Joseph T. Chang

Full reconstruction of Markov models on evolutionary trees: Identifiability and consistency

A Markov model of evolution of characters on a phylogenetic tree consists of a tree topology together with a specification of probability transition matrices on the edges of the tree. Previous work has shown that, under mild conditions, the tree topology may be reconstructed, in the sense that the topology is identifiable from knowledge of the joint distribution of character states at pairs of terminal nodes of the tree. Also, the method of maximum likelihood is statistically consistent for inferring the tree topology. In this article we answer the analogous questions for reconstructing the full model, including the edge transition matrices. Under mild conditions, such full reconstruction is achievable, not by using pairs of terminal nodes, but rather by using triples of terminal nodes. The identifiability result generalizes previous results that were restricted either to characters having two states or to transition matrices having special structure. The proof develops matrix relationships that may be exploited to identify the model. We also use the identifiability result to prove that the method of maximum likelihood is consistent for reconstructing the full model.

Genes Controlling Affiliative Behavior as Candidate Genes for Autism

BACKGROUND Autism spectrum disorders (ASD) are neurodevelopmental disorders of complex etiology, with a recognized substantial contribution of heterogeneous genetic factors; one of the core features of ASD is a lack of affiliative behaviors. METHODS On the basis of the existing literature, in this study we examined the hypothesis of allelic associations between genetic variants in six genes involved in control of maternal and affiliative behaviors (OXT, OXTR, PRL, PRLR, DbetaH, and FOSB). One hundred and seventy-seven probands with ASD from 151 families (n = 527) were assessed with a set of related instruments capturing multiple facets of ASD. Multivariate and univariate phenotypes were constructed from these assessments and subjected to genetic linkage and association analyses with PBAT and FBAT software. RESULTS The resulting pattern of findings, in general, confirmed the hypotheses of the significance of the genes involved in the development of affiliative behaviors in the manifestation of ASD (p values ranging from .000005 to .05); statistically speaking, the strongest results were obtained for allelic associations with the PRL, PRLR, and OXTR genes. CONCLUSIONS These preliminary data provide additional support for the hypothesis that the allelic variants of genes necessary for the development of species-typical affiliative behaviors are associated with ASD. Independent replication of these findings is needed and studies of other genes associated with affiliative behaviors are indicated.

Inconsistency of evolutionary tree topology reconstruction methods when substitution rates vary across characters.

A fundamental problem in reconstructing the evolutionary history of a set of species is to infer the topology of the evolutionary tree that relates those species. A statistical method for estimating such a topology from character data is called consistent if, given data from more and more characters, the method is sure to converge to the true topology. A number of popular methods are based on modeling the evolution of each character as a Markov process along the evolutionary tree. The standard models further assume that each character has in fact evolved according to the same Markov process. This homogeneity assumption is unrealistic; for example, different types of characters are known to experience substitutions at different rates. Certain distance and maximum likelihood methods for topology estimation have been shown to be consistent under the homogeneity assumption. Here we give examples showing that these methods can fail to be consistent when the homogeneity assumption is relaxed. The examples are very simple, requiring only four taxa, binary characters, and characters that evolve at two different rates.

Learning rate schedules for faster stochastic gradient search

The authors propose a new methodology for creating the first automatically adapting learning rates that achieve the optimal rate of convergence for stochastic gradient descent. Empirical tests agree with theoretical expectations that drift can be used to determine whether the crucial parameter c is large enough. Using this statistic, it will be possible to produce the first adaptive learning rates which converge at optimal speed.<<ETX>>

Macrophage migration inhibitory factor and autism spectrum disorders

OBJECTIVE. Autistic spectrum disorders are childhood neurodevelopmental disorders characterized by social and communicative impairment and repetitive and stereotypical behavior. Macrophage migration inhibitory factor (MIF) is an upstream regulator of innate immunity that promotes monocyte/macrophage-activation responses by increasing the expression of Toll-like receptors and inhibiting activation-induced apoptosis. On the basis of results of previous genetic linkage studies and reported altered innate immune response in autism spectrum disorder, we hypothesized that MIF could represent a candidate gene for autism spectrum disorder or its diagnostic components. METHODS. Genetic association between autism spectrum disorder and MIF was investigated in 2 independent sets of families of probands with autism spectrum disorder, from the United States (527 participants from 152 families) and Holland (532 participants from 183 families). Probands and their siblings, when available, were evaluated with clinical instruments used for autism spectrum disorder diagnoses. Genotyping was performed for 2 polymorphisms in the promoter region of the MIF gene in both samples sequentially. In addition, MIF plasma analyses were conducted in a subset of Dutch patients from whom plasma was available. RESULTS. There were genetic associations between known functional polymorphisms in the promoter for MIF and autism spectrum disorder–related behaviors. Also, probands with autism spectrum disorder exhibited higher circulating MIF levels than did their unaffected siblings, and plasma MIF concentrations correlated with the severity of multiple autism spectrum disorder symptoms. CONCLUSIONS. These results identify MIF as a possible susceptibility gene for autism spectrum disorder. Additional research is warranted on the precise relationship between MIF and the behavioral components of autism spectrum disorder, the mechanism by which MIF contributes to autism spectrum disorder pathogenesis, and the clinical use of MIF genotyping.

Modelling the recent common ancestry of all living humans

If a common ancestor of all living humans is defined as an individual who is a genealogical ancestor of all present-day people, the most recent common ancestor (MRCA) for a randomly mating population would have lived in the very recent past. However, the random mating model ignores essential aspects of population substructure, such as the tendency of individuals to choose mates from the same social group, and the relative isolation of geographically separated groups. Here we show that recent common ancestors also emerge from two models incorporating substantial population substructure. One model, designed for simplicity and theoretical insight, yields explicit mathematical results through a probabilistic analysis. A more elaborate second model, designed to capture historical population dynamics in a more realistic way, is analysed computationally through Monte Carlo simulations. These analyses suggest that the genealogies of all living humans overlap in remarkable ways in the recent past. In particular, the MRCA of all present-day humans lived just a few thousand years ago in these models. Moreover, among all individuals living more than just a few thousand years earlier than the MRCA, each present-day human has exactly the same set of genealogical ancestors.

Modeling ChIP Sequencing In Silico with Applications

ChIP sequencing (ChIP-seq) is a new method for genomewide mapping of protein binding sites on DNA. It has generated much excitement in functional genomics. To score data and determine adequate sequencing depth, both the genomic background and the binding sites must be properly modeled. To develop a computational foundation to tackle these issues, we first performed a study to characterize the observed statistical nature of this new type of high-throughput data. By linking sequence tags into clusters, we show that there are two components to the distribution of tag counts observed in a number of recent experiments: an initial power-law distribution and a subsequent long right tail. Then we develop in silico ChIP-seq, a computational method to simulate the experimental outcome by placing tags onto the genome according to particular assumed distributions for the actual binding sites and for the background genomic sequence. In contrast to current assumptions, our results show that both the background and the binding sites need to have a markedly nonuniform distribution in order to correctly model the observed ChIP-seq data, with, for instance, the background tag counts modeled by a gamma distribution. On the basis of these results, we extend an existing scoring approach by using a more realistic genomic-background model. This enables us to identify transcription-factor binding sites in ChIP-seq data in a statistically rigorous fashion.

Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon‐Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information. One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.

Early Generalized Overgrowth in Boys With Autism

CONTEXT Multiple studies have reported an overgrowth in head circumference (HC) in the first year of life in autism. However, it is unclear whether this phenomenon is independent of overall body growth and whether it is associated with specific social or cognitive features. OBJECTIVES To examine the trajectory of early HC growth in autism compared with control groups; to assess whether HC growth in autism is independent of height and weight growth during infancy; and to examine HC growth from birth to 24 months in relationship to social, verbal, cognitive, and adaptive functioning levels. DESIGN Retrospective study. SETTING A specialized university-based clinic. PARTICIPANTS Boys diagnosed as having autistic disorder (n = 64), pervasive developmental disorder-not otherwise specified (n = 34), global developmental delay (n = 13), and other developmental problems (n = 18) and typically developing boys (n = 55). MAIN OUTCOME MEASURES Age-related changes in HC, height, and weight between birth and age 24 months; measures of social, verbal, and cognitive functioning at age 2 years. RESULTS Compared with typically developing controls, boys with autism were significantly longer by age 4.8 months, had a larger HC by age 9.5 months, and weighed more by age 11.4 months (P = .05 for all). None of the other clinical groups showed a similar overgrowth pattern. Boys with autism who were in the top 10% of overall physical size in infancy exhibited greater severity of social deficits (P = .009) and lower adaptive functioning (P = .03). CONCLUSIONS Boys with autism experienced accelerated HC growth in the first year of life. However, this phenomenon reflected a generalized process affecting other morphologic features, including height and weight. The study highlights the importance of studying factors that influence not only neuronal development but also skeletal growth in autism.

cDNA microarray analysis of invasive and tumorigenic phenotypes in a breast cancer model

The fms oncogene encodes the macrophage colony-stimulating factor receptor (CSF1R), a transmembrane tyrosine kinase receptor, which is abnormally expressed in breast cancer. Transfection of wild-type CSF1R into HC11 mammary epithelial cells (HC11-CSF1R) renders the transfectants capable of in vitro local invasion and in vivo tumorigenesis. Transfection with CSF1R mutated to express phe at the tyr-721 autophosphorylation site (HC11-CSF1R-721) creates a phenotype that lacks metastastic competence but maintains local invasiveness. Conversely, HC11 cells transfected with CSF1R mutated at tyr-807 (HC11-CSF1R-807) retain their metastatic competence, but are not locally invasive. Our aims were to determine which genes were differentially expressed with transfection of HC11 with wild-type CSF1R, and to determine the effect of mutation at the autophosphorylation sites on gene expression, using 4.6 K cDNA microarrays. Complementary DNA from HC11, HC11-CSF1R-721 and HC11-CSF1R-807 were each hybridized together with HC11-CSF1R on individual arrays. A principal component spectral method combined with prenormalization procedures was used for sample clustering. Differentially expressed genes were identified by the analysis of variance. Confirmation by Northern blotting was performed for MAP kinase phosphatase-1, WDNM1 (extracellular proteinase inhibitor), Trop 2 (tumor-associated calcium signal transducer-2), procollagen type IV alpha, secretory leukoprotease inhibitor, prenylated snare protein Ykt6, ceruloplasmin and chaperonin 10. Many of these genes have not previously been associated with tumor invasion and metastasis. We have successfully identified genes that can be linked to the invasive phenotypes or to tumorigenesis. These genes provide a basis for further studies of metastatic progression and local invasiveness, and can be evaluated as therapeutic targets.