Ancestral Effective Population Size Research Articles

TRAILS: Tree reconstruction of ancestry using incomplete lineage sorting.

Genome-wide genealogies of multiple species carry detailed information about demographic and selection processes on individual branches of the phylogeny. Here, we introduce TRAILS, a hidden Markov model that accurately infers time-resolved population genetics parameters, such as ancestral effective population sizes and speciation times, for ancestral branches using a multi-species alignment of three species and an outgroup. TRAILS leverages the information contained in incomplete lineage sorting fragments by modelling genealogies along the genome as rooted three-leaved trees, each with a topology and two coalescent events happening in discretized time intervals within the phylogeny. Posterior decoding of the hidden Markov model can be used to infer the ancestral recombination graph for the alignment and details on demographic changes within a branch. Since TRAILS performs posterior decoding at the base-pair level, genome-wide scans based on the posterior probabilities can be devised to detect deviations from neutrality. Using TRAILS on a human-chimp-gorilla-orangutan alignment, we recover speciation parameters and extract information about the topology and coalescent times at high resolution.

A comparison of genomic diversity and demographic history of the North Atlantic and Southwest Atlantic southern right whales.

Right whales (genus Eubalaena) were among the first, and most extensively pursued, targets of commercial whaling. However, understanding the impacts of this persecution requires knowledge of the demographic histories of these species prior to exploitation. We used deep whole genome sequencing (~40×) of 12 North Atlantic (E. glacialis) and 10 Southwest Atlantic southern (E. australis) right whales to quantify contemporary levels of genetic diversity and infer their demographic histories over time. Using coalescent- and identity-by-descent-based modelling to estimate ancestral effective population sizes from genomic data, we demonstrate that North Atlantic right whales have lived with smaller effective population sizes (Ne) than southern right whales in the Southwest Atlantic since their divergence and describe the decline in both populations around the time of whaling. North Atlantic right whales exhibit reduced genetic diversity and longer runs of homozygosity leading to higher inbreeding coefficients compared to the sampled population of southern right whales. This study represents the first comprehensive assessment of genome-wide diversity of right whales in the western Atlantic and underscores the benefits of high coverage, genome-wide datasets to help resolve long-standing questions about how historical changes in effective population size over different time scales shape contemporary diversity estimates. This knowledge is crucial to improve our understanding of the right whales' history and inform our approaches to address contemporary conservation issues. Understanding and quantifying the cumulative impact of long-term small Ne, low levels of diversity and recent inbreeding on North Atlantic right whale recovery will be important next steps.

Demographic history of the Punjab urial and implications for its management

AbstractThe Punjab urial (Ovis vignei punjabiensis) is endemic to Northern Punjab, Pakistan, and is categorized as vulnerable by the International Union for Conservation of Nature Red List of Threatened Species. The urial population has declined by 30% over the last 3 generations. We used non‐invasive fecal samples to identify individuals and estimate population size of Punjab urial in the Kalabagh Game Reserve, Pakistan. We genotyped samples using 12 microsatellite markers to assess genetic variation, population structure, and demographic changes. Microsatellite analysis revealed high levels of genetic variation in urials in terms of expected and observed heterozygosity and allelic diversity. The population structure of the Punjab urial in the Kalabagh Game Reserve, based solely on microsatellite variation using Bayesian clustering, indicated 3 different clusters in the reserve. Results revealed that the urial population may be facing inbreeding pressure because its ancestral effective population size has declined from between 20,000 and 50,000 to ≤1,000 animals today. This reduction has partly occurred because of a bottleneck that occurred about 10,000 years ago. Results also indicate that 1 urial population cluster has the signature of a bottleneck, which may be due to population isolation. The 3 urial clusters are small and broadly dispersed in a large territory, meaning they could be extirpated without any opportunity for natural re‐population through dispersion. The results of our study support a management strategy that encourages maintaining connectivity between urial localities within the Kalabagh Game Reserve, increased diversity so the effective population size may recover from the historical decline, and the use of data generated here as a baseline of urial genetic diversity in the reserve for monitoring diversity over the long term.

Estimation of species divergence times in presence of cross-species gene flow.

Cross-species introgression can have significant impacts on phylogenomic reconstruction of species divergence events. Here, we used simulations to show how the presence of even a small amount of introgression can bias divergence time estimates when gene flow is ignored in the analysis. Using advances in analytical methods under the multispecies coalescent (MSC) model, we demonstrate that by accounting for incomplete lineage sorting and introgression using large phylogenomic data sets this problem can be avoided. The multispecies-coalescent-with-introgression (MSci) model is capable of accurately estimating both divergence times and ancestral effective population sizes, even when only a single diploid individual per species is sampled. We characterize some general expectations for biases in divergence time estimation under three different scenarios: 1) introgression between sister species, 2) introgression between non-sister species, and 3) introgression from an unsampled (i.e., ghost) outgroup lineage. We also conducted simulations under the isolation-with-migration (IM) model and found that the MSci model assuming episodic gene flow was able to accurately estimate species divergence times despite high levels of continuous gene flow. We estimated divergence times under the MSC and MSci models from two published empirical datasets with previous evidence of introgression, one of 372 target-enrichment loci from baobabs (Adansonia), and another of 1000 transcriptome loci from 14 species of the tomato relative, Jaltomata. The empirical analyses not only confirm our findings from simulations, demonstrating that the MSci model can reliably estimate divergence times but also show that divergence time estimation under the MSC can be robust to the presence of small amounts of introgression in empirical datasets with extensive taxon sampling. [divergence time; gene flow; hybridization; introgression; MSci model; multispecies coalescent].

Genetic diversity and structure of a recent fish invasion: Tench (Tinca tinca) in eastern North America.

Introduced and geographically expanding populations experience similar eco-evolutionary challenges, including founder events, genetic bottlenecks, and novel environments. Theory predicts that reduced genetic diversity resulting from such phenomena limits the success of introduced populations. Using 1900 SNPs obtained from restriction-site-associated DNA sequencing, we evaluated hypotheses related to the invasion history and connectivity of an invasive population of Tench (Tinca tinca), a Eurasian freshwater fish that has been expanding geographically in eastern North America for three decades. Consistent with the reported history of a single introduction event, our findings suggest that multiple introductions from distinct genetic sources are unlikely as Tench had a small effective population size (~114 [95% CI=106-123] individuals), no strong population subdivision across time and space, and evidence of a recent genetic bottleneck. The large genetic neighbourhood size (220 km) and weak within-population genetic substructure suggested high connectivity across the invaded range, despite the relatively large area occupied. There was some evidence for a small decay in genetic diversity as the species expanded northward, but not southward, into new habitats. As eradicating the species within a ~112 km radius would be necessary to prevent recolonization, eradicating Tench is likely not feasible at watershed-and possibly local-scales. Management should instead focus on reducing abundance in priority conservation areas to mitigate adverse impacts. Our study indicates that introduced populations can thrive and exhibit relatively high levels of genetic diversity despite severe bottlenecks (<1.5% of the ancestral effective population size) and suggests that landscape heterogeneity and population demographics can generate variability in spatial patterns of genetic diversity within a single range expansion.

Comparative Phylogeography in the Taiwan–Luzon Volcanic Belt Indicates Fast Diversification History of Pachyrhynchus Weevils (Coleoptera: Curculionidae)

Abstract Geological isolation with limited gene flow can shape phenotypic diversification among different populations or species. From Luzon northward to Taiwan lies a series of isolated volcanic islands (the Taiwan–Luzon volcanic belt) where three Pachyrhynchus species [P. sarcitis (Behrens, 1887), P. nobilis (Heller, 1912) and P. semperi (Heller, 1912)] (Coleoptera: Curculionidae: Entiminae: Pachyrhynchini) are sympatrically distributed. With intraspecific color variation across different islands, these three weevil species provide a unique opportunity to study genetic divergence associated with geographic isolation and/or phenotypic differences. In this study, genome-wide single nucleotide polymorphism (SNP) data derived from ddRAD-seq was used to reconstruct the speciation history and to delimit species within each of the three species. Our results indicate all three species have ancient diversification histories in southern islands of the Taiwan–Luzon volcanic belt instead of more recent diversification histories in northern islands. Ancestral effective population size estimations also support a scenario of a series of founder colonization events from southern to northern islands in the volcanic belt. Most island populations are monophyletic, and early-divergent populations with deep genetic structures are supported statistically as distinct species. However, color variations could occur between populations with very recent diversification, indicating a fast-evolving rate in the change of coloration, possibly due to müllerian mimicry or founder effects across this region.

Demographic history and conservation genomics of caribou (Rangifer tarandus) in Québec.

The loss of genetic diversity is a challenge many species are facing, with genomics being a potential tool to inform and prioritize decision-making. Most caribou (Rangifer tarandus) populations have experienced significant recent declines throughout Québec, Canada, and are considered of concern, threatened or endangered. Here, we calculated the ancestral and contemporary patterns of genomic diversity of five representative caribou populations and applied a comparative population genomics framework to assess the interplay between demographic events and genomic diversity. We first calculated a caribou specific mutation rate, μ, by extracting orthologous genes from related ungulates and estimating the rate of synonymous mutations. Whole genome re-sequencing was then completed on 67 caribou: from these data we calculated nucleotide diversity, θ π and estimated the coalescent or ancestral effective population size (N e), which ranged from 12,030 to 15,513. When compared to the census size, N C, the endangered Gaspésie Mountain caribou population had the highest ancestral N e:N C ratio which is consistent with recent work suggesting high ancestral N e:N C is of conservation concern. In contrast, values of contemporary N e, estimated from linkage-disequilibrium, ranged from 11 to 162, with Gaspésie having among the highest contemporary N e:N C ratio. Importantly, classic conservation genetics theory would predict this population to be of less concern based on this ratio. Interestingly, F varied only slightly between populations, and despite evidence of bottlenecks across the province, runs of homozygosity were not abundant in the genome. Tajima's D estimates mirrored the demographic models and current conservation status. Our study highlights how genomic patterns are nuanced and potentially misleading if viewed only through a contemporary lens; we argue a holistic conservation genomics view should integrate ancestral N e and Tajima's D into management decisions.

High genetic diversity and low structure in an endemic long-lived tree, Yucca capensis (Asparagaceae).

Endemic species distributed in fragmented habitats are highly vulnerable to extinction because they may have low genetic diversity. However, some life-history traits can mitigate the effect of genetic drift on populations. We analysed the level and distribution of genetic variation and ancestral population size of Yucca capensis, a long-lived endemic plant of the Baja California Peninsula, Mexico. Its populations are scattered across a habitat that is suffering accelerated transformation. We used six nuclear microsatellites to genotype 224 individuals from 17 locations across the entire species' geographic range. We estimated polymorphisms, heterozygosity and genetic structure. We also evaluated the ancestral and recent effective size and time since the population started to change. We found high heterozygosity, high polymorphism and low differentiation among locations, suggesting a panmictic population across the range. We also detected a large ancestral effective population size, which suffered a strong reduction in the Mid-Holocene. Despite changes in environmental conditions caused by habitat modification, the high diversity and low differentiation in Y. capensis may result from its large ancestral effective size and life-history traits, such as plant longevity, clonal growth and mating system, which reduce the rate of loss of genetic variation. However, the dependence on a specialist pollinator that displays short flight range can reduce gene flow among the plant populations and could, shortly, lead them into an extinction vortex.

Genomic data support multiple introductions and explosive demographic expansions in a highly invasive aquatic insect.

The study of the genetic makeup and demographic fate of alien species is essential to understand their capacity to recover from founder effects, adapt to new environmental conditions and, ultimately, become invasive and potentially damaging. Here, we employ genomic data to gain insights into key demographic processes that might help to explain the extraordinarily successful invasion of the Western Mediterranean region by the North American boatman Trichocorixa verticalis (Hemiptera: Corixidae). Our analyses revealed the genetic distinctiveness of populations from the main areas comprising the invasive range and coalescent-based simulations supported that they originated from independent introductions events probably involving different source populations. Testing of alternative demographic models indicated that all populations experienced a strong bottleneck followed by a recent and instantaneous demographic expansion that restored a large portion (>30%) of their ancestral effective population sizes shortly after introductions took place (<60years ago). Considerable genetic admixture of some populations suggest that hypothetical barriers to dispersal (i.e., land and sea water) are permeable to gene flow and/or that they originated from introductions involving multiple lineages. This study demonstrates the repeated arrival of propagules with different origins and short time lags between arrival and establishment, emphasizing the extraordinary capacity of the species to recover from founder effects and genetically admix in invaded areas. This can explain the demonstrated capacity of this aquatic insect to spread and outcompete native species once it colonizes new suitable regions. Future genomic analyses of native range populations could help to infer the genetic makeup of introduced populations and track invasion routes.

Large ancestral effective population size explains the difficult phylogenetic placement of owl monkeys.

The phylogenetic position of owl monkeys, grouped in the genus Aotus, has been a controversial issue for understanding Neotropical primate evolution. Explanations of the difficult phylogenetic assignment of owl monkeys have been elusive, frequently relying on insufficient data (stochastic error) or scenarios of rapid speciation (adaptive radiation) events. Using a coalescent-based approach, we explored the population-level mechanisms likely explaining these topological discrepancies. We examined the topological variance of 2,192 orthologous genes shared between representatives of the three major Cebidae lineages and the outgroup. By employing a methodological framework that allows for reticulated tree topologies, our analysis explicitly tested for non-dichotomous evolutionary processes impacting the finding of the position of owl monkeys in the cebid phylogeny. Our findings indicated that Aotus is a sister lineage of the callitrichines. Most gene trees (>50%) failed to recover the species tree topology, although the distribution of gene trees mismatching the true species topology followed the standard expectation of the multispecies coalescent without reticulation. We showed that the large effective population size of the common ancestor of Aotus and callitrichines was the most likely factor responsible for generating phylogenetic uncertainty. On the other hand, fast speciation scenarios or introgression played minor roles. We propose that the difficult phylogenetic placement of Aotus is explained by population-level processes associated with the large ancestral effective size. These results shed light on the biogeography of the early cebid diversification in the Miocene, highlighting the relevance of evaluating phylogenetic relationships employing population-aware approaches.

Cox1 barcoding versus multilocus species delimitation: validation of two mite species with contrasting effective population sizes

BackgroundThe cox1-barcoding approach is currently extensively used for high-throughput species delimitation and discovery. However, this method has several limitations, particularly when organisms have large effective population sizes. Paradoxically, most common, abundant, and widely distributed species may be misclassified by this technique.ResultsWe conducted species delimitation analyses for two host-specific lineages of scab mites of the genus Caparinia, having small population sizes. Cox1 divergence between these lineages was high (7.4–7.8%) while that of nuclear genes was low (0.06–0.53%). This system was contrasted with the medically important American house dust mite, Dermatophagoides farinae, a globally distributed species with very large population size. This species has two distinct, sympatric cox1 lineages with 4.2% divergence. We tested several species delimitation algorithms PTP, GMYC, ABGD, BPP, STACEY and PHRAPL, which inferred different species boundaries for these entities. Notably, STACEY recovered the Caparinia lineages as two species and D. farinae as a single species. BPP agreed with these results when the prior on ancestral effective population sizes was set to expected values, although delimitation of Caparinia was still equivocal. No other cox1 species delimitation algorithms inferred D. farinae as a single species, despite the fact that the nuclear CPW2 gene shows some evidence for introgression between the cox1 groups. This indicates that the cox1-barcoding approach may result in excessive species splitting.ConclusionsOur research highlights the importance of using nuclear genes and demographic characteristics to infer species boundaries rather than relying on a single-gene barcoding approach, particularly for putative species having large effective population sizes.

Introgression Makes Waves in Inferred Histories of Effective Population Size

Human populations have a complex history of introgression and of changing population size. Human genetic variation has been affected by both these processes, so that inference of past population size depends upon the pattern of gene flow and introgression among past populations. One remarkable aspect of human population history as inferred from genetics is a consistent of larger effective population size, prior to the bottlenecks and expansions of the last 100,000 years. Here I carry out a series of simulations to investigate how introgression and gene flow from genetically divergent ancestral populations affect the inference of ancestral effective population size. Both introgression and gene flow from an extinct, genetically divergent population consistently produce a wave in the history of inferred effective population size. The time and amplitude of the wave reflect the time of origin of the genetically divergent ancestral populations and the strength of introgression or gene flow. These results demonstrate that even small fractions of introgression or gene flow from ancient populations may have large effects on the inference of effective population size.

Extensive shared polymorphism at non-MHC immune genes in recently diverged North American prairie grouse

Gene polymorphisms shared between recently diverged species are thought to be widespread and most commonly reflect introgression from hybridization or retention of ancestral polymorphism through incomplete lineage sorting. Shared genetic diversity resulting from incomplete lineage sorting is usually maintained for a relatively short period of time, but under strong balancing selection it may persist for millions of years beyond species divergence (balanced trans-species polymorphism), as in the case of the major histocompatibility complex (MHC) genes. However, balancing selection is much less likely to act on non-MHC immune genes. The aim of this study was to investigate the patterns of shared polymorphism and selection at non-MHC immune genes in five grouse species from Centrocercus and Tympanuchus genera. For this purpose, we genotyped five non-MHC immune genes that do not interact directly with pathogens, but are involved in signaling and regulate immune cell growth. In contrast to previous studies with MHC, we found no evidence for balancing selection or balanced trans-species polymorphism among the non-MHC immune genes. No haplotypes were shared between genera and in most cases more similar allelic variants sorted by genus. Between species within genera, however, we found extensive shared polymorphism, which was most likely attributable to introgression or incomplete lineage sorting following recent divergence and large ancestral effective population size (i.e., weak genetic drift). Our study suggests that North American prairie grouse may have attained relatively low degree of reciprocal monophyly at nuclear loci and reinforces the rarity of balancing selection in non-MHC immune genes.

Molecular Population Genetics of the Northern Elephant Seal Mirounga angustirostris.

The northern elephant seal, Mirounga angustirostris, was heavily hunted and declared extinct in the 19th century. However, a colony remained on remote Guadalupe Island, Mexico and the species has since repopulated most of its historical distribution. Here, we present a comprehensive evaluation of genetic variation in the species. First, we assess the effect of the demographic bottleneck on microsatellite variability and compare it with that found in other pinnipeds, demonstrating levels of variation similar to that in species that continue to be threatened with extinction. Next, we use sequence data from these markers to demonstrate that some of the limited polymorphism predates the bottleneck. However, most contemporary variation appears to have arisen recently and persisted due to exponential growth. We also describe how we use the range in allele size of microsatellites to estimate ancestral effective population size before the bottleneck, demonstrating a large reduction in effective size. We then employ a classical method for bacteria to estimate the microsatellite mutation rate in the species, deriving an estimate that is extremely similar to that estimated for a similar set of loci in humans, indicating consistency of microsatellite mutation rates in mammals. Finally, we find slight significant structure between some geographically separated colonies, although its biological significance is unclear. This work demonstrates that genetic analysis can be useful for evaluating the population biology of the northern elephant seal, in spite of the bottleneck that removed most genetic variation from the species.

Estimation of linkage disequilibrium and effective population size in New Zealand sheep using three different methods to create genetic maps

BackgroundInvestments in genetic selection have played a major role in the New Zealand sheep industry competitiveness. Selection may erode genetic diversity, which is a crucial factor for the success of breeding programs. Better understanding of linkage disequilibrium (LD) and ancestral effective population size (Ne) through quantifying this diversity and comparison between populations allows for more informed decisions with regards to selective breeding taking population genetic diversity into account. The estimation of Ne can be determined via genetic markers and requires knowledge of genetic distances between these markers. Single nucleotide polymorphisms (SNP) data from a sample of 12,597 New Zealand crossbred and purebred sheep genotyped with the Illumina Ovine SNP50 BeadChip was used to perform a genome-wide scan of LD and Ne. Three methods to estimate genetic distances were investigated: 1) M1: a ratio fixed across the whole genome of one Megabase per centiMorgan; 2) M2: the ratios of genetic distance (using M3, below) over physical distance fixed for each chromosome; and, 3) M3: a genetic map of inter-SNP distances estimated using CRIMAP software (v2.503).ResultsThe estimates obtained with M2 and M3 showed much less variability between autosomes than those with M1, which tended to give lower Ne results and higher LD decay. The results suggest that Ne has decreased since the development of sheep breeds in Europe and this reduction in Ne has been accelerated in the last three decades. The Ne estimated for five generations in the past ranged from 71 to 237 for Texel and Romney breeds, respectively. A low level of genetic kinship and inbreeding was estimated in those breeds suggesting avoidance of mating close relatives.ConclusionsM3 was considered the most accurate method to create genetic maps for the estimation of LD and Ne. The findings of this study highlight the history of genetic selection in New Zealand crossbred and purebred sheep and these results will be very useful to understand genetic diversity of the population with respect to genetic selection. In addition, it will help geneticists to identify genomic regions which have been preferentially selected within a variety of breeds and populations.

Inferring Demographic History Using Two-Locus Statistics.

Population demographic history may be learned from contemporary genetic variation data. Methods based on aggregating the statistics of many single loci into an allele frequency spectrum (AFS) have proven powerful, but such methods ignore potentially informative patterns of linkage disequilibrium (LD) between neighboring loci. To leverage such patterns, we developed a composite-likelihood framework for inferring demographic history from aggregated statistics of pairs of loci. Using this framework, we show that two-locus statistics are more sensitive to demographic history than single-locus statistics such as the AFS. In particular, two-locus statistics escape the notorious confounding of depth and duration of a bottleneck, and they provide a means to estimate effective population size based on the recombination rather than mutation rate. We applied our approach to a Zambian population of Drosophila melanogaster Notably, using both single- and two-locus statistics, we inferred a substantially lower ancestral effective population size than previous works and did not infer a bottleneck history. Together, our results demonstrate the broad potential for two-locus statistics to enable powerful population genetic inference.

Estimates of linkage disequilibrium and effective population sizes in Chinese Merino (Xinjiang type) sheep by genome-wide SNPs

Knowledge of linkage disequilibrium (LD) is important for effective genome-wide association studies and accurate genomic prediction. Chinese Merino (Xinjiang type) is well-known fine wool sheep breed. However, the extent of LD across the genome remains unexplored. In this study, we calculated autosomal LD based on genome-wide SNPs of 635 Chinese Merino (Xinjiang type) sheep by Illumina Ovine SNP50 BeadChip. A moderate level of LD (r2 ≥ 0.25) across the whole genome was observed at short distances of 0–10 kb. Further, the ancestral effective population size (Ne) was analyzed by extent of LD and found that Ne increased with the increase of generations and declined rapidly within the most recent 50 generations, which is consistent with the history of Chinese Merino sheep breeding, initiated in 1971. We also noted that even when the effective population size was estimated across different single chromosomes, Ne only ranged from 140.36 to 183.33 at five generations in the past, exhibiting a rapid decrease compared with that at ten generations in the past. These results indicated that the genetic diversity in Chinese Merino sheep recently decreased and proper protective measures should be taken to maintain the diversity. Our datasets provided essential genetic information to track molecular variations which potentially contribute to phenotypic variation in Chinese Merino sheep.

Genetic Diversity and Ancestral History of the German Angler and the Red-and-White Dual-Purpose Cattle Breeds Assessed through Pedigree Analysis

Local cattle breeds continue to decline in numbers partly due to the use of high performing breeds in advanced production systems where genetic material of elite animals is widely spread. The objective of this study was to assess the within and across breed genetic diversity of the Angler and Red-and-White dual-purpose (DP) cattle breeds applying different inbreeding concepts. Classical and ancestral inbreeding coefficients were computed from pedigree data using the gene dropping method. Effective population size was calculated based on the increase of classical inbreeding, and based on ancestral inbreeding to obtain what was termed as ancestral effective population size. Furthermore, the effective number of founders and ancestors were computed to assess the disequilibrium of founder contribution in the reference populations. The analyses were performed separately for each breed and for a combined dataset. The Angler pedigree was more complete (88%) in the first parental generation but completeness declined with increasing pedigree depth. Average classical inbreeding coefficients of inbred individuals were 2.19%, 1.94% and 2.07%, while average Ballou’s ancestral inbreeding coefficients were 3.69%, 1.39% and 2.21% for the Angler, Red-and-White DP and the combined breed pedigree analyses, respectively. Ancestral history coefficient is a novel coefficient and its estimates were similar and strongly correlated to Ballou’s coefficients (r = 0.99, p < 0.001). The effective population size estimates ranged from 156 to 170 for the classical inbreeding based method, and as low as from 50 to 54 for the ancestral history coefficient based method. The effective number of founders and ancestors ranged from 310 to 532, and 90 to 189, respectively. Our results show that the Red Holstein breed is a key progenitor of the breed populations under study. This highlights cross breeding schemes introduced to improve the milk trait performance of the Angler and Red-and-White DP breeds some decades ago.

Introgression Makes Waves in Inferred Histories of Effective Population Size.

Human populations have a complex history of introgression and of changing population size. Human genetic variation has been affected by both these processes, so inference of past population size depends upon the pattern of gene flow and introgression among past populations. One remarkable aspect of human population history as inferred from genetics is a consistent "wave" of larger effective population sizes, found in both African and non-African populations, that appears to reflect events prior to the last 100,000 years. I carried out a series of simulations to investigate how introgression and gene flow from genetically divergent ancestral populations affect the inference of ancestral effective population size. Both introgression and gene flow from an extinct, genetically divergent population consistently produce a wave in the history of inferred effective population size. The time and amplitude of the wave reflect the time of origin of the genetically divergent ancestral populations and the strength of introgression or gene flow. These results demonstrate that even small fractions of introgression or gene flow from ancient populations may have visible effects on the inference of effective population size.

Distribution of coalescent histories under the coalescent model with gene flow

We propose a coalescent model for three species that allows gene flow between both pairs of sister populations. The model is designed for multilocus genomic sequence alignments, with one sequence sampled from each of the three species, and is formulated using a Markov chain representation that allows use of matrix exponentiation to compute analytical expressions for the probability density of coalescent histories. The coalescent history distribution as well as the gene tree topology distribution under this coalescent model with gene flow are then calculated via numerical integration. We analyze the model to compare the distributions of gene tree topologies and coalescent histories for species trees with differing effective population sizes and gene flow rates. Our results suggest conditions under which the species tree and associated parameters are not identifiable from the gene tree topology distribution when gene flow is present, but indicate that the coalescent history distribution may identify the species tree and associated parameters. Thus, the coalescent history distribution can be used to infer parameters such as the ancestral effective population sizes and the rates of gene flow in a maximum likelihood (ML) framework. We conduct computer simulations to evaluate the performance of our method in estimating these parameters, and we apply our method to an Afrotropical mosquito data set (Fontaine et al., 2015).