School of Science, Wuhan University of Technology, Wuhan, 430070, PR China.
Wuhan Academy of Agricultural Sciences, Wuhan, 430208, PR China.
Waste Manag. 2023 Sep 1;169:351-362. doi: 10.1016/j.wasman.2023.07.015. Epub 2023 Jul 29.
Aerobic compost is an effective method for the treatment of livestock manure, which is usually accompanied by complex interspecific competition. Describing these competitive relationships through mathematical models can help understand the interaction of microorganisms and analyze the effect of exogenous additive to regulate the composting process. The common model for analyzing competition problem is the Lotka-Volterra model. However, the fixed parameters of the Lotka-Volterra model are not suitable to reflect the dynamic variations of the competitive relationship when the environmental conditions change during composting process. Therefore, this paper establishes a novel fractional grey unequal-interval time-varying Lotka-Volterra model. Firstly, a fractional grey derivate operator is proposed on the basis of the unequal interval of composting data and historical dependence of microbial growth. Secondly, considering the influence of temperature, a time-varying parameter matrix is defined to reflect the variation of competitive relationship at different composting phases, and it is estimated by forgetting factor recursive least squares. Thirdly, the optimal coefficients are optimized by grey prediction evolution algorithm. Finally, the proposed model is employed to analyze the chicken manure composting experiment. The results show that the proposed model has lower error criteria and more accurate trend of fitting curve than the other five existing models. The parameter matrix describes the dynamical variation of microbial competitive relationship in two taxonomic levels and reveals that effect of the exogenous additive is principally reacted in the thermophilic phase and the competitive advantage is shifted from Bacteroidota to Firmicutes after treatment with the exogenous additive.
好氧堆肥是处理牲畜粪便的有效方法，通常伴随着复杂的种间竞争。通过数学模型描述这些竞争关系，可以帮助理解微生物的相互作用，并分析外源性添加剂对调节堆肥过程的影响。分析竞争问题的常用模型是Lotka-Volterra 模型。然而，Lotka-Volterra 模型的固定参数并不适合反映堆肥过程中环境条件变化时竞争关系的动态变化。因此，本文建立了一种新的分数阶灰色不等时变 Lotka-Volterra 模型。首先，在堆肥数据的不等时距和微生物生长的历史依赖性的基础上，提出了分数阶灰色导数算子。其次，考虑到温度的影响，定义了一个时变参数矩阵，以反映不同堆肥阶段竞争关系的变化，并通过遗忘因子递归最小二乘法进行估计。再次，通过灰色预测进化算法对最优系数进行优化。最后，将所提出的模型应用于鸡粪堆肥实验。结果表明，所提出的模型具有更低的误差标准和更准确的拟合曲线趋势，优于其他五个现有模型。参数矩阵描述了两个分类水平的微生物竞争关系的动态变化，并揭示了外源性添加剂的作用主要在高温阶段反应，并且在添加外源性添加剂后，竞争优势从拟杆菌门转移到厚壁菌门。
