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As one of the essential nutrients for plants, nitrogen (N) has a major impact on the yield and quality of wheat worldwide. Due to chemical fertilizer pollution, it has become increasingly important to improve crop yield by increasing N use efficiency (NUE). Therefore, understanding the response mechanisms to low N (LN) stress is essential for the regulation of NUE in wheat. In this study, LN stress significantly accelerated wheat root growth, but inhibited shoot growth. Further transcriptome analysis showed that 8468 differentially expressed genes (DEGs) responded to LN stress. The roots and shoots displayed opposite response patterns, of which the majority of DEGs in roots were up-regulated (66.15%; 2955/4467), but the majority of DEGs in shoots were down-regulated (71.62%; 3274/4565). GO and KEGG analyses showed that nitrate reductase activity, nitrate assimilation, and N metabolism were significantly enriched in both the roots and shoots. Transcription factor (TF) and protein kinase analysis showed that genes such as MYB-related (38/38 genes) may function in a tissue-specific manner to respond to LN stress. Moreover, 20 out of 107 N signaling homologous genes were differentially expressed in wheat. A total of 47 transcriptome datasets were used for weighted gene co-expression network analysis (17,840 genes), and five TFs were identified as the potential hub regulatory genes involved in the response to LN stress in wheat. Our findings provide insight into the functional mechanisms in response to LN stress and five candidate regulatory genes in wheat. These results will provide a basis for further research on promoting NUE in wheat. [ABSTRACT FROM AUTHOR]

We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method. [ABSTRACT FROM AUTHOR]

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results. [ABSTRACT FROM AUTHOR]