Both the additive and multiplicative models of crop yield and water supply are polynomial equations, and the number of parameters increases linearly when the growing period is specified.  However, interactions among multiple parameters occasionally lead to unreasonable estimations of certain parameters, which were water sensitivity coefficients but with negative value.  Additionally, evapotranspiration must be measured as a model input.  To facilitate the application of these models and overcome the aforementioned shortcomings, a simple model with only three parameters was derived in this paper based on certain general quantitative relations of crop yield (Y) and water supply (W).  The new model, Y/Y_m–W^k/(W^k+w_h^k), fits an S or a saturated curve of crop yield with the cumulative amount of water.  Three parameters are related to biological factors: the yield potential (Y_m), the water requirement to achieve half of the yield potential (half-yield water requirement, w_h), and the water sensitivity coefficient (k).  The model was validated with data from 24 maize lines obtained in the present study and 17 maize hybrids published by other authors.  The results showed that the model was well fit to the data, and the normal root of the mean square error (NRMSE) values were 2.8 to 17.8% (average 7.2%) for the 24 maize lines and 2.7 to 12.7% (average 7.4%) for the 17 maize varieties.  According to the present model, the maize water-sensitive stages in descending order were pollen shedding and silking, tasselling, jointing, initial grain ?lling, germination, middle grain ?lling, late grain ?lling, and end of grain ?lling.  This sequence was consistent with actual observations in the maize field.  The present model may be easily used to analyse the water use efficiency and drought tolerance of maize at specific stages.

During meiosis in flowering plants, degradation of the callose wall in tetrads releases newly produced microspores, which develop into mature pollen grains. In this study, we identified zbs1, a male-sterile mutant of naked oat (Avena nuda L.) that displayed complete spikelet sterility due to inviable mature pollen. The abnormal pollen grains originated from microspores with a defective callose wall and cell plate during meiosis. The defective callose wall and cell plate of the zbs1 mutant were detected by the labeling of cell wall epitopes (β-1,3-glucan) with immunogold during meiosis, and an abnormal chromosome configuration was observed by propidium iodide staining. The mature pollen grains of the zbs1 mutant were irregular in shape, and abnormal germination was observed by scanning electron microscopy. Together, our results indicate that the cause of male sterility in zbs1 is abnormal meiosis.

Selection of quantitative characteristics, division of their expression ranges, and selection of example varieties are key issues on developing DUS Test Guidelines, which are more crucial for quantitative characteristics since their expressions vary in different degrees. Taking the development of DUS Test Guideline of Ranunculus asiaticus L. as an example, this paper applied statistic-based approaches for the analyses of quantitative characteristics. We selected 9 quantitative characteristics from 18 pre-selected characteristics, based on within-variety uniformity, stability between different growing cycles, and correlation among characteristics, by the analyses of coefficient of variation, paired-samples t-test and partial correlation. The expression ranges of the 9 selected quantitative characteristics were divided into different states using descriptive statistics and distribution frequency of varieties. Eight of the 9 selected quantitative characteristics were categorized as standard characteristics as they showed one peak in distribution frequency of 120 varieties in various expressions of the characteristics, whereas, plant height can be categorized as grouping characteristic since it gave two peaks, and can group the varieties into pot and cut varieties. Finally, box-plot was applied to visually select the example varieties, and varieties 7, 12, and 28 were determined as the example varieties for plant height. The methods described in this paper are effective for the selection of quantitative characteristics, division of expression ranges, and selection of example varieties in Ranunculus asiaticus L. for DUS test, and may also be interest for other plant genera.