An experimental evaluation with Drosophila melanogaster of a novel dynamic system for the management of subdivided populations in conservation programs

A dynamic method (DM) recently proposed for the management of captive subdivided populations was evaluated using the pilot species Drosophila melanogaster. By accounting for the particular genetic population structure, the DM determines the optimal mating pairs, their contributions to progeny and the migration pattern that minimize the overall coancestry in the population with a control of inbreeding levels. After a pre-management period such that one of the four subpopulations had higher inbreeding and differentiation than the others, three management methods were compared for 10 generations over three replicates: (1) isolated subpopulations (IS), (2) one-migrant-per-generation rule (OMPG), (3) DM aimed to produce the same or lower inbreeding coefficient than OMPG. The DM produced the lowest coancestry and equal or lower inbreeding than the OMPG method throughout the experiment. The initially lower fitness and lower variation for nine microsatellite loci of the highly inbred subpopulation were restored more quickly with the DM than with the OMPG method. We provide, therefore, an empirical illustration of the usefulness of the DM as a conservation protocol for captive subdivided populations when pedigree information is available (or can be deduced) and manipulation of breeding pairs is possible.     

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.     

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.     

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.     

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.     

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.     

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.     

Fine scale population genetic structure of pumas in the Intermountain West

In this study, I examined the population genetic structure of subpopulations of pumas (Puma concolor) in Idaho and surrounding states. Patterns of genetic diversity, population structure, levels of inbreeding, and the relationship between genetic differentiation and dispersal distance within and between 15 subpopulations of pumas were compared. Spatial analyses revealed that the Snake River plain was an important barrier to movement between northern and southern regions of Idaho. In addition, subpopulations south of the Snake River plain exhibited lower levels of genetic diversity, higher levels of inbreeding, and a stronger pattern of isolation by distance relative to subpopulations north of the Snake River plain. Lower levels of diversity and restricted gene flow are likely the result of historically lower population sizes in conjunction with more recent changes in habitat use and available dispersal corridors for movement. The subdivision of puma populations north and south of the Snake River plain, along with the patterns of genetic diversity within regions, indicate that landscape features are affecting the population genetic structure of pumas in Idaho. These results indicate that information about the effects of landscape features on the distribution of genetic diversity should be considered when designing plans for the management and conservation of pumas.     

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.     

Maintaining genetic diversity using molecular coancestry: the effect of marker density and effective population size

Background

The most efficient method to maintain genetic diversity in populations under conservation programmes is to optimize, for each potential parent, the number of offspring left to the next generation by minimizing the global coancestry. Coancestry is usually calculated from genealogical data but molecular markers can be used to replace genealogical coancestry with molecular coancestry. Recent studies showed that optimizing contributions based on coancestry calculated from a large number of SNP markers can maintain higher levels of diversity than optimizing contributions based on genealogical data. In this study, we investigated how SNP density and effective population size impact the use of molecular coancestry to maintain diversity.

Results

At low SNP densities, the genetic diversity maintained using genealogical coancestry for optimization was higher than that maintained using molecular coancestry. The performance of molecular coancestry improved with increasing marker density, and, for the scenarios evaluated, it was as efficient as genealogical coancestry if SNP density reached at least 3 times the effective population size.However, increasing SNP density resulted in reduced returns in terms of maintained diversity. While a benefit of 12% was achieved when marker density increased from 10 to 100 SNP/Morgan, the benefit was only 2% when it increased from 100 to 500 SNP/Morgan.

Conclusions

The marker density of most SNP chips already available for farm animals is sufficient for molecular coancestry to outperform genealogical coancestry in conservation programmes aimed at maintaining genetic diversity. For the purpose of effectively maintaining genetic diversity, a marker density of around 500 SNPs/Morgan can be considered as the most cost effective density when developing SNP chips for new species. Since the costs to develop SNP chips are decreasing, chips with 500 SNPs/Morgan should become available in a short-term horizon for non domestic species.     

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.     

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.     

Positive assortative mating with selection restrictions on group coancestry enhances gain while conserving genetic diversity in long-term forest tree breeding

Selection and mating principles in a closed breeding population (BP) were studied by computer simulation. The BP was advanced, either by random assortment of mates (RAM), or by positive assortative mating (PAM). Selection was done with high precision using clonal testing. Selection considered both genetic gain and gene diversity by "group-merit selection", i.e. selection for breeding value weighted by group coancestry of the selected individuals. A range of weights on group coancestry was applied during selection to vary parent contributions and thereby adjust the balance between gain and diversity. This resulted in a series of scenarios with low to high effective population sizes measured by status effective number. Production populations (PP) were selected only for gain, as a subset of the BP. PAM improved gain in the PP substantially, by increasing the additive variance (i.e. the gain potential) of the BP. This effect was more pronounced under restricted selection when parent contributions to the next generation were more balanced with within-family selection as the extreme, i.e. when a higher status effective number was maintained in the BP. In that case, the additional gain over the BP mean for the clone PP and seed PPs was 32 and 84% higher, respectively, for PAM than for RAM in generation 5. PAM did not reduce gene diversity of the BP but increased inbreeding, and in that way caused a departure from Hardy-Weinberg equilibrium. The effect of inbreeding was eliminated by recombination during the production of seed orchard progeny. Also, for a given level of inbreeding in the seed orchard progeny or in a mixture of genotypes selected for clonal deployment, gain was higher for PAM than for RAM. After including inbreeding depression in the simulation, inbreeding was counteracted by selection, and the enhancement of PAM on production population gain was slightly reduced. In the presence of inbreeding depression the greatest PP gain was achieved at still higher levels of status effective number, i.e. when more gene diversity was conserved in the BP. Thus, the combination of precise selection and PAM resulted in close to maximal short-term PP gain, while conserving maximal gene diversity in the BP.Communicated by O. Savolainen     

Controlling genetic variability by mathematical programming in a selection scheme on an open-pollinated population in Eucalyptus globulus

A model using integer quadratic mathematical programming has been developed to control the inbreeding level (or genetic diversity) through group coancestry in a selection programme for a forestry population structured in terms of maternal families coming from different locations. A method to calculate the average group coancestry between- and within-families for these open-pollinated populations is also proposed. This model has been applied to data from a breeding programme of Australian Eucalyptus globulus. The strategy proved to be effective as reductions of up to 50% for the group coancestry of the selected individuals were reached with a loss of only 5% of the maximum attainable selection differential (corresponding to truncation selection). Received: 14 October 1999 / Accepted: 26 July 2000     

Fixed contributions designs vs. minimization of global coancestry to control inbreeding in small populations

Populations with small census sizes are at risk because of the loss of genetic variability and the increase of inbreeding and its harmful consequences. For situations with different numbers of males and females, several hierarchical designs have been proposed to control inbreeding through the fixation of individuals' contributions. An alternative method, based on the minimization of global coancestry, has been proposed to determine contributions as to yield of the lowest levels of inbreeding in the population. We use computer simulations to assess the relative efficiency of the different methods. The results show that minimizing the global coancestry leads to equal or lower levels of inbreeding in the short and medium term, although one of the hierarchical designs provides lower asymptotic inbreeding rates and, thus, less net inbreeding in the long term. We also investigate the performance of the alternative methods against departures from the ideal conditions, such as inbred or differentially related base individuals and random failures in the expected contributions. The method of minimization of global coancestry turns out to be more flexible and robust under these realistic situations.     

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.     

A comparison of the population genetic structure of parasitic Viscum album from two landscapes differing in degree of fragmentation

Parasite populations do not necessarily conform to expected patterns of genetic diversity and structure. Parasitic plants may be more vulnerable to the negative consequences of landscape fragmentation because of their specialized life history strategies and dependence on host plants, which are themselves susceptible to genetic erosion and reduced fitness following habitat change. We used AFLP genetic markers to investigate the effects of habitat fragmentation on genetic diversity and structure within and among populations of hemiparasitic Viscum album. Comparing populations from two landscapes differing in the amount of forest fragmentation allowed us to directly quantify habitat fragmentation effects. Populations from both landscapes exhibited significant isolation-by-distance and sex ratios biased towards females. The less severely fragmented landscape had larger and less isolated populations, resulting in lower levels of population genetic structure (F _ST = 0.05 vs. 0.09) and inbreeding (F _IS = 0.13 vs. 0.27). Genetic differentiation between host-tree subpopulations was also higher in the more fragmented landscape. We found no significant differences in within-population gene diversity, percentage of polymorphic loci, or molecular variance between the two regions, nor did we find relationships between genetic diversity measures and germination success. Our results indicate that increasing habitat fragmentation negatively affects population genetic structure and levels of inbreeding in V. album, with the degree of isolation among populations exerting a stronger influence than forest patch size.     

Pedigree estimation of the (sub) population contribution to the total gene diversity: the horse coat colour case

A method to quantify the contribution of subpopulations to genetic diversity in the whole population was assessed using pedigree information. The standardization of between- and within-subpopulation mean coancestries was developed to account for the different coat colour subpopulation sizes in the Spanish Purebred (SPB) horse population. The data included 166264 horses registered in the SPB Studbook. Animals born in the past 11 years (1996 to 2006) were selected as the 'reference population' and were grouped according to coat colour into eight subpopulations: grey (64 836 animals), bay (33 633), black (9414), chestnut (1243), buckskin (433), roan (107), isabella (57) and white (37). Contributions to the total genetic diversity were first assessed in the existing subpopulations and later compared with two scenarios with equal subpopulation size, one with the mean population size (13 710) and another with a low population size (100). Ancestor analysis revealed a very similar origin for the different groups, except for six ancestors that were only present in one of the groups likely to be responsible for the corresponding colour. The coancestry matrix showed a close genetic relationship between the bay and chestnut subpopulations. Before adjustment, Nei's minimum distance showed a lack of differentiation among subpopulations (particularly among the black, chestnut and bay subpopulations) except for isabella and white individuals, whereas after adjustment, white, roan and grey individuals appeared less differentiated. Standardization showed that balancing coat colours would contribute preserving the genetic diversity of the breed. The global genetic diversity increased by 12.5% when the subpopulations were size standardized, showing that a progressive increase in minority coats would be profitable for the genetic diversity of this breed. The methodology developed could be useful for the study of the genetic structure of subpopulations with unbalanced sizes and to predict their genetic importance in terms of their contribution to genetic variability.