Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm. to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker. demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

A generalised Bayesian instrumental variable approach under student t-distributed errors with application

Bayesian analysis is given of an instrumental variable model that allows for heteroscedasticity in both the structural equation and the instrument equation. Specifically, the approach for dealing with heteroscedastic errors in Geweke (1993) is extended to the Bayesian instrumental variable estimator outlined in Rossi et al. (2005). Heteroscedasticity is treated by modelling the variance for each error using a hierarchical prior that is Gamma distributed. The computation is carried out by using a Markov chain Monte Carlo sampling algorithm with an augmented draw for the heteroscedastic case. An example using real data illustrates the approach and shows that ignoring heteroscedasticity in the instrument equation when it exists may lead to biased estimates.

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented.

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Landscape state machines: Tools for evolutionary algorithm performance analyses and landscape/algorithm mapping

Many evolutionary algorithm applications involve either fitness functions with high time complexity or large dimensionality (hence very many fitness evaluations will typically be needed) or both. In such circumstances, there is a dire need to tune various features of the algorithm well so that performance and time savings are optimized. However, these are precisely the circumstances in which prior tuning is very costly in time and resources. There is hence a need for methods which enable fast prior tuning in such cases. We describe a candidate technique for this purpose, in which we model a landscape as a finite state machine, inferred from preliminary sampling runs. In prior algorithm-tuning trials, we can replace the 'real' landscape with the model, enabling extremely fast tuning, saving far more time than was required to infer the model. Preliminary results indicate much promise, though much work needs to be done to establish various aspects of the conditions under which it can be most beneficially used. A main limitation of the method as described here is a restriction to mutation-only algorithms, but there are various ways to address this and other limitations.

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.

Sampling uncertainty in gridded sea surface temperature products and Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data

Sea surface temperature (SST) data are often provided as gridded products, typically at resolutions of order 0.05 degrees from satellite observations to reduce data volume at the request of data users and facilitate comparison against other products or models. Sampling uncertainty is introduced in gridded products where the full surface area of the ocean within a grid cell cannot be fully observed because of cloud cover. In this paper we parameterise uncertainties in SST as a function of the percentage of clear-sky pixels available and the SST variability in that subsample. This parameterisation is developed from Advanced Along Track Scanning Radiometer (AATSR) data, but is applicable to all gridded L3U SST products at resolutions of 0.05-0.1 degrees, irrespective of instrument and retrieval algorithm, provided that instrument noise propagated into the SST is accounted for. We also calculate the sampling uncertainty of ~0.04 K in Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) products, using related methods.