Matching data sets from two different spatial samples

Abstract. Methods for coupling two data sets (species composition and environmental variables for example) are well known and often used in ecology. All these methods require that variables of the two data sets have been recorded at the same sample stations. But if the two data sets arise from different sample schemes, sample locations can be different. In this case, scientists usually transform one data set to conform with the other one that is chosen as a reference. This inevitably leads to some loss of information. We propose a new ordination method, named spatial‐RLQ analysis, for coupling two data sets with different spatial sample techniques. Spatial‐RLQ analysis is an extension of co‐inertia analysis and is based on neighbourhood graph theory and classical RLQ analysis. This analysis finds linear combinations of variables of the two data sets which maximize the spatial cross‐covariance. This provides a co‐ordination of the two data sets according to their spatial relationships. A vegetation study concerning the forest of Chizé (western France) is presented to illustrate the method.     

Partitioning the variation in a plot‐by‐species data matrix that is related to n sets of explanatory variables

Abstract. Variation partitioning by (partial) constrained ordination is a popular method for exploratory data analysis, but applications are mostly restricted to simple ecological questions only involving two or three sets of explanatory variables, such as climate and soil, this because of the rapid increase in complexity of calculations and results with an increasing number of explanatory variable sets. The existence is demonstrated of a unique algorithm for partitioning the variation in a set of response variables on n sets of explanatory variables; it is shown how the 2n– 1 non‐overlapping components of variation can be calculated. Methods for evaluation and presentation of variation partitioning results are reviewed, and a recursive algorithm is proposed for distributing the many small components of variation over simpler components. Several issues related to the use and usefulness of variation partitioning with n sets of explanatory variables are discussed with reference to a worked example.     

An exhaustive analysis of heuristic methods for variable selection in ecological niche modeling and species distribution modeling

Ecological niche models and species distribution models are used in many fields of science. Despite their popularity, only recently have important aspects of the modeling process like model selection been developed. Choosing environmental variables with which to create these models is another critical part of the process, but methods currently in use are not consistent in their results and no comprehensive approach exists by which to perform this step. Here, we compared seven heuristic methods of variable selection against a novel approach that proposes to select best sets of variables by evaluating performance of models created with all combinations of variables and distinct parameter settings of the algorithm in concert. Our results were that—except for the jackknife method for one of the 12 species and fluctuation index for two of the 12 species—none of the heuristic methods for variable selection coincided with the exhaustive one. Performance decreased in models created using variables selected with heuristic methods and both underfitting and overfitting were detected when comparing their geographic projections with the ones of models created with variables selected with the exhaustive method. Using the exhaustive approach could be time consuming, so a two-step exercise may be necessary. However, using this method identifies adequate variable sets and parameter settings in concert that are associated with increased model performance.     

Effects of individual activity sequences on prey-predator models

We study the influence of the individual behaviour of animals on predator-prey models. Populations of preys and predators are divided into sub-populations corresponding to different activity classes. The animals are assumed to do many activities all day long such as searching for food of different types. The preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study activity sequences of the animals and also the effect of a change in the average individual behaviour of the animals on Lotka-Volterra prey-predator interactions. Numerical simulations are realized for the whole sets of equations (governing the subpopulations) and are compared to the simulations of the reduced sets of equation (governing the populations). We look for the validity of the method with respect to a scaling factor which measures the differences between the two time scales associated to the fast-varying variables and to the slow-time varying global variables. It is shown that when the two time scales differ of about two orders of magnitude, the approximation is satisfying.     

Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities

This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories calledN-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points.Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.     

Reproductive and socioeconomic determinants of child survival: Confounded,interactive, and age‐dependent effects

Abstract

Studies of infant and child mortality have evolved to distinguish between two sets of explanatory variables—factors related to reproductive or maternal characteristics and socioeconomic factors, generally described as characteristics of the family or household. Almost all multivariate analyses include variables from each of these two sets, but there has been little consideration of the relationship between them. We examine how these two sets of variables jointly affect mortality. We test first for confounded effects by examining socioeconomic effects while excluding and then including reproductive variables in nested multivariate models. Next, we look for age‐dependent effects among the explanatory variables and find that reproductive and socioeconomic factors affect mortality at differing ages of children. Finally, we examine interactive effects of the two sets of variables. We conclude that the higher mortality observed among the low status groups is not a result of greater concentration of poor reproductive patterns in those groups. Instead, higher status groups probably have more resources available for combating the negative effects of the same high‐risk reproductive patterns.     

Reproductive and socioeconomic determinants of child survival: confounded, interactive, and age-dependent effects.

Studies of infant and child mortality have evolved to distinguish between two sets of explanatory variables-factors related to reproductive or maternal characteristics and socioeconomic factors, generally described as characteristics of the family or household. Almost all multivariate analyses include variables from each of these two sets, but there has been little consideration of the relationship between them. We examine how these two sets of variables jointly affect mortality. We test first for confounded effects by examining socioeconomic effects while excluding and then including reproductive variables in nested multivariate models. Next, we look for age-dependent effects among the explanatory variables and find that reproductive and socioeconomic factors affect mortality at differing ages of children. Finally, we examine interactive effects of the two sets of variables. We conclude that the higher mortality observed among the low status groups is not a result of greater concentration of poor reproductive patterns in those groups. Instead, higher status groups probably have more resources available for combating the negative effects of the same high-risk reproductive patterns.     

Between-group analysis of microarray data

MOTIVATION: Most supervised classification methods are limited by the requirement for more cases than variables. In microarray data the number of variables (genes) far exceeds the number of cases (arrays), and thus filtering and pre-selection of genes is required. We describe the application of Between Group Analysis (BGA) to the analysis of microarray data. A feature of BGA is that it can be used when the number of variables (genes) exceeds the number of cases (arrays). BGA is based on carrying out an ordination of groups of samples, using a standard method such as Correspondence Analysis (COA), rather than an ordination of the individual microarray samples. As such, it can be viewed as a method of carrying out COA with grouped data. RESULTS: We illustrate the power of the method using two cancer data sets. In both cases, we can quickly and accurately classify test samples from any number of specified a priori groups and identify the genes which characterize these groups. We obtained very high rates of correct classification, as determined by jack-knife or validation experiments with training and test sets. The results are comparable to those from other methods in terms of accuracy but the power and flexibility of BGA make it an especially attractive method for the analysis of microarray cancer data.     

High‐dimensional data analysis: Selection of variables,data compression and graphics – Application to gene expression

The paper presents effective and mathematically exact procedures for selection of variables which are applicable in cases with a very high dimension as, for example, in gene expression analysis. Choosing sets of variables is an important method to increase the power of the statistical conclusions and to facilitate the biological interpretation. For the construction of sets, each single variable is considered as the centre of potential sets of variables. Testing for significance is carried out by means of the Westfall‐Young principle based on resampling or by the parametric method of spherical tests. The particular requirements for statistical stability are taken into account; each kind of overfitting is avoided. Thus, high power is attained and the familywise type I error can be kept in spite of the large dimension. To obtain graphical representations by heat maps and curves, a specific data compression technique is applied. Gene expression data from B‐cell lymphoma patients serve for the demonstration of the procedures.     

Relationships of overstory to understory cover variables in a Ponderosa pine/Gambel oak ecosystem

Many studies have indicated relationships between individual species, but none have related combinations of overstory variables to understory herbaceous vegetation in a Ponderosa pine/Gambel oak ecosystem. Our objective was to determine not only the general relationships between the two sets of variables, but also identify the hyghest contributing variables. We used canonical correlation analysis to relate overstory variables (canopy cover, basal cover and density) to herbaceous vegetation cover variables. Canopy, basal, and ground cover were measured by the line intercept method using a 12.2 m tape as a sample unit. Tree density was measured by the Point-Center-Quarter method. The analysis was made with selected overstory variables and 5 understory herbaceous cover variables. This analysis revealed a significant canonical correlation between the two canonical variables (r=0.69). The analysis showed that among herbaceous cover variables, Oregon grape, Kentucky bluegrass, sedge, and foxtail barley; and among overstory variables, the density and the basal cover of Ponderosa pine indicated the highest positive contribution to the correlation of the two linear combinations while the density and canopy of Gambel oak negatively affected the canonical correlation.     

Non-linear relations between selected anthropological predictors and psycho-physiological exercise-responses

In this paper, some very useful non-linear-relation procedures are actualized. The authors have defined the characteristic correlations between a set of anthropological characteristics (14 anthropometric and 14 motor-endurance status variables) and a set of psycho-physiological exercise-responses during the hi-lo and during the step aerobic dance training (heart rate, lactate concentration and rating of the perceived exertion). 60 healthy females served as the sample of subjects (mean age 21 +/- 1.4 years). The experiment consisted of two parts. In the first one, the linear correlations between the two sets of the variables were established. In the second part, non-linear (squared) relations, between the variables of the two sets were calculated. Results confirm the statement that the non-linear correlations, in some cases, better determinate the real nature of the relations between the variables, than linear correlation models.     

Integrative analysis of gene expression and copy number alterations using canonical correlation analysis

Background  

With the rapid development of new genetic measurement methods, several types of genetic alterations can be quantified in a high-throughput manner. While the initial focus has been on investigating each data set separately, there is an increasing interest in studying the correlation structure between two or more data sets. Multivariate methods based on Canonical Correlation Analysis (CCA) have been proposed for integrating paired genetic data sets. The high dimensionality of microarray data imposes computational difficulties, which have been addressed for instance by studying the covariance structure of the data, or by reducing the number of variables prior to applying the CCA. In this work, we propose a new method for analyzing high-dimensional paired genetic data sets, which mainly emphasizes the correlation structure and still permits efficient application to very large data sets. The method is implemented by translating a regularized CCA to its dual form, where the computational complexity depends mainly on the number of samples instead of the number of variables. The optimal regularization parameters are chosen by cross-validation. We apply the regularized dual CCA, as well as a classical CCA preceded by a dimension-reducing Principal Components Analysis (PCA), to a paired data set of gene expression changes and copy number alterations in leukemia.     

Simplivariate models: uncovering the underlying biology in functional genomics data

One of the first steps in analyzing high-dimensional functional genomics data is an exploratory analysis of such data. Cluster Analysis and Principal Component Analysis are then usually the method of choice. Despite their versatility they also have a severe drawback: they do not always generate simple and interpretable solutions. On the basis of the observation that functional genomics data often contain both informative and non-informative variation, we propose a method that finds sets of variables containing informative variation. This informative variation is subsequently expressed in easily interpretable simplivariate components.We present a new implementation of the recently introduced simplivariate models. In this implementation, the informative variation is described by multiplicative models that can adequately represent the relations between functional genomics data. Both a simulated and two real-life metabolomics data sets show good performance of the method.     

Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each dataset. However, in high‐dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each dataset, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic dataset.     

Finding a common ordination for several data sets by individual differences scaling

Individual differences scaling is a multidimensional scaling method for finding a common ordination for several data sets. An individual ordination for each data set can then be derived from the common ordination by adjusting the axis lengths so as to maximize the correlations between observed proximities and individual ordination distances. The importance of the various axes for each data set and the mutual similarities and goodness of fit for the individual data sets are described by weight plots. As an example, 46 soft-water lakes in eastern Finland are ordinated on two dimensions according to 3 chemical data sets (water in summer and autumn, sediment) and 4 biological sets (major phytoplankton groups, phytoplankton, surface sediment diatom and cladoceran assemblages). The method seems to be effective as a means of ordination for obtaining the common ordination for the data sets. The major taxonomic groups gave the ordination which differed most clearly from the ordinations of the other data sets. Phytoplankton was most poorly ordinated in all the analyses. The other data sets were fairly coherent. When only biological data sets were ordinated, the diatoms and cladocerans showed rather different patterns. It seems that the cladocerans are best correlated with water chemistry, both according to weights in the joint analysis, and according to correlation between the axes from the biological data sets and the chemical variables.Abbreviations CCA = Canonical correspondence analysis - IDS = Individual differences scaling - MDS = multidimensional scaling - PCA = Principal components analysis     

Niche shift versus niche conservatism? Climatic characteristics of the native and invasive ranges of the Mediterranean house gecko (Hemidactylus turcicus)

Aim The use of ecological niche models (ENMs) to predict potential distributions of species is steadily increasing. A necessary assumption is that climatic niches are conservative, but recent findings of niche shifts during biological invasion indicate that this assumption is not always valid. Selection of predictor variables may be one reason for the observed shifts. In this paper we assess differences in climatic niches in the native and invaded ranges of the Mediterranean house gecko (Hemidactylus turcicus) in terms of commonly applied climate variables in ENMs. We analyse which variables are more conserved versus relaxed (i.e. subject to niche shift). Furthermore, we study the predictive power of different sets of climate variables. Location The Mediterranean region and North America. Methods We developed models using Maxent and various subsets of variables out of 19 bioclimatic layers including: (1) two subsets comprising almost all variables excluding only highly collinear ones; (2) two subsets with minimalistic variable sets of water availability and energy measures; (3) two subsets focused on temperature‐related parameters; (4) two subsets with precipitation‐related parameters; and (5) one subset comprising variables combining temperature and precipitation characteristics. Occurrence data from the native Mediterranean range were used to predict the potential introduced range in North America and vice versa. Degrees of niche similarity and conservatism were assessed using both Schoener's index and Hellinger distances. The significance of the results was tested using null models. Results The degree of niche similarity and conservatism varied greatly among the predictors and variable sets applied. Shifts observed in some variables could be attributed to active habitat selection while others apparently reflected background effects. Main conclusions The study was based on comprehensive occurrence data from all regions where Hemidactylus turcicus is present in Europe and North America, providing a robust foundation. Our results clearly indicate that the degree of conservatism of niches in H. turcicus largely varies among predictors and variable sets applied. Therefore, the extent of niche conservatism of variables applied should always be tested in ENMs. This has an important impact on studies of biological invasion, impacts of climate change and niche evolution.     

Relations between some exogenous factors and anthropometric factors of growth and development of male children and youngsters in the Tuzla region, Bosnia and Herzegovina

Dynamics of growth of male children and youths from the Region of Tuzla influenced by some exogenous factors was researched by a corresponding analysis of the sample which included 751 tested individuals, aged from 11 to 17 years. The analysis performed is primarily based on the scientific elaboration of the registered state in two time-points (1996 and 1999) in the tested part of broader population. This research involved the period of four-year aggression on Bosnia and Herzegovina, taking into consideration the fact that the tested persons spent one period of their growth and development in extremely bad wartime living conditions. By quasicanonic correlative analysis it was established that the next factors participated in connection of variables of both sets (initial and final measurements): mother's standard, total mother's and father's standard of living, mother's age and sequence of births participated to some less extent in connection of both sets of variables. Anthropometric variables that had most significant impact of both sets of variables are: length parameters, body mass, width parameters, circumferences had somewhat less impact, while indexes of head and sitting height had the least impact on this connection.