Efficient maximum likelihood pedigree reconstruction

A simple and efficient algorithm is presented for finding a maximum likelihood pedigree using microsatellite (STR) genotype information on a complete sample of related individuals. The computational complexity of the algorithm is at worst (O(n³2ⁿ)), where n is the number of individuals. Thus it is possible to exhaustively search the space of all pedigrees of up to thirty individuals for one that maximizes the likelihood. A priori age and sex information can be used if available, but is not essential. The algorithm is applied in a simulation study, and to some real data on humans.     

Numerical comparison between powers of maximum likelihood and analysis of variance methods for QTL detection in progeny test designs: the case of monogenic inheritance

Simulations are used to compare four statistics for the detection of a quantitative trait locus (QTL) in daughter and grand-daughter designs as defined by Soller and Genizi (1978) and Weller et al. (1990): (1) the Fisher test of a linear model including a marker effect within sire or grand-sire effect; (2) the likelihood ratio test of a segregation analysis without the information given by the marker; (3) the likelihood ratio test of a segregation analysis considering the information from the marker; and (4) the lod score which is the likelihood ratio test of absence of linkage between the marker and the QTL. In all cases the two segregation analyses are more powerful for QTL detection than are either the linear method or the lod score. The differences in power are generally limited but may be significant (in a ratio of 1 to 3 or 4) when the QTL has a small effect (0.2 standard deviations) and is not closely linked to the marker (recombination rate of 20% or more).     

Comparison of Bayesian and maximum likelihood bootstrap measures of phylogenetic reliability

Owing to the exponential growth of genome databases, phylogenetic trees are now widely used to test a variety of evolutionary hypotheses. Nevertheless, computation time burden limits the application of methods such as maximum likelihood nonparametric bootstrap to assess reliability of evolutionary trees. As an alternative, the much faster Bayesian inference of phylogeny, which expresses branch support as posterior probabilities, has been introduced. However, marked discrepancies exist between nonparametric bootstrap proportions and Bayesian posterior probabilities, leading to difficulties in the interpretation of sometimes strongly conflicting results. As an attempt to reconcile these two indices of node reliability, we apply the nonparametric bootstrap resampling procedure to the Bayesian approach. The correlation between posterior probabilities, bootstrap maximum likelihood percentages, and bootstrapped posterior probabilities was studied for eight highly diverse empirical data sets and were also investigated using experimental simulation. Our results show that the relation between posterior probabilities and bootstrapped maximum likelihood percentages is highly variable but that very strong correlations always exist when Bayesian node support is estimated on bootstrapped character matrices. Moreover, simulations corroborate empirical observations in suggesting that, being more conservative, the bootstrap approach might be less prone to strongly supporting a false phylogenetic hypothesis. Thus, apparent conflicts in topology recovered by the Bayesian approach were reduced after bootstrapping. Both posterior probabilities and bootstrap supports are of great interest to phylogeny as potential upper and lower bounds of node reliability, but they are surely not interchangeable and cannot be directly compared.     

Property and efficiency of the maximum likelihood method for molecular phylogeny

Summary The maximum likelihood (ML) method for constructing phylogenetic trees (both rooted and unrooted trees) from DNA sequence data was studied. Although there is some theoretical problem in the comparison of ML values conditional for each topology, it is possible to make a heuristic argument to justify the method. Based on this argument, a new algorithm for estimating the ML tree is presented. It is shown that under the assumption of a constant rate of evolution, the ML method and UPGMA always give the same rooted tree for the case of three operational taxonomic units (OTUs). This also seems to hold approximately for the case with four OTUs. When we consider unrooted trees with the assumption of a varying rate of nucleotide substitution, the efficiency of the ML method in obtaining the correct tree is similar to those of the maximum parsimony method and distance methods. The ML method was applied to Brown et al.'s data, and the tree topology obtained was the same as that found by the maximum parsimony method, but it was different from those obtained by distance methods.     

Group coancestry-controlled selection in a Pinus sylvestris L. breeding program

 Integer Linear Programming was used to maximize genetic gain from selection at a given level of relatedness. Variances and breeding values for total height were available for 296 plus-trees of Pinus sylvestris which had been evaluated by open-pollinated progeny testing at a single test site in northern Sweden. Second-generation breeding and selection scenarios for this breeding population were evaluated using simulated data derived deterministically from normal distributions of estimated breeding values of progeny around mid-parent family means. The study considered two mating designs, assortative and non-assortative single-pair mating, and two selection criteria, individual phenotype and performance of half-sib progeny. Relatedness (group coancestry) was restricted to a level equivalent to that given by within-family selection of 2 trees per family from each of 25 families (the current standard in Sweden). Selection that allows the best-performing families to contribute a greater number of progeny was superior, both when the breeding population size was limited to 50 individuals and when it was allowed to be larger. The selected set giving the greatest average breeding value under restricted group coancestry included the best individual from families that would have been rejected under application of standard within-family selection. We made a comparison of the present value on retrieved gain between phenotypic selection and evaluation by progeny testing. Received: 24 November 1998 / Accepted: 14 December 1998     

A systems biology approach to genetic studies of complex diseases

Revealing mechanisms underlying complex diseases poses great challenges to biologists. The traditional linkage and linkage disequilibrium analysis that have been successful in the identification of genes responsible for Mendelian traits, however, have not led to similar success in discovering genes influencing the development of complex diseases. Emerging functional genomic and proteomic ('omic') resources and technologies provide great opportunities to develop new methods for systematic identification of genes underlying complex diseases. In this report, we propose a systems biology approach, which integrates omic data, to find genes responsible for complex diseases. This approach consists of five steps: (1) generate a set of candidate genes using gene-gene interaction data sets; (2) reconstruct a genetic network with the set of candidate genes from gene expression data; (3) identify differentially regulated genes between normal and abnormal samples in the network; (4) validate regulatory relationship between the genes in the network by perturbing the network using RNAi and monitoring the response using RT-PCR; and (5) genotype the differentially regulated genes and test their association with the diseases by direct association studies. To prove the concept in principle, the proposed approach is applied to genetic studies of the autoimmune disease scleroderma or systemic sclerosis.     

Application of pattern-mixture models to outcomes that are potentially missing not at random using pseudo maximum likelihood estimation

In this work, we fit pattern-mixture models to data sets with responses that are potentially missing not at random (MNAR, Little and Rubin, 1987). In estimating the regression parameters that are identifiable, we use the pseudo maximum likelihood method based on exponential families. This procedure provides consistent estimators when the mean structure is correctly specified for each pattern, with further information on the variance structure giving an efficient estimator. The proposed method can be used to handle a variety of continuous and discrete outcomes. A test built on this approach is also developed for model simplification in order to improve efficiency. Simulations are carried out to compare the proposed estimation procedure with other methods. In combination with sensitivity analysis, our approach can be used to fit parsimonious semi-parametric pattern-mixture models to outcomes that are potentially MNAR. We apply the proposed method to an epidemiologic cohort study to examine cognition decline among elderly.     

Ab initio maximum likelihood reconstruction from cryo electron microscopy images of an infectious virion of the tailed bacteriophage P22 and maximum likelihood versions of Fourier Shell Correlation appropriate for measuring resolution of spherical or cylindrical objects

A maximum likelihood reconstruction method for an asymmetric reconstruction of the infectious P22 bacteriophage virion is described and demonstrated on a subset of the images used in [Lander, G.C., Tang, L., Casjens, S.R., Gilcrease, E.B., Prevelige, P., Poliakov, A., Potter, C.S., Carragher, B., Johnson, J.E., 2006. The structure of an infectious P22 virion shows the signal for headful DNA packaging. Science 312(5781), 1791–1795]. The method makes no assumptions at any stage regarding the structure of the phage tail or the relative rotational orientation of the phage tail and capsid but rather the structure and the rotation angle are determined as a part of the analysis. A statistical method for determining resolution consistent with maximum likelihood principles based on ideas for cylinders analogous to the ideas for spheres that are embedded in the Fourier Shell Correlation method is described and demonstrated on the P22 reconstruction. With a correlation threshold of .95, the resolution in the tail measured radially is greater than (33.3 Å) and measured axially is greater than (70.6 Å) both with probability p=0.02.     

Current developments and future directions of bio-inspired computation and implications for ecoinformatics

Evolutionary and neural computation has been used widely in solving various problems in biological ecosystems. This paper reviews some of the recent work in evolutionary computation and neural network ensembles that could be explored further in the context of ecoinformatics. Although these bio-inspired techniques were not developed specifically for ecoinformatics, their successes in solving complex problems in other fields demonstrate how these techniques could be adapted and used for tackling difficult problems in ecoinformatics. Firstly, we will review our work in modelling and model calibration, which is an important topic in ecoinformatics. Secondly one example will be given to illustrate how coevolutionary algorithms could be used in problem-solving. Thirdly, we will describe our work on neural network ensembles, which can be used for various classification and prediction problems in ecoinformatics. Finally, we will discuss ecosystem-inspired computational models and algorithms that could be explored as directions of future research.     

Multi-year analysis of stock composition of a loggerhead turtle (<Emphasis Type="Italic">Caretta caretta</Emphasis>) foraging habitat using maximum likelihood and Bayesian methods

Genetic markers have proven useful for determining which sea turtle rookeries contribute to a particular feeding ground. This information is especially relevant when management concerns include anthropogenic mortality of feeding cohorts, and the suspected presence of endangered populations. One such feeding habitat is the Pamlico–Albemarle Estuarine Complex in North Carolina, which was established as an index area in 1995 to monitor population-specific recovery of sea turtles. Pound nets in the study area were surveyed at random from September–December (1995–1997) to enumerate incidental captures of sea turtles as an index of sea turtle abundance. In this study, we estimated the rookery origins of this feeding cohort using both maximum likelihood and Bayesian based stock analysis programs and compare and contrast these different methodologies. The Bayesian methods appear to yield more realistic estimates of percent contribution to the feeding cohort when information regarding relative population sizes was used. Subsequently, we tested for temporal variation in the frequency of mitochondrial DNA haplotypes and resulting estimates of contribution over a 3-year time span. Mixed stock analysis of the combined data indicated that 80 of the individuals originated from the south Florida nesting population, 12 were from the northeast Florida to North Carolina nesting population, 6 from Yucatan, Mexico, and 2 from other rookeries. Although statistically significant shifts in haplotype frequencies were not observed between the three annual sampling periods, estimates of composition indicated subtle differences in the contributions to this foraging area over the sampling period.     

A class of Bayesian shared gamma frailty models with multivariate failure time data

For multivariate failure time data, we propose a new class of shared gamma frailty models by imposing the Box-Cox transformation on the hazard function, and the product of the baseline hazard and the frailty. This novel class of models allows for a very broad range of shapes and relationships between the hazard and baseline hazard functions. It includes the well-known Cox gamma frailty model and a new additive gamma frailty model as two special cases. Due to the nonnegative hazard constraint, this shared gamma frailty model is computationally challenging in the Bayesian paradigm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and it absorbs the nonlinear parameter constraints. The marginal part of the prior specification is free of constraints. The prior distributions allow us to easily compute the full conditionals needed for Gibbs sampling, while incorporating the constraints. This class of shared gamma frailty models is illustrated with a real dataset.