Spatio-temporal heterogeneous analysis and modern phytometry

我的数学和统计学背景与我在麦吉尔大学植物科学系的位置相结合，很好地解释了我的研究计划的两个主轴，称为（A）“时空异质性分析”和（B）“现代植物测量学”。(A)在过去的几年里，我探索了多尺度分析多变量2-D空间数据的地统计方法。我和我的小组开发了一种无偏和有效的估计方法，用于拟合这种方法中的“协区域化线性模型”。我们评估了与参数估计值相关的不确定性以及由此得出的特定于尺度的相关性。我们发表了我们自己的多尺度分析方法，称为“CoRegionalization Analysis with a Drift”（CRAD）;这利用了非空间和小尺度空间变异性和相关性的地统计方法中的变差函数建模，但基于全局或大尺度移动窗口内估计的漂移。在提交的提案中，我解释了对特定尺度相关性的显著性检验的必要性，以及我将如何与一名理科硕士学生一起开发此类检验，以及我打算如何与一名博士生一起将CRAD扩展到3-D空间和时空数据。学生. (B)植物光截获和叶面积之间的关系是传统的Beer-Lambert定律建模，直到叶子的空间分布被纳入通过无叶植物结构的分形维数，估计从一张照片。我和我的团队开发了一种现代植物测量方法，以更完整，更精确地解释植物光截获，基于对冠层收集的计算机断层扫描（CT）扫描数据的处理和分析。金字塔雪松与CT扫描数据构建的三维图像的分形维数的强相关性表明，这些数据包含有关冠层结构几何形状的基本信息。在提交的提案中，我解释了我将如何建立在这个开创性的工作，进行两个原始的树冠CT扫描实验，并探索一个新的途径，称为“木材CT扫描”，在树冠的中心部分：树干。一个硕士，一个博士。学生和一名研究助理都参与其中。

The combination of my background in mathematics and statistics with my location in the Department of Plant Science at McGill University explains for a good part the two main axes of my research program, called (A) "Spatio-Temporal Heterogeneity Analysis" and (B) "Modern Phytometry". (A) In the last years, I explored the geostatistical approach for multi-scale analysis of multivariate 2-D spatial data. My group and I developed an unbiased and efficient estimation method for fitting the "linear model of coregionalization" in this approach. We assessed the uncertainty associated with the parameter estimates and the scale-specific correlations derived from them. We published our own method of multi-scale analysis, called "CoRegionalization Analysis with a Drift" (CRAD); this takes advantage of the variogram modeling in the geostatistical approach for non-spatial and small-scale spatial variability and correlations, but is based on drifts estimated globally or within a moving window at large scale. In the submitted proposal, I explain the need for tests of significance for scale-specific correlations and how I will develop such tests with a M.Sc. student, as well as how I intend to extend CRAD to 3-D spatial and spatio-temporal data with a Ph.D. student. (B) The relationship between plant light interception and leaf area was traditionally modeled with the Beer-Lambert law, until the spatial distribution of leaves was incorporated through the fractal dimension of leafless plant structure, estimated from a photograph. My group and I developed a modern phytometric approach to explain plant light interception more completely and precisely, based on the processing and analysis of computed tomography (CT) scan data collected on canopies. The strong correlation obtained for Pyramidal Cedar with the fractal dimension of skeletonized 3-D images constructed from CT scan data demonstrates that such data contain fundamental information about the canopy architecture geometry. In the submitted proposal, I explain how I will build up on this pioneering work to conduct two original canopy CT scan experiments and explore a new avenue, called "wood CT scan", in the central part of the canopy: the trunk. One M.Sc. and one Ph.D. student plus one research assistant are involved.