Estimating polymorphic growth curve sets with nonchronological data

1. When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data.
2. In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least‐squares method after the log‐transform of the anamorphic growth curve sets were included as special cases.
3. The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction).
4. The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced.

     

Segmented linear regression models applied to the analysis of data from a cross-sectional growth experiment

Several different methods of analysis are applied to data consisting of weight measurements, taken at specified post-treatment times, of harvested thyroids from rats given one of four treatments. Previous studies of this type of data indicated that the growth is initially rapid, and that a second phase of less rapid growth is followed by a final phase in which little additional growth occurs. The data are further characterized by increasing variance through time. The primary purpose of the analysis is to study the effect of the treatments at the end of the study period. One-way analysis of variance tests among groups are performed on each day, but the results are not particularly helpful. However, results from two-way analyses of variance (over subsets of days and groups) are consistent with the three phase model and accordingly indicate significant group differences during each. Finally, maximum likelihood methods are used to fit a three part segmented linear regression model.     

Phylogeny of Mesocyclops (Copepoda: Cyclopidae) inferred from morphological characters

Evolutionary relationships were investigated in the genus Mesocyclops, a pantropical freshwater cyclopid group. In the phylogenetic analyses that involved all 71 known species, and used 81 morphological characters (265 character states) mainly of the adult females, two different approaches were applied: global parsimony, and a new distance method based upon the recognition of sister‐groups on the basis of minimal distances iteratively corrected for unique character states (MICSEQ). In coding of the characters, half of which showed intraspecific variation, the ‘scaled’ method was employed, which assumes that any trait between its absence and fixed presence passes through a polymorphic stage. Impact of the reference points on topology of the trees generated by the parsimony method was tested in three ways where the outgroups comprised: (1) nine species representing six genera of two subfamilies; (2) three species from two genera supposedly not distant from Mesocyclops; and (3) one presumably close and one distant relative of Mesocyclops. The trees generated by the parsimony‐based and corrected distance methods agreed as to the monophyly of the following groups: reidae‐clade (M. reidae, M. chaci, M. yutsil); rarus‐clade (Mesocyclops annae, M. pseudoannae, M. splendidus, M. rarus, M. paludosus, M. darwini, M. dayakorum); annulatus‐clade (Mesocyclops intermedius, M. ellipticus, M. paranaensis, M. annulatus, M. tenuisaccus); meridianus‐clade (Mesocyclops meridionalis, M. varius, M. venezolanus, M. brasilianus, M. pseudomeridianus, M. meridianus); major‐clade (Mesocyclops major, M. pilosus, M. insulensis); dussarti‐clade (M. dussarti, M. dadayi, M. isabellae, M. thermocyclopoides); pubiventris‐clade (M. pubiventris, M. medialis, M. brooksi, M. notius). A majority of the analyses support a clade of the ‘true’Mesocyclops including all ingroup species except the reidae‐group, and point to monophyly of the Old World species lacking medial spine on P1 basipodite. There were, however, some components for which the two procedures, regardless of the outgroup choice and/or character set, suggested different relationships. Basal relationships of Mesocyclops[between M. edax (North and Central America), the Neotropical species (M. longisetus, M. araucanus, M. evadomingoi, meridianus‐ and annulatus‐clade), Old World group (P1 basipodite without medial spine) and the rarus‐clade (Old World; P1 basipodite with medial spine)] remained unresolved. © 2006 The Linnean Society of London, Zoological Journal of the Linnean Society, 2006, 147 , 1–70.     

Spatial auto-correlation and auto-regressive models estimation from sample survey data

Maximum likelihood estimation of the model parameters for a spatial population based on data collected from a survey sample is usually straightforward when sampling and non-response are both non-informative, since the model can then usually be fitted using the available sample data, and no allowance is necessary for the fact that only a part of the population has been observed. Although for many regression models this naive strategy yields consistent estimates, this is not the case for some models, such as spatial auto-regressive models. In this paper, we show that for a broad class of such models, a maximum marginal likelihood approach that uses both sample and population data leads to more efficient estimates since it uses spatial information from sampled as well as non-sampled units. Extensive simulation experiments based on two well-known data sets are used to assess the impact of the spatial sampling design, the auto-correlation parameter and the sample size on the performance of this approach. When compared to some widely used methods that use only sample data, the results from these experiments show that the maximum marginal likelihood approach is much more precise.     

On the use of the substitution method in left-censored environmental data

In risk assessment and environmental monitoring studies, concentration measurements frequently fall below detection limits (DL) of measuring instruments, resulting in left-censored data. The principal approaches for handling censored data include the substitution-based method, maximum likelihood estimation, robust regression on order statistics, and Kaplan-Meier. In practice, censored data are substituted with an arbitrary value prior to use of traditional statistical methods. Although some studies have evaluated the substitution performance in estimating population characteristics, they have focused mainly on normally and lognormally distributed data that contain a single DL. We employ Monte Carlo simulations to assess the impact of substitution when estimating population parameters based on censored data containing multiple DLs. We also consider different distributional assumptions including lognormal, Weibull, and gamma. We show that the reliability of the estimates after substitution is highly sensitive to distributional characteristics such as mean, standard deviation, skewness, and also data characteristics such as censoring percentage. The results highlight that although the performance of the substitution-based method improves as the censoring percentage decreases, its performance still depends on the population's distributional characteristics. Practical implications that follow from our findings indicate that caution must be taken in using the substitution method when analyzing censored environmental data.     

Local estimation of age-dependent variance components from longitudinal twin data

In the study of longitudinal twin and family data, interest is often in the covariance structure of the data and the decomposition of this covariance structure into genetic and environmental components rather than in estimating the mean function. Various parametric models for covariance structures have been proposed but, e.g., in studies of children where growth spurts occur at various ages, it is difficult to a priori determine an appropriate parametric model for the covariance structure. In particular, there is a general lack of the visualization procedures, such as lowess, that are invaluable in the initial stages of constructing a parametric model for a mean function. Here we use kernel smoothing to modify a cross-sectional approach based on the sample covariance matrices to obtain smoothed estimates of the genetic and environmental variances and correlations for longitudinal twin data. The methods are proposed to be exploratory as an aid to parametric modeling rather than inferential, although approximate asymptotic standard errors are derived in the Appendix.     

Attributes and congruence of three molecular data sets: inferring phylogenies among Septoria-related species from woody perennial plants

To improve our understanding of phylogenetic relationships within the anamorphic genus Septoria, three molecular data sets representing 2,417 bp of nuclear and mitochondrial genes were evaluated. Separate gene analyses and combined analyses were performed using first, the maximum parsimony criterion and second, a Bayesian framework. The homogeneity of data partitions was evaluated via a combination of homogeneity partition tests and tree topology incongruence tests before conducting combined analyses. A last incongruence re-evaluation using partitioned Bremer support was performed on the combined tree, which corroborated the previous estimates. After each separate data set attributes were examined, simple explanations were advocated as the causes of the significant incongruences detected. The analysis of multiple gene partitions showed unprecedented phylogenetic resolution within the genus Septoria that supported the results from previously published single gene phylogenies. Specifically, we have delimited distinct but closely related species representing monophyletic groups that frequently correlated with their respective host families. Conversely, the occurrence of well-supported groups including closely related but distinct molecular taxa sampled on unrelated host-plants allowed us to reject, in these particular cases, the co-evolutionary concept expected between a parasite and its host and to discuss alternative evolutionary models recently proposed for these pathogens.     

Likelihood and approximate likelihood analyses of genetic structure in a linear habitat: performance and robustness to model mis-specification

We evaluate the performance of maximum likelihood (ML) analysis of allele frequency data in a linear array of populations. The parameters are a mutation rate and either the dispersal rate in a stepping stone model or a dispersal rate and a scale parameter in a geometric dispersal model. An approximate procedure known as maximum product of approximate conditional (PAC) likelihood is found to perform as well as ML. Mis-specification biases may occur because the importance sampling algorithm is formally defined in term of mutation and migration rates scaled by the total size of the population, and this size may differ widely in the statistical model and in reality. As could be expected, ML generally performs well when the statistical model is correctly specified. Otherwise, mutation rate estimates are much closer to mutation probability scaled by number of demes in the statistical model than scaled by number of demes in reality when mutation probability is high and dispersal is most limited. This mis-specification bias actually has practical benefits. However, opposite results are found in opposite conditions. Migration rate estimates show roughly similar trends, but they may not always be easily interpreted as low-bias estimates of dispersal rate under any scaling. Estimation of the dispersal scale parameter is also affected by mis-specification of the number of demes, and the different biases compensate each other in such a way that good estimation of the so-called neighborhood size (or more precisely the product of population density and mean-squared parent-offspring dispersal distance) is achieved. Results congruent with these findings are found in an application to a damselfly data set.     

Kakusan4 and Aminosan: two programs for comparing nonpartitioned, proportional and separate models for combined molecular phylogenetic analyses of multilocus sequence data

Proportional and separate models able to apply different combination of substitution rate matrix (SRM) and among-site rate variation model (ASRVM) to each locus are frequently used in phylogenetic studies of multilocus data. A proportional model assumes that branch lengths are proportional among partitions and a separate model assumes that each partition has an independent set of branch lengths. However, the selection from among nonpartitioned (i.e., a common combination of models is applied to all-loci concatenated sequences), proportional and separate models is usually based on the researcher's preference rather than on any information criteria. This study describes two programs, 'Kakusan4' (for DNA sequences) and 'Aminosan' (for amino-acid sequences), which allow the selection of evolutionary models based on several types of information criteria. The programs can handle both multilocus and single-locus data, in addition to providing an easy-to-use wizard interface and a noninteractive command line interface. In the case of multilocus data, SRMs and ASRVMs are compared at each locus and at all-loci concatenated sequences, after which nonpartitioned, proportional and separate models are compared based on information criteria. The programs also provide model configuration files for mrbayes, paup*, phyml, raxml and Treefinder to support further phylogenetic analysis using a selected model. When likelihoods are optimized by Treefinder, the best-fit models were found to differ depending on the data set. Furthermore, differences in the information criteria among nonpartitioned, proportional and separate models were much larger than those among the nonpartitioned models. These findings suggest that selecting from nonpartitioned, proportional and separate models results in a better phylogenetic tree. Kakusan4 and Aminosan are available at http://www.fifthdimension.jp/. They are licensed under gnugpl Ver.2, and are able to run on Windows, MacOS X and Linux.     

Estimating population divergence time and phylogeny from single-nucleotide polymorphisms data with outgroup ascertainment bias

The inference of population divergence times and branching patterns is of fundamental importance in many population genetic analyses. Many methods have been developed for estimating population divergence times, and recently, there has been particular attention towards genome-wide single-nucleotide polymorphisms (SNP) data. However, most SNP data have been affected by an ascertainment bias caused by the SNP selection and discovery protocols. Here, we present a modification of an existing maximum likelihood method that will allow approximately unbiased inferences when ascertainment is based on a set of outgroup populations. We also present a method for estimating trees from the asymmetric dissimilarity measures arising from pairwise divergence time estimation in population genetics. We evaluate the methods by simulations and by applying them to a large SNP data set of seven East Asian populations.     

Quantifying the predictive performance of prognostic models for censored survival data with time-dependent covariates

Summary .   Prognostic models in survival analysis typically aim to describe the association between patient covariates and future outcomes. More recently, efforts have been made to include covariate information that is updated over time. However, there exists as yet no standard approach to assess the predictive accuracy of such updated predictions. In this article, proposals from the literature are discussed and a conditional loss function approach is suggested, illustrated by a publicly available data set.     

Phylogenetic systematics of Southeast Asian flying lizards (Iguania: Agamidae: Draco) as inferred from mitochondrial DNA sequence data

Phylogenetic analysis of mitochondrial DNA sequence data using maximum parsimony, minimum evolution (of log-determinant distances), and maximum-likelihood optimality criteria provided a robust estimate of Draco phylogenetic relationships. Although the analyses based on alternative optimality criteria were not entirely congruent, non-parametric bootstrap analyses identified many well-supported clades that were common to the analyses under the three altrenative criteria. Relationships within the major clades are generally well resolved and strongly supported, although this is not the case for the Philippine volans subclade. The hypothesis that a clade composed primarily of Philippine species represents a rapid radiation could not be rejected. A revised taxonomy for Draco is provided.     

Inferring dominance interactions from automatically recorded temporal data

Understanding dominance hierarchies is an important aspect of many studies of animal groups. Collecting the necessary data requires a large amount of time and effort to detect only a small number of interactions. Here, we assess the viability of extracting interactions from a temporal data stream of arrival and departures to a feeder equipped with a radio‐frequency identifier antenna. We show that the interactions extracted from this type of data can create similar dominance hierarchies to those produced by analysing video data of interactions. Additionally, we assessed the amount of temporal data required to obtain a dominance hierarchy and discuss the advantages and disadvantages of utilising temporal data streams to generate dominance hierarchies of animal groups. The code to extract the dominance interactions and test the correlation between different dominance hierarchies is included in the Supporting Information .     

Structured additive regression for categorical space-time data: a mixed model approach

Motivated by a space-time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey.     

A semiparametric empirical likelihood method for data from an outcome-dependent sampling scheme with a continuous outcome

Outcome-dependent sampling (ODS) schemes can be a cost effective way to enhance study efficiency. The case-control design has been widely used in epidemiologic studies. However, when the outcome is measured on a continuous scale, dichotomizing the outcome could lead to a loss of efficiency. Recent epidemiologic studies have used ODS sampling schemes where, in addition to an overall random sample, there are also a number of supplemental samples that are collected based on a continuous outcome variable. We consider a semiparametric empirical likelihood inference procedure in which the underlying distribution of covariates is treated as a nuisance parameter and is left unspecified. The proposed estimator has asymptotic normality properties. The likelihood ratio statistic using the semiparametric empirical likelihood function has Wilks-type properties in that, under the null, it follows a chi-square distribution asymptotically and is independent of the nuisance parameters. Our simulation results indicate that, for data obtained using an ODS design, the semiparametric empirical likelihood estimator is more efficient than conditional likelihood and probability weighted pseudolikelihood estimators and that ODS designs (along with the proposed estimator) can produce more efficient estimates than simple random sample designs of the same size. We apply the proposed method to analyze a data set from the Collaborative Perinatal Project (CPP), an ongoing environmental epidemiologic study, to assess the relationship between maternal polychlorinated biphenyl (PCB) level and children's IQ test performance.