Leaf count overdispersion in coffee seedlings

ABSTRACT: Coffee crops play an important role in Brazilian agriculture, with a high level of social and economic participation resulting from the jobs created in the supply chain and from the income obtained by producers and the revenue generated for the country from coffee bean export. In coffee plant growth, leaves have a determinant role in higher production; therefore, the leaf count per plant provides relevant information to producers for adequate crop management, such as foliar fertilizer applications. To describe count data, the Poisson model is the most commonly employed model; when count data show overdispersion, the negative binomial model has been determined to be more adequate. The objective of this study was to compare the fitness of the Poisson and negative binomial models to data on the leaf count per plant in coffee seedlings. Data were collected from an experiment with a randomized block design with 30 treatments and three replicates and four plants per plot. Data from only one treatment, in which the number of leaves was counted over time, were employed. The first count was conducted on 8 April 2016, and the other counts were performed 18, 32, 47, 62, 76, 95, 116, 133, and 153 days after the first evaluation, for a total of ten measurements. The fitness of the models was assessed based on deviance values and simulated envelopes for residuals. Results of fitness assessment indicated that the Poisson model was inadequate for describing the data due to overdispersion. The negative binomial model adequately fitted the observations and was indicated to describe the number of leaves of coffee plants. Based on the negative binomial model, the expected relative increase in the number of leaves was 0.9768% per day.

摘要：咖啡作物在巴西农业中占据重要地位，其供应链创造的就业岗位、种植户获得的收益以及该国咖啡豆出口带来的国家收入，使其具备极高的社会与经济参与度。在咖啡植株生长过程中，叶片对高产具有决定性作用；因此，单株叶片数量可为种植户开展合理的作物管理（如叶面肥施用）提供关键参考信息。针对计数数据的建模，泊松（Poisson）模型是最常用的方法；当计数数据存在过度分散问题时，负二项（negative binomial）模型则更为适配。本研究旨在对比泊松模型与负二项模型对咖啡幼苗单株叶片计数数据的拟合效果。本研究数据来自一项随机区组设计试验，该试验共设置30个处理、3次重复，每小区种植4株植株。本次分析仅采用其中一个处理组的数据，该组按时间序列统计叶片数量。首次统计于2016年4月8日开展，后续分别在首次评估后的第18、32、47、62、76、95、116、133及153天进行统计，累计完成10次测量。模型拟合效果通过偏差值与残差模拟包络线进行评估。拟合效果评估结果显示，由于数据存在过度分散问题，泊松模型无法适配该数据集。负二项模型则可良好拟合观测数据，适用于咖啡植株叶片数量的建模分析。基于负二项模型，单株叶片数量日均预期相对增幅为0.9768%。