A Faster and More Accurate Algorithm for Calculating Population Genetics Statistics Requiring Sums of Stirling Numbers of the First Kind

Ewen's sampling formula is a foundational theoretical result that connects probability and number theory with molecular genetics and molecular evolution; it was the analytical result required for testing the neutral theory of evolution, and has since been directly or indirectly utilized in a number of population genetics statistics. Ewen's sampling formula, in turn, is deeply connected to Stirling numbers of the first kind. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu's [Formula: see text] By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed

A distribution function from population genetics statistics using Stirling numbers of the first kind: Asymptotics, inversion and numerical evaluation

Stirling numbers of the first kind are common in number theory and combinatorics; through Ewen’s sampling formula, these numbers enter into the calculation of several population genetics statistics, such as Fu’s Fs. In previous papers we have considered an asymptotic estimator for a finite sum of Stirling numbers, which enables rapid and accurate calculation of Fu’s Fs. These sums can also be viewed as cumulative distribution functions, leading directly to the possibility of an inversion function, where, given a value for Fu’s Fs, the goal is to solve for one of the input parameters. We solve this inversion using Newton iteration for small parameters. For large parameters, we have to extend our earlier obtained asymptotic results to solve the inversion problem asymptotically. Numerical experiments are given to show the efficiency of both solving the inversion problem and the expanded asymptotic estimator for sums of Stirling numbers

Detecting inbreeding depression in a severely bottlenecked, recovering species: The little spotted kiwi (Apteryx owenii)

Population bottlenecks reduce genetic variation and population size. Small populations are at greater risk of inbreeding, which further erodes genetic diversity and can lead to inbreeding depression. Inbreeding depression is known to increase extinction risk. Thus, detecting inbreeding depression is important for population viability assessment and conservation management. However, identifying inbreeding depression in wild populations is challenging due to the difficulty of obtaining long-term measures of fitness and error-free measures of individual inbreeding coefficients. I investigated inbreeding depression and our power to detect it in species that have very low genetic variation, using little spotted kiwi (Apteryx owenii) (LSK) as a case study. This endemic New Zealand ratite experienced a bottleneck of, at most, five individuals ~100 years ago and has since been subjected to secondary bottlenecks as a result of introductions to new predator-free locations. There is no behavioural pedigree data available for any LSK population and the status of the species is monitored almost exclusively via population growth. I conducted two seasons of field work to determine hatching success in the two LSK populations with the highest and lowest numbers of founders; Zealandia Sanctuary (40 founders) and Long Island (two founders). I also used simulation-based modelling to assess the feasibility of reconstructing pedigrees based on individual genotypes from LSK populations to calculate pedigree inbreeding coefficients. Finally, I used microsatellite genotypes to measure the genetic erosion in successive filial groupings of Long Island and Zealandia LSK as a result of their respective bottlenecks, and tested for inbreeding depression on Long Island. Hatching success was significantly lower on Long Island than in Zealandia in both years of the study despite significantly higher reproductive effort on Long Island. Although this was suggestive of inbreeding depression on Long Island, simulation results showed that constructing a pedigree for any LSK population based on the genetic markers and samples currently available would lead to inaccurate pedigrees and invalid estimates of individual inbreeding coefficients. Thus, an alternative method of detecting inbreeding and inbreeding depression was required. Microsatellite data showed continued loss of heterozygosity in both populations, but loss of allelic diversity on Long Island only. Individual genotypes indicated that the majority (74%) of the adult Long Island population is comprised of the founding pair (F) and their direct offspring (F1) rather than birds from subsequent generations (F2+). This is not what would be expected if survival was equal between these two filial classes. I suggest that the high levels of inbreeding (≥0.25) in F2+ birds is impacting on their survival, creating a demographic skew in the population and resulting in lower hatching success on average on Long Island when compared to the relatively outbred Zealandia birds. This inbreeding depression appears to have been masked, thus far, by positive population growth on Long Island resulting from the long life span of LSK (27-83 years) and continued reproductive success of the founding pair. Thus, it is likely that the Long Island population will go into decline when the founding pair cease to reproduce. This study highlights the challenges of measuring inbreeding depression in species with very low genetic variation and the importance of assessing the statistical power and reliability of the genetic tools available for those species. It also demonstrates that basic genetic techniques can offer valuable insight when more advanced tools prove error-prone. Monitoring vital rates such as hatching success in conjunction with genetic data is important for assessing the success of conservation translocations and detecting potentially cryptic genetic threats such as inbreeding depression. My results suggest that LSK are being affected by inbreeding depression and that careful genetic management will be required to ensure the long-term viability of this species

Evolutionary genomics : statistical and computational methods

This open access book addresses the challenge of analyzing and understanding the evolutionary dynamics of complex biological systems at the genomic level, and elaborates on some promising strategies that would bring us closer to uncovering of the vital relationships between genotype and phenotype. After a few educational primers, the book continues with sections on sequence homology and alignment, phylogenetic methods to study genome evolution, methodologies for evaluating selective pressures on genomic sequences as well as genomic evolution in light of protein domain architecture and transposable elements, population genomics and other omics, and discussions of current bottlenecks in handling and analyzing genomic data. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of detail and expert implementation advice that lead to the best results. Authoritative and comprehensive, Evolutionary Genomics: Statistical and Computational Methods, Second Edition aims to serve both novices in biology with strong statistics and computational skills, and molecular biologists with a good grasp of standard mathematical concepts, in moving this important field of study forward

Development of tools for tracebility and for assessing the genetic impact of aquaculture

Overexploitation of natural food resources, among which marine resources, put in serious risk the survival of many species and its availability as human food. Reduction of harvest, restocking with farmed fish and farming as alternative source of product, are commonly used to grant high quality food in a sustainable way. Nevertheless, the last two solutions have potential side effects, among which the genetic impact on natural populations that are involved in restocking actions or escapees from fattening cages and farms. Study the genetic structure of the species in the wild and farming environment is a key aspect to understand the real risks related to aquaculture. At the same time, genetic tools developed in the process can be used to trace wild and farmed origin of fish product, which is an aspect that is gaining great interest among consumers. In the study presented in the thesis, genetic analysis based on RAD genotyping allowed the study of more than 1000 wild and farmed samples with 1216 SNP. The results obtained suggest a subdivision of natural samples in four genetically distinct groups: Atlantic, West Mediterranean, Ionian Sea and Aegean Sea. The analysis carried out on many European broodstocks revealed a higher genetic differentiation compared to wild groups, probably due to founder effects and genetic drift; broodstocks are characterized by lower genetic variability, that in some cases fell below the minimum threshold to avoid inbreeding; finally, some of the broodstocks showed genetic traits that could make offspring unfit to the natural environment they would find in case of restocking of escapees. Comparing wild and farmed groups stimulated a discussion on the potential impact of aquaculture on natural populations, considering the reduction in fitness and the loss of inter/intra groups genetic variability, that cause a loss in long-term adaptation potential. The analytical techniques used and the results obtained are important for the development of gilthead sea bream aquaculture in Europe and for the correct management and protection of natural populations from the areas involved in production

An investigation of genetic and reproductive differences between Faroe Plateau and Faroe Bank cod (Gadus morhua L.)

The Atlantic cod (Gadus morhua L.) fishery is of great economic importance to the Faroese economy. There are two separately managed cod stocks around the Faroe Islands, the Faroe Plateau and the Faroe Bank cod. Both have experienced dramatic decreases in size and informed management decisions are vital for both stock viability and exploitation. The stocks are geographically isolated by an 800 m deep channel and water temperatures are on average 1 – 2 ºC higher on the Faroe Bank than on the Faroe Plateau. There are clear phenotypic differences between the stocks; in particular, the markedly higher growth rate for the Faroe Bank cod has caught public and scientific attention. There is continuing debate regarding the relative importance of genetics and environmental contributions to the contrasting phenotypes. Analyses of reproductive parameters (field data and experimental captive spawnings) as well as analyses of microsatellite and single nucleotide polymorphism (SNP) markers were undertaken to better resolve the issue. Field data as well as data from experimental captive spawnings provided evidence of reproductive differences between Faroe Plateau and Faroe Bank cod. Peak spawning occurred earlier on the Faroe Plateau than on the Faroe Bank and this difference in timing of spawning was maintained in captivity. In particular, differences in sizes of eggs (average diameters of 1.40 and 1.30 mm for Faroe Plateau and Faroe Bank cod eggs, respectively) and indirect evidence of greater volumes spawned by the Faroe Bank females suggested stock differences with respect to egg size – egg number trade-off. It was hypothesised that the strategy adopted by cod on the Faroe Bank, with a higher number of smaller eggs, evolved in response to a more hostile environment (bare seabed and higher exposure to predators) experienced by early life stages in this area. Experimental captive spawnings with Faroe Bank cod showed a large interfamily skew in survival rates of cod eggs and fry. Egg size was identified as a useful indicator of survival rates in the egg stage, but egg survival rates could not be used to predict viability in later developmental stages, thus highlighting the importance of employing some sort of genetic monitoring of cod fry to ensure sufficient family representation in the progeny. While no tank effect was evident concerning fry survival, a significant tank effect was identified concerning body sizes of fry. Microsatellite data were analysed using large sample sizes of Faroe Plateau and Faroe Bank cod with the Faroe Plateau divided into two locations, Faroe Plateau North-East and Faroe Plateau West (cod from each of the two were known to belong to separate spawning grounds). Two Norwegian coastal cod samples were included as outlier populations. While no genetic differentiation was detected between the two Faroe Plateau locations, these analyses revealed a detectable, albeit relatively modest, degree of genetic differentiation between cod from the Faroe Plateau and the Faroe Bank (FST = 0.0014 and 0.0018; DJost_EST = 0.0027 and 0.0048; P < 0.0001 and P < 0.001 for the Faroe Plateau North-East – Faroe Bank and the Faroe Plateau West – Faroe Bank comparisons). These values were several times smaller than those between Faroese and Norwegian coastal cod (pairwise FST and DJost_EST values in the range of 0.0061 – 0.0137 and 0.0158 – 0.0386, respectively). Despite recent reductions in census population sizes for Faroe Plateau and, particularly, Faroe Bank cod, genetic diversity estimates were comparable to the ones observed for Norwegian coastal cod and there was no evidence of significant genetic bottlenecks. Lastly, data for one of the markers (Gmo132) indicated genotype-dependent vertical distribution of cod (as investigated for Faroe Plateau North-East cod). Contrary to some previously published studies, analysis of SNPs of two candidate genes for adaptive divergence, the hemoglobin gene Hb-ß1 and the transferrin gene Tf1, failed to detect differentiation between samples of Faroe Plateau and Faroe Bank cod analysed in this thesis. Of 3533 novel SNPs simultaneously discovered and genotyped by restriction-site associated DNA (RAD) sequencing, 58 showed evidence of genetic differentiation between Faroe Plateau North-East and Faroe Bank cod (P 0.25; P < 0.0005) were selected for validation in larger samples, that included cod from both Faroe Plateau areas and the Faroe Bank as well as Norwegian coastal and White Sea cod. Six out of the eight loci amplified successfully with a PCR-based method and there was 100 % concordance between genotypes of individuals screened by both techniques. Due to ascertainment bias, the SNPs should only be applied with caution in a broader geographical context. Nonetheless, these SNPs did confirm the genetic substructure suggested for Faroese cod by microsatellite analyses. While no genetic differentiation was evident between the two Faroe Plateau locations, significant genetic differentiation was evident between Faroe Plateau and Faroe Bank cod at five of the SNPs (FST values in the range of 0.0383 – 0.1914). This panel of five SNPs could confidently be used to trace groups of Faroe Plateau and Faroe Bank cod to their population of origin. In conclusion, multiple lines of evidence demonstrate that Faroe Plateau and Faroe Bank cod are truly two genetically distinct populations. While the findings contribute to a broader understanding of the biology and the genetics of Faroe Plateau and Faroe Bank cod, the novel SNPs developed may provide a valuable resource for potential future demands of i.e. genetic stock identification methods

Genetic diversity in non-native conifer woodlands under Continuous Cover Forestry management in England

Climate change is reshaping ecosystems at a pace that results in tree species not predicted to be able to adapt to new conditions fast enough. The variation in alleles is the main driver of adaptation in response to environmental change. Therefore, estimating the potential adaptability of tree species to Climate Change by monitoring their genetic diversity (GD) is crucial. Tree species appear in forests in varied ways, supporting valuable habitats while providing a full range of ecosystem services, including CO2 capture, maintaining water quality, enhancing biodiversity and landscape, and producing timber. Due to the increasing concern for the future adaptability of forests, the Continuous Cover Forestry (CCF) system presents an opportunity to maintain and enhance forest services by prioritising the management of the ecosystem and encouraging natural regeneration rather than focusing on timber production; for that reason, this approach is being promoted by the UK Forestry Standards to replace other systems such as clear-felling. Therefore, even-aged plantations, usually composed of non-native conifer species are being transformed into CCF; however, there is a lack of studies on the transmission of GD to the naturally regenerated offspring. This thesis aims to understand the GD within and between adults and juveniles under the CCF system. Our hypothesis suggests that in the long-term, the natural regeneration resulting from these plantations may show a low GD reducing the woodland’s potential adaptability to rapid environmental changes. We analysed selected woodlands, focusing on two widely planted species, Pseudotsuga menziesii (Mirb.) Franco and Thuja plicata Donn ex D. Don. The project analysed over 1100 trees from seven woodlands, which required optimised and efficient techniques to process the samples and determine genotypes. We compared the DNA quality, time and plastic-efficiency of two DNA isolation methods and selected the optimal protocol for each species. We designed the genotyping assays using available SNP datasets for P. menziesii and performed a GBS to discover SNPs on T. plicata. We used a high-throughput PCR-based SNP scoring assay to genotype the sample sets. A detailed forestry survey across all sites allowed us to characterise and assess the level of transformation to CCF. We found high levels of heterozygosity overall across species and stands, in both adults and juveniles; however, we found a low effective population size (Ne<500) in every stand for both species. In general, T. plicata stands had lower Ne compared to P. menziesii, in both adults and juveniles, suggesting that this species may have a lower adaptability to rapid environmental changes. In both species, some stands showed lower Ne in juveniles compared to the adults, which may indicate ineffective transmission of GD to the offspring; however, other stands showed the opposite trend, which may be due to pollen from neighbouring stands contributing to the reproductive process. Finally, in some cases, the stands at a late stage of transformation to CCF showed low levels of GD. This may indicate that logging and reducing the number of individuals in favour of species diversity may reduce the adaptive potential in the long-term. The variety of results across stands and species confirms the complexity of this subject and indicates that even though a woodland may appear close-to-nature visually, its genetic makeup may not be sufficiently diverse to adapt to changing climate conditions

Evolutionary Genomics

This open access book addresses the challenge of analyzing and understanding the evolutionary dynamics of complex biological systems at the genomic level, and elaborates on some promising strategies that would bring us closer to uncovering of the vital relationships between genotype and phenotype. After a few educational primers, the book continues with sections on sequence homology and alignment, phylogenetic methods to study genome evolution, methodologies for evaluating selective pressures on genomic sequences as well as genomic evolution in light of protein domain architecture and transposable elements, population genomics and other omics, and discussions of current bottlenecks in handling and analyzing genomic data. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of detail and expert implementation advice that lead to the best results. Authoritative and comprehensive, Evolutionary Genomics: Statistical and Computational Methods, Second Edition aims to serve both novices in biology with strong statistics and computational skills, and molecular biologists with a good grasp of standard mathematical concepts, in moving this important field of study forward

Conservation Genetics for Management of Threatened Plant and Animal Species

This book focuses on conservation genetic (and genomic) papers that demonstrate applied outcomes that inform practical threatened species management. We cover a broad range of species and genetic approaches, but focus on how conservation genetic information is used to underpin management actions for species recovery. Through the exposition of a diversity of approaches, we aim to demonstrate to conservation managers and researchers how conservation genetics can inform on-ground species management