Methods for demographic inference from single-nucleotide polymorphism data

The distribution of the current human population is the result of many complex historical and prehistorical demographic events that have shaped variation in the human genome. Genomic dissimilarities between individuals from different geographical regions can potentially unveil something of these processes. The greatest differences lie between, and within, African populations and most research suggests the origin of modern humans lies within Africa. However, differing models have been proposed to model the evolutionary processes leading to humans inhabiting most of the world. This thesis develops a hypothesis test shown to be powerful in distinguishing between two such models. The first ("migration") model assumes the population of interest is divided into subpopulations that exchange migrants at a constant rate arbitrarily far back in the past, whilst the second ("isolation") model assumes that an ancestral population iteratively segregates into subpopulations that evolve independently. Although both models are simplistic, they do capture key aspects of the opposing theories of the history of modern humans. Given single nucleotide polymorphism (SNP) data from two subpopulations, the method described here tests a global null hypothesis that the data are from an isolation model. The test takes a parametric bootstrap approach, iteratively simulating data under the null hypothesis and computing a set of summary statistics shown to be able to distinguish between the two models. Each summary statistic forms the basis of a statistical hypothesis test where the observed value of the statistic is compared to the simulated values. The global null hypothesis is accepted if each individual test is accepted. A correction for multiple comparisons is used to control the type I error rate of this compound test. Extensions to this hypothesis test are given which adapt it to deal with SNP ascertainment and to better handle large genomic data sets. The methods are illustrated on data from the HapMap project using two Kenyan populations and the Japanese and Yoruba populations, after the method has been validated by simulation, where the `true' model is known

The transfer of IgA from mucus to plasma and the implications for diagnosis and control of nematode infections

Immunoglobulin A (IgA) activity has been associated with reduced growth and fecundity of Teladorsagia circumcincta. IgA is active at the site of infection in the abomasal mucus. However, while IgA activity in abomasal mucus is not easily measured in live animals without invasive methods, IgA activity can be readily detected in the plasma, making it a potentially valuable tool in diagnosis and control. We used a Bayesian statistical analysis to quantify the relationship between mucosal and plasma IgA in sheep deliberately infected with T. circumcincta. The transfer of IgA depends on mucosal IgA activity as well as its interaction with worm number and size; together these account for over 80% of the variation in plasma IgA activity. By quantifying the impact of mucosal IgA and worm number and size on plasma IgA, we provide a tool that can allow more meaningful interpretation of plasma IgA measurements and aid the development of efficient control programmes

Reflections on Designing and Delivering an Online Distance Learning Programme in the Mathematical Sciences

In 2013, the University of Glasgow set out a Blended and Online Learning Development scheme focussing on fully online distance learning programmes and blended programmes. In 2017 the School of Mathematics and Statistics within the University of Glasgow developed part-time, online distance learning programmes (PG Diploma/PG Certificate/MSc) in Data Analytics. The programmes have used considerable innovation in terms of course content, assessment, course management and delivery, and in student support. In this case study, we will reflect our experiences of developing and delivering online distance learning programmes and provide future recommendations considering the recent expansion of remote learning across higher educational institutes globally

A Bayesian generalized random regression model for estimating heritability using overdispersed count data

Background: Faecal egg counts are a common indicator of nematode infection and since it is a heritable trait, it provides a marker for selective breeding. However, since resistance to disease changes as the adaptive immune system develops, quantifying temporal changes in heritability could help improve selective breeding programs. Faecal egg counts can be extremely skewed and difficult to handle statistically. Therefore, previous heritability analyses have log transformed faecal egg counts to estimate heritability on a latent scale. However, such transformations may not always be appropriate. In addition, analyses of faecal egg counts have typically used univariate rather than multivariate analyses such as random regression that are appropriate when traits are correlated. We present a method for estimating the heritability of untransformed faecal egg counts over the grazing season using random regression. Results: Replicating standard univariate analyses, we showed the dependence of heritability estimates on choice of transformation. Then, using a multitrait model, we exposed temporal correlations, highlighting the need for a random regression approach. Since random regression can sometimes involve the estimation of more parameters than observations or result in computationally intractable problems, we chose to investigate reduced rank random regression. Using standard software (WOMBAT), we discuss the estimation of variance components for log transformed data using both full and reduced rank analyses. Then, we modelled the untransformed data assuming it to be negative binomially distributed and used Metropolis Hastings to fit a generalized reduced rank random regression model with an additive genetic, permanent environmental and maternal effect. These three variance components explained more than 80 % of the total phenotypic variation, whereas the variance components for the log transformed data accounted for considerably less. The heritability, on a link scale, increased from around 0.25 at the beginning of the grazing season to around 0.4 at the end. Conclusions: Random regressions are a useful tool for quantifying sources of variation across time. Our MCMC (Markov chain Monte Carlo) algorithm provides a flexible approach to fitting random regression models to non-normal data. Here we applied the algorithm to negative binomially distributed faecal egg count data, but this method is readily applicable to other types of overdispersed data

An explicit immunogenetic model of gastrointestinal nematode infection in sheep

Gastrointestinal nematodes are a global cause of disease and death in humans, wildlife and livestock. Livestock infection has historically been controlled with anthelmintic drugs, but the development of resistance means that alternative controls are needed. The most promising alternatives are vaccination, nutritional supplementation and selective breeding, all of which act by enhancing the immune response. Currently, control planning is hampered by reliance on the faecal egg count (FEC), which suffers from low accuracy and a nonlinear and indirect relationship with infection intensity and host immune responses. We address this gap by using extensive parasitological, immunological and genetic data on the sheep–Teladorsagia circumcincta interaction to create an immunologically explicit model of infection dynamics in a sheep flock that links host genetic variation with variation in the two key immune responses to predict the observed parasitological measures. Using our model, we show that the immune responses are highly heritable and by comparing selective breeding based on low FECs versus high plasma IgA responses, we show that the immune markers are a much improved measure of host resistance. In summary, we have created a model of host–parasite infections that explicitly captures the development of the adaptive immune response and show that by integrating genetic, immunological and parasitological understanding we can identify new immune-based markers for diagnosis and control

Divergent Allele Advantage provides a quantitative model for maintaining alleles with a wide range of intrinsic merits

The Major Histocompatibility Complex (MHC) is the most genetically diverse region of the genome in most vertebrates. Some form of balancing selection is necessary to account for the extreme diversity, but the precise mechanism of balancing selection is unknown. Due to the way MHC molecules determine immune recognition, overdominance (also referred to as heterozygote advantage) has been suggested as the main driving force behind this unrivalled diversity. However, both theoretical results and simulation models have shown that overdominance in its classical form cannot maintain large numbers of alleles unless all alleles confer unrealistically similar levels of fitness. There is increasing evidence that heterozygotes containing genetically divergent alleles allow for broader antigen presentation to immune cells, providing a selective mechanism for MHC polymorphism. By framing competing models of overdominance within a general framework, we show that a model based on Divergent Allele Advantage (DAA) provides a superior mechanism for maintaining alleles with a wide range of intrinsic merits, as intrinsically less fit MHC alleles that are more divergent can survive under DAA. Specifically, our results demonstrate that a quantitative mechanism built from the Divergent Allele Advantage hypothesis is able to maintain polymorphism in the MHC. Applying such a model to both livestock breeding and conservation could provide a better way of identifying superior heterozygotes and quantifying the advantages of genetic diversity at the MHC

Nurturing learning development through student feedback

Student evaluations of both teaching and student services are increasingly embedded into higher education. There is debate surrounding the reliability, effectiveness, and bias of such evaluations (Hefferman, 2022) and National Student Survey (NSS) results show that students typically respond poorly to questions relating to their learning community and their opportunities to give feedback on their experiences (student voice) (Office for Students, 2022). After receiving ethical approval to conduct research on evaluations, four students and a member of staff worked together to address how staff and students within the School of Mathematics and Statistics engage with student evaluations. Two surveys were conducted, the first aimed at staff (63 responses, 90% response rate) and the second at students (53 responses, 17% response rate). The results suggested that both staff and students agreed that evaluations are necessary and useful in building relationships. While staff implement the feedback they receive, students currently do not see it, and their learning may not benefit from being part of this process. When asked to describe the purpose of student evaluations, participating staff expressed that they provide students with opportunities to have direct input to courses, influence their learning environment, and feel part of the school. Students expressed that their feedback could improve a course’s content, quality and delivery, and provide a learning opportunity for lecturers. Students indicated a preference for informal mid-term feedback since they could see their feedback acted upon in real-time. In response, we propose the use of student evaluations as a feedback dialogue tool to encourage and enhance relationships between staff and students and help develop self-regulated learning. We will exemplify a feedback system that uses short, direct, and frequent surveys that students complete at the time of learning (Rowland, 2021), providing time to reflect on learning and creating a line of dialogic communication with the lecturer who can respond to the feedback to inform future learning. The system is applicable to any continuous student-staff learning-focused interaction

Estimation of temporal covariances in pathogen dynamics using Bayesian multivariate autoregressive models

It is well recognised that animal and plant pathogens form complex ecological communities of interacting organisms within their hosts, and there is growing interest in the health implications of such pathogen interactions. Although community ecology approaches have been used to identify pathogen interactions at the within-host scale, methodologies enabling robust identification of interactions from population-scale data such as that available from health authorities are lacking. To address this gap, we developed a statistical framework that jointly identifies interactions between multiple viruses from contemporaneous non-stationary infection time series. Our conceptual approach is derived from a Bayesian multivariate disease mapping framework. Importantly, our approach captures within- and between-year dependencies in infection risk while controlling for confounding factors such as seasonality, demographics and infection frequencies, allowing genuine pathogen interactions to be distinguished from simple correlations. We validated our framework using a broad range of synthetic data. We then applied it to diagnostic data available for five respiratory viruses co-circulating in a major urban population between 2005 and 2013: adenovirus, human coronavirus, human metapneumovirus, influenza B virus and respiratory syncytial virus. We found positive and negative covariances indicative of epidemiological interactions among specific virus pairs. This statistical framework enables a community ecology perspective to be applied to infectious disease epidemiology with important utility for public health planning and preparedness

Estimation of temporal covariances in pathogen dynamics using Bayesian multivariate autoregressive models

It is well recognised that animal and plant pathogens form complex ecological communities of interacting organisms within their hosts, and there is growing interest in the health implications of such pathogen interactions. Although community ecology approaches have been used to identify pathogen interactions at the within-host scale, methodologies enabling robust identification of interactions from population-scale data such as that available from health authorities are lacking. To address this gap, we developed a statistical framework that jointly identifies interactions between multiple viruses from contemporaneous non-stationary infection time series. Our conceptual approach is derived from a Bayesian multivariate disease mapping framework. Importantly, our approach captures within- and between-year dependencies in infection risk while controlling for confounding factors such as seasonality, demographics and infection frequencies, allowing genuine pathogen interactions to be distinguished from simple correlations. We validated our framework using a broad range of synthetic data. We then applied it to diagnostic data available for five respiratory viruses co-circulating in a major urban population between 2005 and 2013: adenovirus, human coronavirus, human metapneumovirus, influenza B virus and respiratory syncytial virus. We found positive and negative covariances indicative of epidemiological interactions among specific virus pairs. This statistical framework enables a community ecology perspective to be applied to infectious disease epidemiology with important utility for public health planning and preparedness

Glycaemic control trends in people with Type 1 diabetes in Scotland 2004-2016

Aims/hypothesis: The aim of this work was to examine whether glycaemic control has improved in those with type 1 diabetes in Scotland between 2004 and 2016, and whether any trends differed by sociodemographic factors. Methods: We analysed records from 30,717 people with type 1 diabetes, registered anytime between 2004 and 2016 in the national diabetes database, which contained repeated measures of HbA1c. An additive mixed regression model was used to estimate calendar time and other effects on HbA1c. Results: Overall, median (IQR) HbA1c decreased from 72 (21) mmol/mol [8.7 (4.1)%] in 2004 to 68 (21) mmol/mol (8.4 [4.1]%) in 2016. However, all of the improvement across the period occurred in the latter 4 years: the regression model showed that the only period of significant change in HbA1c was 2012–2016 where there was a fall of 3 (95% CI 1.82, 3.43) mmol/mol. The largest reductions in HbA1c in this period were seen in children, from 69 (16) mmol/mol (8.5 [3.6]%) to 63 (14) mmol/mol (7.9 [3.4]%), and adolescents, from 75 (25) mmol/mol (9.0 [4.4]%) to 70 (23) mmol/mol (8.6 [4.3]%). Socioeconomic status (according to Scottish Index of Multiple Deprivation) affected the HbA1c values: from the regression model, the 20% of people living in the most-deprived areas had HbA1c levels on average 8.0 (95% CI 7.4, 8.9) mmol/mol higher than those of the 20% of people living in the least-deprived areas. However this difference did not change significantly over time. From the regression model HbA1c was on average 1.7 (95% CI 1.6, 1.8) mmol/mol higher in women than in men. This sex difference did not narrow over time. Conclusions/interpretation: In this high-income country, we identified a modest but important improvement in HbA1c since 2012 that was most marked in children and adolescents. These changes coincided with national initiatives to reduce HbA1c including an expansion of pump therapy. However, in most people, overall glycaemic control remains far from target levels and further improvement is badly needed, particularly in those from more-deprived areas