Use of directed quasi-metric distances for quantifying the information of gene families.

A large hindrance to analyzing information in genetic or protein sequence data has been a lack of a mathematical framework for doing so. In this paper, we present a multinomial probability space as a general foundation for multicategory discrete data, where categories refer to variants/alleles of biosequences. The external information that is infused in order to generate a sample of such data is quantified as a distance on between the prior distribution of data and the empirical distribution of the sample. A number of distances on are treated. All of them have an information theoretic interpretation, reflecting the information that the sampling mechanism provides about which variants that have a selective advantage and therefore appear more frequently compared to prior expectations. This includes distances on based on mutual information, conditional mutual information, active information, and functional information. The functional information distance is singled out as particularly useful. It is simple and has intuitive interpretations in terms of 1) a rejection sampling mechanism, where functional entities are retained, whereas non-functional categories are censored, and 2) evolutionary waiting times. The functional information is also a quasi-metric on , with information being measured in an asymmetric, mountainous landscape. This quasi-metric property is also retained for a robustified version of the functional information distance that allows for mutations in the sampling mechanism. The functional information quasi-metric has been applied with success on bioinformatics data sets, for proteins and sequence alignment of protein families.

What does effective population size tell us about loss of allelic variation?

There are two primary measures of the amount of genetic variation in a population at a locus: heterozygosity and the number of alleles. Effective population size (N e) provides both an expectation of the amount of heterozygosity in a population at drift-mutation equilibrium and the rate of loss of heterozygosity because of genetic drift. In contrast, the number of alleles in a population at drift-mutation equilibrium is a function of both N e and census size (N C). In addition, populations with the same N e can lose allelic variation at very different rates. Allelic variation is generally much more sensitive to bottlenecks than heterozygosity. Expressions used to adjust for the effects of violations of the ideal population on N e do not provide good predictions of the loss of allelic variation. These effects are much greater for loci with many alleles, which are often important for adaptation. We show that there is a linear relationship between the reduction of N C and the corresponding reduction of the expected number of alleles at drift-mutation equilibrium. This makes it possible to predict the expected effect of a bottleneck on allelic variation. Heterozygosity provides good estimates of the rate of adaptive change in the short-term, but allelic variation provides important information about long-term adaptive change. The guideline of long-term N e being greater than 500 is often used as a primary genetic metric for evaluating conservation status. We recommend that this guideline be expanded to take into account allelic variation as well as heterozygosity.

Correcting prevalence estimation for biased sampling with testing errors.

Sampling for prevalence estimation of infection is subject to bias by both oversampling of symptomatic individuals and error-prone tests. This results in naïve estimators of prevalence (ie, proportion of observed infected individuals in the sample) that can be very far from the true proportion of infected. In this work, we present a method of prevalence estimation that reduces both the effect of bias due to testing errors and oversampling of symptomatic individuals, eliminating it altogether in some scenarios. Moreover, this procedure considers stratified errors in which tests have different error rate profiles for symptomatic and asymptomatic individuals. This results in easily implementable algorithms, for which code is provided, that produce better prevalence estimates than other methods (in terms of reducing and/or removing bias), as demonstrated by formal results, simulations, and on COVID-19 data from the Israeli Ministry of Health.

Assessment of the Global Variance Effective Size of Subdivided Populations, and Its Relation to Other Effective Sizes.

The variance effective population size ([Formula: see text]) is frequently used to quantify the expected rate at which a population's allele frequencies change over time. The purpose of this paper is to find expressions for the global [Formula: see text] of a spatially structured population that are of interest for conservation of species. Since [Formula: see text] depends on allele frequency change, we start by dividing the cause of allele frequency change into genetic drift within subpopulations (I) and a second component mainly due to migration between subpopulations (II). We investigate in detail how these two components depend on the way in which subpopulations are weighted as well as their dependence on parameters of the model such a migration rates, and local effective and census sizes. It is shown that under certain conditions the impact of II is eliminated, and [Formula: see text] of the metapopulation is maximized, when subpopulations are weighted proportionally to their long term reproductive contributions. This maximal [Formula: see text] is the sought for global effective size, since it approximates the gene diversity effective size [Formula: see text], a quantifier of the rate of loss of genetic diversity that is relevant for conservation of species and populations. We also propose two novel versions of [Formula: see text], one of which (the backward version of [Formula: see text]) is most stable, exists for most populations, and is closer to [Formula: see text] than the classical notion of [Formula: see text]. Expressions for the optimal length of the time interval for measuring genetic change are developed, that make it possible to estimate any version of [Formula: see text] with maximal accuracy.

Variance effective population size is affected by census size in sub-structured populations.

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (Ne ), and this 'temporal method' provides estimates of Ne referred to as variance effective size (NeV ). We show that NeV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (Nc ). The realized NeV of a local population can either increase or decrease with increasing m, depending on the relationship between Ne and Nc in isolation. This is shown by explicit mathematical expressions for the factors affecting NeV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of Nc on the realized NeV of a local subpopulation is most pronounced at high migration rates. We show that Nc only affects local NeV , whereas NeV for the metapopulation as a whole, inbreeding (NeI ), and linkage disequilibrium (NeLD ) effective size are all independent of Nc . Our results provide a possible explanation to the large variation of Ne /Nc ratios reported in the literature, where Ne is frequently estimated by NeV . They are also important for the interpretation of empirical Ne estimates in genetic management where local NeV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation NeV as a proxy for NeI .

Assessing, Testing and Estimating the Amount of Fine-Tuning by Means of Active Information.

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θf in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis-Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming.

A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning.

Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes' rule. The degree of true belief is quantified by means of active information I+: a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent's strength of belief in a true proposition has increased in comparison with the ignorant person (I+>0), or the strength of belief in a false proposition has decreased (I+<0). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus.

Whole-genome resequencing confirms reproductive isolation between sympatric demes of brown trout (Salmo trutta) detected with allozymes.

The sympatric existence of genetically distinguishable populations of the same species remains a puzzle in ecology. Coexisting salmonid fish populations are known from over 100 freshwater lakes. Most studies of sympatric populations have used limited numbers of genetic markers making it unclear if genetic divergence involves certain parts of the genome. We returned to the first reported case of salmonid sympatry, initially detected through contrasting homozygosity at a single allozyme locus (coding for lactate dehydrogenase A) in brown trout in the small Lakes Bunnersjöarna, Sweden. First, we verified the existence of the two coexisting demes using a 96-SNP fluidigm array. We then applied whole-genome resequencing of pooled DNA to explore genome-wide diversity within and between these demes; nucleotide diversity was higher in deme I than in deme II. Strong genetic divergence is observed with genome-wide FST  ≈ 0.2. Compared with data from populations of similar small lakes, this divergence is of similar magnitude as that between reproductively isolated populations. Individual whole-genome resequencing of two individuals per deme suggests higher inbreeding in deme II versus deme I, indicating different degree of isolation. We located two gene-copies for LDH-A and found divergence between demes in a regulatory section of one of these genes. However, we did not find a perfect fit between the sequence data and previous allozyme results, and this will require further research. Our data demonstrates genome-wide divergence governed mostly by genetic drift but also by diversifying selection in coexisting populations. This type of hidden biodiversity needs consideration in conservation management.

On the waiting time until coordinated mutations get fixed in regulatory sequences.

In this paper we consider the time evolution of a population of size N with overlapping generations, in the vicinity of m genes. We assume that this population is subject to point mutations, genetic drift, and selection. More specifically, we analyze the statistical distribution of the waiting time Tm until the expression of these genes have changed for all individuals, when transcription factors recognize and attach to short DNA-sequences (binding sites) within regulatory sequences in the neighborhoods of the m genes. The evolutionary dynamics is described by a multitype Moran process, where each individual is assigned a m×L regulatory array that consists of regulatory sequences with L nucleotides for all m genes. We study how the waiting time distribution depends on the number of genes, the mutation rate, the length of the binding sites, the length of the regulatory sequences, and the way in which the targeted binding sites are coordinated for different genes in terms of selection coefficients. These selection coefficients depend on how many binding sites have appeared so far, and possibly on their order of appearance. We also allow for back mutations, whereby some acquired binding sites may be lost over time. It is further assumed that the mutation rate is small enough to warrant a fixed state population, so that all individuals have the same regulatory array, at any given time point, until the next successful mutation arrives in some individual and spreads to the rest of the population. We further incorporate stochastic tunneling, whereby successful mutations get mutated before their fixation. A crucial part of our approach is to divide the huge state space of regulatory arrays into a small number of components, assuming that the array component varies as a Markov process over time. This implies that Tm is the time until this Markov process hits an absorbing state, with a phase-type distribution. A number of interesting results can be derived from our general setup, for instance that the expected waiting time increases exponentially with m, for a selectively neutral model, when back-mutations are possible.

Insomnia in the context of short sleep increases suicide risk.

STUDY OBJECTIVES: The relationship between insomnia and suicide risk is not completely understood. We aimed to investigate the influence of insomnia on suicide risk, taking both sleep duration and depression into consideration. METHODS: The present study is based on a Swedish prospective cohort study of 38,786 participants with a mean follow-up time of 19.2 years. Cox proportional hazards models with attained age as time-scale were used to estimate hazard ratios (HRs) of death by suicide with 95% confidence intervals (CI) for participants categorized by frequency of insomnia symptoms. Causal mediation analysis was performed to assess to what extent the relationship between insomnia and suicide risk is mediated by depression. RESULTS: Insomnia was only associated with suicide risk among short sleepers, whereas no significant association was observed among those who slept 7 h/night or more. The total effect of insomnia in the context of short sleep on suicide risk, expressed on the HR scale, was 2.85 (95% CI 1.42-5.74). The direct effect was 2.25 (95% CI 1.12-4.54) and the indirect effect, mediated by depression, was 1.27 (95% CI 1.05-1.53). Of the total effect, 32% was mediated by depression. The association between insomnia and suicide risk became more pronounced with decreasing depressive symptoms (p value for trend <0.05). CONCLUSIONS: Insomnia in the context of short sleep increases suicide risk, both directly and indirectly by affecting the risk of depression. Abnormalities of sleep duration and insomnia symptoms should be evaluated when assessing suicide risk.

The relationship between nightmares, depression and suicide.

OBJECTIVE: Previous studies investigating the association between nightmares and suicide have yielded different results. We aimed to investigate whether nightmares, directly or indirectly, influence the incidence of suicide. METHODS: We used a prospective cohort study, based on 40,902 participants with a mean follow-up duration of 19.0 years. Cox proportional hazards models with attained age as time-scale were fitted to estimate hazard ratios (HR) of suicide with 95% confidence intervals (CI) as a function of the presence or absence of depression and nightmares. Mediation analysis was used to asses to what extent the relationship between nightmares and the incidence rate of suicide could be mediated by depression. RESULTS: No association was observed between nightmares and the incidence of suicide among participants without depression. Compared with non-depressed participants without nightmares, the incidence of suicide among participants with a diagnosis of depression was similar among those with and without nightmares (HR 12.3, 95% CI 5.55-27.2 versus HR 13.2, 95% CI 7.25-24.1). The mediation analysis revealed no significant effects of nightmares on suicide incidence. However, the incidence of depression during follow-up was higher among those who suffered from nightmares than among those who did not (p < 0.001). CONCLUSIONS: Our findings indicate that nightmares have no influence on the incidence rate of suicide, but may reflect pre-existing depression. This is supported by a recent discovery of a strong genetic correlation of nightmares with depressive disorders, with no evidence that nightmares would predispose to psychiatric illness or psychological problems. Interventions targeting both depression and nightmares, when these conditions co-occur, may provide additional therapeutic benefit.

Using statistical methods to model the fine-tuning of molecular machines and systems.

Fine-tuning has received much attention in physics, and it states that the fundamental constants of physics are finely tuned to precise values for a rich chemistry and life permittance. It has not yet been applied in a broad manner to molecular biology. However, in this paper we argue that biological systems present fine-tuning at different levels, e.g. functional proteins, complex biochemical machines in living cells, and cellular networks. This paper describes molecular fine-tuning, how it can be used in biology, and how it challenges conventional Darwinian thinking. We also discuss the statistical methods underpinning fine-tuning and present a framework for such analysis.

Short- and long-term mortality following hypnotic use.

Potential long-term consequences of hypnotics remain controversial. We used the prospective Swedish National March Cohort, a study based on 41,695 participants with a mean follow-up duration of 18.9 years. Logistic regression models and Cox proportional hazards models with attained age as timescale were used to assess associations of hypnotic use with short- and long-term mortality. The proportion of subjects who initiated or discontinued hypnotic use during follow-up was substantial. All groups of hypnotics were associated with increased mortality within 2 years after a first prescription, with an overall OR of 2.38 (95% CI, 2.13-2.66). The association was more pronounced among subjects younger than 60 years (OR, 6.16; 95% CI, 3.98-9.52). There was no association between hypnotic use and long-term mortality. The association between hypnotic use and increased mortality was thus restricted to a relatively short period after treatment initiation, and may be explained in terms of confounding by indication.

The relationship between nightmares, depression and suicide.

Objective: Previous studies investigating the association between nightmares and suicide have yielded different results. We aimed to investigate whether nightmares, directly or indirectly, influence the incidence of suicide. Methods: We used a prospective cohort study, based on 40,902 participants with a mean follow-up duration of 19.0 years. Cox proportional hazards models with attained age as time-scale were fitted to estimate hazard ratios (HR) of suicide with 95% confidence intervals (CI) as a function of the presence or absence of depression and nightmares. Mediation analysis was used to asses to what extent the relationship between nightmares and the incidence rate of suicide could be mediated by depression. Results: No association was observed between nightmares and the incidence of suicide among participants without depression. Compared with non-depressed participants without nightmares, the incidence of suicide among participants with a diagnosis of depression was similar among those with and without nightmares (HR 12.3, 95% CI 5.55-27.2 versus HR 13.2, 95% CI 7.25-24.1). The mediation analysis revealed no significant effects of nightmares on suicide incidence. However, the incidence of depression during follow-up was higher among those who suffered from nightmares than among those who did not (p < 0.001). Conclusions: Our findings indicate that nightmares have no influence on the incidence rate of suicide, but may reflect pre-existing depression. This is supported by a recent discovery of a strong genetic correlation of nightmares with depressive disorders, with no evidence that nightmares would predispose to psychiatric illness or psychological problems. Interventions targeting both depression and nightmares, when these conditions co-occur, may provide additional therapeutic benefit.

Erratum: Withdrawal notice to "The relationship between nightmares, depression and suicide" [Sleep Med: X 2 (2020) 100016].

[This corrects the article DOI: 10.1016/j.sleepx.2020.100016.].

The influence of human leukocyte antigen-DRB1*15:01 and its interaction with smoking in MS development is dependent on DQA1*01:01 status.

BACKGROUND: HLA-DRB1*15:01, absence of HLA-A*02:01, and smoking interact to increase multiple sclerosis (MS) risk. OBJECTIVE: To analyze whether MS-associated human leukocyte antigen (HLA) alleles, apart from DRB1*15:01 and absence of A*02:01, interact with smoking in MS development, and to explore whether the established HLA-smoking interaction is affected by the DQA1*01:01 allele, which confers a protective effect only in the presence of DRB1*15:01. METHODS: In two Swedish population-based case-control studies (5838 cases, 5412 controls), subjects with different genotypes and smoking habits were compared regarding MS risk, by calculating odds ratios with 95% confidence intervals employing logistic regression. Interaction on the additive scale between different genotypes and smoking was evaluated. RESULTS: The DRB1*08:01 allele interacted with smoking to increase MS risk. The interaction between DRB1*15:01 and both the absence of A*02:01 and smoking was confined to DQA1*01:01 negative subjects, whereas no interactions occurred among DQA1*01:01 positive subjects. CONCLUSION: Multifaceted interactions take place between different class II alleles and smoking in MS development. The influence of DRB1*15:01 and its interaction with the absence of A*02:01 and smoking is dependent on DQA1*01:01 status which may be due to differences in the responding T-cell repertoires.

Local fluctuations of genetic processes defined on two time scales, with applications to effective size estimation.

In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes Ne, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy-Weinberg equilibrium.

Interplay between alcohol, smoking and HLA genes in RA aetiology.

Objectives: The relationship between alcohol consumption and risk for rheumatoid arthritis (RA) is incompletely understood. We aimed to determine the influence of alcohol on anticitrullinated protein antibody (ACPA) positive and ACPA-negative RA and investigate potential interactions between alcohol consumption, smoking and the presence of human leucocyte antigen (HLA)-DRB1-shared epitope (SE). Methods: A Swedish population-based case-control study with incident cases of RA was used (3353 cases, 2836 matched controls). Subjects with different HLA-DRB1-SE status, smoking and alcohol consumption were compared regarding risk of ACPA-positive and ACPA-negative RA, by calculating OR with 95% CI employing logistic regression. Interaction on the additive scale between alcohol, HLA-DRB1-SE and smoking was estimated by calculating the attributable proportion (AP) due to interaction. Results: Compared with non-drinking, low and moderate alcohol consumption was dose dependently associated with a reduced risk of ACPA-positive and ACPA-negative RA. Independent of smoking habits, non-drinking and the presence of HLA-DRB1-SE interacted to increase the risk of ACPA-positive RA. Among HLA-DRB1-SE positive subjects, there was also a significant interaction between non-drinking and smoking with regard to risk for ACPA-positive RA. A three-way interaction was observed between alcohol, smoking and HLA-DRB1-SE with regard to risk for ACPA-positive RA (AP 0.7, 95% CI 0.6 to 0.8) that remained significant when the influence from the two-way interactions was removed (AP 0.4, 95% CI 0.2 to 0.6). Conclusions: Our findings emphasize the need to investigate complex interactions between several environmental and genetic factors in order to better understand the etiology of RA. Whereas of great interest in an aetiological perspective, the finding of a protective role of alcohol on risk for RA must, however, be interpreted with caution in a clinical and public health perspective.

Do estimates of contemporary effective population size tell us what we want to know?

Estimation of effective population size (Ne ) from genetic marker data is a major focus for biodiversity conservation because it is essential to know at what rates inbreeding is increasing and additive genetic variation is lost. But are these the rates assessed when applying commonly used Ne estimation techniques? Here we use recently developed analytical tools and demonstrate that in the case of substructured populations the answer is no. This is because the following: Genetic change can be quantified in several ways reflecting different types of Ne such as inbreeding (NeI ), variance (NeV ), additive genetic variance (NeAV ), linkage disequilibrium equilibrium (NeLD ), eigenvalue (NeE ) and coalescence (NeCo ) effective size. They are all the same for an isolated population of constant size, but the realized values of these effective sizes can differ dramatically in populations under migration. Commonly applied Ne -estimators target NeV or NeLD of individual subpopulations. While such estimates are safe proxies for the rates of inbreeding and loss of additive genetic variation under isolation, we show that they are poor indicators of these rates in populations affected by migration. In fact, both the local and global inbreeding (NeI ) and additive genetic variance (NeAV ) effective sizes are consistently underestimated in a subdivided population. This is serious because these are the effective sizes that are relevant to the widely accepted 50/500 rule for short and long term genetic conservation.  The bias can be infinitely large and is due to inappropriate parameters being estimated when applying theory for isolated populations to subdivided ones.

Organic solvents and MS susceptibility: Interaction with MS risk HLA genes.

OBJECTIVE: We hypothesize that different sources of lung irritation may contribute to elicit an immune reaction in the lungs and subsequently lead to multiple sclerosis (MS) in people with a genetic susceptibility to the disease. We aimed to investigate the influence of exposure to organic solvents on MS risk, and a potential interaction between organic solvents and MS risk human leukocyte antigen (HLA) genes. METHODS: Using a Swedish population-based case-control study (2,042 incident cases of MS and 2,947 controls), participants with different genotypes, smoking habits, and exposures to organic solvents were compared regarding occurrence of MS, by calculating odds ratios with 95% confidence intervals using logistic regression. A potential interaction between exposure to organic solvents and MS risk HLA genes was evaluated by calculating the attributable proportion due to interaction. RESULTS: Overall, exposure to organic solvents increased the risk of MS (odds ratio 1.5, 95% confidence interval 1.2-1.8, p = 0.0004). Among both ever and never smokers, an interaction between organic solvents, carriage of HLA-DRB1*15, and absence of HLA-A*02 was observed with regard to MS risk, similar to the previously reported gene-environment interaction involving the same MS risk HLA genes and smoke exposure. CONCLUSION: The mechanism linking both smoking and exposure to organic solvents to MS risk may involve lung inflammation with a proinflammatory profile. Their interaction with MS risk HLA genes argues for an action of these environmental factors on adaptive immunity, perhaps through activation of autoaggressive cells resident in the lungs subsequently attacking the CNS.