Estimating demographic parameters for loggerhead sea turtles using mark–recapture data and a multistate model

The survival for adult loggerhead sea turtles from a saturation tagging study on Bald Head Island, NC, USA, was estimated using a multistate model with unobservable states to relax assumptions that are violated when survival is estimated from multistate models and produce more accurate estimates of survival, recapture, and breeding transition probabilities. The influence of time, trap dependence, and low site fidelity to the study nesting beach on survival and recapture were examined. The best model given the data included an imprecise site-fidelity effect on survival, constrained the reproductive cycle to 4 years, and contained a time effect on recapture rates. The estimate of annual survival for adult females was of 0.85, producing the highest estimate in the literature for loggerhead sea turtles. Multistate models should be applied to other nesting beach data for sea turtles to improve survival estimates and in turn the ability to model and manage populations.     

A method for assessing the fit of a constitutive material model to experimental stress–strain data

Higher-order polynomial functions can be used as a constitutive model to represent the mechanical behaviour of biological materials. The goal of this study was to present a method for assessing the fit of a given constitutive three-dimensional material model. Goodness of fit was assessed using multiple parameters including the root mean square error and Hotelling's T ²-test. Specifically, a polynomial model was used to characterise the stress–strain data, varying the number of model terms used (45 combinations of between 3 and 11 terms) and the manner of optimisation used to establish model coefficients (i.e. determining coefficients either by parameterisation of all data simultaneously or averaging coefficients obtained by parameterising individual data trials). This framework for model fitting helps to ensure that a given constitutive formulation provides the best characterisation of biological material mechanics.     

Buckley–James boosting model based on extreme learning machine and random survival forests

Buckley–James (BJ) model is a typical semiparametric accelerated failure time model, which is closely related to the ordinary least squares method and easy to be constructed. However, traditional BJ model built on linearity assumption only captures simple linear relationships, while it has difficulty in processing nonlinear problems. To overcome this difficulty, in this paper, we develop a novel regression model for right-censored survival data within the learning framework of BJ model, basing on random survival forests (RSF), extreme learning machine (ELM), and L₂ boosting algorithm. The proposed method, referred to as ELM-based BJ boosting model, employs RSF for covariates imputation first, then develops a new ensemble of ELMs—ELM-based boosting algorithm for regression by ensemble scheme of L₂ boosting, and finally, uses the output function of the proposed ELM-based boosting model to replace the linear combination of covariates in BJ model. Due to fitting the logarithm of survival time with covariates by the nonparametric ELM-based boosting method instead of the least square method, the ELM-based BJ boosting model can capture both linear covariate effects and nonlinear covariate effects. In both simulation studies and real data applications, in terms of concordance index and integrated Brier sore, the proposed ELM-based BJ boosting model can outperform traditional BJ model, two kinds of BJ boosting models proposed by Wang et al., RSF, and Cox proportional hazards model.     

Perception–action coupling model for human locomotor pointing

How do humans achieve the precise positioning of the feet during walking, for example, to reach the first step of a stairway? We addressed this question at the visuomotor integration level. Based on the optical specification of the required adaptation, a dynamical system model of the visuomotor control of human locomotor pointing was devised for the positioning of a foot on a visible target on the floor during walking. Visuomotor integration consists of directly linking optical information to a motor command that specifically modulates step length in accordance with the ongoing dynamics of locomotor pattern generation. The adaptation of locomotion emerges from a perception-action coupling type of control based on temporal information rather than on feedforward planning of movements. The proposed model reproduces experimental results obtained for human locomotor pointing.     

A nonlocal kinetic model for predator–prey interactions

We extend the aggregation model from Fetecau (2011) by adding a field of vision to individuals and by including a second species. The two species, assumed to have a predator–prey relationship, have dynamics governed by nonlocal kinetic equations that include advection and turning. The latter is the main mechanism for aggregation and orientation, which results from interactions among individuals of the same species as well as predator–prey relationships. We illustrate numerically a diverse set of predator–prey behaviors that can be captured by this model. We show that a prey’s escape outcome depends on the social interactions between its group members, the prey’s field of vision and the sophistication of the predator’s hunting strategies.     

Scientific data and theories for salmonellosis dose–response assessment

An “expansive” risk assessment approach is illustrated, characterizing dose–response relationships for salmonellosis in light of the full body of evidence for human and murine superorganisms. Risk assessments often require analysis of costs and benefits for supporting public health decisions. Decision-makers and the public need to understand uncertainty in such analyses for two reasons. Uncertainty analyses provide a range of possibilities within a framework of present scientific knowledge, thus helping to avoid undesirable consequences associated with the selected policies. And, it encourages the risk assessors to scrutinize all available data and models, thus helping avoid subjective or systematic errors. Without the full analysis of uncertainty, decisions could be biased by judgments based solely on default assumptions, beliefs, and statistical analyses of selected correlative data. Alternative data and theories that incorporate variability and heterogeneity for the human and murine superorganisms, particularly colonization resistance, are emerging as major influences for microbial risk assessment. Salmonellosis risk assessments are often based on conservative default models derived from selected sets of outbreak data that overestimate illness. Consequently, the full extent of uncertainty of estimates of annual number of illnesses is not incorporated in risk assessments and the presently used models may be incorrect.     

On the effect of sharp rises in blood pressure in the Shah–Humphrey model for intracranial saccular aneurysms

We consider the model originally proposed by Shah and Humphrey (J Biomech 32:593–599, 1999) for a class of intracranial saccular aneurysms and show that for constant pressure the addition of the viscoelastic term corresponding to the presence of cerebral spinal fluid outside the membrane, no matter how small, does ensure convergence to an equilibrium. Our arguments apply to a general equation of this type, and thus also hold for variations of this model such as that proposed by David and Humphrey (J Biomech 36:1143–1150, 2003). On the other hand, it is known that the presence of damping may destabilize periodic orbits of periodically forced systems or even prevent them from existing altogether. We present numerical simulations showing that for some forcing terms the high-frequency oscillations do not die out with time, and a much more complex behaviour may emerge as a discontinuous forcing term is approached. The key point for this situation to occur is related to the derivative of the forcing term, supporting the hypothesis that sharper rises (or falls) in blood pressure may increase the risk of aneurysm rupture.     

Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

In this article, a new approach—namely, the extended Parker–Sochacki method (EPSM)—is presented for solving the Michaelis–Menten nonlinear enzymatic reaction model. The Parker–Sochacki method (PSM) is combined with a new resummation method called the Sumudu–Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge–Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future.     

The model–data fusion pitfall: assuming certainty in an uncertain world

Model–data fusion is a powerful framework by which to combine models with various data streams (including observations at different spatial or temporal scales), and account for associated uncertainties. The approach can be used to constrain estimates of model states, rate constants, and driver sensitivities. The number of applications of model–data fusion in environmental biology and ecology has been rising steadily, offering insights into both model and data strengths and limitations. For reliable model–data fusion-based results, however, the approach taken must fully account for both model and data uncertainties in a statistically rigorous and transparent manner. Here we review and outline the cornerstones of a rigorous model–data fusion approach, highlighting the importance of properly accounting for uncertainty. We conclude by suggesting a code of best practices, which should serve to guide future efforts.     

Dating and localizing an invasion from post-introduction data and a coupled reaction–diffusion–absorption model

Journal of Mathematical Biology - Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in...     

Investigation of Turing instability for the Gierer–Meinhardt model

The dependence of the emergence of Turing instability for a distributed system of nonlinear differential equations that describe hydra morphogenesis based on the oscillatory properties of the corresponding trajectories of the system was investigated. The limits in the parameter space that provide diffusive instability were obtained. The frequency and amplitude dependences of the resulting spatial self oscillations on the values of the main parameters were investigated. Comparative analysis of the properties of the distributed system and corresponding trajectories of the system was carried out and the analytical conclusions were confirmed by the solutions of the system that were found using MATLAB.

     

Pulse waves for a semi-discrete Morris–Lecar type model

 We establish the existence of a pulse traveling wave for an infinite system of ODEs modeling a one dimensional string of nerve cells of identical Morris–Lecar type dynamics:

Probability-based collaborative filtering model for predicting gene–disease associations

Background

Accurately predicting pathogenic human genes has been challenging in recent research. Considering extensive gene–disease data verified by biological experiments, we can apply computational methods to perform accurate predictions with reduced time and expenses.

Methods

We propose a probability-based collaborative filtering model (PCFM) to predict pathogenic human genes. Several kinds of data sets, containing data of humans and data of other nonhuman species, are integrated in our model. Firstly, on the basis of a typical latent factorization model, we propose model I with an average heterogeneous regularization. Secondly, we develop modified model II with personal heterogeneous regularization to enhance the accuracy of aforementioned models. In this model, vector space similarity or Pearson correlation coefficient metrics and data on related species are also used.

Results

We compared the results of PCFM with the results of four state-of-arts approaches. The results show that PCFM performs better than other advanced approaches.

Conclusions

PCFM model can be leveraged for predictions of disease genes, especially for new human genes or diseases with no known relationships.

     

The role of noise in a predator–prey model with Allee effect

The existence and implications of alternative stable states in ecological systems have been investigated extensively within deterministic models. However, it is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. Thus, in this paper, we study the role of noise on the pattern formation of a spatial predator–prey model with Allee effect. The obtained results show that the spatially extended system exhibits rich dynamic behavior. More specifically, the stationary pattern can be induced to be a stable target wave when the noise intensity is small. As the noise intensity is increased, patchy invasion emerges. These results indicate that the dynamic behavior of predator–prey models may be partly due to stochastic factors instead of deterministic factors, which may also help us to understand the effects arising from the undeniable susceptibility to random fluctuations of real ecosystems.     

Brachypodium as an emerging model for cereal–pathogen interactions

Background Cereal diseases cause tens of billions of dollars of losses annually and have devastating humanitarian consequences in the developing world. Increased understanding of the molecular basis of cereal host–pathogen interactions should facilitate development of novel resistance strategies. However, achieving this in most cereals can be challenging due to large and complex genomes, long generation times and large plant size, as well as quarantine and intellectual property issues that may constrain the development and use of community resources. Brachypodium distachyon (brachypodium) with its small, diploid and sequenced genome, short generation time, high transformability and rapidly expanding community resources is emerging as a tractable cereal model.Scope Recent research reviewed here has demonstrated that brachypodium is either susceptible or partially susceptible to many of the major cereal pathogens. Thus, the study of brachypodium–pathogen interactions appears to hold great potential to improve understanding of cereal disease resistance, and to guide approaches to enhance this resistance. This paper reviews brachypodium experimental pathosystems for the study of fungal, bacterial and viral cereal pathogens; the current status of the use of brachypodium for functional analysis of cereal disease resistance; and comparative genomic approaches undertaken using brachypodium to assist characterization of cereal resistance genes. Additionally, it explores future prospects for brachypodium as a model to study cereal–pathogen interactions.Conclusions The study of brachypodium–pathogen interactions appears to be a productive strategy for understanding mechanisms of disease resistance in cereal species. Knowledge obtained from this model interaction has strong potential to be exploited for crop improvement.     

A female head–neck model for rear impact simulations

Several mathematical cervical models of the 50th percentile male have been developed and used for impact biomechanics research. However, for the 50th percentile female no similar modelling efforts have been made, despite females being subject to a higher risk of soft tissue neck injuries. This is a limitation for the development of automotive protective systems addressing Whiplash Associated Disorders (WADs), most commonly caused in rear impacts, as the risk for females sustaining WAD symptoms is double that of males.In this study, a finite element head and neck model of a 50th percentile female was validated in rear impacts. A previously validated ligamentous cervical spine model was complemented with a rigid body head, soft tissues and muscles. In both physiological flexion-extension motions and simulated rear impacts, the kinematic response at segment level was comparable to that of human subjects. Evaluation of ligament stress levels in simulations with varied initial cervical curvature revealed that if an individual assumes a more lordotic posture than the neutral, a higher risk of WAD might occur in rear impact.The female head and neck model, together with a kinematical whole body model which is under development, addresses a need for tools for assessment of automotive protection systems for the group which is at the highest risk to sustain WAD.     

Stimulus–effect relations for left ventricular growth obtained with a simple multi-scale model: the influence of hemodynamic feedback

Cardiac growth is an important mechanism for the human body to respond to changes in blood flow demand. Being able to predict the development of chronic growth is clinically relevant, but so far models to predict growth have not reached consensus on the stimulus–effect relation. In a previously published study, we modeled cardiac and hemodynamic function through a lumped parameter approach. We evaluated cardiac growth in response to valve disease using various stimulus–effect relations and observed an unphysiological decline pump function. Here we extend that model with a model of hemodynamic feedback that maintains mean arterial pressure and cardiac output through adaptation of peripheral resistance and circulatory unstressed volume. With the combined model, we obtain stable growth and restoration of pump function for most growth laws. We conclude that a mixed combination of stress and strain stimuli to drive cardiac growth is most promising since it (1) reproduces clinical observations on cardiac growth well, (2) requires only a small, clinically realistic adaptation of the properties of the circulatory system and (3) is robust in the sense that results were fairly insensitive to the exact choice of the chosen mechanics loading measure. This finding may be used to guide the choice of growth laws in more complex finite element models of cardiac growth, suitable for predicting the response to spatially varying changes in tissue load. Eventually, the current model may form a basis for a tool to predict patient-specific growth in response to spatially homogeneous changes in tissue load, since it is computationally inexpensive.