## CTFS Tutorials

View tutorials at the links below.

**Tutorials: Top Level**- Server Use These are instructions for using the CTFS analytical server to run R programs onCTFS plot data. The principal advantage is in running analyses that take hours to days that wouldotherwise be difficult on your own desktop or laptop. The processors are not especially faster, but there are16 processors, so many programs can be running at once.
It&8217;s a Unix server, so you need to know a few Unix commands to start out, then R will be executed atthe command-line, with no Gui.

- Growth changes The question addressed here is how growth has changed with time, in particular howspecies differ in growth changes. There are two alternative models described:
- Growth rate changing linearly with time
- Growth rate varying from census to census, but not following a consistent change

Both hypotheses will be tested running models with the R function lmer in the package lme4. You willneed to install the package.

- Mortality changes The question addressed here is how tree mortality has changed with time, in particularhow species differ in the changes. There are two alternative models described:
- Mortality rate changing linearly with time
- Mortality rate varying from census to census, but not following a consistent change

Unlike growth analysis, mortality rates cannot be addressed with lmer, due to the variation in timeinterval among trees and among censuses. A proper mortality analysis must take this into account using adifferent death probability for every individual at every census. This can only be done with a Bayesianhierarchical model. The CTFSRPackage has a function lmerBayes which accomplishes the analysis. TheBayesian model has the advantage of producing complete confidence limits easily; the disadvantageis that it runs slowly. Analyses here on big datasets will take a couple hours to complete.

- Mortality vs. dbh Consider a calculation of mortality rate in dbh categories, estimated by countingsurvivors among all trees in each group. This is calculated in the program mortality.spp. The purpose hereis simply graphing results for many species into a pdf.
- Population Changes The question addressed here is how much abundances of all the tree species in a plotfluctuate from census to census. At one extreme, abundances are stabilized, and populations do notchange. In contrast, there may be environmental drivers favoring some species and not others, so that somespecies show marked (ie, more than neutral) increases and others decreases. In between the two extremes isa community in which no external drivers affect abundances but populations fluctuate due to demographicstochasticity: a neutral forest.
The test of these models hinges on a histogram of the rate of population change of every species in theforest. Define λ = , the ratio of a future population N

_{1}to the current N_{0}, and r = little.r = logλ.In a highly stabilized community, λ ≈ 1 for every species, and r = 0, whereas in a forest withenvironmental fluctionas, λ may be distributed widely but ought to be centered close to 1.The neutral community would fall in between, with λ varying a small amount due to chancealone.The distribution of λ and r under neutrality can be predicted mathematically, assumingdeaths are binomially distributed across individuals and a Poisson distribution of births whosemean matches the death rate. Because of this statistical model of neutral fluctuations, anyenvironmentally caused variation can be estimated precisely. In a conceptual sense, it meanssubtracting the predicted neutral variance of λ from the observed variance of λ; what&8217;s left is theenvironmental variances. The neutral prediction depends on the mortality rate, which is also fitted bythe model. The following demonstrates an R program for running this model with forest plotabundances.

The model allows various functional forms for the distribution of population growth. The example belowis based on a power probability distribution, where p(x) ∼ x + 1

^{k}(k &x003C; −1). The exponent k describes howbroad the distribution, with more extreme k (ie, more negative) meaning a narrower distribution. Indeed,frac1k is close to the standard deviation of the distribution of r. The power distribution, though, allows kon the negative size of x to differ from k for x positive. It is thus an asymmetric power distribution. - Biomass This package provides a main function and a series of subroutinesfor calculating above-ground-biomass (AGB) from tree diameter. The base functionscan be used with any tables having diameter and wood density for trees. The top-levelfunctions are designed to CTFS R Analytical tables, and to consult the CTFS wood-densitydatabase, to fill in the agb column with the biomass (dry weight, in Mg) for each tree andstem.
The top level function is biomass.CTFSdb. It must be passed two tables, one with trees, theother with stems. These are the two standard CTFS R Analytical tables, described in the DataFormat section. The function also requires the name of the CTFS wood-density table, available fordownload at http://ctfs.arnarb.harvard.edu/Public/Datasets.

Please note that the CTFS R Analytical Tables already have the agb column filled in, using thisfunction and the default values for the Chave calculation (in the function Chave.AGB).

- Growth vs. DBH The following calculations in R run a model of AGB growth as a function of diameter,or as a function of agb, using a series of discrete size categories and a linear regression within each. Themodel presented here uses log(dbh) or log(agb) as the predictor (independent variable). The locations ofthe categories, or bins, of log(dbh) are not defined in advance, but are fitted as part of the model.
- ImageJ This tutorial demonstrates use of an R program designed to read all quadrat mapscreated by imageJ, converting the digitized pixel to coordinates within a quadrat (local coordinates). Thecommands shown here lead step by step through the process. The input imageJ files must be named in avery specific way, and there must be 4 separate files for each quadrat, in the case of 10x10 m sections of asingle 20x20 m quadrat.
This tutorial is also available for download as a pdf fromhttps://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/tutorials/imageJTutorial/imageJ.pdf.

- Plot maps The map package includes functions for creating maps of tree distributions inCTFS plots. All functions are in a single file, map.r. There are functions for drawing single maps,on which one or more species can be included, and one or more dbh classes. And there are functionsto create many maps, for example of every species in a plot. The functions have many options foradjusting features (point size, colors), and allow maps to be drawn on the screen or exported asvarious graphics file types. All functions use input data in the standard web/data_formatCTFSformat. Most use data in the split format, so having R objects in this format saved already isconvenient.
- Topography The topography package includes just one file, solvetopo.r, whosepurpose is estimating elevation data from survey data. This tutorial illustrates its use,and shows how to use the resulting elevation data to make a contour map. Creationof CTFS Plot elevation data in the standard CTFS format is demonstrated as well.