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Background: Genes exist in a population in a variety of forms (alleles), as a consequence of multiple mutation events that have arisen over the course of time. In this work we consider a locus that is subject to either multiplicative or additive selection, and has n alleles, where n can take the values 2, 3, 4, … . We focus on determining the probability of fixation of each of the n alleles. For n = 2 alleles, analytical results, that are ‘exact’, under the diffusion approximation, can be found for the fixation probability. However generally there are no equally exact results for n ≥ 3 alleles. In the absence of such exact results, we proceed by finding results for the fixation probability, under the diffusion approximation, as a power series in scaled strengths of selection such as R i , j = 2 N e (s i - s j) , where N e is the effective population size, while s i and s j are the selection coefficients associated with alleles i and j, respectively. Results: We determined the fixation probability when all terms up to second order in the R i , j are kept. The truncation of the power series requires that the R i , j cannot be indefinitely large. For magnitudes of the R i , j up to a value of approximately 1, numerical evidence suggests that the results work well. Additionally, results given for the particular case of n = 3 alleles illustrate a general feature that holds for n ≥ 3 alleles, that the fixation probability of a particular allele depends on that allele’s initial frequency, but generally, this fixation probability also depends on the initial frequencies of other alleles at the locus, as well as their selective effects. Conclusions: We have analytically exposed the leading way the probability of fixation, at a locus with multiple alleles, is affected by selection. This result may offer important insights into CDCV traits that have extreme phenotypic variance due to numerous, low-penetrance susceptibility alleles. [ABSTRACT FROM AUTHOR]

To concisely describe how genetic variation, at individual loci or across whole genomes, changes over time, and to follow transitory allelic changes, we introduce a quantity related to entropy, that we term pseudoentropy. This quantity emerges in a diffusion analysis of the mean time a mutation segregates in a population. For a neutral locus with an arbitrary number of alleles, the mean time of segregation is generally proportional to the pseudoentropy of initial allele frequencies. After the initial time point, pseudoentropy generally decreases, but other behaviours are possible, depending on the genetic diversity and selective forces present. For a biallelic locus, pseudoentropy and entropy coincide, but they are distinct quantities with more than two alleles. Thus for populations with multiple biallelic loci, the language of entropy suffices. Then entropy, combined across loci, serves as a concise description of genetic variation. We used individual based simulations to explore how this entropy behaves under different evolutionary scenarios. In agreement with predictions, the entropy associated with unlinked neutral loci decreases over time. However, deviations from free recombination and neutrality have clear and informative effects on the entropy's behaviour over time. Analysis of publicly available data of a natural D. melanogaster population, that had been sampled over seven years, using a sliding-window approach, yielded considerable variation in entropy trajectories of different genomic regions. These mostly follow a pattern that suggests a substantial effective population size and a limited effect of positive selection on genome-wide diversity over short time scales., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

It is unclear how different diets may affect human brain development and if genetic and environmental factors play a part. We investigated diet effects in the UK Biobank data from 18,879 healthy adults and discovered anticorrelated brain-wide gray matter volume (GMV)-association patterns between coffee and cereal intake, coincidence with their anticorrelated genetic constructs. The Mendelian randomization approach further indicated a causal effect of higher coffee intake on reduced total GMV, which is likely through regulating the expression of genes responsible for synaptic development in the brain. The identified genetic factors may further affect people's lifestyle habits and body/blood fat levels through the mediation of cereal/coffee intake, and the brain-wide expression pattern of gene CPLX3, a dedicated marker of subplate neurons that regulate cortical development and plasticity, may underlie the shared GMV-association patterns among the coffee/cereal intake and cognitive functions. All the main findings were successfully replicated. Our findings thus revealed that high-cereal and low-coffee diets shared similar brain and genetic constructs, leading to long-term beneficial associations regarding cognitive, body mass index (BMI), and other metabolic measures. This study has important implications for public health, especially during the pandemic, given the poorer outcomes of COVID-19 patients with greater BMIs., (© The Author(s) 2022. Published by Oxford University Press.)

The Coronavirus Disease 2019 (COVID)-19 pandemic has placed unprecedented pressures on societies around the world. Successful vaccines, developed against the spike protein of the Severe Acute Respiratory Syndrome Virus 2 (SARS-CoV-2) virus, offer hope that new hospitalisations and new deaths will subside. However, vaccination takes place in a dynamic environment. For example, new variants of the disease may occur where the effectiveness of a vaccine lies below that of the original target of the vaccine, while changes in the behaviour of a population are accompanied by a changed basic reproduction number. Here, we aim to understand how changes in values of basic parameters affect the benefits of vaccination at the direct level, of the individuals vaccinated, and at the indirect level, of the wider, unvaccinated community. We work within the framework of a Susceptible-Infected-Recovered model, and produce a metric for the benefits of vaccination, at both direct and indirect levels, in terms of the number of avoided deaths. Taking into account the initial prevalence of a SARS-CoV-2 infection, the mortality rate of the disease, the basic reproduction number, the vaccination rate, and the effectiveness of a vaccine, we explore how these basic parameters affect the benefits of vaccination. We find a range of situations where indirect benefits of vaccination outweigh direct benefits. This especially occurs at lower rates of vaccination (20% - [Formula: see text]) and intermediate values of the basic reproduction number (1-1.5). The indirect benefits can be substantial, in some cases being more than 400% of the direct benefits. For an initial prevalence of SARS-CoV-2 infection of 2%, a basic reproduction number of 1.2, a mortality rate of 2%, and a vaccine effectiveness of 95%, our findings show, for a population of 500,000 people, where 100,000 susceptible individuals are vaccinated, that approximately 2200 deaths are avoided. However, approximately 600 of these deaths are avoided amongst vaccinated individuals, while approximately 1600 deaths are avoided in the wider, unvaccinated community., (© 2022. The Author(s).)

There are many problems in biology and related disciplines involving stochasticity, where a signal can only be detected when it lies above a threshold level, while signals lying below threshold are simply not detected. A consequence is that the detected signal is conditioned to lie above threshold, and is not representative of the actual signal. In this work, we present some general results for the conditioning that occurs due to the existence of such an observational threshold. We show that this conditioning is relevant, for example, to gene-frequency trajectories, where many loci in the genome are simultaneously measured in a given generation. Such a threshold can lead to severe biases of allele frequency estimates under purifying selection. In the analysis presented, within the context of Markov chains such as the Wright-Fisher model, we address two key questions: (1) "What is a natural measure of the strength of the conditioning associated with an observation threshold?" (2) "What is a principled way to correct for the effects of the conditioning?". We answer the first question in terms of a proportion. Starting with a large number of trajectories, the relevant quantity is the proportion of these trajectories that are above threshold at a later time and hence are detected. The smaller the value of this proportion, the stronger the effects of conditioning. We provide an approximate analytical answer to the second question, that corrects the bias produced by an observation threshold, and performs to reasonable accuracy in the Wright-Fisher model for biologically plausible parameter values., (© The Author(s) 2022. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

Background: Most emergency department (ED) patients arrive by their own transport and, for various reasons, may not choose the nearest ED. How far patients travel for ED treatment may reflect both patients' access to care and severity of illness. In this study, we aimed to examine the travel distance and travel time between a patient's home and ED they visited and investigate how these distances/times vary by patient and hospital characteristics., Methods: We randomly sampled and collected data from 14,812 patients discharged to the community (DTC) between January and March 2016 from 50 hospital-based EDs nationwide. We geocoded and calculated the distance and travel time between patient and hospital-based ED addresses, examined the travel distances/ times between patients' home and the ED they visited, and used mixed-effects regression models to investigate how these distances/times vary by patient and hospital characteristics., Results: Patients travelled an average of 8.0 (SD = 10.9) miles and 17.3 (SD = 18.0) driving minutes to the ED. Patients travelled significantly farther to avoid EDs in lower performing hospitals (p < 0.01) and in the West (p < 0.05) and Midwest (p < 0.05). Patients travelled farther when visiting EDs in rural areas. Younger patients travelled farther than older patients., Conclusions: Understanding how far patients are willing to travel is indicative of whether patient populations have adequate access to ED services. By showing that patients travel farther to avoid a low-performing hospital, we provide evidence that DTC patients likely do exercise some choice among EDs, indicating some market incentives for higher-quality care, even for some ED admissions. Understanding these issues will help policymakers better define access to ED care and assist in directing quality improvement efforts. To our knowledge, our study is the most comprehensive nationwide characterization of patient travel for ED treatment to date., (© 2022. The Author(s).)