Local and Regional vs. Global Contingency Testing

Contingency analysis of r × c-tables is systematized as follows: Global contingency testing based on the total chisquare under H₀ of independent row and column variables is least favorable to exhaustive interpretation. Local contingency testing based on chi-square components of the individual cells of an r × c-table and realized in Configural frequency analysis (KRAUTH and LIENERT, 1973) is more favourable to substantive interpretation. Compromising between global and local contingency testing leads to so-called generalized local and regional contingency testing. Every contingency testing (local, regional and naturally global) is including all N individuals of a sample supposed to have been drawn randomly from a defined population. Extension to 3-and t-dimensional contingency analysis is outlined, and biomedical applications are discussed.     

Eutacticity in Sea Urchin Evolution

An eutactic star, in a n-dimensional space, is a set of N vectors which can be viewed as the projection of N orthogonal vectors in a N-dimensional space. By adequately associating a star of vectors to a particular sea urchin, we propose that a measure of the eutacticity of the star constitutes a measure of the regularity of the sea urchin. Then, we study changes of regularity (eutacticity) in a macroevolutive and taxonomic level of sea urchins belonging to the Echinoidea class. An analysis considering changes through geological time suggests a high degree of regularity in the shape of these organisms through their evolution. Rare deviations from regularity measured in Holasteroida order are discussed.     

Screening for partial conjunction hypotheses

SUMMARY: We consider the problem of testing for partial conjunction of hypothesis, which argues that at least u out of n tested hypotheses are false. It offers an in-between approach to the testing of the conjunction of null hypotheses against the alternative that at least one is not, and the testing of the disjunction of null hypotheses against the alternative that all hypotheses are not null. We suggest powerful test statistics for testing such a partial conjunction hypothesis that are valid under dependence between the test statistics as well as under independence. We then address the problem of testing many partial conjunction hypotheses simultaneously using the false discovery rate (FDR) approach. We prove that if the FDR controlling procedure in Benjamini and Hochberg (1995, Journal of the Royal Statistical Society, Series B 57, 289-300) is used for this purpose the FDR is controlled under various dependency structures. Moreover, we can screen at all levels simultaneously in order to display the findings on a superimposed map and still control an appropriate FDR measure. We apply the method to examples from microarray analysis and functional magnetic resonance imaging (fMRI), two application areas where the need for partial conjunction analysis has been identified.     

The identification of critical fluctuations and phase transitions in short term and coarse-grained time series—a method for the real-time monitoring of human change processes

We introduce two complementary measures for the identification of critical instabilities and fluctuations in natural time series: the degree of fluctuations F and the distribution parameter D. Both are valid measures even of short and coarse-grained data sets, as demonstrated by artificial data from the logistic map (Feigenbaum-Scenario). A comparison is made with the application of the positive Lyapunov exponent to time series and another recently developed complexity measure—the Permutation Entropy. The results justify the application of the measures within computer-based real-time monitoring systems of human change processes. Results from process-outcome research in psychotherapy and functional neuroimaging of psychotherapy processes are provided as examples for the practical and scientific applications of the proposed measures.     

How small are small mutation rates?

We consider evolutionary game dynamics in a finite population of size N. When mutations are rare, the population is monomorphic most of the time. Occasionally a mutation arises. It can either reach fixation or go extinct. The evolutionary dynamics of the process under small mutation rates can be approximated by an embedded Markov chain on the pure states. Here we analyze how small the mutation rate should be to make the embedded Markov chain a good approximation by calculating the difference between the real stationary distribution and the approximated one. While for a coexistence game, where the best reply to any strategy is the opposite strategy, it is necessary that the mutation rate μ is less than N ^−1/2exp[−N] to ensure that the approximation is good, for all other games, it is sufficient if the mutation rate is smaller than (N ln N)⁻¹. Our results also hold for a wide class of imitation processes under arbitrary selection intensity.     

Tuned solutions in dynamic neural fields as building blocks for extended EEG models

The most prominent functional property of cortical neurons in sensory areas are their tuned receptive fields which provide specific responses of the neurons to external stimuli. Tuned neural firing indeed reflects the most basic and best worked out level of cognitive representations. Tuning properties can be dynamic on a short time-scale of fractions of a second. Such dynamic effects have been modeled by localised solutions (also called “bumps” or “peaks”) in dynamic neural fields. In the present work we develop an approximation method to reduce the dynamics of localised activation peaks in systems of n coupled nonlinear d-dimensional neural fields with transmission delays to a small set of delay differential equations for the peak amplitudes and widths only. The method considerably simplifies the analysis of peaked solutions as demonstrated for a two-dimensional example model of neural feature selectivity in the brain. The reduced equations describe the effective interaction between pools of local neurons of several (n) classes that participate in shaping the dynamic receptive field responses. To lowest order they resemble neural mass models as they often form the base of EEG-models. Thereby they provide a link between functional small-scale receptive field models and more coarse-grained EEG-models. More specifically, they connect the dynamics in feature-selective cortical microcircuits to the more abstract local elements used in coarse-grained models. However, beside amplitudes the reduced equations also reflect the sharpness of tuning of the activity in a d-dimensional feature space in response to localised stimuli.     

Beyond average: an experimental test of temperature variability on the population dynamics of <Emphasis Type="Italic">Tribolium confusum</Emphasis>

The relationship between ectotherm ecology and climatic conditions has been mainly evaluated in terms of average conditions. Average temperature is the more common climatic variable used in physiological and population studies, and its effect on individual and population-level processes is well understood. However, the intrinsic variability of thermal conditions calls attention to the potential effects that this variability could have in ecological systems. Regarding this point, two hypotheses are proposed. From the allocation principle, it may be inferred that if temperature variability is high enough to induce stress in the organisms, then this extra-cost should reduce the energetic budget for reproduction, which will be reflected in population parameters. Moreover, a mathematical property of non-linear functions, Jensen’s inequality, indicates that, in concave functions, like the temperature–reproduction performance function, variability reduces the expected value of the output variable, and again modifies population parameters. To test these hypotheses, experimental cultures of Tribolium confusum under two different thermal variability regimens were carried out. With these data, we fitted a simple population dynamics model to evaluate the predictions of our hypothesis. The results show that thermal variability reduces the maximum reproductive rate of the population but no other parameters such as carrying capacity or the nonlinear factor in a nonlinear version of the Ricker model, which confirms our hypotheses. This result has important consequences, such as the paradoxical increase in population variability under a decrease in thermal variability and the necessary incorporation of climatic variability to evaluate the net effect of climate change on the dynamics of natural populations.     

Difficulty in Discerning Drivers of Lake Ecosystem Metabolism with High-Frequency Data

High-frequency measurements are increasingly available and used to model ecosystem processes. This growing capability provides the opportunity to resolve key drivers of ecosystem processes at a variety of scales. We use a unique series of high-frequency measures of potential predictors to analyze daily variation in rates of gross primary production (GPP), respiration (R), and net ecosystem production (NEP = GPP − R) for two north temperate lakes. Wind speed, temperature, light, precipitation, mixed layer depth, water column stability, chlorophyll a, chromophoric dissolved organic matter (CDOM), and zooplankton biomass were measured at daily or higher-frequency intervals over two summer seasons. We hypothesized that light, chlorophyll a, and zooplankton biomass would be strongly related to variability in GPP. We also hypothesized that chlorophyll a, CDOM, and temperature would be most strongly related to variability in R, whereas NEP would be related to variation in chlorophyll a and CDOM. Consistent with our hypotheses, chlorophyll a was among the most important drivers of GPP, R, and NEP in these systems. However, multiple regression models did not necessarily include the other variables we hypothesized as most important. Despite the large number of potential predictor variables, substantial variance remained unexplained and models were inconsistent between years and between lakes. Drivers of GPP, R, and NEP were difficult to resolve at daily time scales where strong seasonal dynamics were absent. More complex models with greater integration of physical processes are needed to better identify the underlying drivers of short-term variability of ecosystem processes in lakes and other systems.     

First results from plasma density measurements in the FTU tokamak by means of a two-frequency pulsed time-of-flight refractometer

A pulsed time-of-flight refractometer was developed and tested to determine the mean plasma density in the T-11M tokamak by measuring the propagation time of nanosecond microwave pulses in plasma. Later, it was also proposed to use such an instrument to measure and control the mean plasma density in the ITER tokamak by probing the plasma with an extraordinary wave, the electric field of which is perpendicular to the magnetic field in plasma, in the transparency window at frequencies of 50–100 GHz. To avoid the effect of the density profile shape on the measurement results in the nonlinear mode of refractometer operation (near the cutoff), a system operating at two different probing frequencies was developed and tested. Such a system provides two values of the time delay, which can be used to estimate the peaking factor of the density distribution α and correctly determine the linear density 〈Nl〉, regardless of the density profile (assuming a smooth density profile of the form of N(ρ) = N(0)(1 − ρ²)^α, where N(0) is the central plasma density and ρ = r/a is the normalized plasma radius). The first experiments on density measurements in the FTU tokamak performed with this refractometer are described, and results from these experiments are presented. The formation of a thin dense plasma layer in the zone of a strong magnetic field (the so-called MARFE layer) at a relatively low (for FTU) plasma density of ∼6 × 10¹⁹ m⁻³ was detected. The thickness of this layer, determined from the refractometry data, agrees well with the data obtained using a digital camera.     

Strategies for data analyses in a high resolution 1H NMR based metabolomics study of a mouse model of Batten disease

Using an NMR based approach, employing both solution state and high resolution magic angle spinning (HR MAS) ¹H NMR spectroscopy, in conjunction with an array of statistical methods, we report cerebral metabolic deficits in a mouse model of Batten disease (Cln3 null mutant mice). Batten disease is the most common progressive neurodegenerative disorder of childhood and is caused by mutations in the Cln3 gene. In particular, brain tissue from Cln3 mice was characterised by increased concentrations of glutamine, myo-inositol, scyllo-inositol, aspartate and lactate, alongside decreased concentrations of N-acetyl-l-aspartate (NAA), N-acetyl-l-glutamate (NAG), γ-amino butyric acid (GABA), glutamate and creatine. Accompanying changes in lipid deposition were also detected in intact cortical tissue by HR MAS ¹H NMR spectroscopy. To realise the true potential of metabolomic datasets necessitates a comprehensive analysis of the data, such that useful biological information can be extracted and used to generate hypotheses which can be further tested and refined. We found that using a combination of univariate and multivariate analyses, a maximal number of metabolic deficits were successfully identified. In particular the complementary nature of the statistical approaches allowed the definition of changes which were relative, absolute or simply a change in variance, allowing a greater understanding of the disease processes detected.     

Feeding-patch choice by red deer in relation to foraging efficiency

We tested the idea that ruminants allocate their feeding time to habitat patches in relation to foraging efficiency. We used five tame red deer (Cervus elaphus) in an enclosure planted with four treatment of timothy grass (Phleum pratense) differing in their stage of growth. Older swards offered higher biomass but lower nutritional quality than younger swards. We observed time spent feeding in each treatment during each of seven trials. We measured goodness-of-fit between observed times and predictions from two alternative hypotheses differing in optimization strategy (maximizing versus matching), and a third, null hypothesis. We tested the hypotheses using two alternative currecies: digestible protein, and digestible dry matter or energy. Although digestible protein concentration and dry-matter digestibility were highly correlated (r=0.763, P<0.001), the wider range of digestible protein made it the much more sensitive measure of forage quality. Distributions of feeding time closely matched estimated intake rates of digestible protein (R _infPred ^sup2 =0.899) across all animals and trials. The other hypotheses were rejected. The results have important ecological implications in showing the underlying role of food in the selection of habitat by ruminants, and that simple, mechanistic models of forage intake and digestion can be scaled up to the level of animal behavioural choices.     

Nonlinear time series analysis of food intake in the dab and the rainbow trout

Evidence suggests that dab and rainbow trout are able to quickly adjust their food intake to an appropriate level when offered novel diets. In addition day-to-day and meal-to-meal food intake varies greatly and meal timing is plastic. Why this is the case is not clear: Food intake in fish is influenced by many factors, however the hierarchy and mechanisms by which these interact is not yet fully understood. A model of food intake may be helpful to understand these phenomena; to determine model type it is necessary to understand the qualitative nature of food intake. Food intake can be regarded as an autoregressive (AR) time series, as the amount of food eaten at time t will be influenced by previous meals, and this allows food intake to be considered using time series analyses. Here, time series data were analysed using nonlinear techniques to obtain qualitative information from which evidence for the hierarchy of mechanisms controlling food intake may be drawn. Time series were obtained for a group of dab and individuals and a group of rainbow trout for analysis. Surrogate data sets were generated to test several null hypotheses describing linear processes and all proved significantly different to the real data, suggesting nonlinear dynamics. Examination of topography and recurrence diagrams suggested that all series were deterministic and non-stationary. The point correlation dimension (PD2i) suggested low-dimensional dynamics. Our findings suggest therefore that any model of appetite should create output that is deterministic, non-stationary, low-dimensional and having nonlinear dynamics.     

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. I. USING THE FLURY HIERARCHY

The comparison of additive genetic variance-covariance matrices (G-matrices) is an increasingly popular exercise in evolutionary biology because the evolution of the G-matrix is central to the issue of persistence of genetic constraints and to the use of dynamic models in an evolutionary time frame. The comparison of G-matrices is a nontrivial statistical problem because family structure induces nonindependence among the elements in each matrix. Past solutions to the problem of G-matrix comparison have dealt with this problem, with varying success, but have tested a single null hypothesis (matrix equality or matrix dissimilarity). Because matrices can differ in many ways, several hypotheses are of interest in matrix comparisons. Flury (1988) has provided an approach to matrix comparison in which a variety of hypotheses are tested, including the two extreme hypotheses prevalent in the evolutionary literature. The hypotheses are arranged in a hierarchy and involve comparisons of both the principal components (eigenvectors) and eigenvalues of the matrix. We adapt Flury's hierarchy of tests to the problem of comparing G-matrices by using randomization testing to account for nonindependence induced by family structure. Software has been developed for carrying out this analysis for both genetic and phenotypic data. The method is illustrated with a garter snake test case.     

Invasion Genetics of New World Medflies: Testing Alternative Colonization Scenarios

The Mediterranean fruit fly (Ceratitis capitata) is an invasive agricultural pest with a wide host range and a nearly global distribution. Efforts to forgo the medfly's spread into the United States are dependent on an understanding of population dynamics in newly established populations elsewhere. To explore the potential influence of demographic and historical parameters in six medfly populations distributed from Mexico to Peru, we created population genetic null models using Monte Carlo simulations. Null expectations for genetic differentiation (F _ST) were compared with actual sequence variation from four highly polymorphic nuclear loci. Four colonization scenarios that were modeled led to unique genetic signatures that could be used to interpret empirical data. Unless current gene flow across Latin America was assumed to be very high, we could reject colonizations consisting of multiple introductions, each of low genetic diversity. Further, if simulated populations were small (N _e = 5 × 10² individuals per population), small invasions from a single source consistently produced F _ST values comparable to those currently observed in Latin America. In contrast, only large invasions from diverse sources were compatible with the observed data for large populations (N _e 5 × 10³). This study demonstrates that alternative population genetic hypotheses can be tested empirically even when departures from equilibrium are extreme, and that population genetic theory can be used to explore the processes that underlie biological invasions.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

Limits of a multi-patch SIS epidemic model

 We start from a stochastic SIS model for the spread of epidemics among a population partitioned into M sites, each containing N individuals; epidemic spread occurs through within-site (`local') contacts and global contacts. We analyse the limit behaviour of the system as M and N increase to ∞. Two limit procedures are considered, according to the order in which M and N go to ∞; independently of the order, the limiting distribution of infected individuals across sites is a probability measure, whose evolution in time is governed by the weak form of a PDE. Existence and uniqueness of the solutions to this problem is shown. Finally, it is shown that the infected distribution converges, as time goes to infinity, to a Dirac measure at the value x ^* , the equilibrium of a single-patch SIS model with contact rate equal to the sum of local and global contacts. Received: 18 July 2001 / Revised version: 16 March 2002 / Published online: 26 September 2002 Mathematics Subject Classification (2000): 92D30, 60F99 Key words or phrases: SIS epidemic – Metapopulation – Markov population processes – Weak convergence of measures     

What Can Cross-Cultural Correlations Teach Us about Human Nature?

Many recent evolutionary psychology and human behavioral ecology studies have tested hypotheses by examining correlations between variables measured at a group level (e.g., state, country, continent). In such analyses, variables collected for each aggregation are often taken to be representative of the individuals present within them, and relationships between such variables are presumed to reflect individual-level processes. There are multiple reasons to exercise caution when doing so, including: (1) the ecological fallacy, whereby relationships observed at the aggregate level do not accurately represent individual-level processes; (2) non-independence of data points, which violates assumptions of the inferential techniques used in null hypothesis testing; and (3) cross-cultural non-equivalence of measurement (differences in construct validity between groups). We provide examples of how each of these gives rise to problems in the context of testing evolutionary hypotheses about human behavior, and we offer some suggestions for future research.     

Persistence in metabolic nets

In an attempt to improve the understanding of complex metabolic dynamic phenomena, we have analysed several ‘metabolic networks’, dynamical systems which, under a single formulation, take into account the activity of several catalytic dissipative structures, interconnected by substrate fluxes and regulatory signals. These metabolic networks exhibit a rich variety of self-organized dynamic patterns, with e.g., phase transitions emerging in the whole activity of each network. We apply Hurst’s R/S analysis to several time series generated by these metabolic networks, and measure Hurst exponents H < 0.5 in most cases. This value of H, indicative of antipersistent processes, is detected at very high significance levels, estimated with detailed Monte Carlo simulations. These results show clearly the considered type of metabolic networks exhibit long-term memory phenomena.     

Fast Kalman filtering on quasilinear dendritic trees

Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem—the vector of voltages at every compartment—is very high-dimensional: realistic multicompartmental models often have on the order of N = 10⁴ compartments. Standard implementations of the Kalman filter require O(N ³) time and O(N ²) space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in O(N) time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in O(N) time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require O(N) time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations.