Modeling pollen tube growth of apple

Raw data Sixty flowering shoots of around 0.40 m length were collected from 60 trees that were randomly selected from two commercial orchards of ‘Fuji’ and ‘Gala’ apples in Prosser, Washington (USA). The king flowers were hand pollinated with ‘Red Delicious’ commercial pollen. Pollinated flowers were placed in growth chambers at eight constant temperatures of 4.5, 7, 11.5, 14.5, 21.5, 22.6, 28 and 30°C. At 12, 24, 48, 72 and 96 hours after pollination for lower temperatures, i.e., 4.5, 7, 11.5 and 14.5°C and at 4, 8, 12, 24 and 48 hours after pollination for the warmer temperatures, i.e., 21.5, 22.6, 28 and 30°C; pistils of tree flowers were detached and stored for one night in FAA (5% formalin, 5% acetic acid, 45% ethanol, 45% water: by vol.). The pistils were then washed and boiled for 30 minutes in a solution of sodium sulfite (50 g l-1) and then refrigerated. For evaluation the styles were detached from the ovary, rinsed with distilled water and placed in a water-soluble fluorescent solution of 0.1% Aniline Blue stain and 3.5 g l-1 of tribasic potassium phosphate for three days. Styles were then squashed between two microscope slides with a drop of fluorescent solution. The pollen tube length was measured as the distance between the pollen tube tip and the upper cell layer of the stigma, this process was carried out using a stage micrometer of 10 mm by 0.1 mm, 20X magnification and a fluorescence microscope. Response surface data Pollen tube lengths for each evaluated temperature were adjusted to logarithmic and logistic curves depending of the type of response as a function of the hours after pollination and the derivatives of the curves were calculated to determine the hourly growth rate of the pollen tube and the percentage of penetration of the pollen tube in the style (%) was calculated by dividing the adjusted pollen tube length from logarithmic and logistic curves by the average style length of the sampled flowers, 14.3 mm for ‘Fuji’ and 14 mm for ‘Gala.’ This data was used to fit a segmented nonlinear response surface for each cultivar to estimate the HGR as a function of temperature and style penetration.一、原始数据 从美国华盛顿州普罗斯瑟（Prosser）的两个商业化苹果园（分别种植“富士”（Fuji）与“嘎啦”（Gala）苹果）中，随机选取60株果树，采集了约0.40米长的花枝共60枝。以“红蛇果”（Red Delicious）商品花粉对各花枝的中心花进行人工授粉。将授粉后的花枝置于8个恒定温度（4.5、7、11.5、14.5、21.5、22.6、28及30℃）的生长箱中培养。 针对低温组（4.5、7、11.5及14.5℃），分别在授粉后12、24、48、72及96小时取样；针对高温组（21.5、22.6、28及30℃），则在授粉后4、8、12、24及48小时取样。取样时摘取花的雌蕊，置于FAA固定液（体积占比为5%福尔马林、5%冰乙酸、45%乙醇、45%蒸馏水）中过夜保存。随后将雌蕊取出清洗，置于亚硫酸钠溶液（50 g·L⁻¹）中煮沸30分钟，之后冷藏保存。 用于观测时，将花柱从子房上剥离，用蒸馏水漂洗后，置于由0.1%苯胺蓝（Aniline Blue）染色剂与3.5 g·L⁻¹磷酸三钾组成的水溶性荧光染液中染色3天。随后滴加少量荧光染液，将花柱置于两片载玻片之间压片。花粉管长度定义为花粉管顶端与柱头上层细胞之间的距离，使用规格为10 mm×0.1 mm的载物台测微尺、放大倍数20倍的荧光显微镜完成测量。 二、响应面数据集 针对每个试验温度下测得的花粉管长度，根据其随授粉后时长的响应类型，分别拟合对数曲线与逻辑斯蒂曲线；通过计算曲线的一阶导数，得到花粉管的小时生长速率（hourly growth rate, HGR）。将对数曲线与逻辑斯蒂曲线拟合得到的校正后花粉管长度，除以供试品种的平均花柱长度（“富士”为14.3 mm，“嘎啦”为14 mm），即可算出花粉管在花柱内的穿透百分率（%）。 基于上述数据，为每个品种拟合分段非线性响应面模型，以估算随温度与花柱穿透率变化的小时生长速率（HGR）。