The implicit assumption of symmetry and the species abundance distribution

Species abundance distributions (SADs) have played a historical role in the development of community ecology. They summarize information about the number and the relative abundance of the species encountered in a sample from a given community. For years ecologists have developed theory to characterize species abundance patterns, and the study of these patterns has received special attention in recent years. In particular, ecologists have developed statistical sampling theories to predict the SAD expected in a sample taken from a region. Here, we emphasize an important limitation of all current sampling theories: they ignore species identity. We present an alternative formulation of statistical sampling theory that incorporates species asymmetries in sampling and dynamics, and relate, in a general way, the community-level SAD to the distribution of population abundances of the species integrating the community. We illustrate the theory on a stochastic community model that can accommodate species asymmetry. Finally, we discuss the potentially important role of species asymmetries in shaping recently observed multi-humped SADs and in comparisons of the relative success of niche and neutral theories at predicting SADs.     

Multiple gas washout during jet ventilation

Simultaneous washouts of He, N2, and SF6 were monitored during jet ventilation with tidal volumes of 50-200 ml and rates of 1-2 Hz. Gas concentrations were measured from the trachea and from a lower lobe bronchus in six baboons by mass spectrometry. Washouts using large tidal volumes approximated single exponential decays with the relative exponential rates of decay being He fastest, SF4 slowest, and N2 intermediate. Washouts using smaller tidal volumes demonstrated a two-phase exponential decay pattern. During the fast phase, the relative exponential rates of decay were He slowest, SF6 fastest, and N2 intermediate, the reverse order seen during large-volume washouts. During the slow phase, the relative exponential rates of decay were He fastest, SF4 slowest, and N2 intermediate, the same order seen during large-volume washouts. The magnitude of the first phase observed from the lower lobe bronchus was less than that observed from the trachea. These data are consistent with a serial two-compartment transport model incorporating a limitation of molecular diffusion between the peripheral and proximal compartments. The more rapid clearance of less diffusible gases from the central airways during the first phase of washout was due to slower transport from the alveoli to the central airways rather than faster transport from the central airways to the airway opening.     

The design of a panel study under an alternating Poisson process assumption.

We discuss the design of a panel study for the estimation of the average durations in the two states of an alternating Poisson process. Two types of designs are examined. The first fixes the number of follow-up waves but permits the total length of follow-up to vary, and the second varies the number of follow-up waves with fixed length. Simple expressions for nearly optimal designs are presented, and we compare these with designs allowing for continuous observation. Both equilibrium and nonequilibrium cases are examined. An example is given using morbidity data to illustrate how these results can be applied.     

Correction of inert gas washin or washout for gas solubility in blood

We show that when an inert gas is washed into the lungs its retention in the blood during any one breath is approximately proportional to its solubility. This relationship makes possible the correction of washin or washout data for blood uptake or release, provided that two gases of different solubility are used simultaneously. The method automatically allows for the characteristics of an individual washin or washout and for the occurrence of recirculation within a fairly short washin or washout period. It has been tested in models with nonuniform ventilation and perfusion and closely approximates the behavior of a truly insoluble gas. In the derived ventilation distribution, gas solubility appears as ventilation to units of low turnover. In the case of N2 this effect is small but causes appreciable overestimation of lung volume. The recovered dead space and main alveolar distribution are insignificantly affected.     

Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption

When a flat figure of uniform color and with an elliptic contour is slowly rotated around an axis orthogonal to the plane of the image, an observer set in the frontal position will perceive it first as a rotating ellipse. After a few seconds of inspection, the ellipse appears to deform with an amoeba-like movement until it appears as a rigid, circular disk tilting back and forth in 3-D space; finally it is seen as a rotating ellipsoid tilted in depth at a constant inclination angle with respect to the rotating platform. In an attempt to provide an explanation for the apparent ellipsoid, the authors present a mathematical model based on an hypothesis of velocity differences minimization, successfully used to describe other stereokinetic phenomena, such as the rotating cone and the tilted bar. This technique does not make use of Ullman's ridigity hypothesis for extracting depth from 2-D moving stimuli. A comparison with experimental results supports the validity of the model.     

Analytic determination of the depth effect in stereokinetic phenomena without a rigidity assumption

When a circular disk with an eccentric dot is set in slow rotary motion a compelling impression of a three-dimensional cone is observed. Similarly a line segment of constant length, a bar, rotating on the frontal plane appears slanted in depth. The two stereokinetic phenomena cannot be explained on the basis of Ullman's method of extracting depth from 2-D moving stimuli i.e. the rigidity assumption. A new analytic model is here presented based on the hypothesis that the visual system minimizes the relative velocity differences among all the points of the moving pattern. Two different methods of calculating the depth displacement are described: the velocity field method and the trajectories method. Both lead to the same results. A comparison of the theoretical results with the experimental ones supports the validity of the model.     

Serial determination of lung volume in small animals by nitrogen washout

This report describes the design of an apparatus and the procedures used to serially measure the total lung capacity and the functional residual capacity of small animals utilizing the N2-washout technique. The calibration data indicate that the technique is accurate to within 1 ml and has a variance of less than 5%. The in vivo lung volume measurements of rats were validated by comparing them with values obtained with a water-displacement technique; the means were within 0.3 ml. Examples of the precision and changes in lung volume of animals during studies are included to demonstrate the reliability and usefulness of the technique.     

Automated detection of the phase III slope during inert gas washout testing

We describe a method to determine the phase III slope for the purpose of calculating indexes of ventilation heterogeneity, S(acin) and S(cond), from the multiple breath nitrogen washout test (MBNW). Our automated method applies a recursive, segmented linear regression technique to each breath of the MBNW test and determines the best point of transition, or breakpoint, between each phase of the washout. A sample set of 50 MBNW tests (controls, asthma, and COPD) was used to establish the conditions in which the phase III slope obtained from the automated technique best matched that obtained by two manual interpreters. We then applied our technique to a test set of 30 subjects (with an even number of subjects in each of the above groups) and compared these results against the manual analysis of a third independent manual interpreter. Indexes of ventilation heterogeneity were determined using both methods and compared. The phase III slopes determined by the automatic technique best matched the manual interpreter when the phase III slope was calculated from the phase II-III transition point plus the addition of 50% of the phase II volume to the end of the expiration. Calculation of the indexes S(acin) and S(cond) showed no overall difference between analysis methods in either S(acin) (P = 0.14) or S(cond) (P = 0.59) when the set threshold was applied to our automated analysis. Our analysis method provides an alternate means for rapid quantification of the MBNW test, removing operator dependence without alteration in either S(acin) or S(cond).     

Numerical and experimental study of steady-state CO2 and inert gas washout

The predictions of a single-path trumpet-bell numerical model of steady-state CO2 and infused He and sulfur hexafluoride (SF6) washout were compared with experimental measurements on healthy human volunteers. The mathematical model used was a numerical solution of the classic airway convention-diffusion equation with the addition of a distributed source term at the alveolar end. In the human studies, a static sampling technique was used to measure the exhaled concentrations and phase III slopes of CO2, He, and SF6 during the intravenous infusion of saline saturated with a mixture of the two inert gases. We found good agreement between the experimentally determined normalized slopes (phase III slope divided by mixed expired concentration) and the numerically determined normalized slopes in the model with no free parameters other than the physiological ones of upper airway dead space, tidal volume, breathing frequency, and breathing pattern (sinusoidal). We conclude 1) that the single-path (Weibel) trumpet-bell anatomic model used in conjunction with the airway convection-diffusion equation with a distributed source term is adequate to describe the steady-state lung washout of CO2 and infused He and SF6 in normal lungs and 2) that the interfacial area separating the tidal volume fron from the functional residual capacity gas, through which gas diffusion into the moving tidal volume occurs, exerts a major effect on the normalized slopes of phase III.     

Estimation of blood flow distribution in skeletal muscle from inert gas washout

A new method is evaluated for the estimation of blood flow-to-volume distribution in skeletal muscle from inert gas washout kinetics. Acetylene washout from the isolated, blood-perfused canine gracilis muscle was measured continuously with a blood gas catheter in combination with a mass spectrometer. The washout curves were transformed to flow-to-volume ratio distributions by means of a 50-compartment model. The algorithm fits the expression for the washout curve derived from the model by a least-squares method with enforced smoothing. The algorithm was evaluated using computer simulations in which artificial washout curves were generated by a multicompartment model with a known flow distribution. A wide range of given flow distributions could be recovered from the simulated data. The data were also analyzed using a linear programming technique. Analysis of the experimental data with the least-squares method showed that there is considerable heterogeneity in the distribution of perfusion in resting gracilis muscle. The distribution is characterized by at least two modes and a single compartment with a very low perfusion-to-volume ratio. Experimental noise made it impossible to obtain feasible flow distributions by means of linear programming.     

Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry

A numerical method is developed for simulating unsteady, 3-D, laminar flow through a bileaflet mechanical heart valve with the leaflets fixed. The method employs a dual-time-stepping artificial-compressibility approach together with overset (Chimera) grids and is second-order accurate in space and time. Calculations are carried out for the full 3-D valve geometry under steady inflow conditions on meshes with a total number of nodes ranging from 4 x 10(5) to 1.6 x 10(6). The computed results show that downstream of the leaflets the flow is dominated by two pairs of counter-rotating vortices, which originate on either side of the central orifice in the aortic sinus and rotate such that the common flow of each pair is directed away from the aortic wall. These vortices intensify with Reynolds number, and at a Reynolds number of approximately 1200 their complex interaction leads to the onset of unsteady flow and the break of symmetry with respect to both geometric planes of symmetry. Our results show the highly 3-D structure of the flow; question the validity of computationally expedient assumptions of flow symmetry; and demonstrate the need for highly resolved, fully 3-D simulations if computational fluid dynamics is to accurately predict the flow in prosthetic mechanical heart valves.     

Meta‐analysis of rare events under the assumption of a homogeneous treatment effect

We studied the performance of several meta‐analysis methods in rare event settings, when the treatment effect is assumed to be homogeneous and baseline prevalences are either homogeneous or heterogeneous. We conducted extensive simulations that included the three most common effect sizes with count data: the odds ratio, the relative risk, and the risk difference. We investigated several important scenarios by varying the level of rareness, the value of the trials’ arms unbalance, and the size of the treatment effect. We found that the Mantel–Haenszel method and the Binomial regression model provided the best results across all the scenarios investigated. The Peto method performed satisfactorily only when the true effect size was not too large and the degree of unbalance moderate. Inverse variance was the least reliable method. The use of a continuity correction factor slightly improved the performance of the inverse variance method but deteriorated that of the Peto and Mantel–Haenszel methods. A method based on median unbiased estimators of the probabilities provided similar results to those obtained when using the inverse variance method with a continuity correction. Therefore, when the treatment effect can be assumed to be homogeneous and for either homogeneous or heterogeneous baseline prevalences, we highly recommend using the Mantel‐Haenszel method without continuity correction (for all the effect sizes) or the Binomial regression model (for the odds ratio only) to meta‐analyze the data.     

Reconstructing genealogies of serial samples under the assumption of a molecular clock using serial-sample UPGMA

Reconstruction of evolutionary relationships from noncontemporaneous molecular samples provides a new challenge for phylogenetic reconstruction methods. With recent biotechnological advances there has been an increase in molecular sequencing throughput, and the potential to obtain serial samples of sequences from populations, including rapidly evolving pathogens, is fast being realized. A new method called the serial-sample unweighted pair grouping method with arithmetic means (sUPGMA) is presented that reconstructs a genealogy or phylogeny of sequences sampled serially in time using a matrix of pairwise distances. The resulting tree depicts the terminal lineages of each sample ending at a different level consistent with the sample's temporal order. Since sUPGMA is a variant of UPGMA, it will perform best when sequences have evolved at a constant rate (i.e., according to a molecular clock). On simulated data, this new method performs better than standard cluster analysis under a variety of longitudinal sampling strategies. Serial-sample UPGMA is particularly useful for analysis of longitudinal samples of viruses and bacteria, as well as ancient DNA samples, with the minimal requirement that samples of sequences be ordered in time.     

The validity of different methods of analysis of 133Xe washout curves for the determination of lung function

The influence of different mathematical methods on the analysis of ¹³³Xe washout data, used in the assessment of lung function in the pig, were investigated. When the data were fitted using a bi-exponential or a bi-exponential plus a constant type equation, neither the two clearance rate constants nor the overall 50% clearance time were found totally appropriate for the study of lung function. A new two compartmental model for the in vivo clearance of ¹³³Xe is proposed. The model assumes the whole blood as one compartment and the lung, including the pulmonary blood, as the second compartment. This suggests that the curvature of the xenon clearance curve is the result of recording the summation of the activities from the alveoli and the pulmonary blood and not, as previously described, due to the existence of two different sub-populations of alveoli.