The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MAT-LAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/(Mentaschi et al., 2016).

Effect of temperature, food availability, and estradiol injection on gametogenesis and gender in the pearl oyster Pinctada margaritifera

The black-lip pearl oyster Pinctada margaritifera is a protandrous hermaphrodite species. Its economic value has led to the development of controlled hatchery reproduction techniques, although many aspects remain to be optimized. In order to understand reproductive mechanisms and their controlling factors, two independent experiments were designed to test hypotheses of gametogenesis and sex ratio control by environmental and hormonal factors. In one, pearl oysters were exposed under controlled conditions at different combinations of temperature (24 and 28°C) and food level (10,000 and 40,000 cells mL−1); whereas in the other, pearl oysters were conditioned under natural conditions into the lagoon and subjected to successive 17β-estradiol injections (100 μg per injection). Gametogenesis and sex ratio were assessed by histology for each treatment. In parallel, mRNA expressions of nine marker genes of the sexual pathway (pmarg-foxl2, pmarg-c43476, pmarg-c45042, pmarg-c19309, pmarg-c54338, pmarg-vit6, pmarg-zglp1, pmarg-dmrt, and pmarg-fem1-like) were investigated. Maximum maturation was observed in the treatment combining the highest temperature (28°C) and the highest microalgae concentration (40,000 cells mL−1), where the female sex tended to be maintained. Injection of 17β-estradiol induced a significant increase of undetermined stage proportion 2 weeks after the final injection. These results suggest that gametogenesis and gender in adult pearl oysters can be controlled by environmental factors and estrogens. While there were no significant effects on relative gene expression, the 3-gene-pair expression ratio model of the sexual pathway of P. margaritifera, suggest a probable dominance of genetic sex determinism without excluding a mixed sex determination mode (genetic + environmental)