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，很好地解释了我研究计划的两个主轴，即(A)“时空异质性分析”和(B)“现代植物学”。(A)在过去几年中，我探索了对多变量二维空间数据进行多尺度分析的地质统计学方法。我和我的团队开发了一种无偏见和有效的估计方法，用于在这种方法中拟合“协区域化的线性模型”。我们评估了与参数估计相关的不确定性以及由此得出的特定尺度的相关性。我们发表了我们自己的多尺度分析方法，称为“带漂移的协同区域化分析”(CRAD)；该方法利用地统计学方法中对非空间和小尺度空间变异性和相关性的变异函数建模，但基于全球或大尺度移动窗口内的漂移估计。在提交的提案中，我解释了对特定尺度相关性进行有意义的测试的必要性，以及我将如何与M.Sc一起开发这种测试。学生，以及我打算如何与一位博士生将CRAD扩展到3-D空间和时空数据。(B)植物光截获与叶面积之间的关系传统上用Beer-Lambert定律来模拟，直到通过照片估计的无叶植物结构的分维来反映叶片的空间分布。我和我的团队开发了一种现代植物测量学方法，基于对收集到的树冠上的计算机断层扫描(CT)数据的处理和分析，更全面和准确地解释植物的光截获。从CT扫描数据构建的骨架化3-D图像的分维与金字塔雪松的相关性很强，表明这些数据包含有关树冠结构几何的基本信息。在提交的建议书中，我解释了我将如何在这项开创性工作的基础上进行两项原始树冠CT扫描实验，并在树冠中央部分探索一种新的途径，称为“木材CT扫描”：树干。一名理科硕士。一名博士生和一名研究助理参与其中。

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.