Inference of Gene Flow between Species under Misspecified Models

Genomic sequence data provide a rich source of information about the history of species divergence and interspecific hybridization or introgression. Despite recent advances in genomics and statistical methods, it remains challenging to infer gene flow, and as a result, one may have to estimate introgression rates and times under misspecified models. Here we use mathematical analysis and computer simulation to examine estimation bias and issues of interpretation when the model of gene flow is misspecified in analysis of genomic datasets, for example, if introgression is assigned to the wrong lineages. In the case of two species, we establish a correspondence between the migration rate in the continuous migration model and the introgression probability in the introgression model. When gene flow occurs continuously through time but in the analysis is assumed to occur at a fixed time point, common evolutionary parameters such as species divergence times are surprisingly well estimated. However, the time of introgression tends to be estimated towards the recent end of the period of continuous gene flow. When introgression events are assigned incorrectly to the parental or daughter lineages, introgression times tend to collapse onto species divergence times, with introgression probabilities underestimated. Overall, our analyses suggest that the simple introgression model is useful for extracting information concerning between-specific gene flow and divergence even when the model may be misspecified. However, for reliable inference of gene flow it is important to include multiple samples per species, in particular, from hybridizing species.     

Mathematical model of fructan biosynthesis and polymer length distribution in plants

Background and Aims

There are many unresolved issues concerning the biochemistry of fructan biosynthesis. The aim of this paper is to address some of these by means of modelling mathematically the biochemical processes.

Methods

A model has been constructed for the step-by-step synthesis of fructan polymers. This is run until a steady state is achieved for which a polymer distribution is predicted. It is shown how qualitatively different distributions can be obtained.

Key Results

It is demonstrated how a set of experimental results on polymer distribution can by simulated by a simple parameter adjustments.

Conclusions

Mathematical modelling of fructan biosynthesis can provide a useful tool for helping elucidate the details of the biosynthetic processes.     

Proteins searching for their target on DNA by one-dimensional diffusion: overcoming the “speed-stability” paradox

The sequence dependence of DNA-protein interactions that allows proteins to find the correct reaction site also slows down the 1D diffusion of the protein along the DNA molecule, leading to the so-called “speed-stability paradox,” wherein fast diffusion along the DNA molecule is seemingly incompatible with stable targeting of the reaction site. Here, we develop diffusion-reaction models that use discrete and continuous Gaussian random 1D diffusion landscapes with or without a high-energy cut-off, and two-state models with a transition to and from a “searching” mode in which the protein diffuses rapidly without recognizing the target. We show the conditions under which such considerations lead to a predicted speed-up of the targeting process, and under which the presence of a “searching” mode in a two-state model is nearly equivalent to the existence of a high-energy cut-off in a one-state model. We also determine the conditions under which the search is either diffusion-limited or reaction-limited, and develop quantitative expressions for the rate of successful targeting as a function of the site-specific reaction rate, the roughness of the DNA-protein interaction potential, and the presence of a “searching” mode. In general, we find that a rough landscape is compatible with a fast search if the highest energy barriers can be avoided by “hopping” or by the protein transitioning to a lower-energy “searching” mode. We validate these predictions with the results of Brownian dynamics, kinetic Metropolis, and kinetic Monte Carlo simulations of the diffusion and targeting process, and apply these concepts to the case of T7 RNA polymerase searching for its target site on T7 DNA.     

Composite analysis of black duck breeding population surveys in eastern North America

Waterfowl are monitored in eastern Canada and the northeastern United States with 2 surveys: a transect survey from fixed-wing aircraft and a plot survey conducted from helicopters. The surveys vary in extent, but overlap exists in a core area of 9 strata covering portions of all provinces from Ontario east to Newfoundland. We estimated population change for American black ducks (Anas rubripes) and mallards (Anas platyrhynchos) from these surveys using a log-linear hierarchical model that accommodates differences in sample design and visibility associated with these survey methods. Using a combined analysis of the surveys based on total indicated birds, we estimate the American black duck population to be 901,700 (95% CI: 715,200–1,274,000) in 2011, with 526,900 (95% CI: 357,500–852,300) mallards in the surveyed area. Precision of estimates varies widely by species and region, with transect surveys providing less precise results than plot surveys for black ducks in areas of overlap. The combined survey analysis for black ducks in the eastern survey region produced estimates with an average yearly coefficient of variation (CV) of 12.1% for the entire area and an average CV of 6.9% in the plot survey area. Mallards, which had a more limited distribution in the region, had an average yearly CV of 22.1% over the entire region, and an average CV of 27.7% in the plot survey area. Hierarchical models provide a rich framework for analyzing and combining results from complex survey designs, providing useful spatial and temporal information on population size and change in these economically important species. © 2012 The Wildlife Society.     

Climate oscillations and species interactions: large‐scale congruence but regional differences in the phylogeographic structures of an alpine plant and its monophagous insect

Aim To predict the fate of alpine interactions involving specialized species, using a monophagous beetle and its host plant as a case study. Location The Alps. Methods We investigated genetic structuring of the herbivorous beetle Oreina gloriosa and its specific host‐plant Peucedanum ostruthium. We used genome fingerprinting (in the insect and the plant) and sequence data (in the insect) to compare the distribution of the main gene pools in the two associated species and to estimate divergence time in the insect, a proxy for the temporal origin of the interaction. We quantified the similarity in spatial genetic structures by performing a Procrustes analysis, a tool from shape theory. Finally, we simulated recolonization of an empty space analogous to the deglaciated Alps just after ice retreat by two lineages from two species showing unbalanced dependence, to examine how timing of the recolonization process, as well as dispersal capacities of associated species, could explain the observed pattern. Results Contrasting with expectations based on their asymmetrical dependence, patterns in the beetle and plant were congruent at a large scale. Exceptions occurred at a regional scale in areas of admixture, matching known suture zones in Alpine plants. Simulations using a lattice‐based model suggested these empirical patterns arose during or soon after recolonization, long after the estimated origin of the interaction c. 0.5 million years ago. Main conclusions Species‐specific interactions are scarce in alpine habitats because glacial cycles have limited the opportunities for co‐evolution. Their fate, however, remains uncertain under climate change. Here we show that whereas most dispersal routes are paralleled at a large scale, regional incongruence implies that the destinies of the species might differ under changing climate. This may be a consequence of the host dependence of the beetle, which locally limits the establishment of dispersing insects.     

Analysing covariates with spike at zero: A modified FP procedure and conceptual issues

In epidemiology and in clinical research, risk factors often have special distributions. A common situation is that a proportion of individuals have exposure zero, and among those exposed, we have some continuous distribution. We call this a ‘spike at zero’. Examples for this are smoking, duration of breastfeeding, or alcohol consumption. Furthermore, the empirical distribution of laboratory values and other measurements may have a semi‐continuous distribution as a result of the lower detection limit of the measurement. To model the dose–response function, an extension of the fractional polynomial approach was recently proposed. In this paper, we suggest a modification of the previously suggested FP procedure. We first give the theoretical justification of this modified procedure by investigating relevant distribution classes. Here, we systematically derive the theoretical shapes of dose–response curves under given distributional assumptions (normal, log normal, gamma) in the framework of a logistic regression model. Further, we check the performance of the procedure in a simulation study and compare it to the previously suggested method, and finally we illustrate the procedures with data from a case–control study on breast cancer.     

Analysis of multivariate recurrent event data with time‐dependent covariates and informative censoring

Multivariate recurrent event data are usually encountered in many clinical and longitudinal studies in which each study subject may experience multiple recurrent events. For the analysis of such data, most existing approaches have been proposed under the assumption that the censoring times are noninformative, which may not be true especially when the observation of recurrent events is terminated by a failure event. In this article, we consider regression analysis of multivariate recurrent event data with both time‐dependent and time‐independent covariates where the censoring times and the recurrent event process are allowed to be correlated via a frailty. The proposed joint model is flexible where both the distributions of censoring and frailty variables are left unspecified. We propose a pairwise pseudolikelihood approach and an estimating equation‐based approach for estimating coefficients of time‐dependent and time‐independent covariates, respectively. The large sample properties of the proposed estimates are established, while the finite‐sample properties are demonstrated by simulation studies. The proposed methods are applied to the analysis of a set of bivariate recurrent event data from a study of platelet transfusion reactions.     

Biophoton emission

The phenomenon of ultraweak photon emission from living systems was further investigated in order to elucidate the physical properties of this radiation and its possible source. We obtained evidence that the light has a high degree of coherence because of (1) its photon count statistics, (2) its spectral distribution, (3) its decay behavior after exposure to light illumination, and (4) its transparency through optically thick materials. Moroever, DNA is apparently at least an important source, since conformational changes induced with ethidium bromide in vivo are clearly reflected by changes of the photon emission of cells. The physical properties of the radiation are described, taking DNA as an exciplex laser system, where a stable state can be reached far from thermal equilibrium at threshold.     

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.