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.

Haplotype based testing for a better understanding of the selective architecture

BACKGROUND

The identification of genomic regions affected by selection is one of the most important goals in population genetics. If temporal data are available, allele frequency changes at SNP positions are often used for this purpose. Here we provide a new testing approach that uses haplotype frequencies instead of allele frequencies.

RESULTS

Using simulated data, we show that compared to SNP based test, our approach has higher power, especially when the number of candidate haplotypes is small or moderate. To improve power when the number of haplotypes is large, we investigate methods to combine them with a moderate number of haplotype subsets. Haplotype frequencies can often be recovered with less noise than SNP frequencies, especially under pool sequencing, giving our test an additional advantage. Furthermore, spurious outlier SNPs may lead to false positives, a problem usually not encountered when working with haplotypes. Post hoc tests for the number of selected haplotypes and for differences between their selection coefficients are also provided for a better understanding of the underlying selection dynamics. An application on a real data set further illustrates the performance benefits.

CONCLUSIONS

Due to less multiple testing correction and noise reduction, haplotype based testing is able to outperform SNP based tests in terms of power in most scenarios.

Development and evaluation of an animal health and welfare monitoring system for veterinary supervision of pullet farms

Regular welfare monitoring throughout rearing of pullets may help to identify problems early and take counteractions timely, which helps in guaranteeing good welfare. The aims of our observational study were (i) to establish and test a welfare monitoring system that can be used during (short) routine veterinary and technical staff visits for pullet flocks, (ii) to use the monitoring system to investigate variability between flocks and (iii) to analyse factors that potentially affect pullets' body weight, uniformity in body weight and mortality. The developed monitoring system tries to minimise the time required while not losing important information. Age-specific recording sheets comprise animal-based indicators of welfare and relevant environmental factors (housing, management, care) to allow for identifying causes of problems and targeted action. Finally, the system was implemented in a cross-sectional study and data collected in 100 flocks (67 organic, 33 conventional) on 28 rearing farms in Austria. Linear mixed models were used to identify factors influencing body weight, uniformity and mortality, both including all flocks (A) and only organic flocks (O) and a linear regression model with all flocks to investigate associations within animal-based indicators. High variability was found between flocks in animal-based indicators. Body weight was higher when the pre-rearing period was shorter (p ≤ 0.001, A&O), with higher intensities of light (p = 0.012, O), with only one compared to more stockpersons (p ≤ 0.007, A&O), with a higher number of flock visits per day (p ≤ 0.018, A&O), and a lower avoidance distance (p = 0.034, A). Body weight uniformity increased, with age and decreased with the duration of the light period (p = 0.046, A), and, amongst others, was higher on organic farms (farming type; p = 0.041). The latter may reflect a more uniform level of welfare due to a lower stocking density and lowered effects of social competition. Within organic flocks mortality was lower if pullets had access to a covered veranda (p = 0.025) resulting in an overall lower stocking density inside the barn, while in the model including all farms mortality was higher in cases where a disease had been diagnosed. We conclude that our monitoring system can easily be implemented in regular veterinary and technical staff visits, but could also be used by the farmers'. Several easy-to-record animal-based indicators of animal welfare could be analysed more frequently to increase early detection of problems. Implementation of such a routine-based monitoring system with easy-to-assess animal-based parameters and input measures can contribute to better animal health and welfare in pullets.

Using fecal immmunochemical cartridges for gut microbiome analysis within a colorectal cancer screening program

The colorectal cancer (CRC) screening program B-PREDICT is an invited two-stage screening project using a fecal immunochemical test (FIT) for initial screening followed by a colonoscopy for those with a positive FIT. Since the gut microbiome likely plays a role in the etiology of CRC, microbiome-based biomarkers in combination with FIT could be a promising tool for optimizing CRC screening. Therefore, we evaluated the usability of FIT cartridges for microbiome analysis and compared it to Stool Collection and Preservation Tubes. Corresponding FIT cartridges as well as Stool Collection and Preservation Tubes were collected from participants of the B-PREDICT screening program to perform 16S rRNA gene sequencing. We calculated intraclass correlation coefficients (ICCs) based on center log ratio transformed abundances and used ALDEx2 to test for significantly differential abundant taxa between the two sample types. Additionally, FIT and Stool Collection and Preservation Tube triplicate samples were obtained from volunteers to estimate variance components of microbial abundances. FIT and Preservation Tube samples produce highly similar microbiome profiles which cluster according to subject. Significant differences between the two sample types can be found for abundances of some bacterial taxa (e.g. 33 genera) but are minor compared to the differences between the subjects. Analysis of triplicate samples revealed slightly worse repeatability of results for FIT than for Preservation Tube samples. Our findings indicate that FIT cartridges are appropriate for gut microbiome analysis nested within CRC screening programs.

Multiple haplotype reconstruction from allele frequency data

Because haplotype information is of widespread interest in biomedical applications, effort has been put into their reconstruction. Here, we propose an efficient method, called haploSep, that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes. From a methodological point of view, we model our problem as a multivariate regression problem where both the design matrix and the coefficient matrix are unknown. Compared to other methods, haploSep is very fast, with linear computational complexity in the haplotype length. We illustrate our method on simulated and real data focusing on experimental evolution and microbial data.

Gentle interactions with restrained and free-moving cows: Effects on the improvement of the animal-human relationship

The animal-human relationship is essential for farm animal welfare and production. Generally, gentle tactile and vocal interactions improve the animal-human relationship in cattle. However, cows that are fearful of humans avoid their close presence and touch; thus, the animal-human relationship first has to be improved to a point where the animals accept stroking before their perception of the interactions and consequently the animal-human relationship can become positive. We tested whether the animal-human relationship of cows fearful of humans is improved more effectively by gentle interactions during restraint, allowing physical contact from the beginning, or if the gentle interactions are offered while the animals are free to move, giving them more control over the situation and thus probably a higher level of agency and a more positive perception of the interactions. Thirty-six dairy cows (median avoidance distance 1.6 m) were assigned to three treatments (each n = 12): gentle vocal and tactile interactions during restraint in the feeding rack (LOCK); gentle vocal and, if possible, tactile interactions while free in the barn (FREE); routine management without additional interactions (CON). Treatments were applied for 3 min per cow on 10 d per fortnight for 6 weeks (i.e., three periods). Avoidance and approach behaviour towards humans was tested before the start of the treatment period, and then at 2-week intervals. The recorded variables were reduced to one score by Principal Component Analysis. The resulting relationship score (higher values implying a better relationship with humans) increased in all groups; the increase was stronger in FREE than in CON, with the increase in LOCK being not significantly different from the other treatment groups. Thus, we recommend that gentle interactions with cows should take place while they are unrestrained, if possible.

Talking to Cows: Reactions to Different Auditory Stimuli During Gentle Human-Animal Interactions

The quality of the animal-human relationship and, consequently, the welfare of animals can be improved by gentle interactions such as stroking and talking. The perception of different stimuli during these interactions likely plays a key role in their emotional experience, but studies are scarce. During experiments, the standardization of verbal stimuli could be increased by using a recording. However, the use of a playback might influence the perception differently than "live" talking, which is closer to on-farm practice. Thus, we compared heifers' (n = 28) reactions to stroking while an experimenter was talking soothingly ("live") or while a recording of the experimenter talking soothingly was played ("playback"). Each animal was tested three times per condition and each trial comprised three phases: pre-stimulus, stimulus (stroking and talking) and post-stimulus. In both conditions, similar phrases with positive content were spoken calmly, using long low-pitched vowels. All tests were video recorded and analyzed for behaviors associated with different affective states. Effects on the heifers' cardiac parameters were assessed using analysis of heart rate variability. Independently of the auditory stimuli, longer durations of neck stretching occurred during stroking, supporting our hypothesis of a positive perception of stroking. Observation of ear positions revealed longer durations of the "back up" position and less ear flicking and changes of ear positions during stroking. The predicted decrease in HR during stroking was not confirmed; instead we found a slightly increased mean HR during stroking with a subsequent decrease in HR, which was stronger after stroking with live talking. In combination with differences in HRV parameters, our findings suggest that live talking might have been more pleasurable to the animals and had a stronger relaxing effect than "playback." The results regarding the effects of the degree of standardization of the stimulus on the variability of the data were inconclusive. We thus conclude that the use of recorded auditory stimuli to promote positive affective states during human-animal interactions in experimental settings is possible, but not necessarily preferable.

Effects of Different Stroking Styles on Behaviour and Cardiac Parameters in Heifers

Simple Summary

Positive emotions can improve the welfare of animals. Humans can induce positive emotions in cattle via gentle interactions, such as stroking. While previous studies showed that stroking at the lower side of the neck elicited the most positive reactions in cows, cattle groom each other on different body regions and probably react to each other’s signals. We compared the reactions of dairy heifers to two different stroking styles: stroking exclusively on the lower neck or stroking the whole head/neck region and reactively following the signals of the animal. For both styles, we observed longer durations of behaviours indicating positive emotions and relaxation during stroking, suggesting that the animals enjoyed the treatment. The different stroking styles led to differences in the positions of the heifers’ ears: during “reactive” stroking, the animals held their ears longer in low positions, whereas during stroking of the lower neck, the ears spent longer pointing backwards-upwards. However, we did not observe significant differences in other behaviours, indicating that the manner of stroking of the head/neck region seemed to be not very important for the positive perception of stroking. We conclude that both ways of stroking can elicit positive emotions in cattle and increase the animals’ well-being.

Abstract

Gentle animal–human interactions, such as stroking, can promote positive emotions and thus welfare in cattle. While previous studies showed that stroking at the ventral neck elicited the most positive reactions in cows, intra-specific allogrooming in cattle includes different body regions and is probably guided partly by the receiver. Thus, we compared heifers’ (n = 28) reactions to stroking with the experimenter either reactively responding to perceived momentary preferences of the heifers or exclusively stroking the ventral neck. Independently of the stroking style, longer durations of neck stretching and contact occurred during stroking, supporting our hypothesis of a positive perception of stroking. We did not confirm the predicted decrease in heart rate and increase in heart rate variability, but instead found a slightly increased mean heart rate during stroking. The different stroking styles elicited differences in the heifers’ ear positions: “reactive” stroking led to longer durations of low ear positions during stroking, while during “ventral neck” stroking, the duration of back up increased. However, no other behaviours differed significantly between different stroking styles, indicating that the exact manner of stroking applied in our treatments seemed to be less important in the promotion of positive affective states in cattle through gentle human–animal interactions.

The Effects of Play Behavior, Feeding, and Time of Day on Salivary Concentrations of sIgA in Calves

Simple Summary

The focus of animal welfare science has shifted over the last decades from efforts to avoid negative states to ways of allowing animals the experience of positive emotions. The emotional state of an animal interacts with its immune system. Secretory immunoglobulin A, a class of antibodies present on mucosal surfaces and acting as the first line of defense against infections, is influenced by positive and negative emotions in humans; the few studies of its association with emotions in animals focused almost exclusively on the impact of negative emotions and yielded conflicting results. We present the first study that focuses on salivary immunoglobulin A to investigate a possible relationship between positive emotions and immune functioning in calves. We detected a circadian rhythm of immunoglobulin A concentrations, with lowest levels at 14:00 h. Immunoglobulin A concentrations were decreased directly after feeding, possibly due to increased saliva flow rates, and we did not find higher immunoglobulin A concentrations after play. The results are important for the design of future studies of positive emotions, although they do not support immunoglobulin A as an indicator of positive emotional states.

Abstract

The focus of animal welfare science has shifted over the last decades from efforts to avoid negative states to ways of allowing animals the experience of positive emotions. They may influence physiological processes in farmed animals, potentially providing health benefits; in addition, the physiological changes might be used as indicators of emotional states. We investigated calves’ salivary secretory immunoglobulin A (sIgA) concentrations with regard to a possible circadian rhythm and two situations that elicit positive emotions. Ten saliva samples of 14 calves were taken on two consecutive days; within the course of a day we observed a significant decline in salivary sIgA concentrations at 14:00 h. Further, we probed the animals before and after milk feeding and, contrarily to our prediction, detected lower sIgA concentrations 5 min after feeding than 15 min before. A probable explanation might be an increase in salivary flow rate caused by milk ingestion. We also took samples before and after we stimulated play behavior in calves. There was no significant difference in sIgA concentrations between samples taken before and after play. Although there was a significant correlation between the change in sIgA concentrations and the amount of play behavior shown, the correlation depended on an unexpected decrease of sIgA in animals that played little, and thus, does not support our hypothesis. In general, the data showed a large variability that might arise from different factors that are difficult to standardize in animals. Thus, the use of salivary sIgA concentrations as a marker of positive emotions in calves is not supported conclusively by the present data.

Benchmarking software tools for detecting and quantifying selection in evolve and resequencing studies

BACKGROUND

The combination of experimental evolution with whole-genome resequencing of pooled individuals, also called evolve and resequence (E&R) is a powerful approach to study the selection processes and to infer the architecture of adaptive variation. Given the large potential of this method, a range of software tools were developed to identify selected SNPs and to measure their selection coefficients.

RESULTS

In this benchmarking study, we compare 15 test statistics implemented in 10 software tools using three different scenarios. We demonstrate that the power of the methods differs among the scenarios, but some consistently outperform others. LRT-1, CLEAR, and the CMH test perform best despite LRT-1 and the CMH test not requiring time series data. CLEAR provides the most accurate estimates of selection coefficients.

CONCLUSION

This benchmark study will not only facilitate the analysis of already existing data, but also affect the design of future data collections.

The impact of poly-A microsatellite heterologies in meiotic recombination

Meiosis strongly influences the transmission and evolution of heterozygous poly-A repeats as measured experimentally in a large collection of single recombination products in a human hotspot.

Meiotic recombination has strong, but poorly understood effects on short tandem repeat (STR) instability. Here, we screened thousands of single recombinant products with sperm typing to characterize the role of polymorphic poly-A repeats at a human recombination hotspot in terms of hotspot activity and STR evolution. We show that the length asymmetry between heterozygous poly-A’s strongly influences the recombination outcome: a heterology of 10 A’s (9A/19A) reduces the number of crossovers and elevates the frequency of non-crossovers, complex recombination products, and long conversion tracts. Moreover, the length of the heterology also influences the STR transmission during meiotic repair with a strong and significant insertion bias for the short heterology (6A/7A) and a deletion bias for the long heterology (9A/19A). In spite of this opposing insertion-/deletion-biased gene conversion, we find that poly-A’s are enriched at human recombination hotspots that could have important consequences in hotspot activation.

LDJump: Estimating variable recombination rates from population genetic data

As recombination plays an important role in evolution, its estimation and the identification of hotspot positions is of considerable interest. We propose a novel approach for estimating population recombination rates based on genotyping or sequence data that involves a sequential multiscale change point estimator. Our method also permits demography to be taken into account. It uses several summary statistics within a regression model fitted on suitable scenarios. Our proposed method is accurate, computationally fast, and provides a parsimonious solution by ensuring a type I error control against too many changes in the recombination rate. An application to human genome data suggests a good congruence between our estimated and experimentally identified hotspots. Our method is implemented in the R‐package LDJump, which is freely available at https://github.com/PhHermann/LDJump.

An omnibus test for the global null hypothesis

Global hypothesis tests are a useful tool in the context of clinical trials, genetic studies, or meta-analyses, when researchers are not interested in testing individual hypotheses, but in testing whether none of the hypotheses is false. There are several possibilities how to test the global null hypothesis when the individual null hypotheses are independent. If it is assumed that many of the individual null hypotheses are false, combination tests have been recommended to maximize power. If, however, it is assumed that only one or a few null hypotheses are false, global tests based on individual test statistics are more powerful (e.g. Bonferroni or Simes test). However, usually there is no a priori knowledge on the number of false individual null hypotheses. We therefore propose an omnibus test based on cumulative sums of the transformed p-values. We show that this test yields an impressive overall performance. The proposed method is implemented in an R-package called omnibus.

Quantifying Selection with Pool-Seq Time Series Data

Allele frequency time series data constitute a powerful resource for unraveling mechanisms of adaptation, because the temporal dimension captures important information about evolutionary forces. In particular, Evolve and Resequence (E&R), the whole-genome sequencing of replicated experimentally evolving populations, is becoming increasingly popular. Based on computer simulations several studies proposed experimental parameters to optimize the identification of the selection targets. No such recommendations are available for the underlying parameters selection strength and dominance. Here, we introduce a highly accurate method to estimate selection parameters from replicated time series data, which is fast enough to be applied on a genome scale. Using this new method, we evaluate how experimental parameters can be optimized to obtain the most reliable estimates for selection parameters. We show that the effective population size (N_e) and the number of replicates have the largest impact. Because the number of time points and sequencing coverage had only a minor effect, we suggest that time series analysis is feasible without major increase in sequencing costs. We anticipate that time series analysis will become routine in E&R studies.

Approximate maximum likelihood estimation for population genetic inference

In many population genetic problems, parameter estimation is obstructed by an intractable likelihood function. Therefore, approximate estimation methods have been developed, and with growing computational power, sampling-based methods became popular. However, these methods such as Approximate Bayesian Computation (ABC) can be inefficient in high-dimensional problems. This led to the development of more sophisticated iterative estimation methods like particle filters. Here, we propose an alternative approach that is based on stochastic approximation. By moving along a simulated gradient or ascent direction, the algorithm produces a sequence of estimates that eventually converges to the maximum likelihood estimate, given a set of observed summary statistics. This strategy does not sample much from low-likelihood regions of the parameter space, and is fast, even when many summary statistics are involved. We put considerable efforts into providing tuning guidelines that improve the robustness and lead to good performance on problems with high-dimensional summary statistics and a low signal-to-noise ratio. We then investigate the performance of our resulting approach and study its properties in simulations. Finally, we re-estimate parameters describing the demographic history of Bornean and Sumatran orang-utans.

The long zinc finger domain of PRDM9 forms a highly stable and long-lived complex with its DNA recognition sequence

PR domain containing protein 9 (PRDM9) is a meiosis-specific, multi-domain protein that regulates the location of recombination hotspots by targeting its DNA recognition sequence for double-strand breaks (DSBs). PRDM9 specifically recognizes DNA via its tandem array of zinc fingers (ZnFs), epigenetically marks the local chromatin by its histone methyltransferase activity, and is an important tether that brings the DNA into contact with the recombination initiation machinery. A strong correlation between PRDM9-ZnF variants and specific DNA motifs at recombination hotspots has been reported; however, the binding specificity and kinetics of the ZnF domain are still obscure. Using two in vitro methods, gel mobility shift assays and switchSENSE, a quantitative biophysical approach that measures binding rates in real time, we determined that the PRDM9-ZnF domain forms a highly stable and long-lived complex with its recognition sequence, with a dissociation halftime of many hours. The ZnF domain exhibits an equilibrium dissociation constant (K _D) in the nanomolar (nM) range, with polymorphisms in the recognition sequence directly affecting the binding affinity. We also determined that alternative sequences (15-16 nucleotides in length) can be specifically bound by different subsets of the ZnF domain, explaining the binding plasticity of PRDM9 for different sequences. Finally, longer binding targets are preferred than predicted from the numbers of ZnFs contacting the DNA. Functionally, a long-lived complex translates into an enzymatically active PRDM9 at specific DNA-binding sites throughout meiotic prophase I that might be relevant in stabilizing the components of the recombination machinery to a specific DNA target until DSBs are initiated by Spo11.

Improved Versions of Common Estimators of the Recombination Rate

The scaled recombination parameter [Formula: see text] is one of the key parameters, turning up frequently in population genetic models. Accurate estimates of [Formula: see text] are difficult to obtain, as recombination events do not always leave traces in the data. One of the most widely used approaches is composite likelihood. Here, we show that popular implementations of composite likelihood estimators can often be uniformly improved by optimizing the trade-off between bias and variance. The amount of possible improvement depends on parameters such as the sequence length, the sample size, and the mutation rate, and it can be considerable in some cases. It turns out that approximate Bayesian computation, with composite likelihood as a summary statistic, also leads to improved estimates, but now in terms of the posterior risk. Finally, we demonstrate a practical application on real data from Drosophila.

Cost-effective Screening for Differentially Expressed Genes in Microarray Experiments Based on Normal Mixtures

Microarray experiments allow the monitoring of expression levels for thousands of genes simultaneously. Based on data obtained from the co-hybridization of two mRNA samples, a frequent goal is to find out which genes are differentially expressed. For this purpose, we propose to estimate the distribution of popular test statistics by a mixture of normal distributions. These statistics are calculated for each gene separately. A Bayes classifier is then used to decide upon differential expression. The cut-off for the classifier is chosen according to the number of false positives and negatives when applied to realistic data generating models. In particular, we generate data from a mixture model and from an Empirical Bayes model. By comparing the numbers of false decisions for various test statistics in the context of the considered models, we investigate which of the statistics are particularly suitable with our approach.

Book Reviews

Elements of Large-Sample Theory. (E.L. Lehmann)Mathematical Statistics. (J. Shao)A Practical Guide to Heavy Tails. (R.J. Adler, R.E. Feldmann, M.S. Taqqu)Statistik. DerWeg zur Datenanalyse. (L. Fahrmeir, R. K¨unstler, I. Pigeot, G. Tutz)Einführung in die angewandte Statistik für Biowissenschaftler. (A. Kessel, M. Junge,W. Nachtigall)Data Analysis, Statistical and Computational Methods for Scientists and Engineers.(S. Brandt)Numerical Analysis for Statisticans. (K. Lange)Angewandte Statistik. (L. Sachs)Using SPSS forWindows. Data Analysis and Graphics. (K.E. Voelkl, S. Gerber)Stochastik mit Mathematica. (M. Overbeck-Larisch, W. Dolejsky)Negativauslese und Tarifdifferenzierung im Versicherungssektor. (Ch. Bach)

Ist der Euro fair? Ergebnis einer empirischen Untersuchung

In letzter Zeit sind Medienberichte aufgetaucht, nach denen der Euro keine faire Münze sein soll. Eine Abweichung der Kopfwahrscheinlichkeit von 1/2 wurde insbesondere in Zusammenhang mit dem belgischen und französischen Euro behauptet. Wir präsentieren in diesem Zusammenhang Ergebnisse von Münzwurfexperimenten und diskutieren die Implikationen aus statistischer Sicht.

MtDNA segregation in heteroplasmic tissues is common in vivo and modulated by haplotype differences and developmental stage

The dynamics by which mitochondrial DNA (mtDNA) evolves within organisms are still poorly understood, despite the fact that inheritance and proliferation of mutated mtDNA cause fatal and incurable diseases. When two mtDNA haplotypes are present in a cell, it is usually assumed that segregation (the proliferation of one haplotype over another) is negligible. We challenge this assumption by showing that segregation depends on the genetic distance between haplotypes. We provide evidence by creating four mouse models containing mtDNA haplotype pairs of varying diversity. We find tissue-specific segregation in all models over a wide range of tissues. Key findings are segregation in postmitotic tissues (important for disease models) and segregation covering all developmental stages from prenatal to old age. We identify four dynamic regimes of mtDNA segregation. Our findings suggest potential complications for therapies in human populations: we propose "haplotype matching" as an approach to avoid these issues.

Multiscale DNA partitioning: statistical evidence for segments

MOTIVATION

DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as Guanine/Cytosine (GC) content, local ancestry in population genetics or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen.

RESULTS

Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user-specified probability [Formula: see text] that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as a segmentation method that searches segments of any length (on all scales) simultaneously. It is also accurate in localizing segments: under benchmark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Elhaik et al. In our real data examples, we find segments that often correspond well to features taken from standard University of California at Santa Cruz (UCSC) genome annotation tracks.

AVAILABILITY AND IMPLEMENTATION

Our method is implemented in function smuceR of the R-package stepR available at http://www.stochastik.math.uni-goettingen.de/smuce.

Intra-specific regulatory variation in Drosophila pseudoobscura

It is generally accepted that gene regulation serves an important role in determining the phenotype. To shed light on the evolutionary forces operating on gene regulation, previous studies mainly focused on the expression differences between species and their inter-specific hybrids. Here, we use RNA-Seq to study the intra-specific distribution of cis- and trans-regulatory variation in Drosophila pseudoobscura. Consistent with previous results, we find almost twice as many genes (26%) with significant trans-effects than genes with significant cis-effects (18%). While this result supports the previous suggestion of a larger mutational target of trans-effects, we also show that trans-effects may be subjected to purifying selection. Our results underline the importance of intra-specific analyses for the understanding of the evolution of gene expression.

A genome-wide, fine-scale map of natural pigmentation variation in Drosophila melanogaster

Various approaches can be applied to uncover the genetic basis of natural phenotypic variation, each with their specific strengths and limitations. Here, we use a replicated genome-wide association approach (Pool-GWAS) to fine-scale map genomic regions contributing to natural variation in female abdominal pigmentation in Drosophila melanogaster, a trait that is highly variable in natural populations and highly heritable in the laboratory. We examined abdominal pigmentation phenotypes in approximately 8000 female European D. melanogaster, isolating 1000 individuals with extreme phenotypes. We then used whole-genome Illumina sequencing to identify single nucleotide polymorphisms (SNPs) segregating in our sample, and tested these for associations with pigmentation by contrasting allele frequencies between replicate pools of light and dark individuals. We identify two small regions near the pigmentation genes tan and bric-à-brac 1, both corresponding to known cis-regulatory regions, which contain SNPs showing significant associations with pigmentation variation. While the Pool-GWAS approach suffers some limitations, its cost advantage facilitates replication and it can be applied to any non-model system with an available reference genome.

Phenotypic variation is abundant in natural populations, but its genetic basis is not always well-understood. Here, we examine the genetic basis of body pigmentation in Drosophila, a trait with a long history of study in Drosophila genetics and evolution. We conducted the first genome-wide scan for polymorphism associated with pigmentation variation in a large natural sample of D. melanogaster, and found SNPs near two genes, tan and bric-à-brac 1, affecting the trait. The SNPs associated with pigmentation variation in these genes appear to act by affecting the regulation of the pigmentation genes, rather than their protein coding sequence.

Allelic imbalance metre (Allim), a new tool for measuring allele-specific gene expression with RNA-seq data

Estimating differences in gene expression among alleles is of high interest for many areas in biology and medicine. Here, we present a user-friendly software tool, Allim, to estimate allele-specific gene expression. Because mapping bias is a major problem for reliable estimates of allele-specific gene expression using RNA-seq, Allim combines two different strategies to account for the mapping biases. In order to reduce the mapping bias, Allim first generates a polymorphism-aware reference genome that accounts for the sequence variation between the alleles. Then, a sequence-specific simulation tool estimates the residual mapping bias. Statistical tests for allelic imbalance are provided that can be used with the bias corrected RNA-seq data.

Pool-hmm: a Python program for estimating the allele frequency spectrum and detecting selective sweeps from next generation sequencing of pooled samples

Due to its cost effectiveness, next generation sequencing of pools of individuals (Pool-Seq) is becoming a popular strategy for genome-wide estimation of allele frequencies in population samples. As the allele frequency spectrum provides information about past episodes of selection, Pool-seq is also a promising design for genomic scans for selection. However, no software tool has yet been developed for selection scans based on Pool-Seq data. We introduce Pool-hmm, a Python program for the estimation of allele frequencies and the detection of selective sweeps in a Pool-Seq sample. Pool-hmm includes several options that allow a flexible analysis of Pool-Seq data, and can be run in parallel on several processors. Source code and documentation for Pool-hmm is freely available at https://qgsp.jouy.inra.fr/.

DNA pooling and statistical tests for the detection of single nucleotide polymorphisms

The development of next generation genome sequencers gives the opportunity of learning more about the genetic make-up of human and other populations. One important question involves the location of sites at which variation occurs within a population. Our focus will be on the detection of rare variants. Such variants will often not be present in smaller samples and are hard to distinguish from sequencing errors in larger samples. This is particularly true for pooled samples which are often used as part of a cost saving strategy. The focus of this article is on experiments that involve DNA pooling. We derive experimental designs that optimize the power of statistical tests for detecting single nucleotide polymorphisms (SNPs, sites at which there is variation within a population). We also present a new simple test that calls a SNP, if the maximum number of reads of a prospective variant across lanes exceeds a certain threshold. The value of this threshold is defined according to the number of available lanes, the parameters of the genome sequencer and a specified probability of accepting that there is variation at a site when no variation is present. On the basis of this test, we derive pool sizes which are optimal for the detection of rare variants. This test is compared with a likelihood ratio test, which takes into account the number of reads of a prospective variant from all the lanes. It is shown that the threshold based rule achieves a comparable power to this likelihood ratio test and may well be a useful tool in determining near optimal pool sizes for the detection of rare alleles in practical applications.

Detecting selective sweeps from pooled next-generation sequencing samples

Due to its cost effectiveness, next-generation sequencing of pools of individuals (Pool-Seq) is becoming a popular strategy for characterizing variation in population samples. Because Pool-Seq provides genome-wide SNP frequency data, it is possible to use them for demographic inference and/or the identification of selective sweeps. Here, we introduce a statistical method that is designed to detect selective sweeps from pooled data by accounting for statistical challenges associated with Pool-Seq, namely sequencing errors and random sampling among chromosomes. This allows for an efficient use of the information: all base calls are included in the analysis, but the higher credibility of regions with higher coverage and base calls with better quality scores is accounted for. Computer simulations show that our method efficiently detects sweeps even at very low coverage (0.5× per chromosome). Indeed, the power of detecting sweeps is similar to what we could expect from sequences of individual chromosomes. Since the inference of selective sweeps is based on the allele frequency spectrum (AFS), we also provide a method to accurately estimate the AFS provided that the quality scores for the sequence reads are reliable. Applying our approach to Pool-Seq data from Drosophila melanogaster, we identify several selective sweep signatures on chromosome X that include some previously well-characterized sweeps like the wapl region.

On the inadmissibility of Watterson's estimator

We consider the estimation of the scaled mutation parameter theta, which is one of the parameters of key interest in population genetics. We provide a general result showing when estimators of theta can be improved using shrinkage when taking the mean squared error as the measure of performance. As a consequence, we show that Watterson's estimator is inadmissible, and propose an alternative shrinkage-based estimator that is easy to calculate and has a smaller mean squared error than Watterson's estimator for all possible parameter values 0<theta<infinity. This estimator is admissible in the class of all linear estimators. We then derive improved versions for other estimators of theta, including the MLE. We also investigate how an improvement can be obtained both when combining information from several independent loci and when explicitly taking into account recombination. A simulation study provides information about the amount of improvement achieved by our alternative estimators.

Locating multiple interacting quantitative trait Loci using rank-based model selection

In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL mapping, the performance of the mBIC strongly deteriorates when the trait distribution is heavy tailed or when the data contain a significant proportion of outliers. In the present article, we propose a suitable robust version of the mBIC that is based on ranks. We investigate the properties of the resulting method on the basis of theoretical calculations, computer simulations, and a real data analysis. Our simulation results show that for the sample sizes typically used in QTL mapping, the methods based on ranks are almost as efficient as standard techniques when the data are normal and are much better when the data come from some heavy-tailed distribution or include a proportion of outliers.