On Flexible finite polygenic models for multiple-trait evaluation

Finite polygenic models (FPM) might be an alternative to the infinitesimal model (TIM) for the genetic evaluation of pedigreed multiple-generation populations for multiple quantitative traits. I present a general flexible Bayesian method that includes the number of genes in the FPM as an additional random variable. Markov-chain Monte Carlo techniques such as Gibbs sampling and the reversible jump sampler are used for implementation. Sampling of genotypes of all genes in the FPM is done via the use of segregation indicators. A broad range of FPM models, some combined with TIM, are empirically tested for the estimation of variance components and the number of genes in the FPM. Four simulation scenarios were studied, including genetic models with 5 or 50 additive independent diallelic genes affecting the traits, and random selection or selection on one of the traits was performed. The results in this study were based on ten replicates per simulation scenario. In the case of random selection, uniform priors on additive gene effects led to posterior mean estimates of genetic variance that were positively correlated with the number of genes fitted in the FPM. In the case of trait selection, assuming normal priors on gene effects also led to genetic variance estimates for the selected trait that were negatively correlated with the number of genes in the FPM. This negative correlation was not observed for the unselected trait. Treating the number of genes in the FPM as random revealed a positive correlation between prior and posterior mean estimates of this number, but the prior hardly affected the posterior estimates of genetic variance. Posterior inferences about the number of genes should be considered to be indicative where trait selection seems to improve the power of distinguishing between TIM and FPM. Based on the results of this study, I suggest not replacing TIM by the FPM, but combining TIM and FPM with the number of genes treated as random, to facilitate a highly flexible and thereby robust method for variance component estimation in pedigreed populations. Further study is required to explore the full potential of these models under different genetic model assumption

Cortical Dynamics Underlying Seizure Mapping and Control

In one-third of epilepsy patients, antiepileptic drugs do not effectively control seizures, leaving resective surgery as the primary treatment option. In the absence of discrete focal lesions, long-term outcome after surgery is modest and often associated with side effects. In many cases, surgery cannot be performed due to the lack of a discrete region generating seizures. For these reasons, new therapeutic technologies have been developed to treat drug-resistant epilepsy with electrical stimulation. These devices are promising, but the efficacy of first-generation implants has been limited. The work in this thesis aims to advance current approaches to seizure monitoring and control by developing better hardware and building the foundational knowledge behind the cortical dynamics underlying seizure generation, propagation and neural stimulation. In this thesis, I first develop new technologies that sample local field potentials on the cortical surface with high spatial and temporal resolutions. These devices capture complex spatiotemporal patterns of epileptiform activity that are not detected on current clinical electrodes. By adding stimulation functionalities to these arrays, we position them as an ideal candidate for responsive, therapeutic neurostimulation. Next, I explore the effect of direct electrical stimulation in the cortex by recording responses with high spatial resolution on the surface and within the cortical laminae. The findings detail the capabilities and limitations of electrical stimulation as a means of modulating seizures. Finally, I use the same three-dimensional recording paradigm in feline neocortex to investigate the genesis and propagation of epileptiform activity in an isolated, chemically-induced epilepsy model. These experiments demonstrate that important circuit elements involved in seizure propagation are found deeper in the cortex and are not reflected in surface recordings. My investigations also present potential stimulation strategies to more effectively disrupt the spread of seizures in the neocortex. It is my hope that the results of this work will inform future technologies to better detect and prevent seizures, ultimately improving the lives of drug-resistant epilepsy patients through the next generation of implantable devices

Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

Let Q be a given n×n square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n×K fuzzy memberships matrix P is found by least-squares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of Q are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix P. Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster mode

Searching for interacting QTL in related populations of an outbreeding species

Many important crop species are outbreeding. In outbreeding species the search for genes affecting traits is complicated by the fact that in a single cross up to four alleles may be present at each locus. This paper is concerned with the search for interacting quantitative trait loci (QTL) in populations which have been obtained by crossing a number of parents. It will be assumed that the parents are unrelated, but the methods can be extended easily to allow a pedigree structure. The approach has two goals: (1) finding QTL that are interacting with other loci and also loci which behave additively; (2) finding parents which segregate at two or more interacting QTL. Large populations obtained by crossing these parents can be used to study interactions in detail. QTL analysis is carried out by means of regression on predictions of QTL genotypes

Comparison of analyses of the QTLMAS XIII common dataset. II: QTL analysis

Background - Five participants of the QTL-MAS 2009 workshop applied QTL analyses to the workshop common data set which contained a time-related trait: cumulative yield. Underlying the trait were 18 QTLs for three parameters of a logistic growth curve that was used for simulating the trait. Methods - Different statistical models and methods were employed to detect QTLs and estimate position and effect sizes of QTLs. Here we compare the results with respect to the numbers of QTLs detected, estimated positions and percentage explained variance. Furthermore, limiting factors in the QTL detection are evaluated. Results - All QTLs for the asymptote and the scaling factor of the logistic curve were detected by at least one of the participants. Only one out of six of the QTLs for the inflection point was detected. None of the QTLs were detected by all participants. Dominant, epistatic and imprinted QTLs were reported while only additive QTLs were simulated. The power to map QTLs for the inflection point increased when more time points were added. Conclusions - For the detection of QTLs related to the asymptote and the scaling factor, there were no strong differences between the methods used here. Also, it did not matter much whether the time course data were analyzed per single time point or whether parameters of a growth curve were first estimated and then analyzed. In contrast, the power for detection of QTLs for the inflection point was very low and the frequency of time points appeared to be a limiting factor. This can be explained by a low accuracy in estimating the inflection point from a limited time range and a limited number of time points, and by the low correlation between the simulated values for this parameter and the phenotypic data available for the individual time point