Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed

Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed

Isolation and Characterization of Microsatellite DNA Markers in the Deep-Sea Amphipod Paralicella tenuipes by Illumina MiSeq Sequencing

Funding This work was supported by the HADEEP projects, funded by the Nippon Foundation, Japan (2009765188), the Natural Environmental Research Council, UK (NE/E007171/1) and the Total Foundation, France. We acknowledge additional support from the Marine Alliance for Science and Technology for Scotland (MASTS) funded by the Scottish Funding Council (Ref: HR09011) and contributing institutions. We also acknowledge support from the Leverhulme Trust to SBP. Additional sea time was supported by NIWA’s ‘Impact of Resource Use on Vulnerable Deep-Sea Communities’ project (CO1_0906)

Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

New Advancements of Scalable Statistical Methods for Learning Latent Structures in Big Data

Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.

Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.

Exploring Mechanisms of Bacterial Adaptation to Seasonal Temperature Change

This research examines three potential mechanisms by which bacteria can adapt to different temperatures: changes in strain-level population structure, gene regulation and particle colonization. For the first two mechanisms, I utilize bacterial strains from the Vibrionaceae family due to their ease of culturability, ubiquity in coastal environments and status as a model system for marine bacteria. I first examine vibrio seasonal dynamics in temperate, coastal water and compare the thermal performance of strains that occupy different thermal environments. Our results suggest that there are tradeoffs in adaptation to specific temperatures and that thermal specialization can occur at a very fine phylogenetic scale. The observed thermal specialization over relatively short evolutionary time-scales indicates that few genes or cellular processes may limit expansion to a different thermal niche. I then compare the genomic and transcriptional changes associated with thermal adaptation in closely-related vibrio strains under heat and cold stress. The two vibrio strains have very similar genomes and overall exhibit similar transcriptional profiles in response to temperature stress but their temperature preferences are determined by differential transcriptional responses in shared genes as well as temperature-dependent regulation of unique genes. Finally, I investigate the temporal dynamics of particle-attached and free-living bacterial community in coastal seawater and find that microhabitats exert a stronger forcing on microbial communities than environmental variability, suggesting that particle-attachment could buffer the impacts of environmental changes and particle-associated communities likely respond to the presence of distinct eukaryotes rather than commonly-measured environmental parameters. Integrating these results will offer new perspectives on the mechanisms by which bacteria respond to seasonal temperature changes as well as potential adaptations to climate change-driven warming of the surface oceans.

Ocean acidification affects the phyto-zoo plankton trophic transfer efficiency

The critical role played by copepods in ocean ecology and biogeochemistry warrants an understanding of how these animals may respond to ocean acidification (OA). Whilst an appreciation of the potential direct effects of OA, due to elevated pCO2, on copepods is improving, little is known about the indirect impacts acting via bottom-up(food quality) effects. We assessed, for the first time, the chronic effects of direct and/or indirect exposures to elevated pCO2 on the behaviour, vital rates, chemical and biochemical stoichiometry of the calanoid copepod Acartia tonsa. Bottom-up effects of elevated pCO2 caused species-specific biochemical changes to the phytoplanktonic feed, which adversely affected copepod population structure and decreased recruitment by 30 %. The direct impact of elevated pCO2 caused gender-specific respiratory responses in A.tonsa adults, stimulating an enhanced respiration rate in males (> 2-fold), and a suppressed respiratory response in females when coupled with indirect elevated pCO2 exposures. Under the combined indirect+direct exposure, carbon trophic transfer efficiency from phytoplankton-to-zooplankton declined to < 50 % of control populations, with a commensurate decrease in recruitment. For the first time an explicit role was demonstrated for biochemical stoichiometry in shaping copepod trophic dynamics. The altered biochemical composition of the CO2-exposed prey affected the biochemical stoichiometry of the copepods, which could have ramifications for production of higher tropic levels, notably fisheries. Our work indicates that the control of phytoplankton and the support of higher trophic levels involving copepods have clear potential to be adversely affected under future OA scenarios.

Particle flux measured on deep sea sediment trap VP-2_trap (Appendix A2.7)

A 17 month record of vertical particle flux of dry weight, carbonate and organic carbon were 25.8, 9.4 and 2.4g/m**2/y, respectively. Parallel to trap deployments, pelagic system structure was recorded with high vertical and temporal resolution. Within a distinct seasonal cycle of vertical particle flux, zooplankton faecal pellets of various sizes, shapes and contents were collected by the traps in different proportions and quantities throughout the year (range: 0-4,500 10**3/m**2/d). The remains of different groups of organisms showed distinct seasonal variations in abundance. In early summer there was a small maximum in the diatom flux and this was followed by pulses of tinntinids, radiolarians, foraminiferans and pteropods between July and November. Food web interactions in the water column were important in controlling the quality and quantity of sinking materials. For example, changes in the population structure of dominant herbivores, the break-down of regenerating summer populations of microflagellates and protozooplankton and the collapse of a pteropod dominated community, each resulted in marked sedimentation pulses. These data from the Norwegian Sea indicate those mechanisms which either accelerate or counteract loss of material via sedimentation. These involve variations in the structure of the pelagic system and they operatè on long (e.g. annual plankton succession) and short (e.g. the end of new production, sporadic grazing of swarm feeders) time scales. Connecting investigation of the water column with a high resolution in time in parallel with drifting sediment trap deployments and shipboard experiments with the dominant zooplankters is a promising approach for giving a better understanding of both the origin and the fate of material sinking to the sea floor.

The influence of mussel-modified habitat on Fucus serratus L. a rocky intertidal canopy-forming macroalga

The influence of habitat modification by Mytilus edulis L. on the settlement and development of Fucus serratus populations was investigated on rocky shores of the Isle of Anglesey, North Wales. Settlement of fucoids was higher inside mussel habitat than outside on one of two shores studied. The effect of microhabitat on survival of fucoid germlings was examined by transplanting the germlings into and outside mussel habitats, each with and without the exclusion of grazers. Observation showed that periwinkles and top shells were abundant in mussel habitat, while limpets dominated bare rock. Exclusion of grazers greatly enhanced the survival of fucoid germlings in both habitats, indicating that while mussel habitat supports a different grazer assemblage to bare rock, both assemblages are important in limiting fucoid recruitment. The risk of dislodgement was assessed and compared between fucoids growing on mussel shells and bare rock. In situ pull-tests showed that less force was required to detach large fertile thalli growing on mussel shells than those growing on the rock. Adhesion was generally broken between the mussel and the rock rather than between the holdfast and the mussel. These observations indicate that mussels provide an unstable substrate for mature fucoids. Overall results suggest that a negative effect of mussel-modified habitat on fucoids is profound in adults; but the effect is context-dependent in juveniles and can be positive at settlement. Results from a survey on population structure of fucoids across two shores showed that there were greater numbers of large fertile fucoids growing directly attached to rock than on mussel shells, while there was no difference for juvenile fucoids confirming the experimental results. Moreover thalli larger than 60 cm were found only on the rock but not on shells. This finding suggests that a mussel dominated habitat may have a significant impact on reproductive output in fucoid populations.

The influence of mussel-modified habitat on Fucus serratus L. a rocky intertidal canopy-forming macroalga

The influence of habitat modification by Mytilus edulis L. on the settlement and development of Fucus serratus populations was investigated on rocky shores of the Isle of Anglesey, North Wales. Settlement of fucoids was higher inside mussel habitat than outside on one of two shores studied. The effect of microhabitat on survival of fucoid germlings was examined by transplanting the germlings into and outside mussel habitats, each with and without the exclusion of grazers. Observation showed that periwinkles and top shells were abundant in mussel habitat, while limpets dominated bare rock. Exclusion of grazers greatly enhanced the survival of fucoid germlings in both habitats, indicating that while mussel habitat supports a different grazer assemblage to bare rock, both assemblages are important in limiting fucoid recruitment. The risk of dislodgement was assessed and compared between fucoids growing on mussel shells and bare rock. In situ pull-tests showed that less force was required to detach large fertile thalli growing on mussel shells than those growing on the rock. Adhesion was generally broken between the mussel and the rock rather than between the holdfast and the mussel. These observations indicate that mussels provide an unstable substrate for mature fucoids. Overall results suggest that a negative effect of mussel-modified habitat on fucoids is profound in adults; but the effect is context-dependent in juveniles and can be positive at settlement. Results from a survey on population structure of fucoids across two shores showed that there were greater numbers of large fertile fucoids growing directly attached to rock than on mussel shells, while there was no difference for juvenile fucoids confirming the experimental results. Moreover thalli larger than 60 cm were found only on the rock but not on shells. This finding suggests that a mussel dominated habitat may have a significant impact on reproductive output in fucoid populations.

Directional genetic differentiation and relative migration

Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly used to gather this information. One potential caveat is that these measures assume gene flow to be symmetric. However, asymmetric gene flow is common in nature, especially in systems driven by physical processes such as wind or water currents. As information about levels of asymmetric gene flow among populations is essential for the correct interpretation of the distribution of contemporary genetic diversity within species, this should not be overlooked. To obtain information on asymmetric migration patterns from genetic data, complex models based on maximum-likelihood or Bayesian approaches generally need to be employed, often at great computational cost. Here, a new simpler and more efficient approach for understanding gene flow patterns is presented. This approach allows the estimation of directional components of genetic divergence between pairs of populations at low computational effort, using any of the classical or modern measures of genetic differentiation. These directional measures of genetic differentiation can further be used to calculate directional relative migration and to detect asymmetries in gene flow patterns. This can be done in a user-friendly web application called divMigrate-online introduced in this study. Using simulated data sets with known gene flow regimes, we demonstrate that the method is capable of resolving complex migration patterns under a range of study designs.

Conservation genetics of North Atlantic loggerhead sea turtles: analysis of nuclear and mitochondrial DNA

[EN] Complex population structure has been described for the loggerhead sea turtle (Caretta caretta), revealing lower levels of population genetic structure in nuclear compared to mitochondrial DNA assays. This may result from mating during spatially overlapping breeding migrations, or male-biased dispersal as previously found for the green turtle (Chelonia mydas). To further investigate these multiple possibilities, we carried out a comparative analysis from twelve newly developed microsatellite loci and the mitochondrial DNA control region (~804 bp) in adult females of the Cape Verde Islands (n=158), and Georgia, USA (n=17).

Increasing the power of genome wide association studies in natural populations using repeated measures : evaluation and implementation

1. Genomewide association studies (GWAS) enable detailed dissections of the genetic basis for organisms' ability to adapt to a changing environment. In long-term studies of natural populations, individuals are often marked at one point in their life and then repeatedly recaptured. It is therefore essential that a method for GWAS includes the process of repeated sampling. In a GWAS, the effects of thousands of single-nucleotide polymorphisms (SNPs) need to be fitted and any model development is constrained by the computational requirements. A method is therefore required that can fit a highly hierarchical model and at the same time is computationally fast enough to be useful. 2. Our method fits fixed SNP effects in a linear mixed model that can include both random polygenic effects and permanent environmental effects. In this way, the model can correct for population structure and model repeated measures. The covariance structure of the linear mixed model is first estimated and subsequently used in a generalized least squares setting to fit the SNP effects. The method was evaluated in a simulation study based on observed genotypes from a long-term study of collared flycatchers in Sweden. 3. The method we present here was successful in estimating permanent environmental effects from simulated repeated measures data. Additionally, we found that especially for variable phenotypes having large variation between years, the repeated measurements model has a substantial increase in power compared to a model using average phenotypes as a response. 4. The method is available in the R package RepeatABEL. It increases the power in GWAS having repeated measures, especially for long-term studies of natural populations, and the R implementation is expected to facilitate modelling of longitudinal data for studies of both animal and human populations.

The bottom trawl survey of Lake Victoria, Uganda in July to August 2003

The objective of the bottom trawl survey in July/August 2003, was to monitor the changes in the fish stocks in the Uganda sector of Lake Victoria with particular emphasis on species composition, distribution, abundance and population structure.