Rapid cladogenesis in marine fishes revisited

Lineages that underwent rapid cladogenesis are attractive systems for the study of mechanisms underlying taxonomic, ecological, morphological, and behavioral diversification. Recently developed statistical methods provide insights into historical patterns of diversity and allow distinguishing bursts of cladogenesis from stochastic background rates in the presence of confounding factors such as extinction and incomplete taxon sampling. Here, we compare the dynamics of speciation in several marine fish lineages some of which were previously proposed to have undergone significant changes of cladogenesis through time. We tested for evidence of episodes of rapid cladogenesis using the constant rate and Monte Carlo constant rate tests that are robust to incomplete taxon sampling. These tests employ the statistic gamma to measure the relative position of internal node in a chronogram. For the first time, we conducted a comparative analysis to address the behavior of the statistic under different chronogram-constructing methods (Langley-Fitch, nonparametric rate smoothing, and penalized likelihood). Although estimates of gamma sometimes differ widely among methods, acceptance or rejection of the constant rate model within a particular clade appears to be robust to the choice of method. Bursts of cladogenesis were detected in 14 of 34 studied datasets. Some of these were previously proposed to represent marine fish "radiations," whereas others are identified anew. Our results indicate that the wider application of tree shape methods that are able to detect significantly elevated rates of speciation is useful to more precisely define clades that underwent episodes of rapid cladogenesis in marine fish clades. Contrasting the patterns of phylogenetic diversification in marine fish lineages may facilitate the identification of common evolutionary trajectories versus idiosyncrasies, and ultimately help towards a better understanding of the factors and processes underlying speciation in the marine realm.     

Application Fields of the Empirical Regression - A Case Study

Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density. It is a modelfree mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities. The numerical procedures may be applied for calculation of the mean course of an unknown relation hidden in the measured data. Disregarding the statistical background an other aspect of application is the analyzing of time series, especially smoothing of time series and modelfree recording of the trend component in non-stationary time series. The calculated regression curve provides an objective basis for comparing of different measured courses as well as for a further evaluation, e. g. in respect of a suitable choice of an analytical expression. The possibility of interpolation and the smoothing properties of empirical regression give essential advantages for internal regression as one step in the process of model construction.     

Analysis of interval‐censored recurrent event processes subject to resolution

Interval‐censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. In some settings, chronic disease processes may resolve, and individuals will cease to be at risk of events at the time of disease resolution. We develop an expectation‐maximization algorithm for fitting a dynamic mover‐stayer model to interval‐censored recurrent event data under a Markov model with a piecewise‐constant baseline rate function given a latent process. The model is motivated by settings in which the event times and the resolution time of the disease process are unobserved. The likelihood and algorithm are shown to yield estimators with small empirical bias in simulation studies. Data are analyzed on the cumulative number of damaged joints in patients with psoriatic arthritis where individuals experience disease remission.     

Displacement smoothing for the precise MRI-based measurement of strain in soft biological tissues

Displacement and strain are fundamental quantities that describe the normal and pathological mechanical function of soft biological materials. Non-invasive imaging techniques, including displacement-encoded magnetic resonance imaging (MRI), enable the direct calculation of biomaterial displacements during the application of extrinsic mechanical forces. However, because strain is derived from measured MRI-based displacements, data processing must be accomplished to minimise the propagation and amplification of errors. Here, we evaluate smoothing methods (including averaging filters, splines, finite impulse response filters and wavelets) that enable the calculation of strain in biomaterials from MRI-based displacements for minimal error, defined in terms of bias and precision. Displacement and strain precisions were improved using all smoothing methods studied. Precision generally increased with the number of smoothing iterations (i.e. repeated applications) of a chosen smoothing method. The bias depended on the smoothing method and tended to increase with the number of smoothing iterations. A Gaussian filter characterised complex and heterogeneous strain fields with maximum precision and minimum bias. The results suggest that the optimal choice of smoothing method to compute strain for a given biomaterial or tissue application depends on a careful consideration of trade-offs between the improved precision (with increased data smoothing) and the trending increase in bias.     

Robust estimation for ordinary differential equation models

Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data.     

Identifying when weather influences life-history traits of grazing herbivores

1. There is increasing evidence that density-independent weather effects influence life-history traits and hence the dynamics of populations of animals. Here, we present a novel statistical approach to estimate when such influences are strongest. The method is demonstrated by analyses investigating the timing of the influence of weather on the birth weight of sheep and deer. 2. The statistical technique allowed for the pattern of temporal correlation in the weather data enabling the effects of weather in many fine-scale time intervals to be investigated simultaneously. Thus, while previous studies have typically considered weather averaged across a single broad time interval during pregnancy, our approach enabled examination simultaneously of the relationships with weekly and fortnightly averages throughout the whole of pregnancy. 3. We detected a positive effect of temperature on the birth weight of deer, which is strongest in late pregnancy (mid-March to mid-April), and a negative effect of rainfall on the birthweight of sheep, which is strongest during mid-pregnancy (late January to early February). The possible mechanisms underlying these weather-birth weight relationships are discussed. 4. This study enhances our insight into the pattern of the timing of influence of weather on early development. The method is of much more general application and could provide valuable insights in other areas of ecology in which sequences of intercorrelated explanatory variables have been collected in space or in time.     

Low-rank smoothing splines on complicated domains

Smoothing over a domain with irregular boundaries or interior gaps and holes is addressed. Consider the problem of estimating mercury in sediment concentrations in the estuarine waters in New Hampshire. A modified version of low-rank thin plate splines (LTPS) is introduced where the geodesic distance is applied to evaluate dissimilarity of any two data observations: loosely speaking, distances between locations are not measured as the crow flies, but as the fish swims. The method is compared with competing smoothing techniques, LTPS, and finite element L-splines.     

A General Approach to the Predictability Issue in Survival Analysis with Applications

Very often in survival analysis one has to study martingaleintegrals where the integrand is not predictable and where thecounting process theory of martingales is not directly applicable,as for example in nonparametric and semiparametric applicationswhere the integrand is based on a pilot estimate. We call thisthe predictability issue in survival analysis. The problem hasbeen resolved by approximations of the integrand by predictablefunctions which have been justified by ad hoc procedures. Wepresent a general approach to the solution of this problem.The usefulness of the approach is shown in three applications.In particular, we argue that earlier ad hoc procedures do notwork in higher-dimensional smoothing problems in survival analysis.