The green lineage is reportedly 1,500 million years old, evolving shortly after the endosymbiosis event that gave rise to early photosynthetic eukaryotes. In this study, we unveil the complete genome sequence of an ancient member of this lineage, the unicellular green alga Ostreococcus tauri (Prasinophyceae). This cosmopolitan marine primary producer is the world’s smallest free-living eukaryote known to date. Features likely reflecting optimization of environmentally relevant pathways, including resource acquisition, unusual photosynthesis apparatus, and genes potentially involved in C ₄ photosynthesis, were observed, as was downsizing of many gene families. Overall, the 12.56-Mb nuclear genome has an extremely high gene density, in part because of extensive reduction of intergenic regions and other forms of compaction such as gene fusion. However, the genome is structurally complex. It exhibits previously unobserved levels of heterogeneity for a eukaryote. Two chromosomes differ structurally from the other eighteen. Both have a significantly biased G+C content, and, remarkably, they contain the majority of transposable elements. Many chromosome 2 genes also have unique codon usage and splicing, but phylogenetic analysis and composition do not support alien gene origin. In contrast, most chromosome 19 genes show no similarity to green lineage genes and a large number of them are specialized in cell surface processes. Taken together, the complete genome sequence, unusual features, and downsized gene families, make O. tauri an ideal model system for research on eukaryotic genome evolution, including chromosome specialization and green lineage ancestry.

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

Diversity is a concept central to ecology, and its measurement is essential for any study of ecosystem health. But summarizing this complex and multidimensional concept in a single measure is problematic. Dozens of mathematical indices have been proposed for this purpose, but these can provide contradictory results leading to misleading or incorrect conclusions about a community’s diversity. In this review, we summarize the key conceptual issues underlying the measurement of ecological diversity, survey the indices most commonly used in ecology, and discuss their relative suitability. We advocate for indices that: (i) satisfy key mathematical axioms; (ii) can be expressed as so-called effective numbers; (iii) can be extended to account for disparity between types; (iv) can be parameterized to obtain diversity profiles; and (v) for which an estimator (preferably unbiased) can be found so that the index is useful for practical applications.

Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and applied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand.