Application of a probabilistic model for analysing the abortion of seeds and pods in winter oilseed rape (Brassica napus)

In winter oilseed rape (WOSR), only a subset of ovules can develop into seeds in the majority of pods. Any difficulty during the process of seed production may result in seed or pod abortion. This study aimed to reproduce the process of seed development in WOSR based on a limited number of parameters. As a result of the complexity of the developmental patterns of WOSR, it is challenging to identify the roles of various factors that influence seed production using an experimental approach. Here, we present a stochastic probabilistic model of seed development. The generalised least squares method was implemented to estimate the model parameters using the experimental data. Experiments were done in Grignon (France) in 2008 and 2009. The variations in the parameters were analysed according to the following four factors: year, pod rank, inflorescence position and ramification‐clipping treatment. The year had no effect on the number of ovules per ovary (μ) and the probability of seed viability (p). The proportion of effective pollen grains (k) significantly decreased with pod rank at the end of the main stem. Inflorescence position influenced the number of ovules per ovary (μ: 30.8–33.8 from top to bottom) and the parameter k. The mean number of seeds per pod on the main stem and the bottom ramification along the stem was larger than the other ramifications within one plant. Ramification‐clipping treatment increased the number of ovules per ovary (μ: 31 for control plants and 32 for clipped plants), the parameter k and the number of seeds per pod (p). This effect could be due to the competition for assimilates between the pods and seeds. Furthermore, the distribution parameters of the pollen number per stigma (m) remained stable, and the probability of pod survival (Bo) varied with different factors, including the year, pod rank and inflorescence position. Our results indicate that pollen germination is a factor that determines final seed number. This model can identify the impact of each of the factors that lead to the abortion of seeds and pods in WOSR, which include the position effect, assimilate competition and pollination limitation. However, further studies on the pollination process in WOSR should help to refine this model.