Nanoparticle Anisotropy Increases Targeting Interactions on Live-Cell Membranes.

This paper describes how branch lengths of anisotropic nanoparticles can affect interactions between grafted ligands and cell-membrane receptors. Using live-cell, single-particle tracking, we found that DNA aptamer-gold nanostar nanoconstructs with longer branches showed improved binding efficacy to human epidermal growth factor receptor 2 (HER2) on cancer cell membranes. Inhibiting nanoconstruct-HER2 binding promoted nonspecific interactions, which increased the rotational speed of long-branched nanoconstructs but did not affect that of short-branched constructs. Bivariate analysis of the rotational and translational dynamics showed that longer branch lengths increased the ratio of targeting to nontargeting interactions. We also found that longer branches increased the nanoconstruct-cell interaction times before internalization and decreased intracellular trafficking velocities. Differences in binding efficacy revealed by single-particle dynamics can be attributed to the distinct protein corona distributions on short- and long-branched nanoconstructs, as validated by transmission electron microscopy. Minimal protein adsorption at the high positive curvature tips of long-branched nanoconstructs facilitated binding of DNA aptamer ligands to HER2. Our study reveals the significance of nanoparticle branch length in regulating local chemical environment and interactions with live cells at the single-particle level.

Transmission dynamics variability of lineage 2 Mycobacterium tuberculosis strains in Kobe, Japan, determined using population-based whole-genome sequencing analysis.

Currently, tuberculosis (TB) in Japan is highly prevalent among elderly patients who were born during a time when TB was highly prevalent. Mycobacterium tuberculosis (Mtb) lineage 2 (L2) is the predominant strain in the country. Moreover, the proportion of foreign-born patients with TB has been increasing. This epidemiological situation in Japan motivated us to explore the heterogeneity in transmission dynamics among the sublineages of Mtb L2 within this aging population. For this purpose, we conducted a population-based whole genome sequencing analysis of 550 Mtb strains in Kobe, Japan, and employed pairwise single nucleotide polymorphism (SNP) distance clustering and terminal branch length (TBL) distribution analysis to assess Mtb transmission. The genomic clustering rate with a threshold of ≤5 SNPs was significantly lower in elderly patients aged 70 years or higher than in non-elderly patients. The elderly patient group showed significantly longer TBL than the non-elderly group. These results supported the notion that reactivation of distant infection is a major driving force for the high incidence of TB in elderly individuals. The age group distribution and frequency of lineages/sublineages were found to significantly differ between foreign-born and Japan-born patients. The increased proportion of foreign-born patients might have resulted in more strain diversity in Japan. The L2.2.A sublineage demonstrated a significant association with elderly patients and exhibited lower transmission rates, which indicate to be prone to reactivate from long-term latency. In contrast, L2.2.Modern, showed a strong association with younger and foreign-born patients. This sublineage showed a high genomic cluster rate, suggesting its high transmissibility. The other three major sublineages, namely L2.2.AA2, L2.2.AA3.1, and L2.2.AA3.2, exhibited a consistent increase in cluster rates across varying SNP thresholds, indicating their relatively recent emergence as endemic sublineages in Japan. In conclusion, this study highlights distinct differences in the transmission dynamics of L2 sublineages within an aging society.

Identifying and addressing methodological incongruence in phylogenomics: A review.

The availability of phylogenetic data has greatly expanded in recent years. As a result, a new era in phylogenetic analysis is dawning-one in which the methods we use to analyse and assess our data are the bottleneck to producing valuable phylogenetic hypotheses, rather than the need to acquire more data. This makes the ability to accurately appraise and evaluate new methods of phylogenetic analysis and phylogenetic artefact identification more important than ever. Incongruence in phylogenetic reconstructions based on different datasets may be due to two major sources: biological and methodological. Biological sources comprise processes like horizontal gene transfer, hybridization and incomplete lineage sorting, while methodological ones contain falsely assigned data or violations of the assumptions of the underlying model. While the former provides interesting insights into the evolutionary history of the investigated groups, the latter should be avoided or minimized as best as possible. However, errors introduced by methodology must first be excluded or minimized to be able to conclude that biological sources are the cause. Fortunately, a variety of useful tools exist to help detect such misassignments and model violations and to apply ameliorating measurements. Still, the number of methods and their theoretical underpinning can be overwhelming and opaque. Here, we present a practical and comprehensive review of recent developments in techniques to detect artefacts arising from model violations and poorly assigned data. The advantages and disadvantages of the different methods to detect such misleading signals in phylogenetic reconstructions are also discussed. As there is no one-size-fits-all solution, this review can serve as a guide in choosing the most appropriate detection methods depending on both the actual dataset and the computational power available to the researcher. Ultimately, this informed selection will have a positive impact on the broader field, allowing us to better understand the evolutionary history of the group of interest.

The Major Features of Macroevolution.

Evolutionary dynamics operating across deep time leave footprints in the shapes of phylogenetic trees. For the last several decades, researchers have used increasingly large and robust phylogenies to study the evolutionary history of individual clades and to investigate the causes of the glaring disparities in diversity among groups. Whereas typically not the focal point of individual clade-level studies, many researchers have remarked on recurrent patterns that have been observed across many different groups and at many different time scales. Whereas previous studies have documented various such regularities in topology and branch length distributions, they have typically focused on a single pattern and used a disparate collection (oftentimes, of quite variable reliability) of trees to assess it. Here we take advantage of modern megaphylogenies and unify previous disparate observations about the shapes embedded in the Tree of Life to create a catalog of the "major features of macroevolution." By characterizing such a large swath of subtrees in a consistent way, we hope to provide a set of phenomena that process-based macroevolutionary models of diversification ought to seek to explain.

Machine learning classification reveals robust morphometric biomarker of glial and neuronal arbors.

Neurons and glia are the two main cell classes in the nervous systems of most animals. Although functionally distinct, neurons and glia are both characterized by multiple branching arbors stemming from the cell bodies. Glial processes are generally known to form smaller trees than neuronal dendrites. However, the full extent of morphological differences between neurons and glia in multiple species and brain regions has not yet been characterized, nor is it known whether these cells can be reliably distinguished based on geometric features alone. Here, we show that multiple supervised learning algorithms deployed on a large database of morphological reconstructions can systematically classify neuronal and glial arbors with nearly perfect accuracy and precision. Moreover, we report multiple morphometric properties, both size related and size independent, that differ substantially between these cell types. In particular, we newly identify an individual morphometric measurement, Average Branch Euclidean Length that can robustly separate neurons from glia across multiple animal models, a broad diversity of experimental conditions, and anatomical areas, with the notable exception of the cerebellum. We discuss the practical utility and physiological interpretation of this discovery.

Phylogenies in yeast species descriptions: In defense of neighbor-joining.

The neighbor-joining (NJ) method of tree inference is examined, with special attention to its use in yeast species descriptions. How the often-vilified method works is often misunderstood. More importantly, given the right kind of data, its output is a phylogram that illustrates a hypothetical phylogeny that is just as credible as that obtained by any other method. And as with any other method, the result is greatly affected by sampling intensity, particularly the number of aligned positions used for analysis. I address various allegations, including the claim that the method is phenetic, and, therefore, not phylogenetic. I argue that NJ is the most suitable tree inference method to use in yeast species descriptions, primarily because it is best at visually preserving the extent of sequence divergence between close relatives, which continues to be the primary criterion for yeast species delineation. The relevance of bootstraps in the application of the phylogenetic species concept is discussed.

Competitive performance of Pinus massoniana is related to scaling relationships at the individual plant and branch levels.

PREMISE: Competition is an important driver of tree mortality and thus affects forest structure and dynamics. Tree architectural traits, such as height-to-diameter (H-D) and branch length-to-diameter (L-d) relationships are thought to influence species competitiveness by affecting light capture. Unfortunately, little is known about how the H vs. D and L vs. d scaling exponents are related to tree performance (defined in the context of growth vigor) in competition. METHODS: Using data from field surveys of 1547 individuals and destructive sampling of 51 trees with 1086 first-order branches from a high-density Pinus massoniana forest, we explored whether the H vs. D and the L vs. d scaling exponents respectively differed numerically across tree performance and branch vertical position in crowns. RESULTS: The results indicated that (1) the H vs. D scaling exponent decreased as tree performance declined; (2) the L vs. d scaling exponent differed across tree performance classes (i.e., the scaling exponent of "inferior" trees was significantly larger than that of "moderate" and "superior" trees); (3) the L vs. d scaling exponent decreased as branch position approached ground level; and (4) overall, the branch scaling exponent decreased as tree performance improved in each crown layer, but decreased significantly in the intermediate layer. CONCLUSIONS: This study highlights the variation within (and linkage among) length-to-diameter scaling relationships across tree performance at the individual and branch levels. This linkage provides new insights into potential mechanisms of tree growth variation (and even further mortality) under competition in subtropical forests.

Effect of strip clear-cutting on the natural regeneration of Pinus tabuliformis plantations in northeastern China.

In this study, the effect of strip clear-cutting on the natural regeneration performance of mature Pinus tabuliformis plantations in the three locations in western part of the Liaoning Province was analyzed. Strip clear-cutting, with clear-cut and uncut strip widths of 15, 20, 25 m, and 10 and 18 m, respectively, was conducted in spring 2014, and control, in each study location. Field investigations were conducted in 2017. Fifteen sample plots with sizes of 4 m2 (2 m × 2 m) were established in each clear-cut strip, uncut strip, and control. One to four saplings were randomly selected to measure the current year increment, and the lengths and numbers for branch of the first whorl. Three saplings were randomly selected from the center of the strip to measure the photosynthetic rate. Three sample plots with sizes of 4 m2 (2 m × 2 m) and 1 m2 (1 m × 1 m) were developed in each strip and control to determine the biodiversity of shrubs and herbs as well as the water content of the decomposition and semi-decomposition layer. The results show that the current year increment and branch length of the first whorl can be ordered as follows: clear-cut strips > control > uncut strips. Number of the branches of the first whorl can be ordered as follows: clear-cut strips > uncut strips > control. Strip clear-cutting was a statistically significant treatment for the current year increment and length and number of branches of the first whorl. The saplings from the clear-cut strip with a width of 25 m have the largest photosynthetic capacity compared with those from the other strips and control. The transpiration rates of the large, medium, and small saplings from clear-cut strips are the largest and those of saplings from the control are the smallest. The water content of the decomposition and semi-decomposition layer in the control is the highest, but no significant difference was confirmed between the strip clear-cutting approaches.

UCE Phylogenomics, detection of a putative hybrid population, and one older mitogenomic node age of Batrachuperus salamanders.

The prevalence of incomplete lineage sorting complicates the examination of hybridization and species-level paraphyly with gene trees of a small number of loci. In Asian mountain salamanders of the genus Batrachuperus, possible hybridization and species paraphyly had been identified by utilizing mitochondrial genealogy and fixed allozyme differences. Here we sampled 2909 UCEs in 44 local populations from all six Batrachuperus species, inferred gene and species trees, compared them with mitochondrial and allozyme results, and examined the potential hybridization and species paraphyly. The clustering pattern of single-locus trees, increased proportion of heterozygous SNPs, allele frequency-based migration edge estimation, and intrapopulation long branches (as expected from an increase of genetic lineage and nucleotide diversity) support that an eastern B. karlschmidti population has experienced admixture with B. tibetanus. On the 2909-UCE concatenated and species trees, lower nodal supports were observed when similar proportions of loci agreed with alternative topologies, i.e., a reciprocal monophyly between a Pengxian lineage and the remainder of B. pinchonii (0.379) or a paraphyly of the latter with respect to Pengxian (0.362). The UCE phylogenomics agreed with the relatively recent groupings in the allozyme dendrogram. Despite incomplete lineage sorting, the mitochondrial trees were similar to the UCE trees for deeper relationships of the genus. However, one significant branch-length level discordance was identified. The branch between the common ancestor of B. daochengensis and B. yenyuanensis and common ancestor of the genus was approximately three times shorter on the mitochondrial tree than on the UCE tree, suggesting that the split of the mitochondrial lineages was likely a few million years earlier than the split of species. This finding supports considering possible ancestral polymorphism when interpreting different divergence dates estimated from mitochondrial and genome-wide data.

Different rates of pollen and seed gene flow cause branch-length and geographic cytonuclear discordance within Asian butternuts.

Topological cytonuclear discordance is commonly observed in plant phylogenetic and phylogeographic studies, yet few studies have attempted to detect two other forms of cytonuclear discordance (branch length and geographical) and to uncover the causes of the discordance. We used the whole nuclear and chloroplast genome data from 80 individual Asian butternuts to reveal the pattern and processes of cytonuclear discordance. Our findings indicate that the chloroplast genome had substantially deeper divergence (branch-length discordance) and a steeper cline in the contact zone (geographic discordance) compared with the nuclear genome. After various hypothesis have been tested, the results suggest that incomplete lineage sorting, positive selection and cytonuclear incompatibility are probably insufficient to explain this pattern. However, isolation-by-distance analysis and gene flow estimation point to a much higher level of gene flow by pollen compared with by seeds, which may have slowed down lineage divergence and mediated wider contact for nuclear genome compared with the chloroplast genome. Altogether, this study highlights a critical role of sex-biased dispersal in causing discordance between the nuclear and plastid genome of Asian butternuts. Given its ubiquity among plants, asymmetric gene flow should be given a high priority in future studies of cytonuclear discordance.

Novel Features for Binary Time Series Based on Branch Length Similarity Entropy.

Branch length similarity (BLS) entropy is defined in a network consisting of a single node and branches. In this study, we mapped the binary time-series signal to the circumference of the time circle so that the BLS entropy can be calculated for the binary time-series. We obtained the BLS entropy values for "1" signals on the time circle. The set of values are the BLS entropy profile. We selected the local maximum (minimum) point, slope, and inflection point of the entropy profile as the characteristic features of the binary time-series and investigated and explored their significance. The local maximum (minimum) point indicates the time at which the rate of change in the signal density becomes zero. The slope and inflection points correspond to the degree of change in the signal density and the time at which the signal density changes occur, respectively. Moreover, we show that the characteristic features can be widely used in binary time-series analysis by characterizing the movement trajectory of Caenorhabditis elegans. We also mention the problems that need to be explored mathematically in relation to the features and propose candidates for additional features based on the BLS entropy profile.

Collapsing dubiously resolved gene-tree branches in phylogenomic coalescent analyses.

In two-step coalescent analyses of phylogenomic data, gene-tree topologies are treated as fixed prior to species-tree inference. Although all gene-tree conflict is assumed to be caused by lineage sorting when applying these methods, in empirical datasets much of the conflict can be caused by estimation error. Weakly supported and even arbitrarily resolved clades are important sources of this estimation error for gene trees inferred from few informative characters relative to the number of sampled terminals, and the resulting extraneous conflict among gene trees can negatively impact species-tree inference. In this study, we quantified the relative severity of alternative methods for collapsing gene-tree branches for seven empirical datasets and quantified their effects on species-tree inference. The branch-collapsing methods that we employed were based on the strict consensus of optimal topologies, various bootstrap thresholds, and 0% approximate likelihood ratio test (SH-like aLRT) support. Up to 86% of internal gene-tree branches are dubiously or arbitrarily resolved in reanalyses of these published phylogenomic datasets, and collapsing these branches increased inferred species-tree coalescent branch lengths by up to 455%. For two datasets, the longer inferred branch lengths sometimes impacted inference of anomaly-zone conditions. Although branch-collapsing methods did not consistently affect the species-tree topology, they often increased branch support. The more severe and clearly justified gene-tree branch-collapsing methods, which we recommend be broadly applied for two-step coalescent analyses, are use of the strict consensus in parsimony analyses and the collapse clades with 0% SH-like aLRT support in likelihood analyses. Collapsing dubiously or arbitrarily resolved branches in gene trees sometimes improved congruence between coalescent-based results and concatenation trees. In such cases, we contend that the resolution provided by concatenation should be preferred and that incomplete lineage sorting is a poor explanation for the initial conflict between phylogenetic approaches.

A New Measure to Characterize the Degree of Self-Similarity of a Shape and Its Applicability.

We propose a new measure (Γ) to quantify the degree of self-similarity of a shape using branch length similarity (BLS) entropy which is defined on a simple network consisting of a single node and its branches. To investigate the properties of this measure, we computed the Γ values for 70 object groups (20 shapes in each group) in the MPEG-7 shape database and performed grouping on the values. With relatively high Γ values, identical groups had visually similar shapes. On the other hand, the identical groups with low Γ values had visually different shapes. However, the aspect of topological similarity of the shapes also warrants consideration. The shapes of statistically different groups exhibited significant visual difference from each other. Also, in order to show that the Γ can have a wide variety of applicability when properly used with other variables, we showed that the finger gestures in the (Γ, Z) space are successfully classified. Here, the Z means a correlation coefficient value between entropy profiles for gesture shapes. As shown in the applications, Γ has a strong advantage over conventional geometric measures in that it captures the geometrical and topological properties of a shape together. If we could define the BLS entropy for color, Γ could be used to characterize images expressed in RGB. We briefly discussed the problems to be solved before the applicability of Γ can be expanded to various fields.

Exposure to High Salinity During Seed Development Markedly Enhances Seedling Emergence and Fitness of the Progeny of the Extreme Halophyte Suaeda salsa.

Irrigation with 200 mM NaCl significantly increases vegetative and reproductive growth of the extreme halophyte Suaeda salsa. However, little is known about how the progeny of S. salsa plants grown under a continuous NaCl supply behave in terms of growth and seed set parameters. We investigated various plant growth and reproductive parameters of the progeny that germinated from seeds harvested from mother plants grown under 0 or 200 mM NaCl over three generations. Seedling emergence, plant height, stem diameter, total branch length, flowering branch length, flowering branch ratio, and seed production were all significantly enhanced in the progeny produced by mother plants grown with 200 mM NaCl compared to progeny of mother plants grown on low salinity conditions. Therefore, irrigation with 200 mM of NaCl is beneficial to seed development in the halophyte S. salsa and possibly contributes to population establishment in high salinity environments. Likewise, the prolonged absence of NaCl in the growth environment inhibits seed development, results in lower seed quality, and thus limits seedling growth of the progeny, thereby restricting S. salsa to a high salinity ecological niche.

Disrupted architecture and fast evolution of the mitochondrial genome of Argeia pugettensis (Isopoda): implications for speciation and fitness.

BACKGROUND: Argeia pugettensis is an isopod species that parasitizes other crustaceans. Its huge native geographic range spans the Pacific from China to California, but molecular data are available only for a handful of specimens from North-American populations. We sequenced and characterised the complete mitogenome of a specimen collected in the Yellow Sea. RESULTS: It exhibited a barcode (cox1) similarity level of only 87-89% with North-American populations, which is unusually low for conspecifics. Its mitogenome is among the largest in isopods (≈16.5 Kbp), mostly due to a large duplicated palindromic genomic segment (2 Kbp) comprising three genes. However, it lost a segment comprising three genes, nad4L-trnP-nad6, and many genes exhibited highly divergent sequences in comparison to isopod orthologues, including numerous mutations, deletions and insertions. Phylogenetic and selection analyses corroborated that this is one of the handful of most rapidly evolving available isopod mitogenomes, and that it evolves under highly relaxed selection constraints (as opposed to positive selection). However, its nuclear 18S gene is highly conserved, which suggests that rapid evolution is limited to its mitochondrial genome. The cox1 sequence analysis indicates that elevated mitogenomic evolutionary rates are not shared by North-American conspecifics, which suggests a breakdown of cox1 barcoding in this species. CONCLUSIONS: A highly architecturally disrupted mitogenome and decoupling of mitochondrial and nuclear rates would normally be expected to have strong negative impacts on the fitness of the organism, so the existence of this lineage is a puzzling evolutionary question. Additional studies are needed to assess the phylogenetic breadth of this disrupted mitochondrial architecture and its impact on fitness.

Measuring the external branches of a Kingman tree: A discrete approach.

The Kingman coalescent process is a classical model of gene genealogies in population genetics. It generates Yule-distributed, binary ranked tree topologies - also called histories - with a finite number of n leaves, together with n-1 exponentially distributed time lengths: one for each layer of the history. Using a discrete approach, we study the lengths of the external branches of Yule distributed histories, where the length of an external branch is defined as the rank of its parent node. We study the multiplicity of external branches of given length in a random history of n leaves. A correspondence between the external branches of the ordered histories of size n and the non-peak entries of the permutations of size n-1 provides easy access to the length distributions of the first and second longest external branches in a random Yule history and coalescent tree of size n. The length of the longest external branch is also studied in dependence of root balance of a random tree. As a practical application, we compare the observed and expected number of mutations on the longest external branches in samples from natural populations.

Optimizing taxon addition order and branch lengths in the construction of phylogenetic trees using maximum likelihood.

Taxon addition order and branch lengths are optimized by genetic algorithms (GAS) within the fastDNAml algorithm for constructing phylogenetic trees of high likelihood. Results suggest that optimizing the order in which taxa are added improves the likelihood of the resulting trees.

Maximize Resolution or Minimize Error? Using Genotyping-By-Sequencing to Investigate the Recent Diversification of Helianthemum (Cistaceae).

A robust phylogenetic framework, in terms of extensive geographical and taxonomic sampling, well-resolved species relationships and high certainty of tree topologies and branch length estimations, is critical in the study of macroevolutionary patterns. Whereas Sanger sequencing-based methods usually recover insufficient phylogenetic signal, especially in recently diversified lineages, reduced-representation sequencing methods tend to provide well-supported phylogenetic relationships, but usually entail remarkable bioinformatic challenges due to the inherent trade-off between the number of SNPs and the magnitude of associated error rates. The genus Helianthemum (Cistaceae) is a species-rich and taxonomically complex Palearctic group of plants that diversified mainly since the Upper Miocene. It is a challenging case study since previous attempts using Sanger sequencing were unable to resolve the intrageneric phylogenetic relationships. Aiming to obtain a robust phylogenetic reconstruction based on genotyping-by-sequencing (GBS), we established a rigorous methodological workflow in which we i) explored how variable settings during dataset assembly have an impact on error rates and on the degree of resolution under concatenation and coalescent approaches, ii) assessed the effect of two extreme parameter configurations (minimizing error rates vs. maximizing phylogenetic resolution) on tree topology and branch lengths, and iii) evaluated the effects of these two configurations on estimates of divergence times and diversification rates. Our analyses produced highly supported topologically congruent phylogenetic trees for both configurations. However, minimizing error rates did produce more reliable branch lengths, critically affecting the accuracy of downstream analyses (i.e. divergence times and diversification rates). In addition to recommending a revision of intrageneric systematics, our results enabled us to identify three highly diversified lineages in Helianthemum in contrasting geographical areas and ecological conditions, which started radiating in the Upper Miocene.

A new method for quantifying the phylogenetic redundancy of biological communities.

The increasing use of phylogenetic methods in community ecology recognizes that accumulated evolutionary differences among species mirror, to some extent, ecological processes. The scope of this work is thus to propose a new method for the measurement of community-level phylogenetic redundancy, which takes into account the branching pattern of the underlying phylogeny. Like for functional redundancy, a measure of phylogenetic redundancy can be described as a normalized measure in the range (0-1) that relates the observed community-level phylogenetic diversity to the value of a hypothetical assemblage with the same abundance distribution of the focal community in which all species had independent evolution. Therefore, phylogenetic redundancy can be interpreted as the diversity decrease that is obtained by taking into account the evolutionary relationships among species in the calculation of diversity. The behavior of the proposed method, for which we provide a simple R function called 'phyloredundancy', was evaluated with published data on Alpine plant communities along a primary succession on a glacier foreland in northern Italy. As shown by our results, the method accounts for the length of shared branches in the phylogeny, producing a coherent framework for describing the evolutionary relationships within a species assemblage. Being based on classical diversity measures, which have been used in ecology for decades, it also has a great potential for future research in phylogenetic community ecology.

An Unbiased Estimator of Gene Diversity with Improved Variance for Samples Containing Related and Inbred Individuals of any Ploidy.

Gene diversity, or expected heterozygosity (H), is a common statistic for assessing genetic variation within populations. Estimation of this statistic decreases in accuracy and precision when individuals are related or inbred, due to increased dependence among allele copies in the sample. The original unbiased estimator of expected heterozygosity underestimates true population diversity in samples containing relatives, as it only accounts for sample size. More recently, a general unbiased estimator of expected heterozygosity was developed that explicitly accounts for related and inbred individuals in samples. Though unbiased, this estimator's variance is greater than that of the original estimator. To address this issue, we introduce a general unbiased estimator of gene diversity for samples containing related or inbred individuals, which employs the best linear unbiased estimator of allele frequencies, rather than the commonly used sample proportion. We examine the properties of this estimator, [Formula: see text] relative to alternative estimators using simulations and theoretical predictions, and show that it predominantly has the smallest mean squared error relative to others. Further, we empirically assess the performance of [Formula: see text] on a global human microsatellite dataset of 5795 individuals, from 267 populations, genotyped at 645 loci. Additionally, we show that the improved variance of [Formula: see text] leads to improved estimates of the population differentiation statistic, [Formula: see text] which employs measures of gene diversity within its calculation. Finally, we provide an R script, BestHet, to compute this estimator from genomic and pedigree data.