes to mate with several males despite the dominance hierarchy . This minimizes the effects on Ne due to an uneven male allelic contribution by polygynous behavior [77,78]. However, no studies have been done on the fine-scale population dynamics of TI; therefore, it is unknown at the present time if different groups of animals may act as isolated herds. In this sense, the estimated FIS could be due not only to TI foundation, but also to the Wahlund effect caused by the social structure of the herds in TI. Another factor promoting high levels of genetic diversity is natural selection. Kaeuffer et al.  observed that in a single-pair founded mouflon (Ovis aries) population, genetic diversity could be influenced by natural selection, thus overtaking the effects of genetic drift. In this sense, it has been recognized that natural selection plays an important role in maintaining genetic diversity in bighorn sheep .
Current and ancestral stable inbreeding effective sizes and genetic diversity
In general, we found a positive relationship between HE and Ncrnt. However, the results also showed deviations from this pattern (Table 2). For example, for O. canadensis populations, the TI population showed an Ncrnt estimate larger than SRN; however, SRN had a higher HE than that of TI (Table 2, Table S6). Similarly, RRNM had a relatively low HE, but its Ncrnt was higher than the Ncrnt for all the populations from Oregon (HMO, LGO, SMO, and JDO) (Table 2, Figure 2). The HE reported for the SRA population was ~5% larger than that reported for SRN (Table 2), while the estimated Ncrnt for SRA was about two times larger than that estimated for SRN (Table S6). In the case of bison populations  (Table 2), the reported HE for the three populations were similar, but our Ncrnt estimates were contrasting. The Ncrnt estimate for YNP is larger than that of WCNP, although WCNP had higher HE than YNP (Table 2, Table S6). Instead, YNP has relatively high levels of HE and Ncrnt. This could be explained by the fact that the YNP population had a large census size and was founded using native animals. In contrast, SUH showed a considerably low Ncrnt, even though this population had a HE of 0.604 (Table 2).
The black muntjac (HWCH) and Arabian oryx (MNWSA) populations had the largest Ncrnt estimates, yet they have small census sizes, especially the black muntjac. In the case of HWCH, the population was founded from a single wild source ; thus, the estimated Ncrnt could correspond to the source population and not necessarily to the actual captive population. MNWSA is similar; however, since this population was founded using several sources instead of a single source, MNWSA could offer a better representation of the source or original genetic pool. For both populations (HWCH and MNWSA), it is likely that not enough time has passed to decrease the “effective size signal” by drift or inbreeding depression and, consequently, to erode the genetic diversity [3,10].
The contrasting patterns between the HE and Ncrnt estimates could be attributed to the fact that genetic variation could be restored more rapidly than the Ncrnt. In this sense, the introduction of alleles can promote an increase of HE but not necessarily of Ncrnt. This could be the case for bighorn populations, such as SRN, SUH and WCNP, that showed relatively high levels of HE but lower Ncrnt when compared with other populations. For MNWSA and HWCH, it is clear that the populations could not retain such genetic diversity, so it is imperative to increase the census number of both populations in order to avoid a future reduction of Ncrnt and the associated genetic diversity loss.
The differences observed between Nstbl and Ncrnt were of at least one order of magnitude (Figure 3), suggesting a considerable genetic bottleneck for all species. In the case of the bighorn sheep populations, the TI, RRNM, and SRA Nstbl estimates were similar, while the Californian bighorn sheep populations exhibited the largest and most variable estimates of Nstbl (Table 2, Figure 3). The HMO population was founded with individuals from the Williams Lake population in Canada, while LGO and SMO were founded mostly with individuals from HMO . The Nstbl estimates for these populations actually may represent the ancestral stable effective size of the Williams Lake population, and the differences observed may be due to the sub-sampling represented by the LGO and SMO populations. On the other hand, the difference observed in JDO and SRN could be explained by the fact that these populations were founded from several different sources that could represent a mixed ancestral genetic pool. The bison populations showed similar Nstbl values; however, this was expected considering that bison populations could share the same genetic pool due to translocation history. Nevertheless, the Nstbl estimate for each population is relatively small considering the estimates for the reports of the historical size of bison . These results suggest that in the past, bison populations could have remained as relatively small and isolated demes, so local sampling of herds represented the diversity of each deme. Finally, the non-American species had the largest Nstbl observed by far, which could indicate that their populations were very large and that they had large, interconnected populations that resulted in larger Nstbl estimates.
It is necessary to consider the factors that influence and possibly bias our Nstbl estimates: i) the analyzed populations could have historical genetic flow with other populations, and ii) the antiquity of the ancestral stable population size. Historical interconnections with other populations could lead to an Nstbl overestimation, as MSVAR assumes that the sample represents a closed population [56,57]. In addition, Schwartz et al.  and Beaumont  stated that, on long time-scales, the estimates of Ne obtained from genetic data (in our study, Nstbl) could approach the global Ne for the species, yielding historical Ne estimates very different from actual local census size.
The time of the population size change Tfa, and anthropogenic pressures
The European colonization of the Americas has been considered as one of the most important factors influencing the decline of the bighorn sheep populations . However, our Tfa estimates suggested that other factors besides the European settlement could have affected the bighorn sheep populations (Figure 4, Table 2). It has been reported that the climate changes during the Holocene restricted vegetation cover and water availability [82–86]; however, the climate became less arid in the late Holocene, allowing the artiodactyl populations to grow . Nevertheless, archaeological and paleontological records across North America revealed that, although the environmental conditions were favorable for artiodactyls, the hunting pressures by Native Americans appear to have caused substantial declines in artiodactyl populations [86–89]. The Tfa values obtained could be related to an ancient and continuous population decrease driven mostly by human foragers who took advantage of the increased high artiodactyl densities .
As in the case of the bighorn sheep populations, the Holocene droughts, as well as hunting pressures, could have influenced the bison populations . For example, the Tfa for YNP is in accordance with fossil abundance in the locality, having peaked in the late Holocene . However, more recent Tfa values were found in SUH and WCNP (Figure 4). It has been documented that considerable anthropogenic pressures on bison populations began around 550 years ago and increased 150 years later with the introduction of horses [91,92]. This finding indicates that the SUH and WCNP populations had a strong population-decline signal, primarily driven by hunting in the last centuries, of such magnitude that it overwhelmed the Holocene influence. In contrast, YNP was the only population that had native individuals; thus, its Tfa estimate represents the time of population size change of a relict population, while SUH and WCNP estimates relate to more recent anthropogenic pressures.
Booth et al.  reported that severe droughts at ~4.2 kyr are recorded at multiple mid-latitude and subtropical sites on all other continents of the Northern Hemisphere. This suggests that the Late Holocene climate changes could influence artiodactyls in other continents, including black muntjac. Finally, the MNWSA Tfa value corresponds to another important climatic event, the Younger Dryas (11,000 years ago) . This event is characterized by a striking increase of aridity. This caused a retreat of herbaceous plants in Southwest Asia  that could have influenced oryx populations. The NeI reduction in this species could reflect a severe influence of climatic changes and/or could be partly due to human activities.
The estimation of the effective population size provides additional information about genetic diversity. In this sense, our results showed that past human influences and possibly climatic changes played a major role in demographic trends on the artiodactyls studied here. Moreover, the use of Ncrnt and Nstlb estimates allows a glimpse of the possible fate of genetic diversity in the future (for example, the effects of genetic drift or posterior bottlenecks). Thus, the effective size estimation, along with classic summary statistics, allows us to make better decisions for planning management and conservation strategies.
Schematic representation of the ABC-analysis scenarios. From past to present, the simulations are as follows: Begin with an ancestral population that had a constant effective size (Nstlb); the population had a size change at an exponential rate during the Tfa years (in this case, scaled to generations). Fifteen generations before the present, the TI foundation occurred, represented as the continental (Sonora) and TI population split. Finally, in the present (Ncrnt), 63 samples were taken from TI. We considered the actual information on the TI foundation (16 founders, 30 years ago), and parameters Nstlb, Ncrnt and Tfa were obtained from the MSVAR analysis. To determinate the most likely Ncrnt of the Sonora source population, four scenarios were considered: (A) no genetic bottleneck fixing size at 271 individuals; (B) reduced considering 385 individuals; (C) strong 500; and (D) severe bottleneck 918. Finally, in order to predict the effects on genetic diversity of using TI as source for founding new populations, we simulated the outcome for 64, 32, 16, and 8 founders using the most likely scenario obtained with the ABC-analysis.
Protocols for the amplification and genotyping of the molecular markers used in this study.
Chromosomal position, primer sequences, MgCl2 concentration, alignment temperature, and references of the microsatellite loci used in this study.
Summary statistics of microsatellite markers used in this study.
Allele size and frequencies of microsatellite loci used in this study.
HE and na values obtained from the ABC-analysis.
Current effective inbreeding population size (Ncrnt) obtained form the ABC-analysis simulations.
Paired comparisons of current inbreeding effective population size (Ncrnt) estimates using Robust Bayesian Estimates (RBE).
Paired comparisons of ancestral stable effective population size (Nstbl) estimates using Robust Bayesian Estimates (RBE).
All research was carried out at the Instituto de Ecología (UNAM). This paper is part of the doctoral research of the first author at Programa de Doctorado en Ciencias Biomédicas, UNAM. We want to thank Dr. Erika Aguirre, M.Sc. Laura espinosa and M.Sc. Patricia Padilla for their technical assistance in the laboratory. We are grateful to Felipe Rodríguez, UMA Rincón de La Madera, UMA La Mesa, and the Seri Government for their permission to work on Tiburon Island. Also we are grateful to Dr. R.T. Hanlin for his generous help with the English. We thank Dr. M. S. Boyce, Dr. M. festa-Bianchet, Dr. William Barendse, and three anonymous reviewers for their valuable comments. Finally, we want to thank Dr. Erika Aguirre, M.Sc. Patricia Vélez, M.Sc. Gabriela Castellanos Morales, and Alexander Ochoa for their comments for the improvement of the manuscript.
Conceived and designed the experiments: JGP IC RA LEE. Performed the experiments: JGP RA LEE. Analyzed the data: JGP IC RA LEE. Contributed reagents/materials/analysis tools: JGP IC RA LEE. Wrote the manuscript: JGP LEE.
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