Management of subdivided populations in conservation programs: development of a novel dynamic system

Within the context of a conservation program the management of subdivided populations implies a compromise between the control of the global genetic diversity, the avoidance of high inbreeding levels, and, sometimes, the maintenance of a certain degree of differentiation between subpopulations. We present a dynamic and flexible methodology, based on genealogical information, for the maximization of the genetic diversity (measured through the global population coancestry) in captive subdivided populations while controlling/restricting the levels of inbreeding. The method is able to implement specific restrictions on the desired relative levels of coancestry between and within subpopulations. By accounting for the particular genetic population structure, the method determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals. Computer simulations are used to illustrate the procedure and its performance in a range of reasonable scenarios. The method performs well in most situations and is shown to be more efficient than the commonly accepted one-migrant-per-generation strategy.     

Genetic management of captive populations: the advantages of circular mating

We performed computer simulations to evaluate the effectiveness of circular mating as a genetic management option for captive populations. As a benchmark, we used the method proposed by Fernández and Caballero according to which parental contributions are set to produce minimum coancestry among the offspring and matings are performed so as to minimize mean pairwise coancestry (referred to as the Gc/mc method). In contrast to other methods, fitness does not vary with population size in the case of circular mating, and can be higher than under random mating. Whether circular mating is an effective method in conserving captive populations depends on the trade-off between different considerations. On the one hand, circular mating shows the highest allelic diversity and the lowest mean pairwise coancestry for all population sizes. It also shows a relatively higher efficiency of purging deleterious alleles. More importantly, circular mating can significantly increase the success probability of populations released to the wild relative to the Gc/mc method. On the other hand, circular mating has the drawback of showing high inbreeding rates and low fitness in early generations, which can result to an increase in the extinction probability of the captive populations. However, this increase is slight unless population size and litter size are both very low. Overall, if the slight increase in extinction probability can be tolerated then circular mating fulfils the primary goals of a captive breeding program, i.e., it maintains high levels of genetic diversity and increases the success probability of reintroduced populations.     

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extend of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.     

Genome-Wide Estimates of Coancestry and Inbreeding in a Closed Herd of Ancient Iberian Pigs

Maintaining genetic variation and controlling the increase in inbreeding are crucial requirements in animal conservation programs. The most widely accepted strategy for achieving these objectives is to maximize the effective population size by minimizing the global coancestry obtained from a particular pedigree. However, for most natural or captive populations genealogical information is absent. In this situation, microsatellites have been traditionally the markers of choice to characterize genetic variation, and several estimators of genealogical coefficients have been developed using marker data, with unsatisfactory results. The development of high-throughput genotyping techniques states the necessity of reviewing the paradigm that genealogical coancestry is the best parameter for measuring genetic diversity. In this study, the Illumina PorcineSNP60 BeadChip was used to obtain genome-wide estimates of rates of coancestry and inbreeding and effective population size for an ancient strain of Iberian pigs that is now in serious danger of extinction and for which very accurate genealogical information is available (the Guadyerbas strain). Genome-wide estimates were compared with those obtained from microsatellite and from pedigree data. Estimates of coancestry and inbreeding computed from the SNP chip were strongly correlated with genealogical estimates and these correlations were substantially higher than those between microsatellite and genealogical coefficients. Also, molecular coancestry computed from SNP information was a better predictor of genealogical coancestry than coancestry computed from microsatellites. Rates of change in coancestry and inbreeding and effective population size estimated from molecular data were very similar to those estimated from genealogical data. However, estimates of effective population size obtained from changes in coancestry or inbreeding differed. Our results indicate that genome-wide information represents a useful alternative to genealogical information for measuring and maintaining genetic diversity.     

Effective Size and F-Statistics of Subdivided Populations. II. Dioecious Species

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

Effective Size and F-Statistics of Subdivided Populations. I. Monoecious Species with Partial Selfing

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.     

gesp: A computer program for modelling genetic effective population size,inbreeding and divergence in substructured populations

The genetically effective population size (N_e) is of key importance for quantifying rates of inbreeding and genetic drift and is often used in conservation management to set targets for genetic viability. The concept was developed for single, isolated populations and the mathematical means for analysing the expected N_e in complex, subdivided populations have previously not been available. We recently developed such analytical theory and central parts of that work have now been incorporated into a freely available software tool presented here. gesp (Genetic Effective population size, inbreeding and divergence in Substructured Populations) is R‐based and designed to model short‐ and long‐term patterns of genetic differentiation and effective population size of subdivided populations. The algorithms performed by gesp allow exact computation of global and local inbreeding and eigenvalue effective population size, predictions of genetic divergence among populations (G_ST) as well as departures from random mating (F_IS, F_IT) while varying (i) subpopulation census and effective size, separately or including trend of the global population size, (ii) rate and direction of migration between all pairs of subpopulations, (iii) degree of relatedness and divergence among subpopulations, (iv) ploidy (haploid or diploid) and (v) degree of selfing. Here, we describe gesp and exemplify its use in conservation genetics modelling.     

Methods to estimate effective population size using pedigree data: Examples in dog,sheep, cattle and horse

Background

Effective population sizes of 140 populations (including 60 dog breeds, 40 sheep breeds, 20 cattle breeds and 20 horse breeds) were computed using pedigree information and six different computation methods. Simple demographical information (number of breeding males and females), variance of progeny size, or evolution of identity by descent probabilities based on coancestry or inbreeding were used as well as identity by descent rate between two successive generations or individual identity by descent rate.

Results

Depending on breed and method, effective population sizes ranged from 15 to 133 056, computation method and interaction between computation method and species showing a significant effect on effective population size (P < 0.0001). On average, methods based on number of breeding males and females and variance of progeny size produced larger values (4425 and 356, respectively), than those based on identity by descent probabilities (average values between 93 and 203). Since breeding practices and genetic substructure within dog breeds increased inbreeding, methods taking into account the evolution of inbreeding produced lower effective population sizes than those taking into account evolution of coancestry. The correlation level between the simplest method (number of breeding males and females, requiring no genealogical information) and the most sophisticated one ranged from 0.44 to 0.60 according to species.

Conclusions

When choosing a method to compute effective population size, particular attention should be paid to the species and the specific genetic structure of the population studied.     

Minimization of rate of inbreeding for small populations with overlapping generations

We propose a method that minimizes the rate of inbreeding (delta F) for small unselected populations with overlapping generations and several reproductive age classes. It minimizes the increase in coancestry of parents and optimizes the contribution of each selection candidate. The carrying capacity of the population is limited to a fixed number of animals per year. When survival rate equalled 100%, only animals from the oldest age class were selected, which maximized the number of parents per generation, slowed down the turnover of generations and minimized the increase of coancestry across sublines. However, the population became split into sublines separated by age classes, which substantially increased inbreeding within sublines. Sublines were prevented by a restriction of selecting at least one sire and one dam from the second-oldest age class, which resulted in an L times lower delta F, where L equals the average generation interval of sires and dams. Minimum coancestry mating resulted in lower levels of inbreeding than random mating, but delta F was approximately the same. For schemes where the oldest animals were selected, delta F increased by 18-52% compared with the proposed method.     

METAPOP—A software for the management and analysis of subdivided populations in conservation programs

We introduce a computer program for the dynamic and flexible management of conserved subdivided populations. Using molecular marker data or pedigree information, the software determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals in order to maintain the largest level of gene diversity in the whole population with a desired control in the rate of inbreeding. Restrictions can be introduced for the total number of migrants, and the mating of particular pairs and their contribution. A full genetic diversity analysis of the population is carried out. The optimal contribution from each subpopulation to a pool of maximal gene diversity is also provided by the program.     

Genetic structure analysis of a highly inbred captive population of the African antelope Addax nasomaculatus. Conservation and management implications

The African antelope Addax nasomaculatus is a rare mammal at high risk of extinction, with no more than 300 individuals in the wild and 1,700 captive animals distributed in zoos around the world. In this work, we combine genetic data and genealogical information to assess the structure and genetic diversity of a captive population located at Parque Lecocq Zoo (N=27), originated from only two founders. We amplified 39 microsatellites previously described in other Artiodactyls but new to this species. Seventeen markers were polymorphic, with 2–4 alleles per locus (mean=2.71). Mean expected heterozygosity (He) per locus was between 0.050 (marker ETH3) and 0.650 (marker D5S2), with a global He of 0.43. The mean inbreeding coefficient of the population computed from pedigree records of all registered individuals (N=53) was 0.222. The mean coancestry of the population was 0.298 and F_IS index was ?0.108. These results reflect the importance of an adequate breeding management on a severely bottlenecked captive population, which would benefit by the incorporation of unrelated individuals. Thanks to the successful amplification of a large number of microsatellites commonly used in domestic bovids, this study will provide useful information for the management of this population and serve as future reference for similar studies in other captive populations of this species. Zoo Biol 30:399–411, 2011. © 2010 Wiley‐Liss, Inc.     

Management of genetic diversity in small farm animal populations

Many local breeds of farm animals have small populations and, consequently, are highly endangered. The correct genetic management of such populations is crucial for their survival. Managing an animal population involves two steps: first, the individuals who will be permitted to leave descendants are to be chosen and the number offspring they will be permitted to produce has to be determined; second, the mating scheme has to be identified. Strategies dealing with the first step are directed towards the maximisation of effective population size and, therefore, act jointly on the reduction in the loss of genetic variation and in the increase of inbreeding. In this paper, the most relevant methods are summarised, including the so-called 'Optimum Contribution' methodology (contributions are proportional to the coancestry of each individual with the rest), which has been shown to be the best. Typically, this method is applied to pedigree information, but molecular marker data can be used to complete or replace the genealogy. When the population is subjected to explicit selection on any trait, the above methodology can be used by balancing the response to selection and the increase in coancestry/inbreeding. Different mating strategies also exist. Some of the mating schemes try to reduce the level of inbreeding in the short term by preventing mating between relatives. Others involve regular (circular) schemes that imply higher levels of inbreeding within populations in the short term, but demonstrate better performance in the long term. In addition, other tools such as cryopreservation and reproductive techniques aid in the management of small populations. In the future, genomic marker panels may replace the pedigree information in measuring the coancestry. The paper also includes the results of several experiments and field studies on the effectiveness and on the consequences of the use of the different strategies.     

Conservation genetic management of a critically endangered New Zealand endemic bird: minimizing inbreeding in the Black Stilt Himantopus novaezelandiae

For threatened species with small captive populations, it is advisable to incorporate conservation management strategies that minimize inbreeding in an effort to avoid inbreeding depression. Using multilocus microsatellite genotype data, we found a significant negative relationship between genetic relatedness (inbreeding) and reproductive success (fitness) in a captive population of the critically endangered Black Stilt or KakīHimantopus novaezelandiae. In an effort to avoid inbreeding depression in this iconic New Zealand endemic, we recommend re‐pairing closely related captive birds with less related individuals and pairing new captive birds with distantly related individuals.     

Variable rates of random genetic drift in protected populations of English yew: implications for gene pool conservation

Protecting populations in their natural habitat allows for the maintenance of naturally evolved adaptations and ecological relationships. However, the conservation of genetic resources often requires complementary practices like gene banks, translocations or reintroductions. In order to minimize inbreeding depression and maximize the adaptive potential of future populations, populations chosen for ex situ conservation should be selected according to criteria that will result in a reduction of global coancestry in the population. Generally, large populations should reveal lower coancestry and higher genetic variation than small populations. If detailed knowledge about coancestry is lacking, census population number (N _c ) can be used as a proxy for required characteristics. However, a simple measure of N _c may be misleading in particular cases as genetic processes rely on effective population size (N _e ) rather than N _c and these two measures may differ substantially due to demographic processes. We used an example of English yew to address whether N _c can be a good predictor of genetic parameters when used in conservation programs. Using microsatellite markers, we estimated allelic richness, inbreeding and coancestry coefficients of six relatively large yew populations in Poland. Each population was characterized by N _e using the linkage disequilibrium method. Our results showed that populations of English yew were subject to substantial divergence and genetic drift, with both being inversely proportional to the effective subpopulation size (N _e ). Additionally, allelic richness appeared proportional to N _e but not to N _c . However, the N _e /N ratio differed greatly among populations, which was possibly due to different population histories. From the results we concluded that choosing source populations based only on their census size can be fairly misleading. Implications for conservation are briefly discussed.     

陕西省林麝mtDNA D-loop区序列结构和种群遗传多样性

林麝(Moschus berezovskii)曾广泛分布于中国,由于盗猎和栖息地缩小,秦岭地区野生种群数量迅速下降,圈养繁殖种群已成立了几十年,但大多数圈养种群的遗传背景不清,种群规模增长非常缓慢。为了给这一物种的保护和管理提供有用的信息,调查了陕西省林麝1个圈养种群3个野生种群线粒体DNA(mt DNA)D-Loop 632 bp片段的遗传多样性和种群结构。在69个个体中其碱基组成为A+T的平均含量63.2%高于G+C含量36.8%,共检测到变异位点171个(约占总位点数的27.05%)。核苷酸多样性(Pi)为0.04424,平均核苷酸差异数(K)为19.908。69个个体分属32个单倍型,单倍型间的平均遗传距离(P)为0.070。32个单倍型构建的NJ系统树聚为3个分支,4个林麝群体中的单倍型是随机分布的。4个群体的平均遗传距离为0.043(标准误SE为0.005),凤县养殖场群体与留坝和陇县群体的亲缘关系较远。单倍型间的平均遗传距离为0.043,可见其遗传分化尚未达到种群分化的水平。结果表明,陕西省林麝群体mt DNA D-loop区序列存在着较丰富的变异和遗传多样性,凤县野生群体和凤县养殖场群体的核苷酸多样性和单倍型多样较高,养殖场种群没有出现近亲繁殖及遗传多样性下降的情况。凤县野生群体和凤县养殖场群体两者遗传分化较小,存在着较高的基因流水平。     

Genetic variability and population differentiation in captive baird's Tapirs (Tapirus bairdii)

The objectives of this study were to assess the level of genetic variability and population differentiation within captive populations of an endangered large mammal, Baird's tapir (Tapirus bairdii). We genotyped 37 captive animals from North American (NA) and Central American (CA) zoos and conservation ranches using six polymorphic microsatellite loci. Standard indices of genetic variability (allelic richness and diversity, and heterozygosity) were estimated and compared between captive populations, and between captive and wild population samples. In addition, we evaluated levels of population differentiation using Weir and Cockerham's version of Wright's F-statistics. The results indicate that the NA and CA captive populations of Baird's tapirs have retained levels of genetic variability similar to that measured in a wild population. However, inbreeding coefficients estimated from the molecular data indicate that the CA captive population is at increased risk of losing genetic variability due to inbreeding. Despite this, estimated levels of population differentiation indicate limited divergence of the CA captive population from the wild population. Careful management appears to have kept inbreeding coefficients low in the NA captive population; however, population differentiation levels indicate that the NA population has experienced increased divergence from wild populations due to a founder effect and isolation. Based on these results, we conclude that intermittent exchanges of Baird's tapirs between the NA and CA captive populations will benefit both populations by increasing genetic variability and effective population size, while reducing inbreeding and divergence from wild populations. Zoo Biol 23:521–531, 2004. © 2004 Wiley-Liss, Inc.     

Using genomic tools to maintain diversity and fitness in conservation programmes

Conservation programmes aim at maximizing the survival probability of populations, by minimizing the loss of genetic diversity, which allows populations to adapt to changes, and controlling inbreeding increases. The best known strategy to achieve these goals is optimizing the contributions of the parents to minimize global coancestry in their offspring. Results on neutral scenarios showed that management based on molecular coancestry could maintain more diversity than management based on genealogical coancestry when a large number of markers were available. However, if the population has deleterious mutations, managing using optimal contributions can lead to a decrease in fitness, especially using molecular coancestry, because both beneficial and harmful alleles are maintained, compromising the long‐term viability of the population. We introduce here two strategies to avoid this problem: The first one uses molecular coancestry calculated removing markers with low minor allele frequencies, as they could be linked to selected loci. The second one uses a coancestry based on segments of identity by descent, which measures the proportion of genome segments shared by two individuals because of a common ancestor. We compare these strategies under two contrasting mutational models of fitness effects, one assuming many mutations of small effect and another with few mutations of large effect. Using markers at intermediate frequencies maintains a larger fitness than using all markers, but leads to maintaining less diversity. Using the segment‐based coancestry provides a compromise solution between maintaining diversity and fitness, especially when the population has some inbreeding load.     

Genome-Wide Estimates of Coancestry,Inbreeding and Effective Population Size in the Spanish Holstein Population

Estimates of effective population size in the Holstein cattle breed have usually been low despite the large number of animals that constitute this breed. Effective population size is inversely related to the rates at which coancestry and inbreeding increase and these rates have been high as a consequence of intense and accurate selection. Traditionally, coancestry and inbreeding coefficients have been calculated from pedigree data. However, the development of genome-wide single nucleotide polymorphisms has increased the interest of calculating these coefficients from molecular data in order to improve their accuracy. In this study, genomic estimates of coancestry, inbreeding and effective population size were obtained in the Spanish Holstein population and then compared with pedigree-based estimates. A total of 11,135 animals genotyped with the Illumina BovineSNP50 BeadChip were available for the study. After applying filtering criteria, the final genomic dataset included 36,693 autosomal SNPs and 10,569 animals. Pedigree data from those genotyped animals included 31,203 animals. These individuals represented only the last five generations in order to homogenise the amount of pedigree information across animals. Genomic estimates of coancestry and inbreeding were obtained from identity by descent segments (coancestry) or runs of homozygosity (inbreeding). The results indicate that the percentage of variance of pedigree-based coancestry estimates explained by genomic coancestry estimates was higher than that for inbreeding. Estimates of effective population size obtained from genome-wide and pedigree information were consistent and ranged from about 66 to 79. These low values emphasize the need of controlling the rate of increase of coancestry and inbreeding in Holstein selection programmes.     

Effects of inbreeding on reproductive success,performance, litter size,and survival in captive red wolves (Canis rufus)

Captive‐breeding programs have been widely used in the conservation of imperiled species, but the effects of inbreeding, frequently expressed in traits related to fitness, are nearly unavoidable in small populations with few founders. Following its planned extirpation in the wild, the endangered red wolf (Canis rufus) was preserved in captivity with just 14 founders. In this study, we evaluated the captive red wolf population for relationships between inbreeding and reproductive performance and fitness. Over 30 years of managed breeding, the level of inbreeding in the captive population has increased, and litter size has declined. Inbreeding levels were lower in sire and dam wolves that reproduced than in those that did not reproduce. However, there was no difference in the inbreeding level of actual litters and predicted litters. Litter size was negatively affected by offspring and paternal levels of inbreeding, but the effect of inbreeding on offspring survival was restricted to a positive influence. There was no apparent relationship between inbreeding and method of rearing offspring. The observable effects of inbreeding in the captive red wolf population currently do not appear to be a limiting factor in the conservation of the red wolf population. Additional studies exploring the extent of the effects of inbreeding will be required as inbreeding levels increase in the captive population. Zoo Biol 29:36–49, 2010. © 2009 Wiley‐Liss, Inc.     

An effective rotational mating scheme for inbreeding reduction in captive populations illustrated by the rare sheep breed Kempisch Heideschaap

Within breeds and other captive populations, the risk of high inbreeding rates and loss of diversity can be high within (small) herds or subpopulations. When exchange of animals between different subpopulations is organised according to a rotational mating scheme, inbreeding rates can be restricted. Two such schemes, a breeding circle and a maximum avoidance of inbreeding scheme, are compared. In a breeding circle, flocks are organised in a circle where each flock serves as a donor flock for another flock, and the same donor-recipient combination is used in each breeding season. In the maximum inbreeding avoidance scheme, donor-recipient combinations change each year so that the use of the same combination is postponed as long as possible. Data from the Kempisch Heideschaap were used with computer simulations to determine the long-term effects of different breeding schemes. Without exchanging rams between flocks, high inbreeding rates (>1.5% per year) occurred. Both rotational mating schemes reduced inbreeding rates to on average 0.16% per year and variation across flocks in inbreeding rates, caused by differences in flock size, almost disappeared. Inbreeding rates with maximum inbreeding avoidance were more variable than with a breeding circle. Moreover, a breeding circle is easier to implement and operate. Breeding circles are thus efficient and flexible and can also be efficient for other captive populations, such as zoo populations of endangered wild species.