Estimating species richness from quadrat sampling data: a general approach

We consider the problem of estimating the number of species (denoted by S) of a biological community located in a region divided into n quadrats. To address this question, different hierarchical parametric approaches have been recently developed. Despite a detailed modeling of the underlying biological processes, they all have some limitations. Indeed, some assume that n is theoretically infinite; as a result, n and the sampling fraction are not a part of such models. Others require some prior information on S to be efficiently implemented. Our approach is more general in that it applies without limitation on the size of n, and it can be used in the presence, as well as in the absence, of prior information on S. Moreover, it can be viewed as an extension of the approach of Dorazio and Royle (2005, Journal of the American Statistical Association 100, 389-398) in that n is a part of the model and a prior distribution is placed on S. Despite serious computational difficulties, we have perfected an efficient Markov chain Monte Carlo algorithm, which allows us to obtain the Bayesian estimate of S. We illustrate our approach by estimating the number of species of a bird community located in a forest.     

Radiation protection from external exposure to radionuclides: A Monte Carlo data handbook

The availability of a resource collecting dose factors for the evaluation of the absorbed doses from external exposure during the manipulation of radioactive substances is fundamental for radiological protection purposes. Monte Carlo simulations are useful for the accurate calculation of dose distributions in complex geometries, particularly in presence of extended spectra of multi-radiation sources. We considered, as possible irradiation scenarios, a point source, a uniform planar source resembling a contaminated surface, several source volumes contained in plastic or glass receptacles, and the direct skin contamination case, implementing the corresponding Monte Carlo simulations in GAMOS (GEANT4-based Architecture for Medicine-Oriented Simulations). A set of 50 radionuclides was studied, focusing the attention on those ones mainly used in nuclear medicine, both for diagnostic and therapeutic purposes, in nuclear physics laboratories and for instrument calibration. Skin dose equivalents at 70 μm of depth and deep dose equivalents at 10 mm of depth are reported for different configurations and organized in easy-to-read tables.     

A Monte Carlo study on dose distribution evaluation of Flexisource 192Ir brachytherapy source

Aim

The aim of this study is to evaluate the dose distribution of the Flexisource ¹⁹²Ir source.

Background

Dosimetric evaluation of brachytherapy sources is recommended by task group number 43 (TG. 43) of American Association of Physicists in Medicine (AAPM).

Materials and methods

MCNPX code was used to simulate Flexisource ¹⁹²Ir source. Dose rate constant and radial dose function were obtained for water and soft tissue phantoms and compared with previous data on this source. Furthermore, dose rate along the transverse axis was obtained by simulation of the Flexisource and a point source and the obtained data were compared with those from Flexiplan treatment planning system (TPS).

Results

The values of dose rate constant obtained for water and soft tissue phantoms were equal to 1.108 and 1.106, respectively. The values of the radial dose function are listed in the form of tabulated data. The values of dose rate (cGy/s) obtained are shown in the form of tabulated data and figures. The maximum difference between TPS and Monte Carlo (MC) dose rate values was 11% in a water phantom at 6.0 cm from the source.

Conclusion

Based on dosimetric parameter comparisons with values previously published, the accuracy of our simulation of Flexisource ¹⁹²Ir was verified. The results of dose rate constant and radial dose function in water and soft tissue phantoms were the same for Flexisource and point sources. For Flexisource ¹⁹²Ir source, the results of TPS calculations in a water phantom were in agreement with the simulations within the calculation uncertainties. Furthermore, the results from the TPS calculation for Flexisource and MC calculation for a point source were practically equal within the calculation uncertainties.     

Bayesian estimation of species richness from quadrat sampling data in the presence of prior information

We consider the problem of estimating the number of species of an animal community. It is assumed that it is possible to draw up a list of species liable to be present in this community. Data are collected from quadrat sampling. Models considered in this article separate the assumptions related to the experimental protocol and those related to the spatial distribution of species in the quadrats. Our parameterization enables us to incorporate prior information on the presence, detectability, and spatial density of species. Moreover, we elaborate procedures to build the prior distributions on these parameters from information furnished by external data. A simulation study is carried out to examine the influence of different priors on the performances of our estimator. We illustrate our approach by estimating the number of nesting bird species in a forest.     

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.     

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.     

A Monte Carlo study on dose distribution validation of GZP6 60Co stepping source

Aim

Stepping source in brachytherapy systems is used to treat a target lesion longer than the effective treatment length of the source. Cancerous lesions in the cervix, esophagus and rectum are examples of such a target lesion.

Background

In this study, the stepping source of a GZP6 afterloading intracavitary brachytherapy unit was simulated using Monte Carlo (MC) simulation and the results were used for the validation of the GZP6 treatment planning system (TPS).

Materials and methods

The stepping source was simulated using MCNPX Monte Carlo code. Dose distributions in the longitudinal plane were obtained by using a matrix shift method for esophageal tumor lengths of 8 and 10 cm. A mesh tally has been employed for the absorbed dose calculation in a cylindrical water phantom. A total of 5 × 10⁸ photon histories were scored and the MC statistical error obtained was at the range of 0.008–3.5%, an average of 0.2%.

Results

The acquired MC and TPS isodose curves were compared and it was shown that the dose distributions in the longitudinal plane were relatively coincidental. In the transverse direction, a maximum dose difference of 7% and 5% was observed for tumor lengths of 8 and 10 cm, respectively.

Conclusion

Considering that the certified source activity is given with ±10% uncertainty, the obtained difference is reasonable. It can be concluded that the accuracy of the dose distributions produced by GZP6 TPS for the stepping source is acceptable for its clinical applications.     

A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.     

Insertion and hairpin formation of membrane proteins: a Monte Carlo study.

Some particular effects of a lipid membrane on the partitioning and the concomitant folding processes of model proteins have been investigated using Monte Carlo methods. It is observed that orientational order and lateral density fluctuations of the lipid matrix stabilize the orientation of helical proteins and induce a tendency of spontaneous formation of helical hairpins for helices longer than the width of the membrane. The lateral compression of the lipids on a hairpin leads to the extrusion of a loop at the trans side of the membrane. The stability of the hairpin can be increased by the design of appropriate groups of hydrophilic and hydrophobic residues at the extruded loop. It is shown that in the absence of lipids the orientation of proteins is not stable and the formation of hairpins is absent. Some analogies between the formation of helical hairpins in membranes and the formation of hairpins in polymer liquid crystals are discussed. The simulations indicate that the insertion process follows a well-defined pattern of kinetic steps.     

Multi-particle sampling in Monte Carlo simulations on fluids: efficiency and extended implementations

Various technical aspects affecting the efficiency of a recently proposed novel Monte Carlo (MC) simulation scheme based on biased simultaneous displacements/rotations of all particles of the system are investigated using two polarisable models of water, the Chialvo–Cummings and Brodholt–Sampoli–Vallauri models, as a test case. Necessary expressions for polarisable site–site interaction models are derived along with a novel smoothing of the potential at the cut-off distance. In addition to the common thermodynamic and structural properties, the mean-squared displacements, rotation relaxation, speed of equilibration (translational order parameter, TOP) and autocorrelation coefficients have been computed as well, in order to assess the efficiency of the method. Gain in speed by parallelisation has also been examined. Performance of the method is coumpared with both the standard one-particle move method and the available approximate methods. It is shown that the multi-particle move (MPM) method performs about by a factor of 10 faster for the systems considered when compared with the common MC scheme, and several times faster when compared with the approximate methods. Parallelised codes of the MPM method may then perform about 70 times faster than the conventional MC. These conclusions hold true for the system size simulated (N = 256) because the efficiency of the multi-particle method depends on the size of the system: its efficiency even increases with increasing number of particles.     

A Markov chain Monte Carlo strategy for sampling from the joint posterior distribution of pedigrees and population parameters under a Fisher-Wright model with partial selfing

A simple population genetic model is presented for a hermaphrodite annual species, allowing both selfing and outcrossing. Those male gametes (pollen) responsible for outcrossing are assumed to disperse much further than seeds. Under this model, the pedigree of a sample from a single locality is loop-free. A novel Markov chain Monte Carlo strategy is presented for sampling from the joint posterior distribution of the pedigree of such a sample and the parameters of the population genetic model (including the selfing rate) given the genotypes of the sampled individuals at unlinked marker loci. The computational costs of this Markov chain Monte Carlo strategy scale well with the number of individuals in the sample, and the number of marker loci, but increase exponentially with the age (time since colonisation from the source population) of the local population. Consequently, this strategy is particularly suited to situations where the sample has been collected from a population which is the result of a recent colonisation process.     

Sources of anomalous diffusion on cell membranes: a Monte Carlo study

A stochastic random walk model of protein molecule diffusion on a cell membrane was used to investigate the fundamental causes of anomalous diffusion in two-dimensional biological media. Three different interactions were considered: collisions with fixed obstacles, picket fence posts, and capture by, or exclusion from, lipid rafts. If motion is impeded by randomly placed, fixed obstacles, we find that diffusion can be highly anomalous, in agreement with previous studies. In contrast, collision with picket fence posts has a negligible effect on the anomalous exponent at realistic picket fence parameters. The effects of lipid rafts are more complex. If proteins partition into lipid rafts there is a small to moderate effect on the anomalous exponent, whereas if proteins are excluded from rafts there is a large effect on the anomalous exponent. In combination, these mechanisms can explain the level of anomaly in experimentally observed membrane diffusion, suggesting that anomalous diffusion is caused by multiple mechanisms whose effects are approximately additive. Finally, we show that the long-range diffusion rate, D(macro), estimated from fluorescence recovery after photobleaching studies, can be much smaller than D(micro), the small-scale diffusion rate, and is highly sensitive to obstacle densities and other impeding structures.     

Receptor aggregation by intermembrane interactions: a Monte Carlo study

The lateral organization of receptors on cell surfaces is critically important to their function; many receptors transmit transmembrane signals when redistributed into clusters, while the response of others is potentiated by their aggregation. Cell-cell contact can play a crucial role in receptor aggregation, even when the bonds between receptors on one cell and ligands on the other are monovalent. Monte Carlo simulations on a two-membrane model were carried out to determine whether weak enthalpic interactions among receptors in one membrane, and among ligands in another, can work synergistically to give large-scale clustering when the two membranes are brought into contact. The simulations give support to such a clustering mechanism. In addition, because clustering is a cooperative process akin to a phase separation, individual receptors and ligands may undergo repeated binding and unbinding while in a clustered "phase," and a single ligand could interact with multiple different receptor partners. The results suggest a resolution of the dichotomy between serial triggering and aggregation models of T cell activation.     

Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study.

The lateral diffusion coefficient for mixtures of mobile and immobile particles is obtained from Monte Carlo calculations of random walks by mobile tracers in the presence of immobile obstacles on a triangular lattice. The diffusion coefficient of the mobile species is obtained as a function of the area fractions of mobile and immobile species. The results are applied to diffusion of band 3 in the erythrocyte membrane, and indicate that obstruction of diffusion of mobile band 3 by band 3 and glycophorin attached to the membrane skeleton is not sufficient to explain the observed diffusion coefficient.     

Effect of polyelectrolyte adsorption on lateral distribution and dynamics of anionic lipids: a Monte Carlo study of a coarse-grain model

We employ Monte Carlo simulations to investigate the interaction between an adsorbing linear flexible cationic polyelectrolyte and a ternary mixed fluid membrane containing neutral (phosphatidylcholine, PC), monovalent (phosphatidylserine, PS), and multivalent (phosphatidylinositol, PIP₂) anionic lipids. We systematically explore the influences of polyelectrolyte chain length, polyelectrolyte charge density, polyelectrolyte total charge amount, and salt solution ionic strength on the static and dynamic properties of different anionic lipid species. Our results show that the multivalent PIP₂ lipids dominate the polyelectrolyte–membrane interaction and competitively inhibit polyelectrolyte–PS binding. When the total charge amount of the polyelectrolyte is less than that of the local oppositely charged PIP₂ lipids, the polyelectrolyte can drag the bound multivalent lipids to diffuse on the membrane, but cannot interact with the PS lipids. Under this condition, the diffusion behaviors of the polyelectrolyte closely follow the prediction of the Rouse model, and the polyelectrolyte chain properties determine the adsorption amount, concentration gradients, and hierarchical mobility of the bound PIP₂ lipids. However, when the total charge amount of the polyelectrolyte is larger than that of the local PIP₂ lipids, the polyelectrolyte further binds the PS lipids around the polyelectrolyte–PIP₂ complex to achieve local electrical neutrality. In this condition, parts of the polyelectrolyte desorb from the membrane and show faster mobility, and the bound PS presents much faster mobility than the segregated PIP₂. This work provides an explanation for heterogeneity formation in different anionic lipids induced by polyelectrolyte adsorption.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

A Monte Carlo study of the self-assembly of bacteriorhodopsin

Bacteriorhodopsin (BR) and specific lipid molecules self-assemble into a quasi two-dimensional lattice structure known as the purple membrane (PM). In the PM, BR molecules exist in a trimeric form with lipid molecules present in the space enclosed by each trimeric unit and in the inter-trimer space. These trimeric units, which have a roughly circular cross-section, are arranged in hexagonal patterns with long-ranged crystalline order. In this work, we investigate the self-assembly of BR in the PM via Monte Carlo simulations of a two-dimensional model of the membrane and proteins. The protein molecules are modeled as 120 degrees sectors of a circle and the lipid molecules enter into the model through effective protein-protein interactions. The sectors cannot overlap with each other, and in addition to this excluded volume interaction there are site-site attractive interactions between specific points of the proteins to mimic interactions between helices on the proteins and lipid-induced interactions. At low values of the attractive well depth, the proteins are found in the monomeric form at all concentrations. At moderate and high values of the attractive well depth, trimers are formed as the concentration increases, and with a further increase in concentration the trimers organize into a hexagonal lattice. The interactions between the proteins and those induced by the intra-trimer lipids play an equally important role in the formation of trimers and the lattice. The lipids in the inter-trimer space cause the trimers to orient in a specific direction in the hexagonal crystal lattice.     

A sampling study of the size and power of tests for paired survival data

The paired-t, sign, and signed rank tests were compared for samples from a bivariate exponential distribution. Each is a valid α-level test. One test was not uniformly more powerful than the others for all sample sizes, α levels, correlations, and alternative hypotheses considered, but the signed rank test did well consistently. It was always preferable to the sign test and never was appreciably worse than the paired-t test. The relative performance of the tests depends on α as well as the sample size.