Genome-wide association mapping in a wild avian population identifies a link between genetic and phenotypic variation in a life-history trait

Understanding the genetic basis of traits involved in adaptation is a major challenge in evolutionary biology but remains poorly understood. Here, we use genome-wide association mapping using a custom 50 k single nucleotide polymorphism (SNP) array in a natural population of collared flycatchers to examine the genetic basis of clutch size, an important life-history trait in many animal species. We found evidence for an association on chromosome 18 where one SNP significant at the genome-wide level explained 3.9% of the phenotypic variance. We also detected two suggestive quantitative trait loci (QTLs) on chromosomes 9 and 26. Fitness differences among genotypes were generally weak and not significant, although there was some indication of a sex-by-genotype interaction for lifetime reproductive success at the suggestive QTL on chromosome 26. This implies that sexual antagonism may play a role in maintaining genetic variation at this QTL. Our findings provide candidate regions for a classic avian life-history trait that will be useful for future studies examining the molecular and cellular function of, as well as evolutionary mechanisms operating at, these loci.

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

Aggression and its function as a hub mediating host defense against the slavemaking ant Protomognathus americanus

In meiner Dissertation beschäftigte ich mich mit unterschiedlichen Verteidungsstrategien, derenrnEffektivität und Evolution, der Ameisenart Temnothorax longispinosus (“Sklaven”), gegenüberrneinem sozialen Parasiten - der nahverwandten, sklavenhaltenden Art Protomognathusrnamericanus (“Sklavenhalter”). Wir entdeckten eine neue Kategorie der Verteidigungsstrategie,rnwelche es dem Wirten ermöglicht, flexibel auf die nicht vorhersagbaren Angriffe des Parasitenrnzu reagieren. Darüber hinaus erforschten wir, wie die Wirte ihre kollektive Verteidigung an einernVielzahl unterschiedlicher Angreifer anpassen können. Wir konnten feststellen, dass Wirte in derrnLage sind ihre kollektive Verteidigung dem Grad der Bedrohung anzupassen. Dies weist daraufrnhin, dass Selektion die Verteidigung gegen unterschiedliche Typen von Angreifern voneinanderrnunabhängig beeinflussen könnte. In einer dritten Studie belegten wir experimentell, dass diernParasiten die Evolution der Kolonieaggressivität der Wirtsart direkt beeinflussen. Die letztenrnbeiden Publikationen beschäftigten sich mit Sklavenrebellion, einer rätselhaftenrnVerteidigungsstrategie, da noch unklar ist, wie eine Eigenschaft von nicht reproduzierendenrnIndividuen vererbt werden kann. In einer Metaanalyse konnten wir die weite Verbreitung undrnhohe Variabilität dieser Eigenschaft dokumentieren, und fanden Hinweise, dassrnVerwandtenselektion eine mögliche Erklärung für die Evolution dieses Merkmals darstellenrnkönnte.

Sequential Quantitative Trait Locus Mapping in Experimental Crosses

The etiology of complex diseases is heterogeneous. The presence of risk alleles in one or more genetic loci affects the function of a variety of intermediate biological pathways, resulting in the overt expression of disease. Hence, there is an increasing focus on identifying the genetic basis of disease by sytematically studying phenotypic traits pertaining to the underlying biological functions. In this paper we focus on identifying genetic loci linked to quantitative phenotypic traits in experimental crosses. Such genetic mapping methods often use a one stage design by genotyping all the markers of interest on the available subjects. A genome scan based on single locus or multi-locus models is used to identify the putative loci. Since the number of quantitative trait loci (QTLs) is very likely to be small relative to the number of markers genotyped, a one-stage selective genotyping approach is commonly used to reduce the genotyping burden, whereby markers are genotyped solely on individuals with extreme trait values. This approach is powerful in the presence of a single quantitative trait locus (QTL) but may result in substantial loss of information in the presence of multiple QTLs. Here we investigate the efficiency of sequential two stage designs to identify QTLs in experimental populations. Our investigations for backcross and F2 crosses suggest that genotyping all the markers on 60% of the subjects in Stage 1 and genotyping the chromosomes significant at 20% level using additional subjects in Stage 2 and testing using all the subjects provides an efficient approach to identify the QTLs and utilizes only 70% of the genotyping burden relative to a one stage design, regardless of the heritability and genotyping density. Complex traits are a consequence of multiple QTLs conferring main effects as well as epistatic interactions. We propose a two-stage analytic approach where a single-locus genome scan is conducted in Stage 1 to identify promising chromosomes, and interactions are examined using the loci on these chromosomes in Stage 2. We examine settings under which the two-stage analytic approach provides sufficient power to detect the putative QTLs.

Seasonal Variation in the Capacity for Plant Trait Measures to Predict Grassland Carbon and Water Fluxes

There is a need for accurate predictions of ecosystem carbon (C) and water fluxes in field conditions. Previous research has shown that ecosystem properties can be predicted from community abundance-weighted means (CWM) of plant functional traits and measures of trait variability within a community (FDvar). The capacity for traits to predict carbon (C) and water fluxes, and the seasonal dependency of these trait-function relationships has not been fully explored. Here we measured daytime C and water fluxes over four seasons in grasslands of a range of successional ages in southern England. In a model selection procedure, we related these fluxes to environmental covariates and plant biomass measures before adding CWM and FDvar plant trait measures that were scaled up from measures of individual plants grown in greenhouse conditions. Models describing fluxes in periods of low biological activity contained few predictors, which were usually abiotic factors. In more biologically active periods, models contained more predictors, including plant trait measures. Field-based plant biomass measures were generally better predictors of fluxes than CWM and FDvar traits. However, when these measures were used in combination traits accounted for additional variation. Where traits were significant predictors their identity often reflected seasonal vegetation dynamics. These results suggest that database derived trait measures can improve the prediction of ecosystem C and water fluxes. Controlled studies and those involving more detailed flux measurements are required to validate and explore these findings, a worthwhile effort given the potential for using simple vegetation measures to help predict landscape-scale fluxes.

Structured neural network modelling of multi-valued functions for wind retrieval from scatterometer measurements

A conventional neural network approach to regression problems approximates the conditional mean of the output vector. For mappings which are multi-valued this approach breaks down, since the average of two solutions is not necessarily a valid solution. In this article mixture density networks, a principled method to model conditional probability density functions, are applied to retrieving Cartesian wind vector components from satellite scatterometer data. A hybrid mixture density network is implemented to incorporate prior knowledge of the predominantly bimodal function branches. An advantage of a fully probabilistic model is that more sophisticated and principled methods can be used to resolve ambiguities.

Structured neural network modelling of multi-valued functions for wind retrieval from scatterometer measurements

A conventional neural network approach to regression problems approximates the conditional mean of the output vector. For mappings which are multi-valued this approach breaks down, since the average of two solutions is not necessarily a valid solution. In this article mixture density networks, a principled method to model conditional probability density functions, are applied to retrieving Cartesian wind vector components from satellite scatterometer data. A hybrid mixture density network is implemented to incorporate prior knowledge of the predominantly bimodal function branches. An advantage of a fully probabilistic model is that more sophisticated and principled methods can be used to resolve ambiguities.

Semisupervised learning of hierarchical latent trait models for data visualization

Recently, we have developed the hierarchical Generative Topographic Mapping (HGTM), an interactive method for visualization of large high-dimensional real-valued data sets. In this paper, we propose a more general visualization system by extending HGTM in three ways, which allows the user to visualize a wider range of data sets and better support the model development process. 1) We integrate HGTM with noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM). This enables us to visualize data of inherently discrete nature, e.g., collections of documents, in a hierarchical manner. 2) We give the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode, the user selects "regions of interest," whereas in the automatic mode, an unsupervised minimum message length (MML)-inspired construction of a mixture of LTMs is employed. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. 3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualization plots, since they can highlight the boundaries between data clusters. We illustrate our approach on a toy example and evaluate it on three more complex real data sets. © 2005 IEEE.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Trans-ethnic fine mapping highlights kidney-function genes linked to salt sensitivity

We analyzed genome-wide association studies (GWASs), including data from 71,638 individuals from four ancestries, for estimated glomerular filtration rate (eGFR), a measure of kidney function used to define chronic kidney disease (CKD). We identified 20 loci attaining genome-wide-significant evidence of association (p < 5 × 10(-8)) with kidney function and highlighted that allelic effects on eGFR at lead SNPs are homogeneous across ancestries. We leveraged differences in the pattern of linkage disequilibrium between diverse populations to fine-map the 20 loci through construction of "credible sets" of variants driving eGFR association signals. Credible variants at the 20 eGFR loci were enriched for DNase I hypersensitivity sites (DHSs) in human kidney cells. DHS credible variants were expression quantitative trait loci for NFATC1 and RGS14 (at the SLC34A1 locus) in multiple tissues. Loss-of-function mutations in ancestral orthologs of both genes in Drosophila melanogaster were associated with altered sensitivity to salt stress. Renal mRNA expression of Nfatc1 and Rgs14 in a salt-sensitive mouse model was also reduced after exposure to a high-salt diet or induced CKD. Our study (1) demonstrates the utility of trans-ethnic fine mapping through integration of GWASs involving diverse populations with genomic annotation from relevant tissues to define molecular mechanisms by which association signals exert their effect and (2) suggests that salt sensitivity might be an important marker for biological processes that affect kidney function and CKD in humans.

Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.