High heritability of malaria parasite clearance rate indicates a genetic basis for artemisinin resistance in western Cambodia.

In western Cambodia, malaria parasites clear slowly from the blood after treatment with artemisinin derivatives, but it is unclear whether this results from parasite, host, or other factors specific to this population. We measured heritability of clearance rate by evaluating patients infected with identical or nonidentical parasite genotypes, using methods analogous to human twin studies. A substantial proportion (56%-58%) of the variation in clearance rate is explained by parasite genetics. This has 2 important implications: (1) selection with artemisinin derivatives will tend to drive resistance spread and (2) because heritability is high, the genes underlying parasite clearance rate may be identified by genome-wide association.

Inferred relatedness and heritability in malaria parasites.

Malaria parasites vary in phenotypic traits of biomedical or biological interest such as growth rate, virulence, sex ratio and drug resistance, and there is considerable interest in identifying the genes that underlie this variation. An important first step is to determine trait heritability (H(2)). We evaluate two approaches to measuring H(2) in natural parasite populations using relatedness inferred from genetic marker data. We collected single-clone Plasmodium falciparum infections from 185 patients from the Thailand-Burma border, monitored parasite clearance following treatment with artemisinin combination therapy (ACT), measured resistance to six antimalarial drugs and genotyped parasites using 335 microsatellites. We found strong relatedness structure. There were 27 groups of two to eight clonally identical (CI) parasites, and 74 per cent of parasites showed significant relatedness to one or more other parasites. Initially, we used matrices of allele sharing and variance components (VC) methods to estimate H(2). Inhibitory concentrations (IC(50)) for six drugs showed significant H(2) (0.24 to 0.79, p = 0.06 to 2.85 x 10(-9)), demonstrating that this study design has adequate power. However, a phenotype of current interest--parasite clearance following ACT--showed no detectable heritability (H(2) = 0-0.09, ns) in this population. The existence of CI parasites allows the use of a simple ANOVA approach for quantifying H(2), analogous to that used in human twin studies. This gave similar results to the VC method and requires considerably less genotyping information. We conclude (i) that H(2) can be effectively measured in malaria parasite populations using minimal genotype data, allowing rational design of genome-wide association studies; and (ii) while drug response (IC(50)) shows significant H(2), parasite clearance following ACT was not heritable in the population studied.

Mortality in captive baboons with seizures: a new model for SUDEP?

Because the baboon is a model of primary generalized epilepsy, we were interested in mortality of captive animals with a history of witnessed seizures. Causes of natural death were investigated in 46 seizure baboons (SZ) and 78 nonepileptic controls (CTL), all of which underwent a complete pathologic examination at the Southwest Foundation for Biomedical Research (SFBR) in San Antonio. SZ animals died at a younger age than the control baboons (p < 0.001). Almost all epileptic baboons that died suddenly without an apparent cause (SZ-UKN), had pulmonary congestion or edema without evidence of trauma, systemic illness, or heart disease, compared to nine controls (12%) (p < 0.001), most of which demonstrated evidence of a concurrent illness. Serosanguineous bronchial secretions were found in 15 SZ-UKN baboons (58%), but in only three controls (4%) (p < 0.001). Chronic multifocal fibrotic changes in myocardium were noted in only three (12%) of SZ-UKN baboons and one control baboon. Based upon these results, untreated seizures appear to reduce the life expectancy of captive baboons. Sudden unexpected death in epilepsy (SUDEP) may be a common cause of natural death in epileptic baboons.

Natural Chagas disease in four baboons.

BACKGROUND: Chagas disease is common in Central and South America and the southern United States. The causative agent is Trypanosoma cruzi (order Kinetoplastida, family Trypanosomatidae), a kinetoplastid protozoan parasite of humans and other vertebrates. It is a serious public health issue and the leading cause of heart disease and cardiovascular death in Central and South America. In 1984, a colony baboon was discovered to be infected with T. cruzi. METHODS: As the initial diagnosis was made by microscopic observation of the amastigote forms of T. cruzi in myocardial fibers, T. cruzi amastigotes have been identified in three additional baboons. RESULTS: The primary findings were similar in all four baboons and were congestive heart failure with edema of dependent areas, hydrothorax, hydropericardium, and multifocal to diffuse lymphoplasmacytic myocarditis. CONCLUSIONS: A baboon animal model of Chagas disease could contribute significantly to the development of therapies for the disease in humans.

Identification of promoter variants in baboon endothelial lipase that regulate high-density lipoprotein cholesterol levels.

BACKGROUND: High-density lipoprotein cholesterol (HDL) levels are a major risk factor for cardiovascular disease. Previously we identified a quantitative trait locus on baboon chromosome 18 that regulates HDL. From positional cloning studies and expression studies, we identified the endothelial lipase gene (LIPG) as the primary candidate gene for the quantitative trait locus. The mechanism by which LIPG variation influences HDL levels has not been determined. METHODS AND RESULTS: We identified 164 LIPG polymorphisms in a panel of sibling baboons discordant for HDL1 and genotyped putative regulatory polymorphisms in a population of 951 pedigreed baboons. With the use of quantitative trait nucleotide analysis we identified 3 polymorphisms in the LIPG promoter associated with variation in serum HDL1 levels. In addition, we demonstrated that these 3 polymorphisms affect LIPG promoter activity in vitro. In silico analysis was used to identify putative transcription factors that differentially bind the functional promoter polymorphisms. CONCLUSIONS: These results reveal LIPG variants that specifically contribute to HDL1 levels and demonstrate mechanisms by which these polymorphisms may regulate LIPG promoter activity. Results from the present study provide a mechanism, namely variation in LIPG promoter activity possibly caused by altered transcription factor binding, by which LIPG variation affects HDL levels.

A locus on chromosome 10 influences C-reactive protein levels in two independent populations.

High sensitivity C-reactive protein (hsCRP) is an independent risk factor for cardiovascular disease, such as stroke or coronary artery disease. Genetic factors influence significantly the inter-individual variability of hsCRP. The aim of this study was to identify genomic regions influencing hsCRP levels. A genome scan was performed in two independent studies of Caucasian populations, namely 513 Western-European families ascertained for myocardial infarction (n = 1,406) and 120 French-Canadian families diagnosed with hypertension (n = 758). In the myocardial infarction families, 31% of the inter-individual variation of hsCRP levels was explained by genetic factors (P = 0.0000015) and loci influencing hsCRP were identified on chromosomes 10 (at 141 cM) and 5 (at 150 cM) with multipoint LOD scores of 3.15 and 2.23, respectively. An additional suggestive signal was detected on chromosome 2 in subset analyses. A similar degree of heritability has been observed in a second independent population of French-Canadian hypertensive families for hsCRP (30%) and linkage results for chromosome 10 were confirmed with maximum LOD score of 2.7. We identified a chromosomal region in two independent populations which influences hsCRP in addition to several unique regions. This provides targets for the identification of genes involved in the regulation of hsCRP and the development and progression of vascular disease, including stroke.

Contrasting genetic structure in Plasmodium vivax populations from Asia and South America.

Populations of Plasmodium falciparum show striking differences in linkage disequilibrium, population differentiation and diversity, but only fragmentary data exists on the genetic structure of Plasmodium vivax. We genotyped nine tandem repeat loci bearing 2-8 bp motifs from 345 P. vivax infections collected from three Asian countries and from five locations in Colombia. We observed 9-37 alleles per locus and high diversity (He=0.72-0.79, mean=0.75) in all countries. Numbers of multiple clone infections varied considerably: these were rare in Colombia and India, but > 60% of isolates carried multiple alleles in at least one locus in Thailand and Laos. However, only one or two of the nine loci show >1 allele in many samples, suggesting that mutation within infections may result in overestimation of true multiple carriage rates. Identical nine-locus genotypes were frequently found in Colombian populations, contributing to strong linkage disequilibrium. These identical genotypes were strongly clustered in time, consistent with epidemic transmission of clones and subsequent breakdown of allelic associations, suggesting high rates of inbreeding and low effective recombination rates in this country. In contrast, identical genotypes were rare and loci were randomly associated in all three Asian populations, consistent with higher rates of outcrossing and recombination. We observed low but significant differentiation between different Asian countries (standardized FST = 0.13-0.45). In comparison, we see greater differentiation between collection locations within Colombia (standardized FST = 0.4-0.7), and strong differentiation between continents (standardized FST = 0.48-0.79). The observed heterogeneity in multiple clone carriage rates, linkage disequilibrium and population differentiation are similar in some, but not all, respects to those observed in P. falciparum, and have important implications for the design of association mapping studies, and interpretation of P. vivax epidemiology.

Quantitative trait locus-specific genotype x alcoholism interaction on linkage for evoked electroencephalogram oscillations.

We explored the evidence for a quantitative trait locus (QTL)-specific genotype x alcoholism interaction for an evoked electroencephalogram theta band oscillation (ERP) phenotype on a region of chromosome 7 in participants of the US Collaborative Study on the Genetics of Alcoholism. Among 901 participants with both genotype and phenotype data available, we performed variance component linkage analysis (SOLAR version 2.1.2) in the full sample and stratified by DSM-III-R and Feighner-definite alcoholism categories. The heritability of the ERP phenotype after adjusting for age and sex effects in the combined sample and in the alcoholism classification sub-groups ranged from 40% to 66%. Linkage on chromosome 7 was identified at 158 cM (LOD = 3.8) in the full sample and at 108 in the non-alcoholic subgroup (LOD = 3.1). Further, we detected QTL-specific genotype x alcoholism interaction at these loci. This work demonstrates the importance of considering the complexity of common complex traits in our search for genes that predispose to alcoholism.

Mitochondrial genetic effects on latent class variables associated with susceptibility to alcoholism.

We report the results of statistical genetic analyses of data from the Collaborative Study on the Genetics of Alcoholism prepared for the Genetic Analysis Workshop 14 to detect and characterize maternally inherited mitochondrial genetic effects on variation in latent class psychiatric/behavioral variables employed in the diagnosis of alcoholism. Using published extensions to variance decomposition methods for statistical genetic analysis of continuous and discrete traits we: 1) estimated the proportion of the variance in each trait due to the effects of mitochondrial DNA (mtDNA), 2) tested for pleiotropy, both mitochondrial genetic and residual additive genetic, between trait pairs, and 3) evaluated whether the simultaneous estimation of mitochondrial genetic effects on these traits improves our ability to detect and localize quantitative trait loci (QTL) in the nuclear genome. After correction for multiple testing, we find significant (p < 0.009) mitochondrial genetic contributions to the variance for two latent class variables. Although we do detect significant residual additive genetic correlations between the two traits, there is no evidence of a residual mitochondrial genetic correlation between them. Evidence for autosomal QTL for these traits is improved when linkage screens are conditioned on significant mitochondrial genetic effects. We conclude that mitochondrial genes may contribute to variation in some latent class psychiatric/behavioral variables associated with alcoholism.

Accuracy of haplotype estimation in a region of low linkage disequilibrium.

We compared the accuracy of haplotype inferences at a 6 Mb region on chromosome 7 where significant linkage between a brain oscillation phenotype and a cholinergic muscarinic receptor gene was previously reported. Individual haplotype assignments and haplotype frequencies were estimated using 5, 10, and 14 consecutive Illumina single-nucleotide polymorphisms (SNPs) within the 1-LOD unit support interval of the chromosome 7 linkage peak. Initially, haplotypes were constructed incorporating phase information provided by relatives using the pedigree analysis package MERLIN. Population-based haplotypes were inferred using the haplotype estimation software HAPLO.STATS and PHASE, using unrelated individuals. The 14 SNPs within this region exhibited markedly low linkage disequilibrium, and the average D' estimate between SNPs was 0.18 (range: 0.01-0.97). In comparison to the family-based haplotypes calculated in MERLIN, the computational inferences of individual haplotype assignments were most accurate when considering 5 consecutive SNPs, but decayed dramatically when considering 10 or 14 SNPs in both PHASE and HAPLO.STATS. When comparing the two haplotype inference methods, both PHASE and HAPLO.STATS performed poorly. These analyses underscore the difficulties of haplotype estimation in the presence of low linkage disequilibrium and stress the importance of careful consideration of confidence measures when using estimated haplotype frequencies and individual assignments in biomedical research.

Clinical and EEG phenotypes of epilepsy in the baboon (Papio hamadryas spp.).

Spontaneous seizures have been reported in several baboon subspecies housed at the Southwest Foundation for Biomedical Research (SFBR), including Papio hamadryas anubis as well as cynocephalus/anubis and other hybrids. This study classified clinical and electroencephalographic (EEG) phenotypes in these subspecies based upon interictal and ictal findings, as well as photosensitivity, by scalp EEG. One hundred baboons underwent 1-h EEG studies with photic stimulation (PS), 49 with previously witnessed seizures and 51 without. The animals were classified according to these electroclinical phenotypes: presence or absence of interictal epileptic discharges (IEDs), seizures and photoparoxysmal or photoconvulsive responses. Effects of age, gender, and species on EEG phenotypes were also examined. Six discrete electroclinical phenotypes were identified. Generalized IEDs of 2-3, 4-6, and/or 6-7Hz were identified in 67 baboons. Epileptic seizures were recorded in 40 animals, including myoclonic and generalized tonic-clonic seizures. Thirty-three animals were photosensitive. Although the prevalence of IEDs and seizures were similar in seizure and asymptomatic animals, photosensitivity was more prevalent in the seizure animals (p=0.001). P.h. anubis/cynocephalus hybrids were more likely to be photosensitive than P.h. anubis (p=0.004). The reliable characterization of distinct epileptic phenotypes in this pedigreed colony is critical to the success of future genetic analyses to identify genetic factors underlying their epilepsy.

Discovering schizophrenia endophenotypes in randomly ascertained pedigrees.

BACKGROUND: Although case-control approaches are beginning to disentangle schizophrenia's complex polygenic burden, other methods will likely be necessary to fully identify and characterize risk genes. Endophenotypes, traits genetically correlated with an illness, can help characterize the impact of risk genes by providing genetically relevant traits that are more tractable than the behavioral symptoms that classify mental illness. Here, we present an analytic approach for discovering and empirically validating endophenotypes in extended pedigrees with very few affected individuals. Our approach indexes each family member's risk as a function of shared genetic kinship with an affected individual, often referred to as the coefficient of relatedness. To demonstrate the utility of this approach, we search for neurocognitive and neuroanatomic endophenotypes for schizophrenia in large unselected multigenerational pedigrees. METHODS: A fixed-effects test within the variance component framework was performed on neurocognitive and cortical surface area traits in 1606 Mexican-American individuals from large, randomly ascertained extended pedigrees who participated in the Genetics of Brain Structure and Function study. As affecteds were excluded from analyses, results were not influenced by disease state or medication usage. RESULTS: Despite having sampled just 6 individuals with schizophrenia, our sample provided 233 individuals at various levels of genetic risk for the disorder. We identified three neurocognitive measures (digit-symbol substitution, facial memory, and emotion recognition) and six medial temporal and prefrontal cortical surfaces associated with liability for schizophrenia. CONCLUSIONS: With our novel analytic approach, one can discover and rank endophenotypes for schizophrenia, or any heritable disease, in randomly ascertained pedigrees.

Genetic basis of variation in carotid artery plaque in the San Antonio Family Heart Study.

BACKGROUND AND PURPOSE: In contrast to the commonly used quantitative marker of subclinical atherosclerosis, namely intima-media thickness, we investigated the extent to which the presence or absence of carotid artery plaque (CAP) was under genetic control. METHODS: The study population consisted of 750 individuals distributed across 29 randomly ascertained extended Mexican American pedigrees who participated in the second examination cycle of the San Antonio Family Heart Study. Extracranial focal CAP was identified by B-mode ultrasound bilaterally in the internal carotid artery or the carotid bulb. Using a variance decomposition approach implemented in the SOLAR computer program, we performed genetic analysis on the discrete trait CAP (ie, liability to disease) using a threshold model. Covariates considered in the analysis included age, sex, diabetes, current smoking status, lipid levels, and markers of hypertension and obesity. RESULTS: Fifty-one of 461 women and fifty-seven of 289 men with a mean age of 42.1 years had evidence of a plaque in the right and/or left carotid artery. The age- and sex-adjusted heritability (h(2)+/-SE) for CAP was significant (h(2)=0.28+/-0.15, P=0.01). Furthermore, after adjustment for additional covariates that contributed significantly to the model (P<0.05; diabetes, hypertension, body mass index, waist circumference, and smoking status), heritability remained significant (h(2)=0.23+/-0.15, P=0.03). CONCLUSIONS: Our data indicate that after established cardiovascular risk factors are controlled for, the variation of the discrete trait CAP is under appreciable additive genetic influences.

On different approximations to multilocus identity-by-descent calculations and the resulting power of variance component-based linkage analysis.

An empirical comparison between three different methods for estimation of pair-wise identity-by-descent (IBD) sharing at marker loci was conducted in order to quantify the resulting differences in power and localization precision in variance components-based linkage analysis. On the examined simulated, error-free data set, it was found that an increase in accuracy of allele sharing calculation resulted in an increase in power to detect linkage. Linkage analysis based on approximate multi-marker IBD matrices computed by a Markov chain Monte Carlo approach was much more powerful than linkage analysis based on exact single-marker IBD probabilities. A "multiple two-point" approximation to true "multipoint" IBD computation was found to be roughly intermediate in power. Both multi-marker approaches were similar to each other in accuracy of localization of the quantitative trait locus and far superior to the single-marker approach. The overall conclusions of this study with respect to power are expected to also hold for different data structures and situations, even though the degree of superiority of one approach over another depends on the specific circumstances. It should be kept in mind, however, that an increase in computational accuracy is expected to go hand in hand with a decrease in robustness to various sources of errors.

HDL cholesterol in females in the Framingham Heart Study is linked to a region of chromosome 2q.

BACKGROUND: Despite strong evidence for a genetic component to variation in high-density lipoprotein cholesterol levels (HDL-C), specific polymorphisms associated with normal variation in HDL-C have not been identified. It is known, however, that HDL-C levels are influenced in complex ways by factors related to age and sex. In this paper, we examined the evidence for age- and sex-specific linkage of HDL-C in a longitudinal sample of participants from the Framingham Heart Study. To determine if aging could influence our ability to detect linkage, we explored the evidence for linkage of HDL-C at three time points, t1, t2, and t3, spaced approximately 8 years apart and corresponding respectively to visits 11, 15, and 20 for the original cohort and 1, 2, and 4 for the offspring and spouses. Additionally, to examine the effects of sex on linkage at each time point, we estimated the heritability and genetic correlation of HDL-C, performed linkage analysis of HDL-C, tested for genotype-by-sex interaction at a QTL, and performed linkage analysis of HDL-C in males and females separately. RESULTS AND CONCLUSION: In women, we found evidence for a QTL on chromosome 2q influencing HDL-C variation. Although the QTL could be detected in the combined sample of males and females at the first time point, the linkage was not significant at subsequent time points.

Morphologic and functional characterization of Chagasic heart disease in non-human primates.

Chagasic heart disease has been documented in non-human primates, but noninvasive characterization of systolic and diastolic function has not been previously reported. Seventeen seropositive (12 females; mean age, 20) and 13 age- and gender-matched seronegative baboons underwent Doppler echocardiography. Systolic function indices included left ventricular (LV) fractional shortening (FS %), velocity of circumferential fiber shortening (VCF, circ/sec), LV mass index, and left and right ventricular ejection fractions (RVEF %). Diastolic function indices included transmitral E-wave, A-wave, E/A ratio, E-deceleration time, and isovolumic relaxation time. Twelve-lead electrocardiographic (ECG) recordings were obtained. There were no significant differences between groups for body size or blood pressure. Seropositive and seronegative groups revealed diffuse non-specific T wave changes precluding differentiation; however, tall "P" waves were seen in four seropositive and two seronegative baboons. Four of the 17 (24%) seropositive baboons had decreased FS (25 +/- 8% versus 40 +/- 5%, P < 0.005) and VCF (1.05 +/- 0.36 circ/sec versus 1.84 +/- 0.23 circ/sec, P < 0.0001), prolonged isovolumic relaxation time (71 +/- 16 msec versus 55 +/- 9 msec, P < 0.02), and reduced RVEF (44 +/- 9% versus 54 +/- 4%, P < 0.05), as compared with the other seropositive baboons. We conclude that chagasic heart disease is present in 24% of the naturally infected baboons in this study. ECG evidence of right atrial enlargement was more common in the seropositive animals. There were systolic and diastolic abnormalities of both ventricles. The LV systolic dysfunction may be segmental or diffuse.

Craniofacial trauma as a clinical marker of seizures in a baboon colony.

Baboons provide a natural model of epilepsy. However, spontaneous seizures are usually sporadic, brief, and may not be observed. We hypothesized that various types of craniofacial trauma (CFT) may serve as reliable markers for epilepsy. We evaluated the type, demographics, and clinical significance of CFT in a large baboon colony. CFT was categorized according to somatotopic location, propensity to recur, and association with witnessed seizures or abnormal EEG findings. We divided the baboons with CFT into 2 groups: those with known histories of seizures (CFT+Sz, n = 176) and those without seizure histories (CFTonly; n = 515). In CFT+Sz baboons, the 568 injuries identified included periorbital (57%), scalp (27%), muzzle (12%), and facial (4%) injuries; multiple somatotopic locations or body parts were affected in 21 baboons. The most common CFT injuries associated with seizures were periorbital and scalp lesions (43% for each region). Compared with those in CFTonly animals, EEG abnormalities, including interictal epileptic discharges (IED) and photosensitivity were more prevalent in the CFT+Sz group, particularly among baboons with periorbital or scalp injuries. Compared with CFT+Sz animals, CFTonly baboons tended to have later onset and less frequent recurrence of CFT but higher prevalence of muzzle and tooth injuries. IED and photosensitivity were less prevalent in the CFTonly than the CFT+Sz group, with periorbital injuries carrying the highest and muzzle injuries the lowest association with IED or photosensitivity in both groups. Therefore, CFT in general and periorbital injuries in particular may be markers for seizures in baboons.

Electroclinical phenotypes in a pedigreed baboon colony.

This is the first large-scale epidemiological study evaluating the prevalence of interictal epileptic discharges (IEDs) and photosensitivity (PS) recorded by scalp EEG in a natural nonhuman-primate model of photosensitive, generalized epilepsy. Scalp EEG was used to characterize electroclinical phenotypes in a large baboon pedigree housed at the Southwest National Primate Research Center at the Texas Biomedical Research Institute (Texas Biomed) based upon IEDs and photosensitivity. Scalp EEG studies including intermittent light stimulation (ILS) were performed in 671 baboons. Clinical histories were available for 531 (79%) of the animals. The EEG studies lasted 53 (±11) min, during which the baboons were lightly sedated with intramuscular ketamine doses of 5.6 (±0.8) mg. The animals were further classified according to electroclinical phenotypes recorded by scalp EEG: presence or absence of IEDs, seizures and photoparoxysmal or photoconvulsive responses. Effects of age, gender, and species on EEG phenotypes were compared using (Chi-square, two-sided, α<0.05). Sensitivity and specificity of IEDs and photosensitivity to detect a history of seizures was calculated. Generalized IEDs and photosensitivity were identified in 324 (49%) and 156 (23%) pedigreed baboons, respectively. Only photosensitivity was associated with gender, significantly increased in males. Otherwise, while IEDs were marginally more prevalent among males, there were no other significant associations of IEDs or photosensitivity with age or subspecies. Photosensitivity was significantly associated with IEDs, with demonstrating a possible association with gender and subspecies. Of 531 baboons with histories of clinical events, 91 (17%) had witnessed seizures and 269 (51%) were asymptomatic. IEDs demonstrated sensitivity and specificity of 62% and 57%, and photosensitivity of 40% and 83%, for prediction of seizures, respectively. While these EEG findings mirror the high prevalence of seizures in the colony, the sensitivity and specificity of scalp EEG may have been affected by ketamine's ability to lower the threshold for IEDs and seizures, particularly in animals predisposed to epilepsy. Photosensitivity provides a specific biological marker for epilepsy in future epidemiological, genetic, behavioral and histopathological studies.

A kernel of truth: statistical advances in polygenic variance component models for complex human pedigrees.

Statistical genetic analysis of quantitative traits in large pedigrees is a formidable computational task due to the necessity of taking the nonindependence among relatives into account. With the growing awareness that rare sequence variants may be important in human quantitative variation, heritability and association study designs involving large pedigrees will increase in frequency due to the greater chance of observing multiple copies of rare variants among related individuals. Therefore, it is important to have statistical genetic test procedures that utilize all available information for extracting evidence regarding genetic association. Optimal testing for marker/phenotype association involves the exact calculation of the likelihood ratio statistic which requires the repeated inversion of potentially large matrices. In a whole genome sequence association context, such computation may be prohibitive. Toward this end, we have developed a rapid and efficient eigen simplification of the likelihood that makes analysis of family data commensurate with the analysis of a comparable sample of unrelated individuals. Our theoretical results which are based on a spectral representation of the likelihood yield simple exact expressions for the expected likelihood ratio test statistic (ELRT) for pedigrees of arbitrary size and complexity. For heritability, the ELRT is where h2 and λgi are, respectively, the heritability and eigenvalues of the pedigree-derived genetic relationship kernel (GRK). For association analysis of sequence variants, the ELRT is given by where ht2, hq2, and hr2 are the total, quantitative trait nucleotide, and residual heritabilities, respectively. Using these results, fast and accurate analytical power analyses are possible, eliminating the need for computer simulation. Additional benefits of eigen simplification include a simple method for calculation of the exact distribution of the ELRT under the null hypothesis which turns out to differ from that expected under the usual asymptotic theory. Further, when combined with the use of empirical GRKs-estimated over a large number of genetic markers-our theory reveals potential problems associated with nonpositive semidefinite kernels. These procedures are being added to our general statistical genetic computer package, SOLAR.