Maximum likelihood with multiparameter models of substitution

Maximum-likelihood approaches to phylogenetic estimation have the potential of great flexibility, even though current implementations are highly constrained. One such constraint has been the limitation to one-parameter models of substitution. A general implementation of Newton's maximization procedure was developed that allows the maximum likelihood method to be used with multiparameter models. The Estimate and Maximize (EM) algorithm was also used to obtain a good approximation to the maximum likelihood for a certain class of multiparameter models. The condition for which a multiparameter model will only have a single maximum on the likelihood surface was identified. Two-and three-parameter models of substitution in base-paired regions of RNA sequences were used as examples for computer simulations to show that these implementations of the maximum likelihood method are not substantially slower than one-parameter models. Newton's method is much faster than the EM method but may be subject to divergence in some circumstances. In these cases the EM method can be used to restore convergence.     

A dotplot program for the Atari ST, for the analysis of DNA and protein sequences

A program was written in GFA-BASIC for the Atari ST microcomputeraimed at drawing two-dimensional homology ‘dotplot’patterns for two protein or DNA sequences. The program, builtaround a machine-code subroutine, communicates interactivelywith the user by means of a multi-button dialogue panel andmouse-directed input. A 1000 x 1000 sequence comparison witha 14: 21 stringency window takes 12 s.     

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.     

Global climate change and accuracy of prediction of species' geographical ranges: establishment success of introduced ladybirds (Coccinellidae, Chilocorus spp.) worldwide

AimPredictions of how the geographical ranges of species change implicitly assume that range can be determined without invoking climate change. The aim here was to determine how accurate predictions of range change might be before entertaining global climatic change. LocationWorldwide. MethodsAll the documented global biological control translocations of ladybirds (Coccinellidae: Chilocorus spp.) were analysed with the ecoclimatic program, CLIMEX. This program determines species distributions in relation to climate, and can be used to express the favourableness of different localities for a species. CLIMEX is also a useful exploratory tool for determining the likelihood of establishment of species introduced from one area to another. ResultsPredictive models were developed based on the likelihood of establishment of fifteen Chilocorus spp. relative to their physiological characteristics and climatic tolerances. This likelihood was compared with actual establishment with a resultant range of 0% accuracy to 100% accuracy. Only four (26.7%) species climatic tolerances could the predicted with 100% certainty. The general lack of accurate prediction was because climate is not always the overriding feature determining whether a species will establish or not. Other determinants, such as localized response to microclimate, phenology, host type and availability, presence of natural enemies and hibernation sites play a varying role over and above climate in determining whether a species will establish at a new locality. Main conclusionsThis study shows that even in the absence of climate change, range cannot always be determined, which means that most predictions of range change with climate change are likely to be wrong.     

Maximum Likelihood Estimation of Simultaneous Pairwise Linear Structural Relationships

The problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem. Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re-analysing two data sets in the literature.     

A computer program suitable for fitting linear models when the dependent variable is dichotomous, polichotomous or censored survival and non-linear models when the dependent variable is quantitative.

Given a set of measurements of s explanatory variables corresponding to each experimental unit, a computer program, whose methodological background can be found in [2] has been written in FORTRAN IV language in order to perform regression analyses when the dependent variable is: (i) dichotomous; (ii) polichotomous; (iii) censored survival. In the two former the Cox's [6] linear logistic models are used while in the third one it has been resorted to the models suggested by Feigl and Zelen [8]. The statistical estimation procedure is maximum likelihood and among the different algorithms developed to reach this goal, the one published by Van der Voort and Dorpema [3], has been utilized. Furthermore, when the dependent variable is quantitative, the program is suitable to fit any function non-linear in the parameters; the pertinent function and its first and second derivatives must be provided by the user. In the present version, implemented on a Univac 1106 machine, the program fits directly the Gompertz function.     

A computer program for the statistical analysis of disease prevalence data from survival/sacrifice experiments

This paper presents a computer program for analyzing disease prevalence data from animal survival experiments in which there may also be some serial sacrifice. The method has been described in Biometrics 35 (1979) 221-234. The user is interrogated about the details of particular models he wishes to fit. Then a generalized EM algorithm is used to compute maximum likelihood estimates of various quantities of interest concerning the effects of treatment, time and presence of other diseases on the prevalences and lethalities of specific diseases of interest.     

Testing hypotheses in case-control studies--equivalence of Mantel-Haenszel statistics and logit score tests.

The two approaches in common use for the analysis of case-control studies are cross-classification by confounding variables, and modeling the logarithm of the odds ratio as a function of exposure and confounding variables. We show here that score statistics derived from the likelihood function in the latter approach are identical to the Mantel-Haenszel test statistics appropriate for the former approach. This identity holds in the most general situation considered, testing for marginal homogeneity in mK tables. This equivalence is demonstrated by a permutational argument which leads to a general likelihood expression in which the exposure variable may be a vector of discrete and/or continuous variables and in which more than two comparison groups may be considered. This likelihood can be used in analyzing studies in which there are multiple controls for each case or in which several disease categories are being compared. The possibility of including continuous variables makes this likelihood useful in situations that cannot be treated using the Mantel-Haenszel cross-classification approach.     

Maximum likelihood analysis of a general latent variable model with hierarchically mixed data

A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at both levels, as well as the effects of fixed covariates in the measurement and structural equations at both levels, can be analyzed within the framework. Moreover, the methodology can be applied to hierarchically mixed continuous, dichotomous, and polytomous data. A Monte Carlo EM algorithm is implemented to produce the maximum likelihood estimate. The E-step is completed by approximating the conditional expectations through observations that are simulated by Markov chain Monte Carlo methods, while the M-step is completed by conditional maximization. A procedure is proposed for computing the complicated observed-data log likelihood and the BIC for model comparison. The methods are illustrated by using a real data set.     

A FORTRAN subroutine to compute inbreeding and kinship coefficients according to the number of ancestral generations

This paper presents a FORTRAN IV subroutine to calculate inbreedingand kinship coefficients from pedigree information in a diploidpopulation without self-fertilization. The user can specifythe number of ancestral generations to be taken into account.It is thus possible to determine contributions of succeedingancestral generations to the inbreeding and kinship coefficientsunder consideration. The subroutine is based on a recursiveprocedure that generates systematically all paths connectingtwo individuals, NP and NM, whose kinship coefficient is tobe calculated (or between the father NP and the mother NM ofthe individual whose inbreeding coefficient is to be calculated).These paths obey the following conditions: (i) a given pathdoes not contain the same parent—offspring link more thanonce; (ii) the vertex of a path is an ancestor common to individualsNP and NM, with a rank lower or equal to the parameter specifiedin input. Constraints regarding the size of the corpus of genealogicaldata and the storage method are discussed, as well as the interestof this subroutine compared to the existing ones. An exampleof application is given. Received on October 20, 1988; accepted on March 21, 1989     

Using Confidence Set Heuristics During Topology Search Improves the Robustness of Phylogenetic Inference

We examine the impact of likelihood surface characteristics on phylogenetic inference. Amino acid data sets simulated from topologies with branch length features chosen to represent varying degrees of difficulty for likelihood maximization are analyzed. We present situations where the tree found to achieve the global maximum in likelihood is often not equal to the true tree. We use the program covSEARCH to demonstrate how the use of adaptively sized pools of candidate trees that are updated using confidence tests results in solution sets that are highly likely to contain the true tree. This approach requires more computation than traditional maximum likelihood methods, hence covSEARCH is best suited to small to medium-sized alignments or large alignments with some constrained nodes. The majority rule consensus tree computed from the confidence sets also proves to be different from the generating topology. Although low phylogenetic signal in the input alignment can result in large confidence sets of trees, some biological information can still be obtained based on nodes that exhibit high support within the confidence set. Two real data examples are analyzed: mammal mitochondrial proteins and a small tubulin alignment. We conclude that the technique of confidence set optimization can significantly improve the robustness of phylogenetic inference at a reasonable computational cost. Additionally, when either very short internal branches or very long terminal branches are present, confident resolution of specific bipartitions or subtrees, rather than whole-tree phylogenies, may be the most realistic goal for phylogenetic methods. [Reviewing Editor: Dr. Nicolas Galtier]     

A New Method for Estimation of Resource Selection Probability Function

ABSTRACT Weighted distributions can be used to fit various forms of resource selection probability functions (RSPF) under the use-versus-available study design (Lele and Keim 2006). Although valid, the numerical maximization procedure used by Lele and Keim (2006) is unstable because of the inherent roughness of the Monte Carlo likelihood function. We used a combination of the methods of partial likelihood and data cloning to obtain maximum likelihood estimators of the RSPF in a numerically stable fashion. We demonstrated the methodology using simulated data sets generated under the log—log RSPF model and a reanalysis of telemetry data presented in Lele and Keim (2006) using the logistic RSPF model. The new method for estimation of RSPF can be used to understand differential selection of resources by animals, an essential component of studies in conservation biology, wildlife management, and applied ecology.     

A set of programs for analysis of kinetic and equilibrium data

A program package that can be used for analysis of a wide rangeof kinetic and equilibrium data is described. The four programswere written in Turbo Pascal and run on PC, XT, AT and compatibles.The first of the programs allows the user to fit data with 16predefined and one user-defined function, using two differentnon-linear least-squares procedures. Two additional programsare used to test both the evaluation of model functions andthe least-squares fits. One of these programs uses two simpleprocedures to generate a Gaussian-distributed random variablethat is used to simulate the experimental error of measurements.The last program simulates kinetics described by differentialequations that cannot be solved analytically, using numericalintegration. This program helps the user to judge the validityof steady-state assumptions or treatment of kinetic measurementsas relaxations. Received on September 19, 1989; accepted on March 16, 1990     

Automatic generation of user material subroutines for biomechanical growth analysis

The analysis of the biomechanics of growth and remodeling in soft tissues requires the formulation of specialized pseudoelastic constitutive relations. The nonlinear finite element analysis package ABAQUS allows the user to implement such specialized material responses through the coding of a user material subroutine called UMAT. However, hand coding UMAT subroutines is a challenge even for simple pseudoelastic materials and requires substantial time to debug and test the code. To resolve this issue, we develop an automatic UMAT code generation procedure for pseudoelastic materials using the symbolic mathematics package MATHEMATICA and extend the UMAT generator to include continuum growth. The performance of the automatically coded UMAT is tested by simulating the stress-stretch response of a material defined by a Fung-orthotropic strain energy function, subject to uniaxial stretching, equibiaxial stretching, and simple shear in ABAQUS. The MATHEMATICA UMAT generator is then extended to include continuum growth by adding a growth subroutine to the automatically generated UMAT. The MATHEMATICA UMAT generator correctly derives the variables required in the UMAT code, quickly providing a ready-to-use UMAT. In turn, the UMAT accurately simulates the pseudoelastic response. In order to test the growth UMAT, we simulate the growth-based bending of a bilayered bar with differing fiber directions in a nongrowing passive layer. The anisotropic passive layer, being topologically tied to the growing isotropic layer, causes the bending bar to twist laterally. The results of simulations demonstrate the validity of the automatically coded UMAT, used in both standardized tests of hyperelastic materials and for a biomechanical growth analysis.     

Computer simulation for teaching membrane potential fundamentals

A computer simulation of membrane potential generation is presented. It allows the user to vary the intra and extracellular concentrations of sodium, potassium and chloride ions (Na⁺, K⁺ and Cl⁻), and determine the membrane potential and the equilibrium potential for each ion. The permeability coefficients for the ionic species considered, and the temperature may also be changed at will. Concentration-potential curves may be obtained at any time. The user may also select a voltage clamp option, which allows him to impose a certain membrane potential value, and study the resulting driving force for each ion. The use of the program in general physiology courses has shown it to be a useful aid for teaching the principles of membrane potential generation.     

Joint analysis of longitudinal data with informative right censoring

Longitudinal data arise when subjects are followed over a period of time. A commonly encountered complication in the analysis of such data is the variable length of follow-up due to right censorship. This can be further exacerbated by the possible dependency between the censoring time and the longitudinal measurements. This article proposes a combination of a semiparametric transformation model for the censoring time and a linear mixed effects model for the longitudinal measurements. The dependency is handled via latent variables which are naturally incorporated. We show that the likelihood function has an explicit form and develops a two-stage estimation procedure to avoid direct maximization over a high-dimensional parameter space. The resulting estimators are shown to be consistent and asymptotically normal, with a closed form for the variance-covariance matrix that can be used to obtain a plug-in estimator. Finite sample performance of the proposed approach is assessed through extensive simulations. The method is applied to renal disease data.     

A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood

The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximum- likelihood principle, which clearly satisfies these requirements. The core of this method is a simple hill-climbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distance-based method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment of the topology and branch lengths, only a few iterations are sufficient to reach an optimum. We used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches. The reduction of computing time is dramatic in comparison with other maximum-likelihood packages, while the likelihood maximization ability tends to be higher. For example, only 12 min were required on a standard personal computer to analyze a data set consisting of 500 rbcL sequences with 1,428 base pairs from plant plastids, thus reaching a speed of the same order as some popular distance-based and parsimony algorithms. This new method is implemented in the PHYML program, which is freely available on our web page: http://www.lirmm.fr/w3ifa/MAAS/.     

Computer-aided instruction at the Ottawa General Hospital

We have reviewed our experiences with the first systematic use of CAI at the University of Ottawa Medical School. The Bleich acid-base and electrolyte program was employed by senior clinical clerks in the Department of Medicine during the past year using APL version of the program, an IBM 360-65 computer linked by acoustic coupler to the typewriter-style IBM 2741 terminal. We have been impressed with the importance of: (1) minimizing technical difficulties, (2) enhancing the teaching capacity of the program (as opposed to its consultant function) and (3) carefully ensuring that the user understands its limitations. This pilot project in clinical CAI has identified problems which will likely be experienced in other medical centres and has suggested important areas for further development.     

Symbolic Kinship Program

This paper discusses a computerized algorithm to derive the formula for the likelihood ratio for a kinship problem with any arbitrarily defined relationships based on genetic evidence. The ordinary paternity case with the familiar likelihood formula 1/2(q) is the commonest example. More generally, any miscellaneous collection of people can be genetically tested to help settle some argument about how they are related, what one might call a ``kinship' case. Examples that geneticists and DNA identification laboratories run into include sibship, incest, twin, inheritance, motherless, and corpse identification cases. The strength of the genetic evidence is always described by a likelihood ratio. The general method is described by which the computer program finds the formulas appropriate to these various situations. The benefits and the interest of the program are discussed using many examples, including analyses that have previously been published, some practical problems, and simple and useful rules for dealing with scenarios in which ancestral or fraternal types substitute for those of the alleged father.