Convergence to genetically uniform state in stepping stone models of population genetics

We investigate continuous time stepping stone models. Extending the models treated in population genetics, we consider the system described by the following infinite dimensional stochastic differential equation, $$dx_k (t) = a_k (x_k )dB_k + \left\{ {\sum\limits_{j \in S} {q_{k,jXj} } } \right\}dt, k \in S$$ which contains the effects of random sampling drift and a kind of stochastic fluctuation in selection. We obtain a necessary and sufficient condition for the system to converge to a genetically uniform state.     

Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian computation

Approximate Bayesian computation (ABC) substitutes simulation for analytic models in Bayesian inference. Simulating evolutionary scenarios under Kimura’s stepping stone model (KSS) might therefore allow inference over spatial genetic process where analytical results are difficult to obtain. ABC first creates a reference set of simulations and would proceed by comparing summary statistics over KSS simulations to summary statistics from localities sampled in the field, but: comparison of which localities and stepping stones? Identical stepping stones can be arranged so two localities fall in the same stepping stone, nearest or diagonal neighbours, or without contact. None is intrinsically correct, yet some choice must be made and this affects inference. We explore a Bayesian strategy for mapping field observations onto discrete stepping stones. We make Sundial, for projecting field data onto the plane, available. We generalize KSS over regular tilings of the plane. We show Bayesian averaging over the mapping between a continuous field area and discrete stepping stones improves the fit between KSS and isolation by distance expectations. We make Tiler Durden available for carrying out this Bayesian averaging. We describe a novel parameterization of KSS based on Wright’s neighbourhood size, placing an upper bound on the geographic area represented by a stepping stone and make it available as m Vector. We generalize spatial coalescence recursions to continuous and discrete space cases and use these to numerically solve for KSS coalescence previously examined only using simulation. We thus provide applied and analytical resources for comparison of stepping stone simulations with field observations.     

Herbgenomics: A stepping stone for research into herbal medicine

From the prehistoric era until the publishing of the Compendium of Materia Medica and the first scientific Nobel Prize in the Chinese mainland for Tu's discovery on anti-malarial tablets, each milestone and stepping stone in the developmental history of herbal medicine involved intrepid exploration, bold hypothesis formulation, and cautious verification. After thousands of years of discovery and development, herbal research has entered a new era—the era of herbgenomics. Herbgenomics combines herbal and genomic research, bridging the gap between traditional herbal medicine and cutting-edge omics studies. Therefore, it provides a general picture of the genetic background of traditional herbs, enabling researchers to investigate the mechanisms underlying the prevention and treatment of human diseases from an omics perspective.     

Stochastic models for an enzyme reaction in an open linear system

A stochastic model is developed for an enzyme reaction in an open linear system. The proposed model assumes that the open system maintains the concentration of substrate and inhibitor at constant levels and that the product molecules are removed from the system by a first order reaction. Stochastic models for several enzyme reactions occurring in this open system are shown to correspond to special cases of theGI/M/∞ queue. Takács’ (1958) results for this queueing system are used to obtain the stochastic properties of the enzyme systems. A specific model we studied assumed completely competitive inhibition in an open system. The stationary distribution for the number of product molecules in the system is obtained. The enzyme reaction which incorporated the “intermediate chain hypothesis” can also be investigated by the queueing theory approach. It is shown that for this open system, if the model which incorporated the intermediate chain hypothesis has the same deterministic properties as the Michaelis-Menten model, then the latter has greater stochastic variation than the former. Research supported by the NIH Training Grant No. GM 1237-05 awarded to the Department of Statistics, The Johns Hopkins University. This paper in whole or in part may be reproduced for any purpose of the United States Government.     

A framework for estimating the fixation time of an advantageous allele in stepping-stone models

Determining how population subdivision increases the fixation time of an advantageous allele is an important problem in evolutionary genetics as this influences many processes. Here, I lay out a framework for calculating the fixation time of a positively selected allele in a subdivided population, as a function of the number of demes present, the migration rate between them and the manner in which they are connected. Using this framework, it becomes clear that a beneficial allele's fixation time is significantly reduced through migration continuously introducing copies of the allele into a newly colonized subpopulation, increasing its frequency within these demes. The effect that migration has on allele frequency needs to be explicitly taken into account to produce a realistic estimate of fixation time. This behaviour is most prominent when demes are arranged on a two-dimensional torus, in comparison with populations where demes are arranged in a circle. This is because each subpopulation is connected to several neighbours over a torus, so that there are multiple paths that an allele can take in order to fix. As a consequence, some demes experience a greater influx and efflux of migrants than others. Analytical results are found to be very accurate when compared to stochastic simulations, and are generally robust if there are a large number of demes, or if the allele is weakly selected for.     

Diagnostic laboratory parasitology--a stepping stone to medical research in tropical Africa.

African countries can concentrate mainly on operational and problem-solving type of medical research using as a basis routine diagnostic laboratory parasitology which can be elevated to research level by incorporating all relevant techniques backed by statistically-based programming. Because of high incidence of parasitic infections and the peculiar host-parasite relationship, co-operation between all departments of any major hospital will be required to deal with the diseases due to them. Longitudinal studies on some parasites will enable generalisation and specific views to be formed on some infections. Multiplicity and wide variety of available techniques offer several research possibilities of clinico-pathological and epidemiological significance. Routine laboratory-based research offers the right environment for training various types of laboratory workers from technicians to medical parasitologists, through on-the-job training on techniques, investigative studies and research, backed by formal lectures and practicals at various levels. Trainee medical parasitologists can obtain higher degrees locally or abroad. The research can be organised around micro and mini research units. This approach is cost-beneficial because it minimises administrative difficulties and so avoids wastage. The results can be used to monitor impact of national development on parasitic infection prevalence and to formulate a policy on parasitic disease management.     

The Hawaiian Archipelago is a stepping stone for dispersal in the Pacific: an example from the plant genus Melicope (Rutaceae)

Aim Pacific biogeographical patterns in the widespread plant genus Melicope J.R. Forst. & G. Forst. (Rutaceae) were examined by generating phylogenetic hypotheses based on chloroplast and nuclear ribosomal sequence data. The aims of the study were to identify the number of colonization events of Melicope to the Hawaiian Islands and to reveal the relationship of Hawaiian Melicope to the Hawaiian endemic genus Platydesma H. Mann. The ultimate goal was to determine if the Hawaiian Islands served as a source area for the colonization of Polynesia. Location Nineteen accessions were sampled in this study, namely eight Melicope species from the Hawaiian Islands, four from the Marquesas Islands, one species each from Tahiti, Australia and Lord Howe Island, two Australian outgroups and two species of the Hawaiian endemic genus Platydesma. To place our results in a broader context, 19 sequences obtained from GenBank were included in an additional analysis, including samples from Australia, Papua New Guinea, New Zealand, Southeast Polynesia and Asia. Methods DNA sequences were generated across 19 accessions for one nuclear ribosomal and three chloroplast gene regions. Maximum parsimony analyses were conducted on separate and combined data sets, and a maximum likelihood analysis was conducted on the combined nuclear ribosomal and chloroplast data set. A broader nuclear ribosomal maximum parsimony analysis using sequences obtained from GenBank was also performed. Geographic areas were mapped onto the combined chloroplast and nuclear ribosomal tree, as well as onto the broader tree, using the parsimony criterion to determine the dispersal patterns. Results Phylogenetic analyses revealed that Platydesma is nested within Melicope and is sister to the Hawaiian members of Melicope. The Hawaiian Melicope + Platydesma lineage was a result of a single colonization event, probably from the Austral region. Finally, Marquesan Melicope descended from at least one, and possibly two, colonization events from the Hawaiian Islands. Main conclusions These data demonstrate a shifting paradigm of Pacific oceanic island biogeography, in which the patterns of long‐distance dispersal and colonization in the Pacific are more dynamic than previously thought, and suggest that the Hawaiian Islands may act as a stepping stone for dispersal throughout the Pacific.     

Residual analysis for linear mixed models

Residuals are frequently used to evaluate the validity of the assumptions of statistical models and may also be employed as tools for model selection. For standard (normal) linear models, for example, residuals are used to verify homoscedasticity, linearity of effects, presence of outliers, normality and independence of the errors. Similar uses may be envisaged for three types of residuals that emerge from the fitting of linear mixed models. We review some of the residual analysis techniques that have been used in this context and propose a standardization of the conditional residual useful to identify outlying observations and clusters. We illustrate the procedures with a practical example.     

Subset selection for linear mixed models

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates—while accounting for this structured dependence—remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single “best” subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.     

Score test for linkage in generalized linear models

We derive a test for linkage in a Generalized Linear Mixed Model (GLMM) framework which provides a natural adjustment for marginal covariate effects. The method boils down to the score test of a quasi-likelihood derived from the GLMM, it is computationally inexpensive and can be applied to arbitrary pedigrees. In particular, for binary traits, relative pairs of different nature (affected and discordant) and individuals with different covariate values can be naturally combined in a single test. The model introduced could explain a number of situations usually described as gene by covariate interaction phenomena, and offers substantial gains in efficiency compared to methods classically used in those instances.     

Analysis of linear determinacy for spread in cooperative models

 The discrete-time recursion system $\u_{n+1}=Q[\u_n]$ with $\u_n(x)$ a vector of population distributions of species and $Q$ an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an equilibrium of cooperating species by a new species or mutant. It is found that, in general, the resulting change in the equilibrium density of each species spreads at its own asymptotic speed, with the speed of the invader the slowest of the speeds. Conditions on $Q$ are given which insure that all species spread at the same asymptotic speed, and that this speed agrees with the more easily calculated speed of a linearized problem for the invader alone. If this is true we say that the recursion has a single speed and is linearly determinate. The conditions are such that they can be verified for a class of reaction-diffusion models. Received: 7 August 2000 / Revised version: 5 January 2002 / Published online: 17 July 2002