Population Genetic Inference Research Articles

Effect of microsatellite selection on individual and population genetic inferences: an empirical study using cross-specific and species-specific amplifications.

Although whole-genome sequencing is becoming more accessible and feasible for nonmodel organisms, microsatellites have remained the markers of choice for various population and conservation genetic studies. However, the criteria for choosing microsatellites are still controversial due to ascertainment bias that may be introduced into the genetic inference. An empirical study of red deer (Cervus elaphus) populations, in which cross-specific and species-specific microsatellites developed through pyrosequencing of enriched libraries, was performed for this study. Two different strategies were used to select the species-specific panels: randomly vs. highly polymorphic markers. The results suggest that reliable and accurate estimations of genetic diversity can be obtained using random microsatellites distributed throughout the genome. In addition, the results reinforce previous evidence that selecting the most polymorphic markers leads to an ascertainment bias in estimates of genetic diversity, when compared with randomly selected microsatellites. Analyses of population differentiation and clustering seem less influenced by the approach of microsatellite selection, whereas assigning individuals to populations might be affected by a random selection of a small number of microsatellites. Individual multilocus heterozygosity measures produced various discordant results, which in turn had impacts on the heterozygosity-fitness correlation test. Finally, we argue that picking the appropriate microsatellite set should primarily take into account the ecological and evolutionary questions studied. Selecting the most polymorphic markers will generally overestimate genetic diversity parameters, leading to misinterpretations of the real genetic diversity, which is particularly important in managed and threatened populations.

Vegetation and environmental responses to climate forcing during the Last Glacial Maximum and deglaciation in the East Carpathians: attenuated response to maximum cooling and increased biomass burning

The Carpathian Mountains were one of the main mountain reserves of the boreal and cool temperate flora during the Last Glacial Maximum (LGM) in East-Central Europe. Previous studies demonstrated Lateglacial vegetation dynamics in this area; however, our knowledge on the LGM vegetation composition is very limited due to the scarcity of suitable sedimentary archives. Here we present a new record of vegetation, fire and lacustrine sedimentation from the youngest volcanic crater of the Carpathians (Lake St Anne, Lacul Sfânta Ana, Szent-Anna-tó) to examine environmental change in this region during the LGM and the subsequent deglaciation. Our record indicates the persistence of boreal forest steppe vegetation (with Pinus, Betula, Salix, Populus and Picea) in the foreland and low mountain zone of the East Carpathians and Juniperus shrubland at higher elevation. We demonstrate attenuated response of the regional vegetation to maximum global cooling. Between ∼22,870 and 19,150 cal yr BP we find increased regional biomass burning that is antagonistic with the global trend. Increased regional fire activity suggests extreme continentality likely with relatively warm and dry summers. We also demonstrate xerophytic steppe expansion directly after the LGM, from ∼19,150 cal yr BP, and regional increase in boreal woodland cover with Pinus and Betula from 16,300 cal yr BP. Plant macrofossils indicate local (950 m a.s.l.) establishment of Betula nana and Betula pubescens at 15,150 cal yr BP, Pinus sylvestris at 14,700 cal yr BP and Larix decidua at 12,870 cal yr BP. Pollen data furthermore support population genetic inferences regarding the regional presence of some temperate deciduous trees during the LGM (Fagus sylvatica, Corylus avellana, Fraxinus excelsior). Our sedimentological data also demonstrate intensified aeolian dust accumulation between 26,000 and 20,000 cal yr BP.

Viewing Protein Fitness Landscapes Through a Next-Gen Lens

High-throughput sequencing has enabled many powerful approaches in biological research. Here, we review sequencing approaches to measure frequency changes within engineered mutational libraries subject to selection. These analyses can provide direct estimates of biochemical and fitness effects for all individual mutations across entire genes (and likely compact genomes in the near future) in genetically tractable systems such as microbes, viruses, and mammalian cells. The effects of mutations on experimental fitness can be assessed using sequencing to monitor time-dependent changes in mutant frequency during bulk competitions. The impact of mutations on biochemical functions can be determined using reporters or other means of separating variants based on individual activities (e.g., binding affinity for a partner molecule can be interrogated using surface display of libraries of mutant proteins and isolation of bound and unbound populations). The comprehensive investigation of mutant effects on both biochemical function and experimental fitness provide promising new avenues to investigate the connections between biochemistry, cell physiology, and evolution. We summarize recent findings from systematic mutational analyses; describe how they relate to a field rich in both theory and experimentation; and highlight how they may contribute to ongoing and future research into protein structure-function relationships, systems-level descriptions of cell physiology, and population-genetic inferences on the relative contributions of selection and drift.

Detection and removal of PCR duplicates in population genomic ddRAD studies by addition of a degenerate base region (DBR) in sequencing adapters.

Restriction-site associated DNA sequencing (RAD) has emerged as a powerful marker system for studying genome-wide DNA polymorphisms using next-generation sequencing. A recent technical facilitation of RAD is double-digest RAD (ddRAD), which utilizes two restriction enzymes for library preparation. The more flexible and balanced ddRAD allows analysis of genomic loci in hundreds of individuals. However, in contrast to paired-end sequencing of traditional RAD libraries, PCR duplicates cannot be detected with ddRAD. This is a concern because duplicates can contribute substantially to read coverage data and erroneously inflate the proportion of homozygous loci (allele dropout). Allele dropout can bias population genetic parameter inference and complicate the detection of outlier loci under selection. Here we outline a simple and straightforward approach to detecting PCR duplicates from ddRAD libraries. Our approach introduces a degenerate base region (DBR, 12,288 unique combinations) in the sequencing adapter. We demonstrate the high efficiency and low rate of false positives in simulations. In addition, a pilot study was performed to test this approach on six aquatic invertebrates, sequenced on a HiSeq 2500 sequencer. The reads of the ddRAD libraries consisted of 33.48% PCR duplicates distributed on 19.40% of the loci. A disproportionate number of PCR duplicates were detected in only 4.66% of the loci. While this should not be a concern for general parameter inference, outlier loci detection in particular would be improved by the DBR technique. Given the easy and straightforward application of the technique in other RAD protocols as well, we suggest that DBR regions should generally be included in PCR-based RAD studies.

Biogeography of speciation of two sister species of neotropical amazona (Aves, Psittaciformes) based on mitochondrial sequence data.

Coalescent theory provides powerful models for population genetic inference and is now increasingly important in estimates of divergence times and speciation research. We use molecular data and methods based on coalescent theory to investigate whether genetic evidence supports the hypothesis of A. pretrei and A. tucumana as separate species and whether genetic data allow us to assess which allopatric model seems to better explain the diversification process in these taxa. We sampled 13 A. tucumana from two provinces in northern Argentina and 28 A. pretrei from nine localities of Rio Grande do Sul, Brazil. A 491 bp segment of the mitochondrial gene cytochrome c oxidase I was evaluated using the haplotype network and phylogenetic methods. The divergence time and other demographic quantities were estimated using the isolation and migration model based on coalescent theory. The network and phylogenetic reconstructions showed similar results, supporting reciprocal monophyly for these two taxa. The divergence time of lineage separation was estimated to be approximately 1.3 million years ago, which corresponds to the lower Pleistocene. Our results enforce the current taxonomic status for these two Amazon species. They also support that A. pretrei and A. tucumana diverged with little or no gene flow approximately 1.3 million years ago, most likely after the establishment of a small population in the Southern Yungas forest by dispersion of a few founders from the A. pretrei ancestral population. This process may have been favored by habitat corridors formed in hot and humid periods of the Quaternary. Considering that these two species are considered threatened, the results were evaluated for their implications for the conservation of these two species.

Population genetics inference for longitudinally-sampled mutants under strong selection.

Longitudinal allele frequency data are becoming increasingly prevalent. Such samples permit statistical inference of the population genetics parameters that influence the fate of mutant variants. To infer these parameters by maximum likelihood, the mutant frequency is often assumed to evolve according to the Wright–Fisher model. For computational reasons, this discrete model is commonly approximated by a diffusion process that requires the assumption that the forces of natural selection and mutation are weak. This assumption is not always appropriate. For example, mutations that impart drug resistance in pathogens may evolve under strong selective pressure. Here, we present an alternative approximation to the mutant-frequency distribution that does not make any assumptions about the magnitude of selection or mutation and is much more computationally efficient than the standard diffusion approximation. Simulation studies are used to compare the performance of our method to that of the Wright–Fisher and Gaussian diffusion approximations. For large populations, our method is found to provide a much better approximation to the mutant-frequency distribution when selection is strong, while all three methods perform comparably when selection is weak. Importantly, maximum-likelihood estimates of the selection coefficient are severely attenuated when selection is strong under the two diffusion models, but not when our method is used. This is further demonstrated with an application to mutant-frequency data from an experimental study of bacteriophage evolution. We therefore recommend our method for estimating the selection coefficient when the effective population size is too large to utilize the discrete Wright–Fisher model.

Error-prone polymerase activity causes multinucleotide mutations in humans.

About 2% of human genetic polymorphisms have been hypothesized to arise via multinucleotide mutations (MNMs), complex events that generate SNPs at multiple sites in a single generation. MNMs have the potential to accelerate the pace at which single genes evolve and to confound studies of demography and selection that assume all SNPs arise independently. In this paper, we examine clustered mutations that are segregating in a set of 1092 human genomes, demonstrating that the signature of MNM becomes enriched as large numbers of individuals are sampled. We estimate the percentage of linked SNP pairs that were generated by simultaneous mutation as a function of the distance between affected sites and show that MNMs exhibit a high percentage of transversions relative to transitions, findings that are reproducible in data from multiple sequencing platforms and cannot be attributed to sequencing error. Among tandem mutations that occur simultaneously at adjacent sites, we find an especially skewed distribution of ancestral and derived alleles, with GC → AA, GA → TT, and their reverse complements making up 27% of the total. These mutations have been previously shown to dominate the spectrum of the error-prone polymerase Pol ζ, suggesting that low-fidelity DNA replication by Pol ζ is at least partly responsible for the MNMs that are segregating in the human population. We develop statistical estimates of MNM prevalence that can be used to correct phylogenetic and population genetic inferences for the presence of complex mutations.

Validation of statistical imputation of allele-level multilocus phased genotypes from ambiguous HLA assignments.

Genetic matching for loci in the human leukocyte antigen (HLA) region between a donor and a patient in hematopoietic stem cell transplantation (HSCT) is critical to outcome; however, methods for HLA genotyping of donors in unrelated stem cell registries often yield results with allelic and phase ambiguity and/or do not query all clinically relevant loci. We present and evaluate a statistical method for in silico imputation of HLA alleles and haplotypes in large ambiguous population data from the Be The Match(®) Registry. Our method builds on haplotype frequencies estimated from registry populations and exploits patterns of linkage disequilibrium (LD) across HLA haplotypes to infer high resolution HLA assignments. We performed validation on simulated and real population data from the Registry with non-trivial ambiguity content. While real population datasets caused some predictions to deviate from expectation, validations still showed high percent recall for imputed results with average recall >76% when imputing HLA alleles from registry data. We simulated ambiguity generated by several HLA genotyping methods to evaluate the imputation performance on several levels of typing resolution. On average, imputation percent recall of allele-level HLA haplotypes was >95% for allele-level typing, >92% for intermediate resolution typing and >58% for serology (low-resolution) typing. Thus, allele-level HLA assignments can be imputed through the application of a set of statistical and population genetics inferences and with knowledge of haplotype frequencies and self-identified race and ethnicities.

Inferring human population size and separation history from multiple genome sequences.

The availability of complete human genome sequences from populations across the world has given rise to new population genetic inference methods that explicitly model their ancestral relationship under recombination and mutation. So far, application of these methods to evolutionary history more recent than 20-30 thousand years ago and to population separations has been limited. Here we present a new method that overcomes these shortcomings. The Multiple Sequentially Markovian Coalescent (MSMC) analyses the observed pattern of mutations in multiple individuals, focusing on the first coalescence between any two individuals. Results from applying MSMC to genome sequences from nine populations across the world suggest that the genetic separation of non-African ancestors from African Yoruban ancestors started long before 50,000 years ago, and give information about human population history as recently as 2,000 years ago, including the bottleneck in the peopling of the Americas, and separations within Africa, East Asia and Europe.

Population-Genetic Inference from Pooled-Sequencing Data

Although pooled-population sequencing has become a widely used approach for estimating allele frequencies, most work has proceeded in the absence of a proper statistical framework. We introduce a self-sufficient, closed-form, maximum-likelihood estimator for allele frequencies that accounts for errors associated with sequencing, and a likelihood-ratio test statistic that provides a simple means for evaluating the null hypothesis of monomorphism. Unbiased estimates of allele frequencies (where N is the number of individuals sampled) appear to be unachievable, and near-certain identification of a polymorphism requires a minor-allele frequency . A framework is provided for testing for significant differences in allele frequencies between populations, taking into account sampling at the levels of individuals within populations and sequences within pooled samples. Analyses that fail to account for the two tiers of sampling suffer from very large false-positive rates and can become increasingly misleading with increasing depths of sequence coverage. The power to detect significant allele-frequency differences between two populations is very limited unless both the number of sampled individuals and depth of sequencing coverage exceed 100.

Enhanced methods for local ancestry assignment in sequenced admixed individuals.

Inferring the ancestry at each locus in the genome of recently admixed individuals (e.g., Latino Americans) plays a major role in medical and population genetic inferences, ranging from finding disease-risk loci, to inferring recombination rates, to mapping missing contigs in the human genome. Although many methods for local ancestry inference have been proposed, most are designed for use with genotyping arrays and fail to make use of the full spectrum of data available from sequencing. In addition, current haplotype-based approaches are very computationally demanding, requiring large computational time for moderately large sample sizes. Here we present new methods for local ancestry inference that leverage continent-specific variants (CSVs) to attain increased performance over existing approaches in sequenced admixed genomes. A key feature of our approach is that it incorporates the admixed genomes themselves jointly with public datasets, such as 1000 Genomes, to improve the accuracy of CSV calling. We use simulations to show that our approach attains accuracy similar to widely used computationally intensive haplotype-based approaches with large decreases in runtime. Most importantly, we show that our method recovers comparable local ancestries, as the 1000 Genomes consensus local ancestry calls in the real admixed individuals from the 1000 Genomes Project. We extend our approach to account for low-coverage sequencing and show that accurate local ancestry inference can be attained at low sequencing coverage. Finally, we generalize CSVs to sub-continental population-specific variants (sCSVs) and show that in some cases it is possible to determine the sub-continental ancestry for short chromosomal segments on the basis of sCSVs.

Cryptosporidium,Giardia, Cryptococcus, Pneumocystis genetic variability: cryptic biological species or clonal near-clades?

An abundant literature dealing with the population genetics and taxonomy of Giardia duodenalis, Cryptosporidium spp., Pneumocystis spp., and Cryptococcus spp., pathogens of high medical and veterinary relevance, has been produced in recent years. We have analyzed these data in the light of new population genetic concepts dealing with predominant clonal evolution (PCE) recently proposed by us. In spite of the considerable phylogenetic diversity that exists among these pathogens, we have found striking similarities among them. The two main PCE features described by us, namely highly significant linkage disequilibrium and near-clading (stable phylogenetic clustering clouded by occasional recombination), are clearly observed in Cryptococcus and Giardia, and more limited indication of them is also present in Cryptosporidium and Pneumocystis. Moreover, in several cases, these features still obtain when the near-clades that subdivide the species are analyzed separately (“Russian doll pattern”). Lastly, several sets of data undermine the notion that certain microbes form clonal lineages simply owing to a lack of opportunity to outcross due to low transmission rates leading to lack of multiclonal infections (“starving sex hypothesis”). We propose that the divergent taxonomic and population genetic inferences advanced by various authors about these pathogens may not correspond to true evolutionary differences and could be, rather, the reflection of idiosyncratic practices among compartmentalized scientific communities. The PCE model provides an opportunity to revise the taxonomy and applied research dealing with these pathogens and others, such as viruses, bacteria, parasitic protozoa, and fungi.

Exact vs. Approximate Computation: Reconciling Different Estimates of Mycobacterium tuberculosis Epidemiological Parameters

Exact computational methods for inference in population genetics are intuitively preferable to approximate analyses. We reconcile two starkly different estimates of the reproductive number of tuberculosis from previous studies that used the same genotyping data and underlying model. This demonstrates the value of approximate analyses in validating exact methods.

Integrating genetic data and population viability analyses for the identification of harbour seal (Phoca vitulina) populations and management units

Identification of populations and management units is an essential step in the study of natural systems. Still, there is limited consensus regarding how to define populations and management units, and whether genetic methods allow for inference at the relevant spatial and temporal scale. Here, we present a novel approach, integrating genetic, life history and demographic data to identify populations and management units in southern Scandinavian harbour seals. First, 15 microsatellite markers and model- and distance-based genetic clustering methods were used to determine the population genetic structure in harbour seals. Second, we used harbour seal demographic and life history data to conduct population viability analyses (PVAs) in the vortex simulation model in order to determine whether the inferred genetic units could be classified as management units according to Lowe and Allendorf's (Molecular Ecology, 19, 2010, 3038) 'population viability criterion' for demographic independence. The genetic analyses revealed fine-scale population structuring in southern Scandinavian harbour seals and pointed to the existence of several genetic units. The PVAs indicated that the census population size of each of these genetic units was sufficiently large for long-term population viability, and hence that the units could be classified as demographically independent management units. Our study suggests that population genetic inference can offer the same degree of temporal and spatial resolution as 'nongenetic' methods and that the combined use of genetic data and PVAs constitutes a promising approach for delineating populations and management units.

Improving the inference of population genetic structure in the presence of related individuals.

It is well known that the presence of related individuals can affect the inference of population genetic structure from molecular data. This has been verified, for example, on the unsupervised Bayesian clustering algorithm implemented in the software STRUCTURE. This methodology assumes, among others, Hardy-Weinberg and linkage equilibrium within subpopulations. The existence of groups of close relatives, such as full-sib families, may prevent these assumptions to be fulfilled, causing the algorithm to work suboptimally. The purpose of this study was to evaluate the effect of the presence of related individuals on a different methodology (implemented in CLUSTER_DIST) for population genetic structure inference. This approach arranges individuals to maximize the genetic distance between groups and does not make Hardy-Weinberg and linkage equilibrium assumptions. We study the robustness of this approach to the presence of close relatives in a sample using simulated scenarios involving combinations of several factors, including the number of subpopulations, the level of differentiation between them, the number, size and type (full or half-sibs) of families in a sample, and the type and number of molecular markers available for clustering analysis. Results indicate that the methodology that maximizes the genetic distance between subpopulations is less influenced by the presence of related individuals than the program STRUCTURE. Therefore, the former can be used, in combination with the program STRUCTURE, to analyse population genetic structure when related individuals are suspected to be present in a sample.

Introgression and Phenotypic Assimilation in Zimmerius Flycatchers (Tyrannidae): Population Genetic and Phylogenetic Inferences from Genome-Wide SNPs

Genetic introgression is pervasive in nature and may lead to large-scale phenotypic assimilation and/or admixture of populations, but there is limited knowledge on whether large phenotypic changes are typically accompanied by high levels of introgression throughout the genome. Using bioacoustic, biometric, and spectrophotometric data from a flycatcher (Tyrannidae) system in the Neotropical genus Zimmerius, we document a mosaic pattern of phenotypic admixture in which a population of Zimmerius viridiflavus in northern Peru (henceforth "mosaic") is vocally and biometrically similar to conspecifics to the south but shares plumage characteristics with a different species (Zimmerius chrysops) to the north. To clarify the origins of the mosaic population, we used the RAD-seq approach to generate a data set of 37,361 genome-wide single nucleotide polymorphisms (SNPs). A range of population-genetic diagnostics shows that the genome of the mosaic population is largely indistinguishable from southern Z. viridiflavus and distinct from northern Z. chrysops, and the application of parsimony and species tree methods to the genome-wide SNP data set confirms the close affinity of the mosaic population with southern Z. viridiflavus. Even so, using a subset of 2710 SNPs found across all sampled lineages in configurations appropriate for a recently proposed statistical ("ABBA/BABA") test that distinguishes gene flow from incomplete lineage sorting, we detected low levels of gene flow from northern Z. chrysops into the mosaic population. Mapping the candidate loci for introgression from Z. chrysops into the mosaic population to the zebra finch genome reveals close linkage with genes significantly enriched in functions involving cell projection and plasma membranes. Introgression of key alleles may have led to phenotypic assimilation in the plumage of mosaic birds, suggesting that selection may have been a key factor facilitating introgression.

Characterizing Bias in Population Genetic Inferences from Low-Coverage Sequencing Data

The site frequency spectrum (SFS) is of primary interest in population genetic studies, because the SFS compresses variation data into a simple summary from which many population genetic inferences can proceed. However, inferring the SFS from sequencing data is challenging because genotype calls from sequencing data are often inaccurate due to high error rates and if not accounted for, this genotype uncertainty can lead to serious bias in downstream analysis based on the inferred SFS. Here, we compare two approaches to estimate the SFS from sequencing data: one approach infers individual genotypes from aligned sequencing reads and then estimates the SFS based on the inferred genotypes (call-based approach) and the other approach directly estimates the SFS from aligned sequencing reads by maximum likelihood (direct estimation approach). We find that the SFS estimated by the direct estimation approach is unbiased even at low coverage, whereas the SFS by the call-based approach becomes biased as coverage decreases. The direction of the bias in the call-based approach depends on the pipeline to infer genotypes. Estimating genotypes by pooling individuals in a sample (multisample calling) results in underestimation of the number of rare variants, whereas estimating genotypes in each individual and merging them later (single-sample calling) leads to overestimation of rare variants. We characterize the impact of these biases on downstream analyses, such as demographic parameter estimation and genome-wide selection scans. Our work highlights that depending on the pipeline used to infer the SFS, one can reach different conclusions in population genetic inference with the same data set. Thus, careful attention to the analysis pipeline and SFS estimation procedures is vital for population genetic inferences.

Assessing the effect of sequencing depth and sample size in population genetics inferences.

Next-Generation Sequencing (NGS) technologies have dramatically revolutionised research in many fields of genetics. The ability to sequence many individuals from one or multiple populations at a genomic scale has greatly enhanced population genetics studies and made it a data-driven discipline. Recently, researchers have proposed statistical modelling to address genotyping uncertainty associated with NGS data. However, an ongoing debate is whether it is more beneficial to increase the number of sequenced individuals or the per-sample sequencing depth for estimating genetic variation. Through extensive simulations, I assessed the accuracy of estimating nucleotide diversity, detecting polymorphic sites, and predicting population structure under different experimental scenarios. Results show that the greatest accuracy for estimating population genetics parameters is achieved by employing a large sample size, despite single individuals being sequenced at low depth. Under some circumstances, the minimum sequencing depth for obtaining accurate estimates of allele frequencies and to identify polymorphic sites is , where both alleles are more likely to have been sequenced. On the other hand, inferences of population structure are more accurate at very large sample sizes, even with extremely low sequencing depth. This all points to the conclusion that under various experimental scenarios, in cost-limited population genetics studies, large sample sizes at low sequencing depth are desirable to achieve high accuracy. These findings will help researchers design their experimental set-ups and guide further investigation on the effect of protocol design for genetic research.

SNP ascertainment bias in population genetic analyses: Why it is important, and how to correct it

Whole genome sequencing and SNP genotyping arrays can paint strikingly different pictures of demographic history and natural selection. This is because genotyping arrays contain biased sets of pre-ascertained SNPs. In this short review, we use comparisons between high-coverage whole genome sequences of African hunter-gatherers and data from genotyping arrays to highlight how SNP ascertainment bias distorts population genetic inferences. Sample sizes and the populations in which SNPs are discovered affect the characteristics of observed variants. We find that SNPs on genotyping arrays tend to be older and present in multiple populations. In addition, genotyping arrays cause allele frequency distributions to be shifted towards intermediate frequency alleles, and estimates of linkage disequilibrium are modified. Since population genetic analyses depend on allele frequencies, it is imperative that researchers are aware of the effects of SNP ascertainment bias. With this in mind, we describe multiple ways to correct for SNP ascertainment bias.

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n - An(t) follows a Poisson distribution, and as m → n, $$n\left(n-1\right){T}_{m}/2N\left(0\right)$$ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.