An Alternative Approach to Modelling the Assortative Mating Process

In this article we demonstrate how the difficulties encountered from consideration of two-sided assortation for a characteristic (or set of characteristics) in human populations can be overcome. This is achieved, essentially, by postulating a socio-environmental variable (based on an individual's lifetime experiences) over which individuals are mating assortatively. The value an individual has on this scale determines his mean value for the characteristic under consideration. In other words, there is a relationship between the characteristic and the socioenvironmental scale. As well, individuals may be mating assortatively for the characteristic under consideration (although not necessarily). Thus we achieve assortative mating for a single characteristic as a result of mixing, simultaneously, over more than just one variable. Expansions to more ‘mixing’ scales than a single socio-environmental variable are quite straightforward.     

Simplified models for gas exchange in the human lungs

This paper presents a hierarchy of models with increasing complexity for gas exchange in the human lungs. The models span from a single compartment, inflexible lung to a single compartment, flexible lung with pulmonary gas exchange. It is shown how the models are related to well-known models in the literature. A long-term purpose of this work is to study nonlinear phenomena seen in the cardio-respiratory system (for example, synchronization between ventilation rate and heart rate, and Cheyne-Stokes respiration). The models developed in this paper can be regarded as the controlled system (plant) and provide a mathematical framework to link between "molecular-level", and "systems-level" models. It is shown how changes in molecular level affect the alveolar partial pressure. Two assumptions that have previously been made are re-examined: (1) the hidden assumption that the air flow through the mouth is equal to the rate of volume change in the lungs, and, (2) the assumption that the process of oxygen binding to hemoglobin is near equilibrium. Conditions under which these assumptions are valid are studied. All the parameters in the models, except two, are physiologically realistic. Numerical results are consistent with published experimental observations.     

Modeling Reconsolidation in Kernel Associative Memory

Memory reconsolidation is a central process enabling adaptive memory and the perception of a constantly changing reality. It causes memories to be strengthened, weakened or changed following their recall. A computational model of memory reconsolidation is presented. Unlike Hopfield-type memory models, our model introduces an unbounded number of attractors that are updatable and can process real-valued, large, realistic stimuli. Our model replicates three characteristic effects of the reconsolidation process on human memory: increased association, extinction of fear memories, and the ability to track and follow gradually changing objects. In addition to this behavioral validation, a continuous time version of the reconsolidation model is introduced. This version extends average rate dynamic models of brain circuits exhibiting persistent activity to include adaptivity and an unbounded number of attractors.     

Spotting altruistic dictator game players and mingling with them: the elective assortation of classmates

Altruism can evolve through assortation if the selfish advantage of egoistic individuals is outcompeted by the benefits of mutual cooperation between altruists. This selection process is possible if (a) individuals can distinguish altruists from egoists and (b) altruists cooperate electively with other altruists, leaving egoists no chance but to mingle with each other. This study investigates whether these two conditions are fulfilled in a natural setting. One hundred twenty-two students of six secondary school classes (age 10 to 19 years) played an anonymous dictator game, which functioned as a measure of altruism. Afterwards and unannounced, the students had to estimate their classmates' decisions and did so better than chance. Sociometry revealed that the accuracy of predictions depended on social closeness. Friends and disliked classmates were judged more accurately than liked classmates or those met with indifference. Moreover, altruists were friends with more altruistic persons than were egoists. The results confirm the existence of the two prerequisites for the evolution of altruism through assortation: the predictability of altruistic behavior and the association of altruists.     

Calculating spatial statistics for velocity jump processes with experimentally observed reorientation parameters

Mathematical modelling of the directed movement of animals, microorganisms and cells is of great relevance in the fields of biology and medicine. Simple diffusive models of movement assume a random walk in the position, while more realistic models include the direction of movement by assuming a random walk in the velocity. These velocity jump processes, although more realistic, are much harder to analyse and an equation that describes the underlying spatial distribution only exists in one dimension. In this communication we set up a realistic reorientation model in two dimensions, where the mean turning angle is dependent on the previous direction of movement and bias is implicitly introduced in the probability distribution for the direction of movement. This model, and the associated reorientation parameters, is based on data from experiments on swimming microorganisms. Assuming a transport equation to describe the motion of a population of random walkers using a velocity jump process, together with this realistic reorientation model, we use a moment closure method to derive and solve a system of equations for the spatial statistics. These asymptotic equations are a very good match to simulated random walks for realistic parameter values.     

Cascading extinctions and community collapse in model food webs

Species loss in ecosystems can lead to secondary extinctions as a result of consumer–resource relationships and other species interactions. We compare levels of secondary extinctions in communities generated by four structural food-web models and a fifth null model in response to sequential primary species removals. We focus on various aspects of food-web structural integrity including robustness, community collapse and threshold periods, and how these features relate to assumptions underlying different models, different species loss sequences and simple measures of diversity and complexity. Hierarchical feeding, a fundamental characteristic of food-web structure, appears to impose a cost in terms of robustness and other aspects of structural integrity. However, exponential-type link distributions, also characteristic of more realistic models, generally confer greater structural robustness than the less skewed link distributions of less realistic models. In most cases for the more realistic models, increased robustness and decreased levels of web collapse are associated with increased diversity, measured as species richness S, and increased complexity, measured as connectance C. These and other results, including a surprising sensitivity of more realistic model food webs to loss of species with few links to other species, are compared with prior work based on empirical food-web data.     

Incorporating phenotype-dependent growth rates into the color-shift model for preneoplastic hepatocellular lesions

Multi-stage models occupy a central position in modeling the carcinogenesis process. These models formalize the hypothesis that cells have to undergo several transformations on their way to malignancy. This hypothesis assumes that a preneoplastic cell of a later stage arises through a mutational event of a single cell of a previous stage and that preneoplastic cells proliferate clonally. However, there is some evidence that multi-stage models cannot adequately describe the formation and the progression of preneoplastic lesions at least in certain organs [Math. Biosci. 168 (2000) 167]. An alternative model assuming that all cells in a colony of altered hepatocytes change their phenotype more or less simultaneously rather than by mutation of single cells has already been introduced [Math. Biosci. 148 (1998) 181] and is called color-shift model (CSM). This model assumed deterministic phenotype-independent growth for the foci once they are generated. An expansion of the CSM allowing for variability between deterministic growth behaviour of phenotypically different colonies is presented (modCSM) and the model is applied to focal lesion data from a rat hepatocarcinogenesis experiment. The fit of the originally proposed and the modCSM are compared with respect to their ability to predict numbers and radii of preneoplastic cell foci.     

A statistical approach to quasi-extinction forecasting

Forecasting population decline to a certain critical threshold (the quasi-extinction risk) is one of the central objectives of population viability analysis (PVA), and such predictions figure prominently in the decisions of major conservation organizations. In this paper, we argue that accurate forecasting of a population's quasi-extinction risk does not necessarily require knowledge of the underlying biological mechanisms. Because of the stochastic and multiplicative nature of population growth, the ensemble behaviour of population trajectories converges to common statistical forms across a wide variety of stochastic population processes. This paper provides a theoretical basis for this argument. We show that the quasi-extinction surfaces of a variety of complex stochastic population processes (including age-structured, density-dependent and spatially structured populations) can be modelled by a simple stochastic approximation: the stochastic exponential growth process overlaid with Gaussian errors. Using simulated and real data, we show that this model can be estimated with 20-30 years of data and can provide relatively unbiased quasi-extinction risk with confidence intervals considerably smaller than (0,1). This was found to be true even for simulated data derived from some of the noisiest population processes (density-dependent feedback, species interactions and strong age-structure cycling). A key advantage of statistical models is that their parameters and the uncertainty of those parameters can be estimated from time series data using standard statistical methods. In contrast for most species of conservation concern, biologically realistic models must often be specified rather than estimated because of the limited data available for all the various parameters. Biologically realistic models will always have a prominent place in PVA for evaluating specific management options which affect a single segment of a population, a single demographic rate, or different geographic areas. However, for forecasting quasi-extinction risk, statistical models that are based on the convergent statistical properties of population processes offer many advantages over biologically realistic models.     

Continous administration of short-lived radioisotope tracers and the analogous Laplace transform.

Short-lived radioactive tracers are used because of the low radiation dose to patients. Another advantage finding increasing use, however, is that the equilibrium activities achieved by continuous administration to a steady state contain kinetic information. This is not the case with long-lived isotopes.The derivation of quantitative kinetic information in the form of rate constants or flows requires the formulation of a model of the system being studied. Several approaches to this have been published based on a model of single compartments with simultaneous arrival of tracer. To deal with more realistic models a method is proposed which uses the analogy between the procedure of continuous administration of short-lived tracer and the Laplace transform. If f(t) is the activity of a long-lived tracer in any part of a system after administration of unit activity to the input, then

$\text{∫}\text{o}\text{∞}\text{e}{}^{\mathrm{?st}}\text{f(t)}\text{d}\text{t=}\text{f}\text{(s)}$

is the “equilibrium” activity of the part after continuous administration of a short-lived tracer of decay constant $\text{f}\text{(f)}$ is also a value of the Laplace transform of (t).This analogy permits all the theorems of Laplace transform theory to be applied to the analysis of measured activities. The basis of the analogy is explained and examples are given of its application to a number of models which represent actual physiology more realistically than single compartment models. In these applications the transformed equations representing the model, with measured values of activity inserted for each transform, are solved to derive the rate constants. This is different from the use of Laplace transforms where the constant coefficients are known and the initial value problem is solved to find the behaviour of the variables.     

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size.

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.     

Spectrin properties and the elasticity of the red blood cell membrane skeleton

Two models of spectrin elasticity are developed and compared to experimental measurements of the red blood cell (RBC) membrane shear modulus through the use of an elastic finite element model of the RBC membrane skeleton. The two molecular models of spectrin are: (i) An entropic spring model of spectrin as a flexible chain. This is a model proposed by several previous authors. (ii) An elastic model of a helical coiled-coil which expands by increasing helical pitch. In previous papers, we have computed the relationship between the stiffness of a single spectrin molecule (K) and the shear modulus of a network (μ), and have shown that this behavior is strongly dependent upon network topology. For realistic network models of the RBC membrane skeleton, we equate μ to micropipette measurements of RBCs and predict K for spectrin that is consistent with the coiled-coil molecular model. The value of spectrin stiffness derived from the entropic molecular model would need to be at least 30 times greater to match the experimental results. Thus, the conclusion of this study is that a helical coiled-coil model for spectrin is more realistic than a purely entropic model.     

Community versus single‐species distribution models for British plants

Aim Species distribution models are increasingly used to predict the impacts of global change on whole ecological communities by modelling the individualistic niche responses of large numbers of species. However, it is not clear whether this single‐species ensemble approach is preferable to community‐wide strategies that represent interspecific associations or shared responses to environmental gradients. Here, we test the performance of two multi‐species modelling approaches against equivalent single‐species models. Location Great Britain. Methods Single‐ and multi‐species distribution models were fitted for 701 native British plant species at a 10‐km grid scale. Two machine learning methods were used – classification and regression trees (CARTs) and artificial neural networks (ANNs). The single‐species versions are widely used in ecology but their multivariate extensions are less well known and have not previously been evaluated against one another. We compared their abilities to predict species distributions, community compositions and species richness in an independent geographical region reserved from model‐fitting. Results The single‐ and multi‐species models performed similarly, although the community models gave slightly poorer predictive accuracy by all measures. However, from the point of view of the whole community they were much simpler than the array of single‐species models, involving orders of magnitude fewer parameters. Multi‐species approaches also left greater residual spatial autocorrelation than the individualistic models and, contrary to expectation, were relatively less accurate for rarer species. However, the fitted multi‐species response curves had lower tendency for pronounced discontinuities that are unlikely to be a feature of realized niche responses. Main conclusions Although community distribution models were slightly less accurate than single‐species models, they offered a highly simplified way of modelling spatial patterns in British plant diversity. Moreover, an advantage of the multi‐species approach was that the modelling of shared environmental responses resolved more realistic response curves. However, there was a slight tendency for community models to predict rare species less accurately, which is potentially disadvantageous for conservation applications. We conclude that multi‐species distribution models may have potential for understanding and predicting the structure of ecological communities, but were slightly inferior to single‐species ensembles for our data.     

Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman-Scott clustering process

Spatially explicit models relating to plant populations have developed little since Felsenstein (1975) pointed out that if limited seed dispersal causes clustering of individuals, such models cannot reach an equilibrium. This paper aims to resolve this issue by modifying the Neyman-Scott cluster point process. The new point processes are dynamic models with random immigration, and the continuous increase in the clustering of individuals stops at some level. Hence, an equilibrium state is achieved, and new individual-based spatially explicit neutral coalescent models are established. By fitting the spatial structure at equilibrium to individual spatial distribution data, we can indirectly estimate seed dispersal and effective population density. These estimates are improved when genetic data are available, and become even more sophisticated if spatial distribution and genetic data pertaining to the offspring are also available.     

A Stochastic Regression Model for General Trend Analysis of Longitudinal Continuous Data

A predictive continuous time model is developed for continuous panel data to assess the effect of time‐varying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an Ornstein–Uhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time first‐order autoregressive regression model with time‐varying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasi‐likelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasi‐likelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a follow‐up study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.     

Distributed body weight over the whole spine for improved inference in spine modelling

Numerous models used to investigate the causes of low back pain are based upon the concept of the lever model that considers equilibrium of forces and moments about a single intervertebral joint. Consideration of forces and moments at each intervertebral joint is essential if a more realistic idea of the loading on the spine is to be obtained. This will also allow the role of the curvature of the spine to be investigated. A distributed loading pattern for forces due to body weight for the whole spine has not been investigated before. In this paper, a distributed loading pattern for the whole spine for various postures is investigated and the potential impact on the calculations is discussed.     

Statistical multi‐path exposure method for assessing the whole‐body SAR in a heterogeneous human body model in a realistic environment

Assessing the whole‐body absorption in a human in a realistic environment requires a statistical approach covering all possible exposure situations. This article describes the development of a statistical multi‐path exposure method for heterogeneous realistic human body models. The method is applied for the 6‐year‐old Virtual Family boy (VFB) exposed to the GSM downlink at 950 MHz. It is shown that the whole‐body SAR does not differ significantly over the different environments at an operating frequency of 950 MHz. Furthermore, the whole‐body SAR in the VFB for multi‐path exposure exceeds the whole‐body SAR for worst‐case single‐incident plane wave exposure by 3.6%. Moreover, the ICNIRP reference levels are not conservative with the basic restrictions in 0.3% of the exposure samples for the VFB at the GSM downlink of 950 MHz. The homogeneous spheroid with the dielectric properties of the head suggested by the IEC underestimates the absorption compared to realistic human body models. Moreover, the variation in the whole‐body SAR for realistic human body models is larger than for homogeneous spheroid models. This is mainly due to the heterogeneity of the tissues and the irregular shape of the realistic human body model compared to homogeneous spheroid human body models. Bioelectromagnetics 34:240–251, 2013. © 2012 Wiley Periodicals, Inc.     

Cooperativity of ligand binding as a function of monomer-dimer equilibrium parameters and acceptor concentration

A general monomer-dimer equilibrium system involving ligand interactions ispresented. Cooperativity features of specific limited models are analyzed by selecting the appropriate family of equilibrium constants from this general scheme. Each system is then characterized in terms of Hill coefficient dependency on alterations in values of equilibrium constants and total acceptor concentration. This method permits comparison of predicted cooperativity trends between systems. Contrasting reports concerning cooperativity dependencies for certain defined equilibrium systems are compared and the discrepancies resolved. Characteristics of cooperativity binding patterns are shown to include symmetry about dimerization association constant values, both positive and negative cooperativity for a single set of parameters, and significant changes in cooperativity features with relatively small changes in equilibrium parameters.