Construction of Partially Balanced Incomplete Block Designs with Nested Rows and Columns

A number of methods of construction of partially balanced incomplete block designs with nested rows and columns are developed and new balanced incomplete block designs with nested rows and columns are obtained as a by-product.     

Model Building and Analysis for Block Designs with Nested Rows and Columns

The paper deals with two main problems: it gives a unified approach to model building for observations obtained in a block design with nested rows and columns and it provides the analysis of variance for such data. Also, some statistical properties of the design are examined.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

Characterisation of Certain Split-Block Designs with a Control

The paper deals with an incomplete split-block design in which one or two factors are split into two parts, the first one containing test treatments and the second one — a control treatment. The aim of the experiment carried out in such design is to compare the average of the test treatment effects with the control treatment effect and the test treatment effects with the control treatment effect individually. All those comparisons can be expressed by contrasts, elementary or basic ones. The aim of the paper is to characterise particular cases of the incomplete split-block designs with respect to general balance and to efficiency factors of the design with respect to the contrasts. In the paper we restrict our attention to the designs in which each block has two rows or/and two columns only. These designs are suitable for certain agricultural experiments.     

Optimal nested row-column designs with specified components

We consider nested row-column designs where each of the rowand column component designs is specified. For the case thateach of the component designs has second-order balance, we definesuch a nested row-column design to be special if it is generallybalanced, with the smallest possible number of canonical treatmentcontrasts having the lower canonical efficiency factor in bothcomponents. We show that if any special row-column design existsthen it is A-optimal over all nested row-column designs withthe given components.     

Pooled Genomic Indexing (PGI): analysis and design of experiments.

Pooled Genomic Indexing (PGI) is a novel method for physical mapping of clones onto known sequences. PGI is carried out by pooling arrayed clones and generating shotgun sequence reads from the pools. The shotgun sequences are compared to a reference sequence. In the simplest case, clones are placed on an array and are pooled by rows and columns. If a shotgun sequence from a row pool and another shotgun sequence from a column pool match the reference sequence at a close distance, they are both assigned to the clone at the intersection of the two pools. Accordingly, the clone is mapped onto the region of the reference sequence between the two matches. A probabilistic model for PGI is developed, and several pooling designs are described and analyzed, including transversal designs and designs from linear codes. The probabilistic model and the pooling schemes are validated in simulated experiments where 625 rat bacterial artificial chromosome (BAC) clones and 207 mouse BAC clones are mapped onto homologous human sequence.     

Efficiency of cohort sampling designs: some surprising results.

Cohort sampling designs are proposed which one would intuitively expect to be more efficient than nested case-control sampling. Two of these designs start with a nested case-control sample and distribute controls to sampled risk sets other than those for which they were picked. The third design has the goal of maximizing the number of distinct persons in a nested case-control sample. Simulation results show surprisingly little gain, and more often a loss in efficiency of these new designs relative to nested case-control sampling. This is due to the sampling-induced covariance between score terms. We conclude that the often stated intuition that nested case-control sampling does not make good use of sampled individuals' covariate histories is false.     

False Correlates of Nested Patterns: A Case Study Using Temporary Pond Microcrustaceans

Nestedness analysis is a popular tool for inferring spatial species distributions, and therefore has management and conservation relevance. Ecologists frequently compute nestedness and subsequently use Spearman rank correlations for inferring relationships between the observed nested ranks of sites with biogeographic and environmental variables. Using temporary pond microcrustaceans hatched from microcosms as a case study, this paper shows that the application of this method can be problematic. While the overall degree and significance of nestedness was robust against a statistical error, the results obtained from randomly generated matrices, in which community structure from the original microcrustacean incidence matrix was maintained (fixed rows –fixed columns constraints), showed that rank correlations of observed nested patterns can be vulnerable to a Type 1 error (detecting an effect when there is none). Using expected nestedness patterns derived from rarefied original matrices to control for sample size effects did not change this result. This problem may have arisen as a result of a quantitative bias related to the disproportionate impact of rank positions of individual ponds in the analysis. Future extensive simulations studies, involving different community structures, should help identify the general reliability of rank correlation results in nestedness analyses. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A protocol to compare nestedness among submatrices

Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null-models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined.     

The Dynamics of Nestedness Predicts the Evolution of Industrial Ecosystems

In economic systems, the mix of products that countries make or export has been shown to be a strong leading indicator of economic growth. Hence, methods to characterize and predict the structure of the network connecting countries to the products that they export are relevant for understanding the dynamics of economic development. Here we study the presence and absence of industries in international and domestic economies and show that these networks are significantly nested. This means that the less filled rows and columns of these networks'' adjacency matrices tend to be subsets of the fuller rows and columns. Moreover, we show that their nestedness remains constant over time and that it is sustained by both, a bias for industries that deviate from the networks'' nestedness to disappear, and a bias for the industries that are missing according to nestedness to appear. This makes the appearance and disappearance of individual industries in each location predictable. We interpret the high level of nestedness observed in these networks in the context of the neutral model of development introduced by Hidalgo and Hausmann (2009). We show that the model can reproduce the high level of nestedness observed in these networks only when we assume a high level of heterogeneity in the distribution of capabilities available in countries and required by products. In the context of the neutral model, this implies that the high level of nestedness observed in these economic networks emerges as a combination of both, the complementarity of inputs and heterogeneity in the number of capabilities available in countries and required by products. The stability of nestedness in industrial ecosystems, and the predictability implied by it, demonstrates the importance of the study of network properties in the evolution of economic networks.     

Experimental design considerations: a determinant of acute neonatal toxicity

Few studies have investigated the potential developmental differences resulting from treating neonatal rat pups in either split-litter or whole-litter (nested) experimental designs. We directly compared rat pups dosed with triethyl lead (TEL) via both split-litter (representing all dosage groups within a single litter) and nested (all pups randomly assigned to a single litter receive the same dose) designs. The nested design was chosen to produce a uniform behavioral pattern across pups within each litter, whereas the split-litter design was chosen to promote pup competition and differential maternal care. On postpartum day 5, pups were administered either 12, 13, 14, or 15 mg/kg TEL, with each design represented by 12 litters. Although the LD50 values for the two designs were not significantly different, there were significantly more deaths in the 12 mg/kg dosage group within the split-litter design than in the nested design group. Preweaning survival times for split-litter dosed animals were also decreased. In addition, significant growth reduction (7-16%) was observed in the split-litter group, relative to the nested design animals during the preweaning period. These results suggest that neonatal toxicity is not independent from experimental design considerations, and that the factors of littermate competition and/or pup-induced maternal care deserve further study.     

A similarity ring for amino acids based on their evolutionary substitution rates

A similarity ring for amino acids is obtained by reordering the rows and columns of their substitution probability matrix so as to minimize the variance of the matric elements about the main diagonal.     

ScalaParBiBit: scaling the binary biclustering in distributed-memory systems

Cluster Computing - Biclustering is a data mining technique that allows us to find groups of rows and columns that are highly correlated in a 2D dataset. Although there exist several software...     

Power to detect higher-order epistatic interactions in a metabolic pathway using a new mapping strategy

Epistatic interactions among quantitative trait loci (QTL) contribute substantially to the variation in complex traits. The main objectives of this study were to (i) compare three- vs. four-step genome scans to identify three-way epistatic interactions among QTL belonging to a metabolic pathway, (ii) investigate by computer simulations the power and proportion of false positives (PFP) for detecting three-way interactions among QTL in recombinant inbred line (RIL) populations derived from a nested mating design, and (iii) compare these estimates to those obtained for detecting three-way interactions among QTL in RIL populations derived from diallel and different partial diallel mating designs. The single-nucleotide polymorphism haplotype data of B73 and 25 diverse maize inbreds were used to simulate the production of various RIL populations. Compared to the three-step genome scan, the power to detect three-way interactions was higher with the four-step genome scan. Higher power to detect three-way interactions was observed for RILs derived from optimally allocated distance-based designs than from nested designs or diallel designs. The power and PFP to detect three-way interactions using a nested design with 5000 RILs were for both the 4-QTL and the 12-QTL scenario of a magnitude that seems promising for their identification.     

Sequential and combinatorial inputs from Nodal, Delta2/Notch and FGF/MEK/ERK signalling pathways establish a grid-like organisation of distinct cell identities in the ascidian neural plate

The ascidian neural plate has a grid-like organisation, with six rows and eight columns of aligned cells, generated by a series of stereotypical cell divisions. We have defined unique molecular signatures for each of the eight cells in the posterior-most two rows of the neural plate - rows I and II. Using a combination of morpholino gene knockdown, dominant-negative forms and pharmacological inhibitors, we tested the role of three signalling pathways in defining these distinct cell identities. Nodal signalling at the 64-cell stage was found to be required to define two different neural plate domains - medial and lateral - with Nodal inducing lateral and repressing medial identities. Delta2, an early Nodal target, was found to then subdivide each of the lateral and medial domains to generate four columns. Finally, a separate signalling system along the anteroposterior axis, involving restricted ERK1/2 activation, was found to promote row I fates and repress row II fates. Our results reveal how the sequential integration of three signalling pathways - Nodal, Delta2/Notch and FGF/MEK/ERK - defines eight different sub-domains that characterise the ascidian caudal neural plate. Most remarkably, the distinct fates of the eight neural precursors are each determined by a unique combination of inputs from these three signalling pathways.     

Construction of Resolvable Designs with Nested Treatment Structure

The construction of resolvable incomplete block and row-column designs is investigated when the treatments have a nested structure. Some theoretical results are derived for lattice designs. Efficient designs for unequal-sized treatment groups are obtained by defining a multiple objective function and carrying out a computer search using an interchange algorithm.     

Sampling design and the shape of species–area curves on the regional scale

Species–area relationships (SARs) are one of the fundamental patterns in ecology. However, how the way they were constructed influences resulting SAR shapes has gained astonishingly little attention. We use data of the distribution atlas of Polish butterflies to compare SARs constructed from four different designs: adding up species numbers of independent areas (species accumulation curves using contiguous and non-contiguous areas), using a nested design, and comparing species numbers of independent areas of different sizes. It appeared that the way of constructing SARs influences the outcome. We attribute this influence to the pronounced faunal dissimilarities of more distant areas (spatial species turnover). The nested design resulted in significantly higher slopes and lower intercepts of power function SARs than the other designs. SARs from all four sampling designs showed a pronounced downward curvature on small spatial scales. Only the nested design predicted species densities correctly. The implications of these results for the use of SARs in bioconservation are discussed.     

The Probability Density Functions of the Contingency Coefficients,defined by KRAMER and PEARSON,in a 2-Dimensional Frequency Distribution of Grouped Bivariate Normal Variables. I

Two general measures for the degree of association in a contingency table are the contingency coefficients defined by PEARSON and KRAMER. In the case of a standardized bivariate normal distribution with correlation coefficient of the variables, whose realizations constitute the rows and columns of the table, the density functions of the two listed association measures are derived.     

The presence–absence matrix reloaded: the use and interpretation of range–diversity plots

Aim A great deal of information on distribution and diversity can be extracted from presence–absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range–diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity. Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co‐occurrence of species and of similarity among sites. Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness.     

Large-scale ion-exchange column chromatography of proteins. Comparison of different formats

This review describes the performance of various column designs available to process-scale users of low-pressure chromatography for protein purification. By carrying out a range of ion-exchange separations using Whatman microgranular ion-exchange celluloses we are able to compare and contrast the practical performance issues associated with several designs of axial and radial flow columns.