Locally adaptive function estimation for binary regression models

In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.     

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.     

Interspecific variation of body shape and sexual dimorphism in three coexisting species of the genus <Emphasis Type="Italic">Petrotilapia</Emphasis> (Teleostei: Cichlidae) from Lake Malawi

Differences in color patterns have been the most used feature in describing cichlid species belonging to genus Petrotilapia from Lake Malawi. In this study, we quantified morphological variation in body shape within and among three coexisting Petrotilapia species using landmark-based geometric morphometric methods. Statistic analyses revealed significant body shape differences among species but not between sexes. Post hoc multiple comparisons based on Mahalanobis distances revealed that P. nigra was significantly different from P. genalutea and Petrotilapia sp., whereas the latter two were not significantly different. The splines generated showed that the most pronounced variation was in the head region, in which P. nigra had a relatively longer and deeper head than the other two. The most clear-cut distinction was in gape length; P. genalutea had the longest gape, followed by Petrotilapia sp., whereas P. nigra had the shortest gape. Body depth was shallower in P. nigra than the others. When comparing sexes by their centroid size, ANOVA revealed that males were bigger than females. Therefore, we conclude that color is not the only feature that can distinguish these congeners. We discuss the observed sexual dimorphism in terms of sexual selection and relate morphological variation among species to feeding behavior, which may help explain their coexistence in nature.     

An example of a regular inbreeding system with cubic ancestral growth that preserves some genetic variability

A specific regular inbreeding system of quadruple half-second cousin mating is considered. A regular inbreeding system can be thought of as a graph which satisfies certain natural homogeneity properties. Random walks X _n and Y _n are introduced on the nodes of the graph; the event {X _n=Y_n} is a renewal event by the homogeneity properties. In Arzberger (1985) it is shown that 1) graphs associated with left cancellative semigroups are regular, and 2) for regular systems, the population becomes genetically uniform if and only if the event {X _n=Y_n} is recurrent. In Arzberger (1986) the system of quadruple half-second cousin mating is associated with a cancellative semigroup, thus the system is regular. In this paper we show that 1) A_n is asymptotically of the form cn ³, where A _n is the number of ancestors n generations into the past, 2) {X _n=Y_n} is not recurrent (this is shown by associating (X _n, Y _n) with a random walk in Z ³, 3) P[X _3n =Y _3n ] is asymptotically of the form cn ^–3/2. Thus, in this example, genetic heterogeneity is maintained, with a cubic rate of growth for A_n, not by an exponential growth rate, as in all previous examples of regular inbreeding systems in which genetic heterogeneity is maintained.     

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.     

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.     

Ontogenetic shifts in morphology and resource use of cisco Coregonus artedi

Two previously described lacustrine cisco Coregonus spp. morphs [i.e. a small (<300 mm fork length, L_F), low‐gillraker (≤44) morph and a large (≥300 mm L_F), high‐gillraker (≥45) morph] from Great Slave Lake, NT, Canada, were found to be synonymous with cisco Coregonus artedi. Geometric body shape did not differ between the two size classes nor could they be differentiated by 24 size‐corrected linear measurements, indicating that the two groups had similar phenotypes. Strong, positive correlations between all linear characters and geometric centroid size (a composite variable of fish body length, mass and age) suggested that body morphology changed with age as fish grew. Total gillraker number (N_GR) increased with L_F according to: N_GR = 36·3 + 0·034L_F. Differences in gillraker number and phenotype with age and size were explained by shifts in habitat and trophic resource use. Relative abundance within 0–30, 30–60, 60–90 and >90 m depth strata differed between size classes suggesting that morphology changed when fish shifted their habitat as they grew older. Large C. artedi had lower δ¹³C and slightly higher δ¹⁵N, indicating greater reliance on pelagic prey resources (i.e. more or larger zooplankton, such as Mysis spp.), compared to small C. artedi, which relied slightly more on benthic prey. Gillraker shape and number have always been used as key diagnostic characters in coregonine taxonomy; based on the findings presented here, ontogenetic shifts should be accounted for in resulting classifications.     

Smoothing population size estimates for time-stratified mark-recapture experiments using Bayesian P-splines

Petersen-type mark-recapture experiments are often used to estimate the number of fish or other animals in a population moving along a set migration route. A first sample of individuals is captured at one location, marked, and returned to the population. A second sample is then captured farther along the route, and inferences are derived from the numbers of marked and unmarked fish found in this second sample. Data from such experiments are often stratified by time (day or week) to allow for possible changes in the capture probabilities, and previous methods of analysis fail to take advantage of the temporal relationships in the stratified data. We present a Bayesian, semiparametric method that explicitly models the expected number of fish in each stratum as a smooth function of time. Results from the analysis of historical data from the migration of young Atlantic salmon (Salmo salar) along the Conne River, Newfoundland, and from a simulation study indicate that the new method provides more precise estimates of the population size and more accurate estimates of uncertainty than the currently available methods.