One of the approaches to plant development description involves phenological curves, which represent the time variations of certain traits. Most models applied to various plant taxa and life forms describe their phenology, including flowering, at the population level, and insufficient attention is paid to the modeling at the individual one. Individual modeling is more complicated than populational one owing to the multilevel structure of a phenotype. And as a result, it is accompanied by a significant increase in the number of model parameters, many of which are both interdependent and non-transferable between species. Here, we present a simple structural-dynamic data-driven model to describe the flowering patterns of individual monocarpic shoots of herbaceous plants with multi-flowered inflorescences. This model is nonparametric, thus being convenient and applicable to various plant species. Our results showed the operability of the proposed model and its potential in the detection of hidden trends in the input data. This is illustrated by the example of the herbaceous polycarpic Campanula sarmatica, Campanulaceae family, whose inflorescences demonstrate a wide variability in the structure and dynamics of flowering. For example, using our model, we found that the shape of the flowering curve of C. sarmatica shoots as a whole is determined by only two factors, the ratio of the number of flowers on the main and lateral axes, and the time of the flowering shift from the main axis to the lateral axes. The proposed model accurately mimics the individual flowering pattern with due natural variability. It can be used to simulate the flowering of a group of individuals in cenopopulational studies or practical tasks, e.g., in landscape design. Flowering patterns that characterize inflorescence development at the individual level can serve as informative phenotypic traits in anthoecological and developmental studies, and in inflorescence diagnostics.

中文翻译：

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草本多花单果树枝条花型分析的非参数模型

植物发育描述的方法之一涉及物候曲线，它代表某些性状的时间变化。大多数应用于各种植物分类群和生命形式的模型在种群水平上描述了它们的物候学，包括开花，而对个体的建模关注不够。由于表型的多级结构，个体建模比群体建模更复杂。结果，伴随着模型参数数量的显着增加，其中许多参数既相互依赖又不可在物种之间转移。在这里，我们提出了一个简单的结构动态数据驱动模型来描述具有多花花序的草本植物单果枝的开花模式。这个模型是非参数的，从而方便和适用于各种植物物种。我们的结果显示了所提出模型的可操作性及其在检测输入数据中隐藏趋势方面的潜力。以桔梗科草本多果风铃草为例说明了这一点，其花序在开花结构和动态方面表现出很大的变异性。例如，使用我们的模型，我们发现 C. sarmatica 芽整体的开花曲线形状仅由两个因素决定，即主轴和横轴上的花数比，以及开花时间开花从主轴转移到侧轴。所提出的模型准确地模拟了具有适当自然可变性的个体开花模式。它可用于在种群研究或实际任务（例如，景观设计）中模拟一组个体的开花。在个体水平上表征花序发育的开花模式可以作为植物生态学和发育研究以及花序诊断中的信息表型特征。