Embedding of Markov matrices for d ⩽ 4.

The embedding problem of Markov matrices in Markov semigroups is a classic problem that regained a lot of impetus and activities through recent needs in phylogeny and population genetics. Here, we give an account for dimensions d ⩽ 4 , including a complete and simplified treatment of the case d = 3 , and derive the results in a systematic fashion, with an eye on the potential applications. Further, we reconsider the setup of the corresponding problem for time-inhomogeneous Markov chains, which is needed for real-world applications because transition rates need not be constant over time. Additional cases of this more general embedding occur for any d ⩾ 3 . We review the known case of d = 3 and describe the setting for future work on d = 4 .

Genetic characterization of cucumber genetic resources in the NARO Genebank indicates their multiple dispersal trajectories to the East.

KEY MESSAGE: Genotyping-by-sequencing of 723 worldwide cucumber genetic resources revealed that cucumbers were dispersed eastward via at least three distinct routes, one to Southeast Asia and two from different directions to East Asia. The cucumber (Cucumis sativus) is an economically important vegetable crop cultivated and consumed worldwide. Despite its popularity, the manner in which cucumbers were dispersed from their origin in South Asia to the rest of the world, particularly to the east, remains a mystery due to the lack of written records. In this study, we performed genotyping-by-sequencing (GBS) on 723 worldwide cucumber accessions, mainly deposited in the Japanese National Agriculture and Food Research Organization (NARO) Genebank, to characterize their genetic diversity, relationships, and population structure. Analyses based on over 60,000 genome-wide single-nucleotide polymorphisms identified by GBS revealed clear genetic differentiation between Southeast and East Asian populations, suggesting that they reached their respective region independently, not progressively. A deeper investigation of the East Asian population identified two subpopulations with different fruit characteristics, supporting the traditional classification of East Asian cucumbers into two types thought to have been introduced by independent routes. Finally, we developed a core collection of 100 accessions representing at least 93.2% of the genetic diversity present in the entire collection. The genetic relationships and population structure, their associations with geographic distribution and phenotypic traits, and the core collection presented in this study are valuable resources for elucidating the dispersal history and promoting the efficient use and management of genetic resources for research and breeding in cucumber.

Population genetics assessment of two pocilloporid coral species from the northern red sea: Implications for urbanized reef sustainability.

Understanding the genetic makeup of key coral species is vital for effective coral reef management, as heightened genetic diversity directly influences long-term survival and resilience against environmental changes. This study focused on two widespread Indo-Pacific branching corals, Pocillopora damicornis (referred as Pocillopora cf. damicornis (as identified only morphologically) and Seriatopora hystrix, by genotyping 222 and 195 colonies, respectively, from 10 sites in the northern Gulf of Eilat, Red Sea, using six and five microsatellite markers, respectively. Both species exhibited low observed heterozygosity (0.47 for P. cf. damicornis, 0.32 for S. hystrix) and similar expected heterozygosity (0.576 for P. cf. damicornis, 0.578 for S. hystrix). Pocillopora cf. damicornis showed minimal deviations from Hardy-Weinberg equilibrium (HWE) and low but positive F values, indicating high gene flow, while S. hystrix exhibited higher diversion from HWE and positive F values, suggesting isolation by distance and possible non-random mating or genetic drift. As the Gulf of Eilat undergoes rapid urbanization, this study highlights the anthropogenic impacts on the population genetics of key ecosystem engineering species and emphasizes the importance of managing genetics of Marine Protected Areas while implementing active coral reef restoration. The differences in reproductive traits between the two species (S. hystrix being a brooder, while P. cf. damicornis a broadcast spawner), underscore the need for sustainable population genetics management of the coral reefs for the future and resilience of the coral reef ecosystem of the northern Red Sea region.

On the estimation of genome-average recombination rates.

The rate at which recombination events occur in a population is an indicator of its effective population size and the organism's reproduction mode. It determines the extent of linkage disequilibrium along the genome and, thereby, the efficacy of both purifying and positive selection. The population recombination rate can be inferred using models of genome evolution in populations. Classic methods based on the patterns of linkage disequilibrium provide the most accurate estimates, providing large sample sizes are used and the demography of the population is properly accounted for. Here, the capacity of approaches based on the sequentially Markov coalescent (SMC) to infer the genome-average recombination rate from as little as a single diploid genome is examined. SMC approaches provide highly accurate estimates even in the presence of changing population sizes, providing that (1) within genome heterogeneity is accounted for and (2) classic maximum-likelihood optimization algorithms are employed to fit the model. SMC-based estimates proved sensitive to gene conversion, leading to an overestimation of the recombination rate if conversion events are frequent. Conversely, methods based on the correlation of heterozygosity succeed in disentangling the rate of crossing over from that of gene conversion events, but only when the population size is constant and the recombination landscape homogeneous. These results call for a convergence of these two methods to obtain accurate and comparable estimates of recombination rates between populations.

Global assessment of effective population sizes: Consistent taxonomic differences in meeting the 50/500 rule.

Effective population size (Ne) is a particularly useful metric for conservation as it affects genetic drift, inbreeding and adaptive potential within populations. Current guidelines recommend a minimum Ne of 50 and 500 to avoid short-term inbreeding and to preserve long-term adaptive potential respectively. However, the extent to which wild populations reach these thresholds globally has not been investigated, nor has the relationship between Ne and human activities. Through a quantitative review, we generated a dataset with 4610 georeferenced Ne estimates from 3829 populations, extracted from 723 articles. These data show that certain taxonomic groups are less likely to meet 50/500 thresholds and are disproportionately impacted by human activities; plant, mammal and amphibian populations had a <54% probability of reaching N ̂ e = 50 and a <9% probability of reaching N ̂ e = 500. Populations listed as being of conservation concern according to the IUCN Red List had a smaller median N ̂ e than unlisted populations, and this was consistent across all taxonomic groups. N ̂ e was reduced in areas with a greater Global Human Footprint, especially for amphibians, birds and mammals, however relationships varied between taxa. We also highlight several considerations for future works, including the role that gene flow and subpopulation structure plays in the estimation of N ̂ e in wild populations, and the need for finer-scale taxonomic analyses. Our findings provide guidance for more specific thresholds based on Ne and help prioritise assessment of populations from taxa most at risk of failing to meet conservation thresholds.

The expected sample allele frequencies from populations of changing size via orthogonal polynomials.

In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for stepwise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

Phase-type distributions in mathematical population genetics: An emerging framework.

A phase-type distribution is the time to absorption in a continuous- or discrete-time Markov chain. Phase-type distributions can be used as a general framework to calculate key properties of the standard coalescent model and many of its extensions. Here, the 'phases' in the phase-type distribution correspond to states in the ancestral process. For example, the time to the most recent common ancestor and the total branch length are phase-type distributed. Furthermore, the site frequency spectrum follows a multivariate discrete phase-type distribution and the joint distribution of total branch lengths in the two-locus coalescent-with-recombination model is multivariate phase-type distributed. In general, phase-type distributions provide a powerful mathematical framework for coalescent theory because they are analytically tractable using matrix manipulations. The purpose of this review is to explain the phase-type theory and demonstrate how the theory can be applied to derive basic properties of coalescent models. These properties can then be used to obtain insight into the ancestral process, or they can be applied for statistical inference. In particular, we show the relation between classical first-step analysis of coalescent models and phase-type calculations. We also show how reward transformations in phase-type theory lead to easy calculation of covariances and correlation coefficients between e.g. tree height, tree length, external branch length, and internal branch length. Furthermore, we discuss how these quantities can be used for statistical inference based on estimating equations. Providing an alternative to previous work based on the Laplace transform, we derive likelihoods for small-size coalescent trees based on phase-type theory. Overall, our main aim is to demonstrate that phase-type distributions provide a convenient general set of tools to understand aspects of coalescent models that are otherwise difficult to derive. Throughout the review, we emphasize the versatility of the phase-type framework, which is also illustrated by our accompanying R-code. All our analyses and figures can be reproduced from code available on GitHub.

kalis: a modern implementation of the Li & Stephens model for local ancestry inference in R.

BACKGROUND: Approximating the recent phylogeny of N phased haplotypes at a set of variants along the genome is a core problem in modern population genomics and central to performing genome-wide screens for association, selection, introgression, and other signals. The Li & Stephens (LS) model provides a simple yet powerful hidden Markov model for inferring the recent ancestry at a given variant, represented as an N × N distance matrix based on posterior decodings. RESULTS: We provide a high-performance engine to make these posterior decodings readily accessible with minimal pre-processing via an easy to use package kalis, in the statistical programming language R. kalis enables investigators to rapidly resolve the ancestry at loci of interest and developers to build a range of variant-specific ancestral inference pipelines on top. kalis exploits both multi-core parallelism and modern CPU vector instruction sets to enable scaling to hundreds of thousands of genomes. CONCLUSIONS: The resulting distance matrices accessible via kalis enable local ancestry, selection, and association studies in modern large scale genomic datasets.

SNVstory: inferring genetic ancestry from genome sequencing data.

BACKGROUND: Genetic ancestry, inferred from genomic data, is a quantifiable biological parameter. While much of the human genome is identical across populations, it is estimated that as much as 0.4% of the genome can differ due to ancestry. This variation is primarily characterized by single nucleotide variants (SNVs), which are often unique to specific genetic populations. Knowledge of a patient's genetic ancestry can inform clinical decisions, from genetic testing and health screenings to medication dosages, based on ancestral disease predispositions. Nevertheless, the current reliance on self-reported ancestry can introduce subjectivity and exacerbate health disparities. While genomic sequencing data enables objective determination of a patient's genetic ancestry, existing approaches are limited to ancestry inference at the continental level. RESULTS: To address this challenge, and create an objective, measurable metric of genetic ancestry we present SNVstory, a method built upon three independent machine learning models for accurately inferring the sub-continental ancestry of individuals. We also introduce a novel method for simulating individual samples from aggregate allele frequencies from known populations. SNVstory includes a feature-importance scheme, unique among open-source ancestral tools, which allows the user to track the ancestral signal broadcast by a given gene or locus. We successfully evaluated SNVstory using a clinical exome sequencing dataset, comparing self-reported ethnicity and race to our inferred genetic ancestry, and demonstrate the capability of the algorithm to estimate ancestry from 36 different populations with high accuracy. CONCLUSIONS: SNVstory represents a significant advance in methods to assign genetic ancestry, opening the door to ancestry-informed care. SNVstory, an open-source model, is packaged as a Docker container for enhanced reliability and interoperability. It can be accessed from https://github.com/nch-igm/snvstory .

Assessment of the Genetic Diversity and Structure of the Korean Endemic Freshwater Fish Microphysogobio longidorsalis (Gobioninae) Using Microsatellite Markers: A First Glance from Population Genetics.

Microphysogobio longidorsalis is endemic to South Korea and inhabits small areas of the Namhangang, Bukhangang, and Imjingang Rivers in the Hangang River water system. Endemic species usually are more vulnerable than species with a wide distribution. Notably, there is a lack of basic conservation data for M. longidorsalis. We analyzed 19 microsatellite loci in six populations of M. longidorsalis in South Korea to characterize their population structure and genetic diversity. The genetic diversity of the microsatellites was 0.741-0.779, which is lower than that of other freshwater fishes. The pairwise genetic differentiation of microsatellite (FST) values ranged from 0.007 to 0.041, suggesting low genetic differentiation between the populations. The Jojongicheon stream population (CP) had an effective population size of <100. Therefore, conservation efforts are required to prevent inbreeding depression in M. longidorsalis. Discriminant analysis of principal components showed that the Hangang River water system would be a single management unit (MU). Our findings provide fundamental genetic insights for the formulation of conservation strategies for M. longidorsalis.

Diversity assessment of a lesser known buffalo population from Central India and its comparative evaluation reveals presence of sufficient genetic variation and absence of selection.

Planned breeding and conservation strategies for a lesser-known population require an assessment of complete genetic diversity and population structure analysis in addition to its morphometric characteristics. In the present study, a comparative analysis of the genetic structure of a rare buffalo population, namely Chhattisgarhi, was extensively studied using a panel of FAO-recommended microsatellite markers along with well-established breeds namely Murrah, Nili-Ravi, Gojri, Kalahandi, and Nagpuri. Mode shift analysis indicated the absence of genetic bottleneck in the recent past. Assessment of genetic diversity indices across all loci indicated the presence of sufficient genetic variation within and between populations. Analysis of molecular variance between the six different buffalo populations attributed 19.05% of the variations to between-population differentiation. Cluster analyses using DAPC and Bayesian approach along with the phylogenetic tree based on UPGMA grouped six populations into three groups. The Chhattisgarhi population was revealed to be genetically closer to Nagpuri and Kalahandi populations. The study reveals the presence of sufficient genetic diversity within the Chhattisgarhi population and indicates the absence of a systematic selection program. We suggest improvement and conservation programs should be planned for this breed in the near future through short-term selection.

Demographic history shapes North American gray wolf genomic diversity and informs species' conservation.

Effective population size estimates are critical information needed for evolutionary predictions and conservation decisions. This is particularly true for species with social factors that restrict access to breeding or experience repeated fluctuations in population size across generations. We investigated the genomic estimates of effective population size along with diversity, subdivision, and inbreeding from 162,109 minimally filtered and 81,595 statistically neutral and unlinked SNPs genotyped in 437 grey wolf samples from North America collected between 1986 and 2021. We found genetic structure across North America, represented by three distinct demographic histories of western, central, and eastern regions of the continent. Further, grey wolves in the northern Rocky Mountains have lower genomic diversity than wolves of the western Great Lakes and have declined over time. Effective population size estimates revealed the historical signatures of continental efforts of predator extermination, despite a quarter century of recovery efforts. We are the first to provide molecular estimates of effective population size across distinct grey wolf populations in North America, which ranged between Ne ~ 275 and 3050 since early 1980s. We provide data that inform managers regarding the status and importance of effective population size estimates for grey wolf conservation, which are on average 5.2-9.3% of census estimates for this species. We show that while grey wolves fall above minimum effective population sizes needed to avoid extinction due to inbreeding depression in the short term, they are below sizes predicted to be necessary to avoid long-term risk of extinction.

Evidence of recent and ongoing admixture in the U.S. and influences on health and disparities.

Many researchers in genetics and social science incorporate information about race in their work. However, migrations (historical and forced) and social mobility have brought formerly separated populations of humans together, creating younger generations of individuals who have more complex and diverse ancestry and race profiles than older age groups. Here, we sought to better understand how temporal changes in genetic admixture influence levels of heterozygosity and impact health outcomes. We evaluated variation in genetic ancestry over 100 birth years in a cohort of 35,842 individuals with electronic health record (EHR) information in the Southeastern United States. Using the software STRUCTURE, we analyzed 2,678 ancestrally informative markers relative to three ancestral clusters (African, East Asian, and European) and observed rising levels of admixture for all clinically-defined race groups since 1990. Most race groups also exhibited increases in heterozygosity and long-range linkage disequilibrium over time, further supporting the finding of increasing admixture in young individuals in our cohort. These data are consistent with United States Census information from broader geographic areas and highlight the changing demography of the population. This increased diversity challenges classic approaches to studies of genotype-phenotype relationships which motivated us to explore the relationship between heterozygosity and disease diagnosis. Using a phenome-wide association study approach, we explored the relationship between admixture and disease risk and found that increased admixture resulted in protective associations with female reproductive disorders and increased risk for diseases with links to autoimmune dysfunction. These data suggest that tendencies in the United States population are increasing ancestral complexity over time. Further, these observations imply that, because both prevalence and severity of many diseases vary by race groups, complexity of ancestral origins influences health and disparities.

Assessment of genetic diversity, population structure and wolf-dog hybridisation in the Eastern Romanian Carpathian wolf population.

The Carpathian Mountains have been constantly inhabited by grey wolves and present one of the largest distribution areas in Europe, comprising between 2300 and 2700 individuals in Romania. To date, however, relatively little is known about the Romanian wolf population. We aimed to provide a first assessment of genetic diversity, population structure and wolf-dog hybridisation based on 444 mostly non-invasively collected samples in the Eastern Romanian Carpathians. Pack reconstruction and analysis of population genetic parameters were performed with mitochondrial DNA control-region sequencing and microsatellite genotyping. We found relatively high levels of genetic diversity, which is similar to values found in previous studies on Carpathian wolves from Poland and Slovakia, as well as to the long-lasting Dinaric-Balkan wolf population. We found no significant population structure in our study region, suggesting effective dispersal and admixture. Analysis of wolf-dog hybridisation using a Single Nucleotide Polymorphism panel optimised for hybrid detection revealed low rates of admixture between wolves and domestic dogs. Our results provide evidence for the existence of a genetically viable wolf population in the Romanian Carpathians. The genetic data obtained in this study may serve as valuable baseline information for the elaboration of monitoring standards and management plans for wolves in Romania.

Theory matters for identifying a causal role for genetic factors in socioeconomic outcomes.

Any empirical claim about the role of genes in socioeconomic outcomes involves successfully addressing the identification problem. This commentary argues that socioeconomic outcomes such as education are sufficiently complex, involving so many mechanisms, that understanding the role genes requires the use of formal theoretical structures.

Genetic Polymorphism and Population Genetic Structure Analysis of 21 Autosomal STR Loci for a Han-Chinese Population from Luzhou of Southwest China.

The Han nationality is an ancient and populous people, and different places in China may have their distinct group relationships. Luzhou area, as a crossroads of several provinces in Southwest China, lacks autosomal short tandem repeat (STR) research and population genetics research. In this study, 21 autosomal STR loci were evaluated in 1959 Han-Chinese individuals from Luzhou area. There was no substantial linkage disequilibrium (LD) among the 21 autosomal STR markers, and all markers were in Hardy-Weinberg equilibrium (HWE). The total discrimination power (TDP) and cumulative probability of exclusion (CPE) of the 21 autosomal STR loci were calculated to be 1-9.8505 × 10-16 and 1-1.9406 × 10-9, respectively. There were 333 alleles for 21 STRs with allelic frequencies ranging from 0.00026 to 0.51302, and the number of alleles ranged from 7 in locus TPOX to 29 in locus Penta E. According to the results of population comparison and population differentiation, historical influences, geographical distribution, cultural integration, and economic development may have an impact on the Luzhou Han population and other Chinese populations. These 21 STR loci were found to enrich autosomal STR information in forensic databases and provide highly informative polymorphisms for our forensic practice in China, including personal identification and parentage testing.

Mitochondrial DNA reveals shallow population genetic structure in economically important Cyprinid fish Labeo rohita (Hamilton, 1822) from South and Southeast Asia.

BACKGROUND: Assessment of genetic diversity and population genetic structure is important for species that are economically important, threatened, and are at global conservation priority. Analysis of mitochondrial DNA is broadly used in species identification and population genetics studies due to the availability of sufficient reference data and better evolutionary dynamics for phylogeographic investigation. Labeo rohita (Rohu) is an economically important species cultured under carp polyculture systems in Asia. The present study explores the genetic diversity, phylogeography, and population structure of L. rohita from different countries using cytochrome oxidase subunit I (COI) gene. METHODS AND RESULTS: A total of 17 L. rohita specimens were sampled from River Beas, India. For the genetic study, we amplified and sequenced COI mitochondrial DNA region. The obtained genetic data was combined with 268 COI records available in the NCBI and BOLD databases originating from multiple populations/countries across South and Southeast Asia. As a result, 33 haplotypes were identified that displayed low nucleotide (π = 0.0233) and moderate haplotype diversity (Hd = 0.523). Tajima (D) was found to be negative (P > 0.05), whereas Fu's Fs showed a positive value (P > 0.05). The overall FST value between studied populations was 0.481 (P < 0.05). CONCLUSION: AMOVA analysis indicated higher variation within than among the population examined. The neutrality tests suggested the presence of rare haplotypes and stable demography within studied populations of L. rohita. The Bayesian skyline plot indicated steady population growth until 1 Mya followed by population decline, whereas FST values indicated significant genetic differentiation. High heterogeneity was observed in the Pakistan population which could be indicative of long-term isolation and excessive culturing to meet market demands. The present results are the first global comparative analysis of L. rohita and pave the way forward for detailed genomic and ecological studies aimed at the development of improved stock and effective conservation plans. The study also makes recommendations to conserve the genetic integrity of wild species from aquaculture-reared fishes.

Inferring genetic structure when there is little: population genetics versus genomics of the threatened bat Miniopterus schreibersii across Europe.

Despite their paramount importance in molecular ecology and conservation, genetic diversity and structure remain challenging to quantify with traditional genotyping methods. Next-generation sequencing holds great promises, but this has not been properly tested in highly mobile species. In this article, we compared microsatellite and RAD-sequencing (RAD-seq) analyses to investigate population structure in the declining bent-winged bat (Miniopterus schreibersii) across Europe. Both markers retrieved general patterns of weak range-wide differentiation, little sex-biased dispersal, and strong isolation by distance that associated with significant genetic structure between the three Mediterranean Peninsulas, which could have acted as glacial refugia. Microsatellites proved uninformative in individual-based analyses, but the resolution offered by genomic SNPs illuminated on regional substructures within several countries, with colonies sharing migrators of distinct ancestry without admixture. This finding is consistent with a marked philopatry and spatial partitioning between mating and rearing grounds in the species, which was suspected from marked-recaptured data. Our study advocates that genomic data are necessary to properly unveil the genetic footprints left by biogeographic processes and social organization in long-distant flyers, which are otherwise rapidly blurred by their high levels of gene flow.

Social injustice unveiled by genetic analysis: Argentina as a case study.

BACKGROUND: The population of the American countries is genetically heterogeneous, whose genesis result from of recent admixture events. In this process, the transoceanic European component displaced the original inhabitants of the continent. AIM: To investigate whether socially differentiated cohorts exhibit underlying ancestry components within an urban admixed population, two cohorts of individuals inhabiting Argentina were studied. One cohort included genetically unrelated individuals involved in voluntary paternity testing while the other included sexual or blood-crime suspects. MATERIALS & METHODS: We analyzed over 2500 unrelated individuals: four Native American maternal lineage mtDNA markers in 1024 samples, five Y chromosome haplogroups in 658 male samples, 24 autosomal ancestry informative markers (AIMs) in 205 samples, and 15 autosomal short tandem repeats (STRs) in 1557 samples; countrywide and divided by regions. RESULTS: While our results confirm a tricontinental ethnic contribution to both cohorts, their proportions showed statistically significant differences, with a higher proportion of Native American ancestry in the cohort linked to violent crimes compared to those in paternity testing. This hallmark was observed with all the marker sets used and at various levels of analysis. DISCUSSION: Since paternity tests are costly, socio-economic differences might help to interpret our observations. The effect of discrimination against descendants of Native American minorities, and exposure to violent social environments, might link marginal groups to criminality. CONCLUSION: Our findings underscore the relevance of proper social management since only by improving living conditions, reducing discrimination, promoting education, and providing job opportunities will it be possible to attain equality in a heterogeneous society. Genetic markers proved to be highly informative in unveiling unexpected social differences.