Predicting long-term response to selection

Lande's equation for predicting the response of trait means to a shift in optimal trait values is tested using a stochastic simulation model. The simulated population is finite, and each individual has a finite number of loci. Therefore, selection may cause allele frequencies and distributions to change over time. Since the equation assumes constant genetic parameters, the degree to which such allelic changes affect predictions can be examined. Predictions are based only on information available at generation zero of directional selection. The quality of the predictions depends on the nature of allelic distributions in the original population. If allelic effects are approximately normally distributed, as assumed in Lande's Gaussian approximation to the continuum-of-alleles model, the predictions are very accurate, despite small changes in the G matrix. If allelic effects have a leptokurtic distribution, as is likely in Turelli's 'house-of-cards' approximation, the equation underestimates the rate of response and correlated response, and overestimates the time required for the trait means to reach their equilibrium values. Models with biallelic loci have limits as to the amount of trait divergence possible, since only two allelic values are available at each of a finite set of loci. If the new optimal trait values lie within these limits, predictions are good, if not, singularity in the G matrix results in suboptimal equilibria, despite the presence of genetic variance for each individual trait.     

Slip-induced fall-risk assessment based on regular gait pattern in older adults

Aging-associated fall-risk assessment is crucial for fall prevention. Thus, this study aimed to develop a prognostic model to predict fall-risk following an unexpected over-ground slip perturbation based on normal gait pattern in healthy older adults. 112 healthy older adults who experienced a novel slip in a safe laboratory environment were included. Their slip trial and natural walking trial immediately prior to it were analyzed. To identify the best fall-risk predictive model, gait related variables including step length, segment angles, center of mass state, and ground reaction force (GRF) were determined and inputted into a stepwise logistic regression. The optimal slip-induced fall prediction model was based on the right thigh angle at slipping foot touchdown (TD), the maximum GRF of the slipping limb after TD, and the momentum change from TD to recovery foot liftoff (LO), with an overall prediction accuracy of 75.9%, predicting 74.5% of falls (sensitivity) and 77.2% of recoveries (specificity). Conversely, a model based on clinical and demographic measures predicted 78.2% of falls and 47.4% of recoveries, resulting in a much lower overall accuracy of 62.5%. The fall-risk model based on normal gait pattern which was developed for slip-induced perturbations in healthy older adults was able to provide a high predictive accuracy. This information could provide insight about the ideal normal gait measures which could be used to contribute towards development of therapeutic strategies related to dynamic balance and fall prevention to enhance preventive interventions in populations with high-risk for slip-induced falls.     

Correction of the inertial effect resulting from a plate moving under low-friction conditions

The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 (body weight) during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint-moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip.     

Effects of obesity on slip-induced fall risks among young male adults

Obesity is associated with structural and functional limitations with impairment of normal gait. Although falls have been identified as the most common cause of injuries in the obese, the mechanisms associated with increased fall risk among the obese population are still unknown. The purpose of this study was to investigate the influence of gait adaptations of the obese individuals and its implication on risk of slip initiations as measured by friction demand characteristics. To exclude the aging and gender effects, a total of ten healthy young male adults participated in the study. Kinematic and kinetic data were collected using a three-dimensional motion analysis system and force plates while subjects were walking at their self-selected walking pace. Results indicated that young obese adults walked similarly as their lean counterparts except for exhibiting greater step width and higher transversal friction demand, suggesting that slip-induced fall risks are similar along the horizontal direction, but increased along the transversal direction under certain floor conditions.     

Can stability really predict an impending slip-related fall among older adults?

The primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices, obtained during normal walking among community-dwelling older adults. One hundred and eighty seven community-dwelling older adults participated in the study. After walking regularly for 20 strides on a walkway, participants were subjected to an unannounced slip during gait under the protection of a safety harness. Full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates. Stability variables, including feasible-stability-region measurement, margin of stability, the maximum Floquet multiplier, the Lyapunov exponents (short- and long-term), and the variability of gait parameters (including the step length, step width, and step time), were calculated for each subject. Sensitivity of predicting slip outcome (fall vs. recovery) was examined for each stability variable using logistic regression. Results showed that the feasible-stability-region measurement predicted fall incidence among these subjects with the highest sensitivity (68.4%). Except for the step width (with an sensitivity of 60.2%), no other stability variables could differentiate fallers from those who did not fall for the sample included in this study. The findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible-stability-region measurement or variability of the step width.     

Predicted threshold against backward balance loss following a slip in gait

The purpose of this study was to use a 7-link, moment-actuated human model to predict, at liftoff of the trailing foot in gait, the threshold of the center of mass (COM) velocity relative to the base of support (BOS) required to prevent backward balance loss during single stance recovery from a slip. Five dynamic optimization problems were solved to find the minimum COM velocities that would allow the simulation to terminate with the COM above the BOS when the COM started 0.25, 0.5, 0.75, 1.0, and 1.25 foot lengths behind the heel of the stance foot (i.e., behind the BOS). The initial joint angles of the model were based on averaged data from experimental trials. Foot-ground contact was modeled using 16 visco-elastic springs distributed under the stance foot. Slipping was modeled by setting the sliding coefficient of friction of these springs to 0.02. The forward velocity of the COM necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non-slip conditions. The predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking. In all trials in which a subject's COM had a velocity below the predicted threshold, the subject's recovery foot landed posterior to the slipping foot as predicted. Finally, combining experimental data with optimization, we verified that the 7-link model could more accurately predict gait stability than a 2-link model.     

Time Inhomogeneous Mutation Models with Birth Date Dependence

The classic Luria–Delbrück model for fluctuation analysis is extended to the case where the split instant distributions of cells are not i.i.d.: the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. In particular, it is possible to consider subprobability distributions and to model non-exponential growth. The extended model leads to a family of probability distributions which depend on the expected number of mutations, the death probability of mutant cells, and the split instant distributions of normal and mutant cells. This is deduced from the Bellman–Harris integral equation, written for the birth date inhomogeneous case. A new theorem of convergence for the final mutant counts is proved, using an analytic method. Particular examples like the Haldane model or the case where hazard functions of the split-instant distributions are proportional are studied. The Luria–Delbrück distribution with cell deaths is recovered. A computation algorithm for the probabilities is provided.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity. The concluding discussion argues against the random walk equation because it embodies a constraint that is not valid, and because it implies specific parameters that may be spurious.     

A semiparametric Bayesian approach for structural equation models

In the development of structural equation models (SEMs), observed variables are usually assumed to be normally distributed. However, this assumption is likely to be violated in many practical researches. As the non‐normality of observed variables in an SEM can be obtained from either non‐normal latent variables or non‐normal residuals or both, semiparametric modeling with unknown distribution of latent variables or unknown distribution of residuals is needed. In this article, we find that an SEM becomes nonidentifiable when both the latent variable distribution and the residual distribution are unknown. Hence, it is impossible to estimate reliably both the latent variable distribution and the residual distribution without parametric assumptions on one or the other. We also find that the residuals in the measurement equation are more sensitive to the normality assumption than the latent variables, and the negative impact on the estimation of parameters and distributions due to the non‐normality of residuals is more serious. Therefore, when there is no prior knowledge about parametric distributions for either the latent variables or the residuals, we recommend making parametric assumption on latent variables, and modeling residuals nonparametrically. We propose a semiparametric Bayesian approach using the truncated Dirichlet process with a stick breaking prior to tackle the non‐normality of residuals in the measurement equation. Simulation studies and a real data analysis demonstrate our findings, and reveal the empirical performance of the proposed methodology. A free WinBUGS code to perform the analysis is available in Supporting Information.     

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

The replicator equation model for the evolution of individual behaviors in a single species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional continuously stable strategy (CSS) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger neighborhood invader strategy (NIS) concept is needed if the supports are arbitrary.     

Influence of simulated neuromuscular noise on movement variability and fall risk in a 3D dynamic walking model

People at risk of falling exhibit increased gait variability, which may predict future falls. However, the causal mechanisms underlying these correlations are not well known. Increased neuronal noise associated with aging likely leads to increased gait variability, which could in turn lead to increased fall risk. This paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling, and aims to determine the extent to which changes in gait variability directly predict fall risk. We used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability. Noise was applied to this controller to approximate neuromuscular noise in humans. Noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell. With increases in noise amplitude, the model fell more often and after fewer steps. Gait variability increased with noise amplitude and predicted increased probability of falling. Importantly, these relationships were not linear. At either low gait variability or very high gait variability, small increases in noise and variability affected probability of falling very little. Conversely, at intermediate noise and/or variability levels, the same small increases resulted in large increases in probability of falling. Our results validate the idea that age-related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk. However, neuromuscular noise remains only one of many important factors that need to be considered. These findings have important implications for fall prevention research and practice.     

General models for segregation analysis.

Theoretical details are given of various oligogenic models for segregation analysis that are available as a general segregation analysis ("GENSEG") package, programmed in FORTRAN iv. The models allow for up to two autosomal loci and one X-linked locus, normally distributed or dichotomous phenotypes, variable age of onset, and various ascertainment functions (including one that allows the probability of becoming a proband to be dependent on the age of onset). Current programs are limited to the analysis of 2-generational data, using the joint likelihood of the sibship and parental phenotypes, unless it can be assumed that the pedigrees being analyzed are a random sample from the population; half-sibships and twins, however, are explicitly allowed.     

Computational wear prediction of a total knee replacement from in vivo kinematics

Wear of ultra-high molecular weight polyethylene bearings in total knee replacements remains a major limitation to the longevity of these clinically successful devices. Few design tools are currently available to predict mild wear in implants based on varying kinematics, loads, and material properties. This paper reports the implementation of a computer modeling approach that uses fluoroscopically measured motions as inputs and predicts patient-specific implant damage using computationally efficient dynamic contact and tribological analyses. Multibody dynamic simulations of two activities (gait and stair) with two loading conditions (70-30 and 50-50 medial-lateral load splits) were generated from fluoroscopic data to predict contact pressure and slip velocity time histories for individual elements on the tibial insert surface. These time histories were used in a computational wear analysis to predict the depth of damage due to wear and creep experienced by each element. Predicted damage areas, volumes, and maximum depths were evaluated against a tibial insert retrieved from the same patient who provided the in vivo motions. Overall, the predicted damage was in close agreement with damage observed on the retrieval. The gait and stair simulations separately predicted the correct location of maximum damage on the lateral side, whereas a combination of gait and stair was required to predict the correct location on the medial side. Predicted maximum damage depths were consistent with the retrieval as well. Total computation time for each damage prediction was less than 30 min. Continuing refinement of this approach will provide a robust tool for accurately predicting clinically relevant wear in total knee replacements.     

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.     

Effects of vibration training in reducing risk of slip-related falls among young adults with obesity

This study examined the effects of controlled whole-body vibration training on reducing risk of slip-related falls in people with obesity. Twenty-three young adults with obesity were randomly assigned into either the vibration or placebo group. The vibration and placebo groups respectively received 6-week vibration and placebo training on a side-alternating vibration platform. Before and after the training, the isometric knee extensors strength capacity was measured for the two groups. Both groups were also exposed to a standardized slip induced by a treadmill during gait prior to and following the training. Dynamic stability and fall incidences responding to the slip were also assessed. The results indicated that vibration training significantly increased the muscle strength and improved dynamic stability control at recovery touchdown after the slip occurrence. The improved dynamic stability could be resulted from the enhanced trunk segment movement control, which may be attributable to the strength increment caused by the vibration training. The decline of the fall rates from the pre-training slip to the post-training one was greater among the vibration group than the placebo group (45% vs. 25%). Vibration-based training could be a promising alternative or additional modality to active exercise-based fall prevention programs for people with obesity.     

Weather limitations on the application of dinoseb-in-oil for cane vigour control in raspberry

Data on crop growth suggested that only 8 days are available for timely spraying of dinoseb-in-oil for control of cane vigour in raspberry in east-central Scotland. Crop records were linked with meteorological data to indicate the dates between which this 8-day period might fall. The meteorological data were then examined to assess the probability and likely duration of conditions suitable for spraying within the period when the crop is amenable to the spray treatment. The results indicated that unfavourable weather conditions may severely restrict the opportunities available for spray application by conventional equipment, the main limitation being high wind speed. The likelihood of rain after application putting the spray treatment at risk was found to be low. The infinitely compound Poisson distribution was found to be suitable for graduating the observed frequency distributions of suitable spraying conditions. Diagrams of frequency distributions were produced which can be used to assess the spraying capacity required to ensure timely application over the total area of a grower's plantations. It is suggested that the approach used in this investigation could be satisfactorily applied to a wider range of crops and spraying operations.     

The size distribution of human hematogenous metastases.

The development of primary cancers and their subsequent metastases occur through a complex sequence of discrete steps. A hypothesis is proposed here whereby the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertz-normal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agreement, correcting for this over-representation. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertz-normal distributions for the size distribution of metastases.     

Disturbance type and gait speed affect fall direction and impact location

Since falling to the side and impacting on or near the hip increase hip fracture risk, we examined the fall direction and pelvis impact location resulting from four disturbances (faint, slip, step down, trip) at three gait speeds (fast, normal, slow) in 14 young adults instructed not to attempt recovery. We hypothesized that certain disturbances such as faints and slips and slow walking speed were more likely to result in an impact on the hip. For each trial, the fall direction, impact location and pelvis impact velocity were measured. The results showed that both disturbance type and gait speed significantly affected fall direction and impact location (analysis of covariance with repeated measures, p< or =0.0001) with a significant interaction (p<0.05). Trips and steps down usually resulted in forward falls, with frontal impacts regardless of gait speed. At fast gait speed, slips and faints also usually resulted in forward falls, with frontal impacts. As gait speed decreased, however, slips usually resulted in sideways or backward falls, with impact on the hip or buttocks, and faints resulted in a greater number of sideways falls, with impact near the hip. Therefore, compared to other disturbances and gait speeds, slipping or fainting while walking slowly was more likely to result in an impact on the hip, suggesting a greater risk for hip fracture. Furthermore, 56% of the impact velocities generated were within one standard deviation of the estimate of the mean impact velocity needed to fracture an elderly femur.