Statistical evaluation of alternative models of human evolution

An appropriate model of recent human evolution is not only important to understand our own history, but it is necessary to disentangle the effects of demography and selection on genome diversity. Although most genetic data support the view that our species originated recently in Africa, it is still unclear if it completely replaced former members of the Homo genus, or if some interbreeding occurred during its range expansion. Several scenarios of modern human evolution have been proposed on the basis of molecular and paleontological data, but their likelihood has never been statistically assessed. Using DNA data from 50 nuclear loci sequenced in African, Asian and Native American samples, we show here by extensive simulations that a simple African replacement model with exponential growth has a higher probability (78%) as compared with alternative multiregional evolution or assimilation scenarios. A Bayesian analysis of the data under this best supported model points to an origin of our species approximate to 141 thousand years ago (Kya), an exit out-of-Africa approximate to 51 Kya, and a recent colonization of the Americas approximate to 10.5 Kya. We also find that the African replacement model explains not only the shallow ancestry of mtDNA or Y-chromosomes but also the occurrence of deep lineages at some autosomal loci, which has been formerly interpreted as a sign of interbreeding with Homo erectus.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

Effect of internal partitioning on room air quality with mixing ventilation-statistical analysis

In designing modern office buildings, building spaces are frequently zoned by introducing internal partitioning, which may have a significant influence on the room air environment. This internal partitioning was studied by means of model test, numerical simulation, and statistical analysis as the final stage. In this paper, the results produced from the statistical analysis are summarized and presented.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Relation between neuronal morphology and electrophysiology in the Kainate lesion model of Alzheimer's Disease

This paper describes a computational and statistical study of the influence of morphological changes on the electrophysiological response of neurons from an animal model of Alzheimer's Disease (AD). We combined experimental morphological data from rat hippocampal CA1 pyramidal cells with a well-established model of active membrane properties. Dendritic morphology and the somatic response to simulated current clamp conditions were then compared for cells from the control and the AD group. The computational approach allowed us to single out the influences of neuromorphology on neuronal response by eliminating the effects of active channel variability. The results did not reveal a simple relationship between morphological changes associated with AD and changes in neural response. However, they did suggest the existence of more complex than anticipated relationships between dendritic morphology and single-cell electrophysiology.

Low-order dynamical behavior in the martian atmosphere: Diagnosis of general circulation model results

The hypothesis of a low dimensional martian climate attractor is investigated by the application of the proper orthogonal decomposition (POD) to a simulation of martian atmospheric circulation using the UK Mars general circulation model (UK-MGCM). In this article we focus on a time series of the interval between autumn and winter in the northern hemisphere, when baroclinic activity is intense. The POD is a statistical technique that allows the attribution of total energy (TE) to particular structures embedded in the UK-MGCM time-evolving circulation. These structures are called empirical orthogonal functions (EOFs). Ordering the EOFs according to their associated energy content, we were able to determine the necessary number to account for a chosen amount of atmospheric TE. We show that for Mars a large fraction of TE is explained by just a few EOFs (with 90% TE in 23 EOFs), which apparently support the initial hypothesis. We also show that the resulting EOFs represent classical types of atmospheric motion, such as thermal tides and transient waves. Thus, POD is shown to be an efficient method for the identification of different classes of atmospheric modes. It also provides insight into the non-linear interaction of these modes.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Case-to-case variability of predictability of deep convection in a mesoscale model

Successful quantitative precipitation forecasts under convectively unstable conditions depend on the ability of the model to capture the location, timing and intensity of convection. Ensemble forecasts of two mesoscale convective outbreaks over the UK are examined with a view to understanding the nature and extent of their predictability. In addition to a control forecast, twelve ensemble members are run for each case with the same boundary conditions but with perturbations added to the boundary layer. The intention is to introduce perturbations of appropriate magnitude and scale so that the large-scale behaviour of the simulations is not changed. In one case, convection is in statistical equilibrium with the large-scale flow. This places a constraint on the total precipitation, but the location and intensity of individual storms varied. In contrast, the other case was characterised by a large-scale capping inversion. As a result, the location of individual storms was fixed, but their intensities and the total precipitation varied strongly. The ensemble shows case-to-case variability in the nature of predictability of convection in a mesoscale model, and provides additional useful information for quantitative precipitation forecasting.

Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods

A precipitation downscaling method is presented using precipitation from a general circulation model (GCM) as predictor. The method extends a previous method from monthly to daily temporal resolution. The simplest form of the method corrects for biases in wet-day frequency and intensity. A more sophisticated variant also takes account of flow-dependent biases in the GCM. The method is flexible and simple to implement. It is proposed here as a correction of GCM output for applications where sophisticated methods are not available, or as a benchmark for the evaluation of other downscaling methods. Applied to output from reanalyses (ECMWF, NCEP) in the region of the European Alps, the method is capable of reducing large biases in the precipitation frequency distribution, even for high quantiles. The two variants exhibit similar performances, but the ideal choice of method can depend on the GCM/reanalysis and it is recommended to test the methods in each case. Limitations of the method are found in small areas with unresolved topographic detail that influence higher-order statistics (e.g. high quantiles). When used as benchmark for three regional climate models (RCMs), the corrected reanalysis and the RCMs perform similarly in many regions, but the added value of the latter is evident for high quantiles in some small regions.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.