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Regulatory relationships between transcription factors (TFs) and their target genes lie at the heart of cellular identity and function; however, uncovering these relationships is often labor-intensive and requires perturbations. Here, we propose a principled framework to systematically infer gene regulation for all TFs simultaneously in cells at steady state by leveraging the intrinsic variation in the transcriptional abundance across single cells. Through modeling and simulations, we characterize how transcriptional bursts of a TF gene are propagated to its target genes, including the expected ranges of time delay and magnitude of maximum covariation. We distinguish these temporal trends from the time-invariant covariation arising from cell states, and we delineate the experimental and technical requirements for leveraging these small but meaningful cofluctuations in the presence of measurement noise. While current technology does not yet allow adequate power for definitively detecting regulatory relationships for all TFs simultaneously in cells at steady state, we investigate a small-scale dataset to inform future experimental design. This study supports the potential value of mapping regulatory connections through stochastic variation, and it motivates further technological development to achieve its full potential.

Single-cell quantification of RNAs is important for understanding cellular heterogeneity and gene regulation, yet current approaches suffer from low sensitivity for individual transcripts, limiting their utility for many applications. Here we present Hybridization of Probes to RNA for sequencing (HyPR-seq), a method to sensitively quantify the expression of hundreds of chosen genes in single cells. HyPR-seq involves hybridizing DNA probes to RNA, distributing cells into nanoliter droplets, amplifying the probes with PCR, and sequencing the amplicons to quantify the expression of chosen genes. HyPR-seq achieves high sensitivity for individual transcripts, detects nonpolyadenylated and low-abundance transcripts, and can profile more than 100,000 single cells. We demonstrate how HyPR-seq can profile the effects of CRISPR perturbations in pooled screens, detect time-resolved changes in gene expression via measurements of gene introns, and detect rare transcripts and quantify cell-type frequencies in tissue using low-abundance marker genes. By directing sequencing power to genes of interest and sensitively quantifying individual transcripts, HyPR-seq reduces costs by up to 100-fold compared to whole-transcriptome single-cell RNA-sequencing, making HyPR-seq a powerful method for targeted RNA profiling in single cells.

Human genetics has been haunted by the mystery of “missing heritability” of common traits. Although studies have discovered >1,200 variants associated with common diseases and traits, these variants typically appear to explain only a minority of the heritability. The proportion of heritability explained by a set of variants is the ratio of ( i ) the heritability due to these variants (numerator), estimated directly from their observed effects, to ( ii ) the total heritability (denominator), inferred indirectly from population data. The prevailing view has been that the explanation for missing heritability lies in the numerator—that is, in as-yet undiscovered variants. While many variants surely remain to be found, we show here that a substantial portion of missing heritability could arise from overestimation of the denominator, creating “phantom heritability.” Specifically, ( i ) estimates of total heritability implicitly assume the trait involves no genetic interactions (epistasis) among loci; ( ii ) this assumption is not justified, because models with interactions are also consistent with observable data; and ( iii ) under such models, the total heritability may be much smaller and thus the proportion of heritability explained much larger. For example, 80% of the currently missing heritability for Crohn's disease could be due to genetic interactions, if the disease involves interaction among three pathways. In short, missing heritability need not directly correspond to missing variants, because current estimates of total heritability may be significantly inflated by genetic interactions. Finally, we describe a method for estimating heritability from isolated populations that is not inflated by genetic interactions.

We recently used in situ Hi-C to create kilobase-resolution 3D maps of mammalian genomes. Here, we combine these maps with new Hi-C, microscopy, and genome-editing experiments to study the physical structure of chromatin fibers, domains, and loops. We find that the observed contact domains are inconsistent with the equilibrium state for an ordinary condensed polymer. Combining Hi-C data and novel mathematical theorems, we show that contact domains are also not consistent with a fractal globule. Instead, we use physical simulations to study two models of genome folding. In one, intermonomer attraction during polymer condensation leads to formation of an anisotropic "tension globule." In the other, CCCTC-binding factor (CTCF) and cohesin act together to extrude unknotted loops during interphase. Both models are consistent with the observed contact domains and with the observation that contact domains tend to form inside loops. However, the extrusion model explains a far wider array of observations, such as why loops tend not to overlap and why the CTCF-binding motifs at pairs of loop anchors lie in the convergent orientation. Finally, we perform 13 genome-editing experiments examining the effect of altering CTCF-binding sites on chromatin folding. The convergent rule correctly predicts the affected loops in every case. Moreover, the extrusion model accurately predicts in silico the 3D maps resulting from each experiment using only the location of CTCF-binding sites in the WT. Thus, we show that it is possible to disrupt, restore, and move loops and domains using targeted mutations as small as a single base pair.

The epithelial-to-mesenchymal transition (EMT) produces cancer cells that are invasive, migratory, and exhibit stem cell characteristics, hallmarks of cells that have the potential to generate metastases. Inducers of the EMT include several transcription factors (TFs), such as Goosecoid, Snail, and Twist, as well as the secreted TGF-β1. Each of these factors is capable, on its own, of inducing an EMT in the human mammary epithelial (HMLE) cell line. However, the interactions between these regulators are poorly understood. Overexpression of each of the above EMT inducers up-regulates a subset of other EMT-inducing TFs, with Twist, Zeb1, Zeb2, TGF-β1, and FOXC2 being commonly induced. Up-regulation of Slug and FOXC2 by either Snail or Twist does not depend on TGF-β1 signaling. Gene expression signatures (GESs) derived by overexpressing EMT-inducing TFs reveal that the Twist GES and Snail GES are the most similar, although the Goosecoid GES is the least similar to the others. An EMT core signature was derived from the changes in gene expression shared by up-regulation of Gsc, Snail, Twist, and TGF-β1 and by down-regulation of E-cadherin, loss of which can also trigger an EMT in certain cell types. The EMT core signature associates closely with the claudin-low and metaplastic breast cancer subtypes and correlates negatively with pathological complete response. Additionally, the expression level of FOXC1, another EMT inducer, correlates strongly with poor survival of breast cancer patients.

We recently showed that the mammalian genome encodes1,000 large intergenic noncoding (linc)RNAs that are clearly conserved across mammals and, thus, functional. Gene expression patterns have implicated these lincRNAs in diverse biological processes, including cell-cycle regulation, immune surveillance, and embryonic stem cell pluripotency. However, the mechanism by which these lincRNAs function is unknown. Here, we expand the catalog of human lincRNAs to approximately 3,300 by analyzing chromatin-state maps of various human cell types. Inspired by the observation that the well-characterized lincRNA HOTAIR binds the polycomb repressive complex (PRC)2, we tested whether many lincRNAs are physically associated with PRC2. Remarkably, we observe that approximately 20% of lincRNAs expressed in various cell types are bound by PRC2, and that additional lincRNAs are bound by other chromatin-modifying complexes. Also, we show that siRNA-mediated depletion of certain lincRNAs associated with PRC2 leads to changes in gene expression, and that the up-regulated genes are enriched for those normally silenced by PRC2. We propose a model in which some lincRNAs guide chromatin-modifying complexes to specific genomic loci to regulate gene expression.

Comprehensive knowledge of the genomic alterations that underlie cancer is a critical foundation for diagnostics, prognostics, and targeted therapeutics. Systematic efforts to analyze cancer genomes are underway, but the analysis is hampered by the lack of a statistical framework to distinguish meaningful events from random background aberrations. Here we describe a systematic method, called Genomic Identification of Significant Targets in Cancer (GISTIC), designed for analyzing chromosomal aberrations in cancer. We use it to study chromosomal aberrations in 141 gliomas and compare the results with two prior studies. Traditional methods highlight hundreds of altered regions with little concordance between studies. The new approach reveals a highly concordant picture involving ≈35 significant events, including 16–18 broad events near chromosome-arm size and 16–21 focal events. Approximately half of these events correspond to known cancer-related genes, only some of which have been previously tied to glioma. We also show that superimposed broad and focal events may have different biological consequences. Specifically, gliomas with broad amplification of chromosome 7 have properties different from those with overlapping focal EGFR amplification: the broad events act in part through effects on MET and its ligand HGF and correlate with MET dependence in vitro . Our results support the feasibility and utility of systematic characterization of the cancer genome.

Conserved noncoding elements (CNEs) constitute the majority of sequences under purifying selection in the human genome, yet their function remains largely unknown. Experimental evidence suggests that many of these elements play regulatory roles, but little is known about regulatory motifs contained within them. Here we describe a systematic approach to discover and characterize regulatory motifs within mammalian CNEs by searching for long motifs (12–22 nt) with significant enrichment in CNEs and studying their biochemical and genomic properties. Our analysis identifies 233 long motifs (LMs), matching a total of ≈60,000 conserved instances across the human genome. These motifs include 16 previously known regulatory elements, such as the histone 3′-UTR motif and the neuron-restrictive silencer element, as well as striking examples of novel functional elements. The most highly enriched motif (LM1) corresponds to the X-box motif known from yeast and nematode. We show that it is bound by the RFX1 protein and identify thousands of conserved motif instances, suggesting a broad role for the RFX family in gene regulation. A second group of motifs (LM2*) does not match any previously known motif. We demonstrate by biochemical and computational methods that it defines a binding site for the CTCF protein, which is involved in insulator function to limit the spread of gene activation. We identify nearly 15,000 conserved sites that likely serve as insulators, and we show that nearby genes separated by predicted CTCF sites show markedly reduced correlation in gene expression. These sites may thus partition the human genome into domains of expression.

Large-scale tumor sequencing projects enabled the identification of many new cancer gene candidates through computational approaches. Here, we describe a general method to detect cancer genes based on significant 3D clustering of mutations relative to the structure of the encoded protein products. The approach can also be used to search for proteins with an enrichment of mutations at binding interfaces with a protein, nucleic acid, or small molecule partner. We applied this approach to systematically analyze the PanCancer compendium of somatic mutations from 4,742 tumors relative to all known 3D structures of human proteins in the Protein Data Bank. We detected significant 3D clustering of missense mutations in several previously known oncoproteins including HRAS, EGFR, and PIK3CA. Although clustering of missense mutations is often regarded as a hallmark of oncoproteins, we observed that a number of tumor suppressors, including FBXW7, VHL, and STK11, also showed such clustering. Beside these known cases, we also identified significant 3D clustering of missense mutations in NUF2, which encodes a component of the kinetochore, that could affect chromosome segregation and lead to aneuploidy. Analysis of interaction interfaces revealed enrichment of mutations in the interfaces between FBXW7-CCNE1, HRAS-RASA1, CUL4B-CAND1, OGT-HCFC1, PPP2R1A-PPP2R5C/PPP2R2A, DICER1-Mg2+, MAX-DNA, SRSF2-RNA, and others. Together, our results indicate that systematic consideration of 3D structure can assist in the identification of cancer genes and in the understanding of the functional role of their mutations.

The evolutionary origin of the conserved noncoding elements (CNEs) in the human genome remains poorly understood but may hold important clues to their biological functions. Here, we report the discovery of a CNE family with approximately 124 instances in the human genome that demonstrates a clear signature of having been derived from an ancient transposon. The CNE family is also present in the chicken genome, although typically not at orthologous locations. The CNE family is closely related to the active transposon SINE3 in zebrafish and also to a previously uncharacterized transposon in the coelacanth, the so-called "living fossil" belonging to the lobe-finned fish lineage. The mammal, bird, zebrafish, and coelacanth families all share a highly similar core element of approximately 180 bp but have important differences in their 5' and 3' ends. The core element has thus been preserved over 450 million years of evolution, implying an important biological function. In addition, we identify 95 additional CNE families that likely predate the mammalian radiation. The results highlight both the creative role of transposons and the importance of CNE families.

Genome-wide association studies (GWASs), also called common variant association studies (CVASs), have uncovered thousands of genetic variants associated with hundreds of diseases. However, the variants that reach statistical significance typically explain only a small fraction of the heritability. One explanation for the “missing heritability” is that there are many additional disease-associated common variants whose effects are too small to detect with current sample sizes. It therefore is useful to have methods to quantify the heritability due to common variation, without having to identify all causal variants. Recent studies applied restricted maximum likelihood (REML) estimation to case–control studies for diseases. Here, we show that REML considerably underestimates the fraction of heritability due to common variation in this setting. The degree of underestimation increases with the rarity of disease, the heritability of the disease, and the size of the sample. Instead, we develop a general framework for heritability estimation, called phenotype correlation–genotype correlation (PCGC) regression, which generalizes the well-known Haseman–Elston regression method. We show that PCGC regression yields unbiased estimates. Applying PCGC regression to six diseases, we estimate the proportion of the phenotypic variance due to common variants to range from 25% to 56% and the proportion of heritability due to common variants from 41% to 68% (mean 60%). These results suggest that common variants may explain at least half the heritability for many diseases. PCGC regression also is readily applicable to other settings, including analyzing extreme-phenotype studies and adjusting for covariates such as sex, age, and population structure.

Identifying the genes responsible for human diseases requires combining information about gene position with clues about biological function. The recent availability of whole-genome data sets of RNA and protein expression provides powerful new sources of functional insight. Here we illustrate how such data sets can expedite disease-gene discovery, by using them to identify the gene causing Leigh syndrome, French-Canadian type (LSFC, Online Mendelian Inheritance in Man no. 220111), a human cytochrome c oxidase deficiency that maps to chromosome 2p16-21. Using four public RNA expression data sets, we assigned to all human genes a “score” reflecting their similarity in RNA-expression profiles to known mitochondrial genes. Using a large survey of organellar proteomics, we similarly classified human genes according to the likelihood of their protein product being associated with the mitochondrion. By intersecting this information with the relevant genomic region, we identified a single clear candidate gene, LRPPRC . Resequencing identified two mutations on two independent haplotypes, providing definitive genetic proof that LRPPRC indeed causes LSFC. LRPPRC encodes an mRNA-binding protein likely involved with mtDNA transcript processing, suggesting an additional mechanism of mitochondrial pathophysiology. Similar strategies to integrate diverse genomic information can be applied likewise to other disease pathways and will become increasingly powerful with the growing wealth of diverse, functional genomics data.

We describe a strategy to obtain highly enriched long-term repopulating (LTR) hematopoietic stem cells (HSCs) from bone marrow side-population (SP) cells by using a transgenic reporter gene driven by a stem cell enhancer. To analyze the gene-expression profile of the rare HSC population, we developed an amplification protocol termed “constant-ratio PCR,” in which sample and control cDNAs are amplified in the same PCR. This protocol allowed us to identify genes differentially expressed in the enriched LTR-HSC population by oligonucleotide microarray analysis using as little as 1 ng of total RNA. Endoglin, an ancillary transforming growth factor β receptor, was differentially expressed by the enriched HSCs. Importantly, endoglin-positive cells, which account for 20% of total SP cells, contain all the LTR-HSC activity within bone marrow SP. Our results demonstrate that endoglin, which plays important roles in angiogenesis and hematopoiesis, is a functional marker that defines LTR HSCs. Our overall strategy may be applicable for the identification of markers for other tissue-specific stem cells.

To assess the extent of abnormal gene expression in clones, we assessed global gene expression by microarray analysis on RNA from the placentas and livers of neonatal cloned mice derived by nuclear transfer (NT) from both cultured embryonic stem cells and freshly isolated cumulus cells. Direct comparison of gene expression profiles of more than 10,000 genes showed that for both donor cell types ≈4% of the expressed genes in the NT placentas differed dramatically in expression levels from those in controls and that the majority of abnormally expressed genes were common to both types of clones. Importantly, however, the expression of a smaller set of genes differed between the embryonic stem cell- and cumulus cell-derived clones. The livers of the cloned mice also showed abnormal gene expression, although to a lesser extent, and with a different set of affected genes, than seen in the placentas. Our results demonstrate frequent abnormal gene expression in clones, in which most expression abnormalities appear common to the NT procedure whereas others appear to reflect the particular donor nucleus.

The optimal treatment of patients with cancer depends on establishing accurate diagnoses by using a complex combination of clinical and histopathological data. In some instances, this task is difficult or impossible because of atypical clinical presentation or histopathology. To determine whether the diagnosis of multiple common adult malignancies could be achieved purely by molecular classification, we subjected 218 tumor samples, spanning 14 common tumor types, and 90 normal tissue samples to oligonucleotide microarray gene expression analysis. The expression levels of 16,063 genes and expressed sequence tags were used to evaluate the accuracy of a multiclass classifier based on a support vector machine algorithm. Overall classification accuracy was 78%, far exceeding the accuracy of random classification (9%). Poorly differentiated cancers resulted in low-confidence predictions and could not be accurately classified according to their tissue of origin, indicating that they are molecularly distinct entities with dramatically different gene expression patterns compared with their well differentiated counterparts. Taken together, these results demonstrate the feasibility of accurate, multiclass molecular cancer classification and suggest a strategy for future clinical implementation of molecular cancer diagnostics.

We have generated a molecular taxonomy of lung carcinoma, the leading cause of cancer death in the United States and worldwide. Using oligonucleotide microarrays, we analyzed mRNA expression levels corresponding to 12,600 transcript sequences in 186 lung tumor samples, including 139 adenocarcinomas resected from the lung. Hierarchical and probabilistic clustering of expression data defined distinct subclasses of lung adenocarcinoma. Among these were tumors with high relative expression of neuroendocrine genes and of type II pneumocyte genes, respectively. Retrospective analysis revealed a less favorable outcome for the adenocarcinomas with neuroendocrine gene expression. The diagnostic potential of expression profiling is emphasized by its ability to discriminate primary lung adenocarcinomas from metastases of extra-pulmonary origin. These results suggest that integration of expression profile data with clinical parameters could aid in diagnosis of lung cancer patients.

In an effort to develop a genomics-based approach to the prediction of drug response, we have developed an algorithm for classification of cell line chemosensitivity based on gene expression profiles alone. Using oligonucleotide microarrays, the expression levels of 6,817 genes were measured in a panel of 60 human cancer cell lines (the NCI-60) for which the chemosensitivity profiles of thousands of chemical compounds have been determined. We sought to determine whether the gene expression signatures of untreated cells were sufficient for the prediction of chemosensitivity. Gene expression-based classifiers of sensitivity or resistance for 232 compounds were generated and then evaluated on independent sets of data. The classifiers were designed to be independent of the cells' tissue of origin. The accuracy of chemosensitivity prediction was considerably better than would be expected by chance. Eighty-eight of 232 expression-based classifiers performed accurately (with P < 0.05) on an independent test set, whereas only 12 of the 232 would be expected to do so by chance. These results suggest that at least for a subset of compounds genomic approaches to chemosensitivity prediction are feasible.

Although nonsteroidal antiinflammatory drugs (NSAIDs) show great promise as therapies for colon cancer, a dispute remains regarding their mechanism of action. NSAIDs are known to inhibit cyclooxygenase (COX) enzymes, which convert arachidonic acid (AA) to prostaglandins (PGs). Therefore, NSAIDs may suppress tumorigenesis by inhibiting PG synthesis. However, various experimental studies have suggested the possibility of PG-independent mechanisms. Notably, disruption of the mouse group IIA secretory phospholipase A 2 locus ( Pla2g2a ), a potential source of AA for COX-2, increases tumor number despite the fact that the mutation has been predicted to decrease PG production. Some authors have attempted to reconcile the results by suggesting that the level of the precursor (AA), not the products (PGs), is the critical factor. To clarify the role of AA in tumorigenesis, we have examined the effect of deleting the group IV cytosolic phospholipase A 2 (cPLA 2 ) locus (Pla2g4). We report that Apc Min/+ , cPLA 2 −/− mice show an 83% reduction in tumor number in the small intestine compared with littermates with genotypes Apc Min/+ , cPLA 2 +/− and Apc Min/+ , cPLA 2 +/+ . This tumor phenotype parallels that of COX-2 knockout mice, suggesting that cPLA 2 is the predominant source of AA for COX-2 in the intestine. The protective effect of cPLA 2 deletion is thus most likely attributed to a decrease in the AA supply to COX-2 and a resultant decrease in PG synthesis. The tumorigenic effect of sPLA 2 mutations is likely to be through a completely different pathway.

Generating human single-nucleotide polymorphisms (SNPs) is no longer a rate-limiting step for genetic studies of disease. The number of SNPs in public databases already exceeds 200,000, and the total is expected to exceed 1,000,000 within a year. Rather, progress is limited by the inability to genotype large numbers of SNPs. Current genotyping methods are suitable for studying individual loci or at most a handful at a time. Here, we describe a method for parallel genotyping of SNPs, called single base extension–tag array on glass slides, SBE-TAGS. The principle is as follows. SNPs are genotyped by single base extension (SBE), using bifunctional primers carrying a unique sequence tag in addition to a locus-specific sequence. Because each locus has a distinct tag, the genotyping reactions can be performed in a highly multiplexed fashion, and the resulting product can then be “demultiplexed” by hybridization to the reverse complements of the sequence tags arrayed on a glass slide. SBE-TAGS is simple and inexpensive because of the high degree of multiplexing and the use of an easily generated, generic tag array. The method is also highly accurate: we genotyped over 100 SNPs, obtaining over 5,000 genotypes, with approximately 99% accuracy.

Hybrid mice carrying oncogenic transgenes afford powerful systems for investigating loss of heterozygosity (LOH) in tumors. Here, we apply this approach to a neoplasm of key importance in human medicine: mammary carcinoma. We performed a whole genome search for LOH using the mouse mammary tumor virus/v-Ha- ras mammary carcinoma model in female (FVB/N × Mus musculus castaneus )F 1 mice. Mammary tumors developed as expected, as well as a few tumors of a second type (uterine leiomyosarcoma) not previously associated with this transgene. Genotyping of 94 anatomically independent tumors revealed high-frequency LOH (≈38%) for markers on chromosome 4. A marked allelic bias was observed, with M. musculus castaneus alleles almost exclusively being lost. No evidence of genomic imprinting effects was noted. These data point to the presence of a tumor suppressor gene(s) on mouse chromosome 4 involved in mammary carcinogenesis induced by mutant H- ras expression, and for which a significant functional difference may exist between the M. musculus castaneus and FVB/N alleles. Provisional subchromosomal localization of this gene, designated Loh-3 , can be made to a distal segment having syntenic correspondence to human chromosome 1p; LOH in this latter region is observed in several human malignancies, including breast cancers. Evidence was also obtained for a possible second locus associated with LOH with less marked allele bias on proximal chromosome 4.

A genome-wide scan for loss of heterozygosity (LOH) in tumors provides a powerful route to the identification of genes involved in tumorigenesis. This approach has not previously been applied to transgenic mice, despite the considerable advantages they afford for genetic dissection. Here, we report a genome-wide LOH analysis of insulinomas and carcinoid tumors in transgenic mice expressing the simian virus 40 large tumor oncogene. Although the overall genome-wide rate of LOH was quite low, chromosomes 9 and 16 showed high rates of allelic loss. About one-third of tumors showed partial LOH, allowing localization of the likely tumor suppressor genes to intervals of approximately 11 centimorgans. The locus on chromosome 9, named Loh-1, lies in a region with synteny conservation to human chromosomes 3q, 6q12, 15q24, and 3p21, while the locus on chromosome 16, named Loh-2, lies in a region corresponding to human chromosomes 3q and 22q. Of particular note is the synteny conservation with human 3p21, which shows frequent loss in human cancers. These regions do not encode two tumor suppressors, pRB and p53, known to interact with large tumor oncoprotein, suggesting the presence of new genes whose loss of function contributes to multistage tumorigenesis.

Human genetic linkage maps are most accurately constructed by using information from many loci simultaneously. Traditional methods for such multilocus linkage analysis are computationally prohibitive in general, even with supercomputers. The problem has acquired practical importance because of the current international collaboration aimed at constructing a complete human linkage map of DNA markers through the study of three-generation pedigrees. We describe here several alternative algorithms for constructing human linkage maps given a specified gene order. One method allows maximum-likelihood multilocus linkage maps for dozens of DNA markers in such three-generation pedigrees to be constructed in minutes.

High-density genetic maps of individual human chromosomes will permit accurate localization of disease-associated genes and provide signposts that will be useful in the construction of physical maps. We have constructed a genetic map of chromosome 7 with 63 polymorphic DNA markers by using segregation data from 23 three-generation families and recently developed multilocus linkage-analysis techniques. The map spans 250 centimorgans in females and 170 centimorgans in males, with much of the difference being concentrated in a few intervals. The density and informativeness of the markers are such that there is a high probability of detecting linkage to any disease gene on this chromosome for which 20 phase-known meioses are available.

Simple single-gene disorders in humans can be genetically mapped by using traditional methods of linkage analysis and increasingly abundant restriction fragment length polymorphisms (RFLPs). Many human diseases and traits, however, can be expected to be genetically heterogeneous (i.e., caused by any one of several genes), and traditional linkage analysis is much less effective in such circumstances. We present two methods, interval mapping and simultaneous search, designed to exploit the full power of a linkage map of the DNA markers. For the simplest situations, only 1/3 as many affected families are needed to map a heterogeneous trait by using these methods. Only 1/5-1/50 as many are needed to detect that genetic heterogeneity is present.