# Summary

### Author

Will Cornwell

### Summary

Statistical methods for manipulating and analyzing data for application to environmental and ecological plant physiology. In general, these methods are designed to connect raw measurements with quantitative theory, that is, bridge the gap between the raw output from a measurement technique and the variable of conceptual interest. We are also interested collecting interesting and elegant methods for visualizing data.

In the broadest sense, in environmental and ecological plant physiology there are two sets of statistical problems. The first are relatively direct applications of general analyzes that have been developed in detail by statisticians. For these sets of problems (e.g., frequentist inference using classical ANOVA) there are already freely-available, open-source resources for statistical analysis are already freely-available on the web. We recognize that the choice or applicability of an existing statistical approach for a specific problem in environmental and ecological plant physiology may be subject to some discussion and critique, and so will provide the opportunity for scripts for particular applications to be uploaded and discussed.

Second, there are many problems in environmental and ecological plant physiology that are specific enough to have required substantial new development of statistical methods. Two prominent examples of this are non-linear curve fits (e.g., the fit of an *A*–*c _{i}* curve) and the choice of model for linear regression relative to the particular problem. For these approaches, many of which have become quite intricate, there has been extensive development of specific approaches and software unique to environmental and ecological plant physiology. We focus more attention on these methods and offer the forum for further development.

General classes of statistical methods developed for environmental and ecological plant physiology:

1) Fitting approaches. There are three main problems that have spurred the development of specific methods for environmental and ecological plant physiology. First, are when the fitting approach is conceptually to a specific application in environmental and ecological plant physiology (e.g. OLS regression). Second, when the conceptual model is so complex that standard, off-the-shelf fitting approaches perform poorly (e.g. A-ci curves). Third, there is often a substantial gap between the raw measurement and the quantity of interest. All three of these problems may lead to disparate methods developing in different labs across the globe.

2) Phlyogenetic methods. All plant traits are the product of evolution. The structure of evolution-a conservative branching process-is particularly ill-suited to classical inferential statistics. A specific field has developed matching measurable quantities (e.g. a trait of individual or species) to estimates of evolutionary processes.

3) Spatial statistics. Often, the goal of environmental and ecological plant physiology is to upscale measurements to large areas. This is a particularly difficult statistical problem because of spatial auto-correlation and other associated problems. A specific field of statistical field approaches and methods has developed around this question.