Generalized n-dimensional biomechanical field analysis using statistical parametric mapping

A variety of biomechanical data are sampled from smooth n-dimensional spatiotemporal fields. These data are usually analyzed discretely, by extracting summary metrics from particular points or regions in the continuum. It has been shown that, in certain situations, such schemes can compromise the spatiotemporal integrity of the original fields. An alternative methodology called statistical parametric mapping (SPM), designed specifically for continuous field analysis, constructs statistical images that lie in the original, biomechanically meaningful sampling space. The current paper demonstrates how SPM can be used to analyze both experimental and simulated biomechanical field data of arbitrary spatiotemporal dimensionality. Firstly, 0-, 1-, 2-, and 3-dimensional spatiotemporal datasets derived from a pedobarographic experiment were analyzed using a common linear model to emphasize that SPM procedures are (practically) identical irrespective of the data's physical dimensionality. Secondly two probabilistic finite element simulation studies were conducted, examining heel pad stress and femoral strain fields, respectively, to demonstrate how SPM can be used to probe the significance of field-wide simulation results in the presence of uncontrollable or induced modeling uncertainty. Results were biomechanically intuitive and suggest that SPM may be suitable for a wide variety of mechanical field applications. SPM's main theoretical advantage is that it avoids problems associated with a priori assumptions regarding the spatiotemporal foci of field signals. SPM's main practical advantage is that a unified framework, encapsulated by a single linear equation, affords comprehensive statistical analyses of smooth scalar fields in arbitrarily bounded n-dimensional spaces.     

The effect of leg preference on postural stability in healthy athletes

In research regarding postural stability, leg preference is often tested and controlled for. However, leg preference may vary between tasks. As athletes are a group of interest for postural stability testing, we evaluated the effect of five leg preference tasks categorization (step up, hop, ball kick, balance, pick up) on single-leg postural stability of 16 field hockey athletes. The ‘center of pressure speed’ was calculated as the primary outcome variable of single-leg postural stability. Secondary variables were ‘mean length of the GRF vector in the horizontal plane’, ‘mean length of the ankle angular velocity vector’, and ‘mean length of the hip angular velocity vector’, as well as the separate outcomes per degree of freedom. Results showed that leg preference was inconsistent between leg preference tasks. Moreover, the primary and secondary variables yielded no significant difference between the preferred and non-preferred legs, regardless of the applied leg preference task categorization (p>0.05). The present findings do not support the usability of leg preference tasks in controlling for bias of postural stability. In conclusion, none of the applied leg preference tasks revealed a significant effect on postural stability in healthy field hockey athletes.     

May random processes explain mating success in leks?

The object of this paper is to verify whether in specific cases the variance of mating success among lekking males may be due exclusively to a random mechanism, as opposed to the adaptive mechanisms of mate choice which are usually postulated in the literature in the framework of sexual selection theory. In fact, some studies attempted to compare observed distributions of male mating success with a Poisson ‘null’ distribution based on the conjecture of random mating; the conjecture is usually rejected. In this paper we construct a plausible model (the ‘null’ hypothesis) for a strictly random non-adaptive pattern of social behaviour of lekking males and females and we perform several simulations for reasonable choices of parameter values. It should be observed that some of the simulations based on our random model lead to a distribution of male mating success which is Poisson-like. However, contrary to predictions, in several simulations a random process of mate choice lead to non-Poissonian distributions. Accordingly, the fact that, when performing a statistical test on several sets of field data, we find both cases which are in agreement with Poisson distribution, or a normal one, and cases which are not, does not allow us to reject the assumption of random male reproductive success. Thus it is legitimate to conjecture that in many cases the inter-individual variability of male mating success might indeed be determined by random processes. If this conjecture were to be confirmed by further studies, the actual significance of sexual selection in the evolution of lekking species should be reassessed, and a novel approach in the analysis of field data would be called for.     

Likelihood-based genetic mark-recapture estimates when genotype samples are incomplete and contain typing errors

Genotypes produced from samples collected non-invasively in harsh field conditions often lack the full complement of data from the selected microsatellite loci. The application to genetic mark-recapture methodology in wildlife species can therefore be prone to misidentifications leading to both ‘true non-recaptures’ being falsely accepted as recaptures (Type I errors) and ‘true recaptures’ being undetected (Type II errors). Here we present a new likelihood method that allows every pairwise genotype comparison to be evaluated independently. We apply this method to determine the total number of recaptures by estimating and optimising the balance between Type I errors and Type II errors. We show through simulation that the standard error of recapture estimates can be minimised through our algorithms. Interestingly, the precision of our recapture estimates actually improved when we included individuals with missing genotypes, as this increased the number of pairwise comparisons potentially uncovering more recaptures. Simulations suggest that the method is tolerant to per locus error rates of up to 5% per locus and can theoretically work in datasets with as little as 60% of loci genotyped. Our methods can be implemented in datasets where standard mismatch analyses fail to distinguish recaptures. Finally, we show that by assigning a low Type I error rate to our matching algorithms we can generate a dataset of individuals of known capture histories that is suitable for the downstream analysis with traditional mark-recapture methods.     

Exploring interactions by second-stage community analyses

Many biological data sets, from field observations and manipulative experiments, involve crossed factor designs, analysed in a univariate context by higher-way analyses of variance which partition out ‘main’ and ‘interaction’ effects. Indeed, tests for significance of interactions among factors, such as differing Before-After responses at Control and Impact sites, are the basis of the widely used BACI strategy for detecting impacts in the environment. There are difficulties, however, in generalising simple univariate definitions of interaction, from classic linear models, to the robust, non-parametric multivariate methods that are commonly required in handling assemblage data. The size of an interaction term, and even its existence at all, depends crucially on the measurement scale, so it is fundamentally a parametric construct. Despite this, certain forms of interaction can be examined using non-parametric methods, namely those evidenced by changing assemblage patterns over many time periods, for replicate sites from different experimental conditions (types of ‘Beyond BACI’ design) - or changing multivariate structure over space, at many observed times. Second-stage MDS, which can be thought of as an MDS plot of the pairwise similarities between MDS plots (e.g. of assemblage time trajectories), can be used to illustrate such interactions, and they can be formally tested by second-stage ANOSIM permutation tests. Similarities between (first-stage) multivariate patterns are assessed by rank-based matrix correlations, preserving the fully non-parametric approach common in marine community studies. The method is exemplified using time-series data on corals from Thailand, macrobenthos from Tees Bay, UK, and macroalgae from a complex recolonisation experiment carried out in the Ligurian Sea, Italy. The latter data set is also used to demonstrate how the analysis copes straightforwardly with certain repeated-measures designs.     

Relating the classical covariance adjustment techniques of multivariate growth curve models to modern univariate mixed effects models

The relationship between the modern univariate mixed model for analyzing longitudinal data, popularized by Laird and Ware (1982, Biometrics 38, 963-974), and its predecessor, the classical multivariate growth curve model, summarized by Grizzle and Allen (1969, Biometrics 25, 357-381), has never been clearly established. Here, the link between the two methodologies is derived, and balanced polynomial and cosinor examples cited in the literature are analyzed with both approaches. Relating the two models demonstrates that classical covariance adjustment for higher-order terms is analogous to including them as random effects in the mixed model. The polynomial example clearly illustrates the relationship between the methodologies and shows their equivalence when all matrices are properly defined. The cosinor example demonstrates how results from each method may differ when the total variance-covariance matrix is positive definite, but that the between-subjects component of that matrix is not so constrained by the growth curve approach. Additionally, advocates of each approach tend to consider different covariance structures. Modern mixed model analysts consider only those terms in a model's expectation (or linear combinations), and preferably the most parsimonious subset, as candidates for random effects. Classical growth curve analysts automatically consider all terms in a model's expectation as random effects and then investigate whether "covariance adjusting" for higher-order terms improves the model. We apply mixed model techniques to cosinor analyses of a large, unbalanced data set to demonstrate the relevance of classical covariance structures that were previously conceived for use only with completely balanced data.     

A Note on the Bias of O'Brien's OLS Test

O'Brien's Ordinary Least Squares (OLS) test is a well known procedure for testing the multivariate one-sided hypothesis when the covariance matrix is unknown. Simulation results have been reported where the actual test level exceeds the nominal one. Here it is shown analytically that the actual level is always larger than the nominal one if the covariance matrix is nonnegative.     

Random effects modeling of multiple binomial responses using the multivariate binomial logit-normal distribution

The multivariate binomial logit-normal distribution is a mixture distribution for which, (i) conditional on a set of success probabilities and sample size indices, a vector of counts is independent binomial variates, and (ii) the vector of logits of the parameters has a multivariate normal distribution. We use this distribution to model multivariate binomial-type responses using a vector of random effects. The vector of logits of parameters has a mean that is a linear function of explanatory variables and has an unspecified or partly specified covariance matrix. The model generalizes and provides greater flexibility than the univariate model that uses a normal random effect to account for positive correlations in clustered data. The multivariate model is useful when different elements of the response vector refer to different characteristics, each of which may naturally have its own random effect. It is also useful for repeated binary measurement of a single response when there is a nonexchangeable association structure, such as one often expects with longitudinal data or when negative association exists for at least one pair of responses. We apply the model to an influenza study with repeated responses in which some pairs are negatively associated and to a developmental toxicity study with continuation-ratio logits applied to an ordinal response with clustered observations.     

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.     

Conspicuous males suffer higher predation risk: visual modelling and experimental evidence from lizards

Colour pattern variation is a striking and widespread phenomenon. Differential predation risk between individuals is often invoked to explain colour variation, but empirical support for this hypothesis is equivocal. We investigated differential conspicuousness and predation risk in two species of Australian rock dragons, Ctenophorus decresii andC. vadnappa . To humans, the coloration of males of these species varies between ‘bright’ and ‘dull’. Visual modelling based on objective colour measurements and the spectral sensitivities of avian visual pigments showed that dragon colour variants are differentially conspicuous to the visual system of avian predators when viewed against the natural background. We conducted field experiments to test for differential predation risk, using plaster models of ‘bright’ and ‘dull’ males. ‘Bright’ models were attacked significantly more often than ‘dull’ models suggesting that differential conspicuousness translates to differential predation risk in the wild. We also examined the influence of natural geographical range on predation risk. Results from 22 localities suggest that predation rates vary according to whether predators are familiar with the prey species. This study is among the first to demonstrate both differential conspicuousness and differential predation risk in the wild using an experimental protocol. Copyright 2003 Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour.      

Estimation of a covariance matrix with zeros

We consider estimation of the covariance matrix of a multivariaterandom vector under the constraint that certain covariancesare zero. We first present an algorithm, which we call iterativeconditional fitting, for computing the maximum likelihood estimateof the constrained covariance matrix, under the assumption ofmultivariate normality. In contrast to previous approaches,this algorithm has guaranteed convergence properties. Droppingthe assumption of multivariate normality, we show how to estimatethe covariance matrix in an empirical likelihood approach. Theseapproaches are then compared via simulation and on an exampleof gene expression.     

Passage order through different pathways in groups of schooling fish,and the diversified leadership hypothesis

The diversified leadership hypothesis proposes that different individuals within a school of fish act as leaders in different circumstances. This ‘circumstantial leadership’ results from inter-individual behavioral variability and a ‘cohesion-dispersion’ tendency modulated by ‘failure-success’ contingencies. The hypothesis predicts that when offered different pathways to escape the restriction of their swimming space, individuals within a group of fish will show

1.

(a) consistent passage orders in each pathway, but     

A novel definition of the multivariate coefficient of variation

The coefficient of variation CV (%) is widely used to measure the relative variation of a random variable to its mean or to assess and compare the performance of analytical techniques/equipments. A review is made of the existing multivariate extensions of the univariate CV where, instead of a random variable, a random vector is considered, and a novel definition is proposed. The multivariate CV obtained only requires the calculation of the mean vector, the covariance matrix and simple quadratic forms. No matrix inversion is needed which makes the new approach equally attractive in high dimensional as in very small sample size problems. As an illustration, the method is applied to electrophoresis data from external quality assessment in laboratory medicine, to phenotypic characteristics of pocket gophers and to a microarray data set.     

A comparison of video and point intercept transect methods for monitoring subtropical coral communities

This study evaluated the use of video transects obtained from SCUBA divers or remote operated vehicle (ROV) and point intercept transect (PIT) method from divers for monitoring subtropical coral communities. Comparisons were made between the datasets obtained by the ROV and SCUBA diver video transect (‘Diver’) and the PIT method on three nearby coral sites with different hydrographies, scleractinian coral composition, dominant species and percentage cover. There was no significant difference between the ROV and ‘Diver’ datasets whereas the PIT method tended to over-estimate percentage cover at sites where corals are not extensive. Power analysis showed that the minimum detectable change in coral percentage cover, δ, had low mean values between 0.39% and 1.65% for the ROV dataset, 0.66% for the “Diver’ dataset, and 12.11% for the PIT dataset. This implied that the ROV and SCUBA survey methods can produce higher precision in terms of detecting temporal changes in coral communities and are thus more suitable for scientific research and management purposes than the PIT method. Other advantages of using video transects by SCUBA divers or ROV include provision of permanent records for subsequent studies and public information, less field time incurred and wider survey areas.     

Samuel Butler and human long term memory: Is the cupboard bare?

Memory studies in biological systems distinguish three informational processes that are generally sequential—production/acquisition, storage, and retrieval/use. Identification of DNA as a storage form for hereditary information accelerated progress in that field. Assuming the path of successful elucidation in one memory field (heredity) to be heuristic for elucidation in another (brain), then progress in neuroscience should accelerate when a storage form is identified. In the 19th century Ewald Hering and Samuel Butler held that heredity and brain memory both involved the storage of information and that the two forms of storage were the same. Hering specified storage as ‘molecular vibrations’ but, while making a fuller case, Butler was less committal. In the 20th century, the ablation studies of Karl Lashley failed to identify unique sites for storage of brain information, and Donald Hebb's ‘synaptic plasticity’ hypothesis of distributed storage over a neuronal network won favor. In the 21st century this has come under attack, and the idea that brain and hereditary information are stored as DNA is advocated. Thus, albeit without attribution, Butler's idea is reinstated. Yet, while the case is still open, the synaptic plasticity and DNA hypotheses have problems. Two broad alternatives remain on the table. Long term memory is located: (1) in the brain, either in some other macromolecular form (e.g. protein, lipid) or in some sub-molecular form (e.g. quantum computing and ‘brain as holograph’ hypotheses) or (2) outside the brain. The suggestion of the medieval physician Avicenna that the brain ‘cupboard’ is bare—i.e. the brain is a perceptual, not storage, organ—is consistent with a mysterious ‘universe as holograph’ model. Understanding how Butler came to contribute could be heuristic for future progress in a field fraught with ‘fractionation and disunity’.     

Kinetics of the Multistep Rupture of Fibrin ‘A-a’ Polymerization Interactions Measured Using Atomic Force Microscopy

Fibrin, the structural scaffold of blood clots, spontaneously polymerizes through the formation of ‘A-a’ knob-hole bonds. When subjected to external force, the dissociation of this bond is accompanied by two to four abrupt changes in molecular dimension observable as rupture events in a force curve. Herein, the configuration, molecular extension, and kinetic parameters of each rupture event are examined. The increases in contour length indicate that the D region of fibrinogen can lengthen by ∼50% of the length of a fibrin monomer before rupture of the ‘A-a’ interaction. The dependence of the dissociation rate on applied force was obtained using probability distributions of rupture forces collected at different pull-off velocities. These distributions were fit using a model in which the effects of the shape of the binding potential are used to quantify the kinetic parameters of forced dissociation. We found that the weak initial rupture (i.e., event 1) was not well approximated by these models. The ruptured bonds comprising the strongest ruptures, events 2 and 3, had kinetic parameters similar to those commonly found for the mechanical unfolding of globular proteins. The bonds ruptured in event 4 were well described by these analyses, but were more loosely bound than the bonds in events 2 and 3. We propose that the first event represents the rupture of an unknown interaction parallel to the ‘A-a’ bond, events 2 and 3 represent unfolding of structures in the D region of fibrinogen, and event 4 is the rupture of the ‘A-a’ knob-hole bond weakened by prior structural unfolding. Comparison of the activation energy obtained via force spectroscopy measurements with the thermodynamic free energy of ‘A-a’ bond dissociation indicates that the ‘A-a’ bond may be more resistant to rupture by applied force than to rupture by thermal dissociation.     

One-Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations

When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, SRIVASTAVA and AWAN (1982) develop one-way ANOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, KABE (1965), (1974).     

Active choice, passive attraction and the cognitive machinery of acoustic preferences

Female preferences for loud calls are widespread among animals that communicate acoustically, but their ‘strategic’ role is still controversial. According to the ‘passive attraction’ hypothesis, females are more likely to respond to loud calls simply because these calls are more effective at stimulating their acoustic receptors and primary neurons. The ‘active choice’ hypothesis, however, assumes that females use sound intensity as a cue to assess the power and location of sound sources and to respond accordingly. To test which hypothesis could best explain the preference for loud calls of female green toads, Bufo viridis, we carried out multitrial discrimination experiments, in which females were given a choice between two stimuli differing in either the power or the distance of their sources or both. In the laboratory, females could discern differences in intensity caused by differences in power or location of the acoustic sources. This ability increased in field experiments, when the speakers and receivers were further apart than in the laboratory experiments. Phonotactic behaviour did not vary significantly between females, but did within females: in their second trial, females were more likely to approach the closer speaker than in the first trial. These findings suggest that sound intensity plays a more complex role in female mate choice than that recognized by the passive attraction hypothesis. To understand female preferences and, ultimately, mate choice, attention should be focused directly on the computational processes of the female's central nervous system.