The sitree package provides a framework to implement Single Tree forest growth models in a fast and memory efficient way. It keep tracks of all alive, dead, and removed trees in a robust and efficient way. SiTree is designed to run single tree simulations where trees can be defined by two time-dependent variables (such as diameter (or basal area), and height), and on time-independent variable, such as tree species. SiTree simulates birth, growth, and death of trees as well as management. Functions can also be defined that affect characteristics of the stand (external modifiers), such as climate change, or fertilization.
The easiest way to start with your own simulation is probably to modify the example functions provided (see the Test Equations vignette).
Two types of input are required by SiTree: tree level and stand level. Tree level information is passed in tree.df, while stand level information is passed in stand.df.
tree.df should be a data frame with four columns named plot.id, treeid, dbh, height, and tree.sp, which correspond to a stand/plot ID, a tree ID, diameter, height, and tree species.
Plot and stand data is passed in stand.df, which should be a data frame or a list, with at least a column or element named plot.id which should contain all the plot IDs present in tree.df. Typical information provided in stand.df are plot size, elevation, site index, plot coordinates, distance to road, temperature or precipitation.
An example of tree data and stand data are provided.
library(sitree)## Loading required package: ggplot2head(tr)## plot.id treeid dbh height tree.sp
## 1 91 108286 149 118 53
## 2 91 137120 133 107 53
## 3 91 108287 55 52 53
## 4 91 108268 235 151 49
## 5 91 137124 187 137 53
## 6 91 108271 162 124 49head(fl)## $plot.id
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100
##
## $SI.m
## [1] 11 11 8 11 8 8 6 14 11 11 8 23 6 6 11 11 17 14 8 8 8 6 17 8 6
## [26] 6 20 11 11 8 11 11 8 11 17 8 8 8 14 11 14 14 11 17 11 11 26 14 11 14
## [51] 11 11 6 14 17 8 8 11 8 17 14 14 14 14 17 8 8 8 14 11 11 20 17 17 11
## [76] 14 11 8 11 8 8 8 8 17 8 11 8 6 11 6 8 8 8 23 17 11 8 14 8 8
##
## $SI.spp
## [1] 2 2 3 3 3 3 3 3 3 3 2 1 2 3 3 3 1 3 3 3 3 2 3 3 2 2 2 2 3 2 2 2 2 2 1 2 2
## [38] 3 3 3 2 3 3 3 3 3 1 3 2 2 3 3 3 3 1 3 2 2 3 3 3 3 2 3 1 3 3 3 2 2 2 1 2 1
## [75] 3 3 3 2 3 3 2 2 3 3 3 3 2 3 3 2 3 3 3 1 3 2 3 1 2 1
##
## $prop.plot
## [1] 5 5 0 0 0 0 5 0 5 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
## [38] 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 0 0 0 0 0 0 6
## [75] 4 5 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 5 7 0 0 0 0 0
##
## $ha2total
## [1] 450.6190 450.6190 901.2380 901.2380 901.2380 901.2380 450.6190
## [8] 901.2380 450.6190 901.2380 901.2380 901.2380 901.2380 630.8666
## [15] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [22] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [29] 901.2380 360.4952 901.2380 901.2380 901.2380 901.2380 901.2380
## [36] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [43] 901.2380 901.2380 901.2380 270.3714 901.2380 901.2380 901.2380
## [50] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [57] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [64] 901.2380 901.2380 630.8666 270.3714 901.2380 901.2380 901.2380
## [71] 901.2380 901.2380 901.2380 540.7428 360.4952 450.6190 901.2380
## [78] 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380 901.2380
## [85] 901.2380 901.2380 901.2380 630.8666 901.2380 901.2380 901.2380
## [92] 2693.6380 901.2380 450.6190 630.8666 901.2380 901.2380 901.2380
## [99] 901.2380 901.2380
##
## $tree2ha
## [1] 80.00000 80.00000 40.00000 40.00000 40.00000 40.00000 80.00000
## [8] 40.00000 80.00000 40.00000 40.00000 40.00000 40.00000 57.14286
## [15] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [22] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [29] 40.00000 100.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [36] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [43] 40.00000 40.00000 40.00000 133.33333 40.00000 40.00000 40.00000
## [50] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [57] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [64] 40.00000 40.00000 57.14286 133.33333 40.00000 40.00000 40.00000
## [71] 40.00000 40.00000 40.00000 66.66667 100.00000 80.00000 40.00000
## [78] 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000 40.00000
## [85] 40.00000 40.00000 40.00000 57.14286 40.00000 40.00000 40.00000
## [92] 40.00000 40.00000 80.00000 57.14286 40.00000 40.00000 40.00000
## [99] 40.00000 40.00000Many of the main functions in a simulation use plot-level variables, like competition indices (e.g. plot-level basal area). In order to make the code more transparent, compact, and robust all variables required in the sub-models that can be estimated from tree, stand and plot variables are calculated in one place. The fn.prep.common.vars function.
For example, if diameter increment is estimated as a function of initial diameter, stand basal area and number of trees per ha, both stand basal area variable and number of trees per ha should be calculated in fn.prep.common.vars. Other typical examples of variables calculated in the fn.prep.common.vars are top height (the mean height of the trees with the largest diameter in a stand), basal area of larger trees, or tree volume.
The fn.prep.common.vars function should be provided by the user, so it fits the particular needs of the growth model selected and the data. Calculating the most common variables used in forestry should be straight forward as they are already provided in either the SiTree or the SiTreeE package.
An example of a fn.prep.common.vars is provided in SiTree.
prep.common.vars.fun## function (tr, fl, i.period, this.period, common.vars, vars.required,
## period.length, n.periods, ...)
## {
## if (length(common.vars) > 1)
## res <- common.vars
## else res <- list()
## others <- list(...)
## all.plot.vars <- data.table(plot.id = fl$plot.id, SI.m = fl$SI.m,
## SI.spp = fl$SI.spp, tree2ha = fl$tree2ha, ha2total = fl$ha2total,
## kom = fl$kom)
## res$i.stand <- match(tr$data[["plot.id"]], fl[["plot.id"]])
## res$i.tree <- match(fl$plot.id, tr$data$plot.id)
## res$tree.BA.m2 <- pi * (tr$data[["dbh.mm"]][, this.period]/1000/2)^2
## res$SBA.m2.ha <- tapply(res$tree.BA.m2 * fl[["tree2ha"]][res$i.stand],
## list(plot.id = tr$data[["plot.id"]]), FUN = sum)
## i.match.tapply <- match(tr$data[["plot.id"]], names(res$SBA.m2.ha))
## res$SBA.m2.ha <- as.vector(res$SBA.m2.ha[i.match.tapply])
## res$spp <- sp.classification(tree.sp = tr$data[["tree.sp"]],
## species.spruce = c(1, 2, 3), species.pine = c(10, 11,
## 20, 21, 29), species.harw = c(30, 31))
## all.tree.vars <- data.table(treeid = tr$data$treeid, plot.id = tr$data$plot.id,
## dbh.mm = tr$data$dbh.mm[, this.period], height.dm = tr$data$height.dm[,
## this.period], tree.sp = tr$data$tree.sp)
## all.tree.vars[all.plot.vars, `:=`(tree2ha, i.tree2ha), on = list(plot.id)]
## all.tree.vars[, `:=`(BA.m2, pi * (dbh.mm/1000/2)^2)]
## QMD.cm <- tapply(tr$data[["dbh.mm"]][, this.period], list(tr$data[["plot.id"]]),
## function(x.mm) {
## x.mm <- x.mm[is.finite(x.mm)]
## (sqrt(sum((x.mm/10)^2)/length(x.mm)))
## })
## res$QMD.cm <- as.vector(QMD.cm[i.match.tapply])
## tph <- tapply(fl[["tree2ha"]][res$i.stand], tr$data[["plot.id"]],
## sum)
## res$tph <- as.vector(tph[i.match.tapply])
## res$SDI <- res$tph * (res$QMD.cm/(10 * 2.54))^1.605
## pr.spp.ba <- data.frame(spru = rep(0, length(res$i.stand)),
## pine = 0, harw = 0, birch = 0, other = 0)
## pr.spp.ba$spru[res$spp == "spruce"] <- 1
## pr.spp.ba$pine[res$spp == "pine"] <- 1
## pr.spp.ba$birch[res$spp %in% c("birch")] <- 1
## pr.spp.ba$other[res$spp %in% c("other")] <- 1
## pr.spp.ba$harw[res$spp %in% c("birch", "other")] <- 1
## pr.spp.ba <- pr.spp.ba * res$tree.BA.m2
## dum.s <- tapply(pr.spp.ba$spru, tr$data$plot.id, sum)
## dum.p <- tapply(pr.spp.ba$pine, tr$data$plot.id, sum)
## dum.h <- tapply(pr.spp.ba$harw, tr$data$plot.id, sum)
## dum.b <- tapply(pr.spp.ba$birch, tr$data$plot.id, sum)
## dum.o <- tapply(pr.spp.ba$other, tr$data$plot.id, sum)
## pr.spp.ba <- data.frame(spru = as.vector(dum.s), pine = as.vector(dum.p),
## harw = as.vector(dum.h), birch = as.vector(dum.b), other = as.vector(dum.o))
## pr.spp.ba <- pr.spp.ba/with(pr.spp.ba, spru + pine + harw)
## pr.spp.ba <- pr.spp.ba[match(tr$data$plot.id, names(dum.s)),
## ] * 100
## res$pr.spp.ba <- pr.spp.ba
## rm(pr.spp.ba)
## res$PBAL.m2.ha <- ave(res$tree.BA.m2 * 10000/fl[["plot.size.m2"]][res$i.stand],
## tr$data$plot.id, FUN = function(X) {
## ord.x <- order(X)
## X <- sum(X[ord.x]) - cumsum(X[ord.x])
## X <- X[match(1:length(X), ord.x)]
## return(X)
## })
## previous.period <- paste0("t", i.period - 1)
## if ("stand.age.years" %in% names(fl)) {
## if (i.period == 0 & !is.data.frame(fl$stand.age.years)) {
## my.age <- fl$stand.age.years
## fl$stand.age.years <- data.frame(matrix(NA, ncol = n.periods,
## nrow = length(fl$plot.id)))
## names(fl$management) <- paste0("t", 1:n.periods)
## fl$stand.age.years[, this.period] <- my.age
## }
## if (i.period > 0 & "stand.age.years" %in% names(fl)) {
## fl$stand.age.years[, this.period] <- fl$stand.age.years[,
## previous.period] + 5
## stand.age.dt <- data.table(plot.id = fl$plot.id,
## SI.spp = fl$SI.spp, SI.m = fl$SI.m, stand.age.years = fl$stand.age.years[,
## this.period], waiting.time = 15)
## if (any(!is.na(fl$management[, this.period]))) {
## stand.age.dt[, `:=`(stands.ff, !substr(fl$management[,
## this.period], 1, 1) %in% c("0", "3"))]
## stand.age.dt[stands.ff == TRUE, `:=`(stand.age.years,
## -waiting.time + period.length/2)]
## stand.age.dt[, `:=`(dev.class, calculate.development.class(SI.spp = SI.spp,
## SI.m = SI.m, stand.age.years = stand.age.years))]
## }
## fl$stand.age.years[, this.period] <- stand.age.dt[,
## stand.age.years]
## if (any(is.na(stand.age.dt$stand.age.years)))
## browser()
## }
## res$dev.class <- calculate.development.class(SI.spp = fl$SI.spp,
## SI.m = fl$SI.m, stand.age.years = fl$stand.age.years[,
## this.period])
## res$tree.age <- data.table(age.years = fl$stand.age.years[,
## this.period][match(tr$data$plot.id, fl$plot.id)],
## treeid = tr$data$treeid)
## table(fl$stand.age.years[, this.period], useNA = "always")
## }
## vuprha.m3.ha <- NULL
## all.tree.vars[all.plot.vars, `:=`(kom, kom), on = "plot.id"]
## all.tree.vars[tree.sp == 12, `:=`(tree.sp, 10)]
## all.tree.vars[dbh.mm > 0, `:=`(c("vol.w.tr.m3", "vol.wo.tr.m3"),
## volume.norway(dbh.mm, height.dm, as.numeric(levels(tree.sp))[tree.sp],
## kom))]
## vuprha.m3.ha <- NULL
## all.tree.vars[all.plot.vars, `:=`(kom, i.kom), on = "plot.id"]
## all.tree.vars[tree.sp == 12, `:=`(tree.sp, 10)]
## all.tree.vars[dbh.mm > 0, `:=`(c("vol.w.tr.m3", "vol.wo.tr.m3"),
## volume.norway(dbh.mm, height.dm, as.numeric(levels(tree.sp))[tree.sp],
## kom))]
## all.tree.vars[, `:=`(vuprha.m3.ha, vol.wo.tr.m3 * tree2ha)]
## vuprha.m3.ha <- all.tree.vars[, sum(vuprha.m3.ha, na.rm = TRUE),
## by = plot.id]
## all.plot.vars[vuprha.m3.ha, `:=`(vuprha.m3.ha, V1), on = "plot.id"]
## all.plot.vars[is.na(vuprha.m3.ha), `:=`(vuprha.m3.ha, 0)]
## res$vuprha.m3.ha <- all.plot.vars$vuprha.m3.ha
## res$vol.wo.tr.m3.ha <- all.tree.vars$vuprha.m3.ha
## if (i.period == 0) {
## time.intern <- rep(NA, length.out = length(fl$plot.id))
## }
## else {
## time.intern <- fl$time.since.final.felling
## harv.last <- substr(fl$management[, this.period], 1,
## 1) %in% c("1", "2")
## time.intern[harv.last] <- period.length/2
## time.intern[!harv.last & !is.na(time.intern)] <- time.intern[!harv.last &
## !is.na(time.intern)] + period.length
## }
## fl$time.since.final.felling <- time.intern
## invisible(list(res = res, fl = fl))
## }
## <environment: namespace:sitree>trList and trListDead classesIn order to efficiently store the list of all individual live and dead (and removed) trees, two Reference classes (or refclasses) are defined in SiTree. Refclases is chosen instead of S3 or S4 classes because refclasses objects are mutable and the usual R copy on modify semantics do not apply. When simulating for long periods, or for large datasets (e.g. a whole national forest inventory) the risk of running out of memory is not negligible. Using refclasses aim at maintaining the memory needs to the minimum by using mutable objects for storing the larger objects such as represented by the tree lists.
There are two Reference Classes implemented in the sitree package, one for live trees (trList) and other for dead trees (trListDead).
trList This class has two fields, data and nperiods. Under data basic information for each tree is stored (a unique stand ID plot.id, a unique tree ID treeid, and dbh and height for each period, dbh.mm, and height.dm). The nperiods field is an integer that stores the number of periods to be simulated.
trListDead This class extends trList. DBH and heights measured while the tree was alive are stored under the data field. Also under this field information on how long the tree has been in the simulation can be found (yrs.sim). In this class the new field last.measurement stores the dimensions of the tree when it died or was removed. How these dimensions are calculated is defined on the dead.trees.growth function.
Reference Classes objects are mutable, they don’t use R’s usual copy-on-modify semantics, but are modified in place.
We have provided a function to convert the sitree() output containing trList and *trListDead** objects to a data frame, the sitree2dataframe function. The resulting data frame follows the usual R copy on modify semantics, and most users might be more comfortable with it.
result.sitree <- sitree (tree.df = stand.west.tr,
stand.df = stand.west.st,
functions = list(
fn.growth = 'grow.dbhinc.hgtinc',
fn.mort = 'mort.B2007',
fn.recr = 'recr.BBG2008',
fn.management = NULL,
fn.tree.removal = NULL,
fn.modif = NULL,
fn.prep.common.vars = 'prep.common.vars.fun'
),
n.periods = 12,
period.length = 5,
mng.options = NA,
print.comments = FALSE,
fn.dbh.inc = 'dbhi.BN2009',
fn.hgt.inc = 'height.korf'
)
str(result.sitree$live)## Reference class 'trList' [package "sitree"] with 2 fields
## $ data :List of 6
## ..$ plot.id : num [1:857] 2 2 2 2 2 2 2 2 1 1 ...
## ..$ treeid : int [1:857] 2 3 4 5 6 7 11 12 15 16 ...
## ..$ dbh.mm :'data.frame': 857 obs. of 13 variables:
## .. ..$ t0 : num [1:857] 50 50 50 50 116 50 90 58 113 116 ...
## .. ..$ t1 : num [1:857] 61 61 61 61 138 61 108 71 134 137 ...
## .. ..$ t2 : num [1:857] 71 71 71 71 157 71 124 82 152 155 ...
## .. ..$ t3 : num [1:857] 80 80 80 80 174 80 138 92 168 171 ...
## .. ..$ t4 : num [1:857] 89 89 89 89 189 89 151 102 183 186 ...
## .. ..$ t5 : num [1:857] 97 97 97 97 203 97 163 111 197 200 ...
## .. ..$ t6 : num [1:857] 105 105 105 105 216 105 174 120 210 213 ...
## .. ..$ t7 : num [1:857] 113 113 113 113 228 113 185 128 222 225 ...
## .. ..$ t8 : num [1:857] 120 120 120 120 239 120 195 136 233 236 ...
## .. ..$ t9 : num [1:857] 127 127 127 127 250 127 205 144 244 247 ...
## .. ..$ t10: num [1:857] 134 134 134 134 260 134 214 152 254 257 ...
## .. ..$ t11: num [1:857] 141 141 141 141 270 141 223 159 264 267 ...
## .. ..$ t12: num [1:857] 148 148 148 148 279 148 232 166 273 276 ...
## ..$ height.dm:'data.frame': 857 obs. of 13 variables:
## .. ..$ t0 : num [1:857] 42 21 8 42 113 53 104 60 117 113 ...
## .. ..$ t1 : num [1:857] 52 31 18 52 128 63 118 72 131 127 ...
## .. ..$ t2 : num [1:857] 61 40 27 61 140 72 129 81 142 138 ...
## .. ..$ t3 : num [1:857] 69 48 35 69 150 80 138 89 151 147 ...
## .. ..$ t4 : num [1:857] 76 55 42 76 158 87 146 97 159 155 ...
## .. ..$ t5 : num [1:857] 82 61 48 82 165 93 153 104 166 162 ...
## .. ..$ t6 : num [1:857] 88 67 54 88 171 99 159 110 173 168 ...
## .. ..$ t7 : num [1:857] 94 73 60 94 177 105 165 115 179 174 ...
## .. ..$ t8 : num [1:857] 99 78 65 99 182 110 170 120 184 179 ...
## .. ..$ t9 : num [1:857] 104 83 70 104 187 115 175 125 189 184 ...
## .. ..$ t10: num [1:857] 109 88 75 109 191 120 179 130 193 188 ...
## .. ..$ t11: num [1:857] 114 93 80 114 195 125 183 134 197 192 ...
## .. ..$ t12: num [1:857] 118 97 84 118 199 129 187 138 201 196 ...
## ..$ yrs.sim : num [1:857] 60 60 60 60 60 60 60 60 60 60 ...
## ..$ tree.sp : Factor w/ 29 levels "1","2","3","10",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ nperiods: int 12
## and 19 methods, of which 5 are possibly relevant:
## addTrees, as.list, extractTrees, getTrees, show#envRefClasshead(sitree2dataframe(result.sitree$live))## treeid plot.id tree.sp period dbh.mm height.dm
## 1 2 2 1 t0 50 42
## 2 3 2 1 t0 50 21
## 3 4 2 1 t0 50 8
## 4 5 2 1 t0 50 42
## 5 6 2 1 t0 116 113
## 6 7 2 1 t0 50 53The sitree() function is the core function of the SiTree package. It is the function that runs the simulations. It requires tree data (tree.df), stand/plot data (stand.df), and a list of functions to be used in the simulation (functions), the number of periods for which to run the simulation (n.periods), and the period length (period.length). Management options can be passed through the mng.options argument, and it is also possible to print comments about the progress of the simulation selecting print.comments = TRUE. Additional arguments needed by the selected functions go into the ellipsis (‘…’) and can be retrieved by simply converting it to a list, e.g. arguments <- list(...).
The functions argument must be a list containing at least 7 elements:
fn.growth the name of the function that implements the growth sub-modelfn.mort the name of the function that implements the mortality sub-modelfn.recr the name of the function that implements the recruitment sub-model: ingrowth, and natural and artificial regenerationfn.management the name of the function that implements the management (e.g. harvest), can be NULLfn.tree.removal the name of the function that implements the management at the tree level, that is the selection of trees to be fell, can be NULL.fn.modif the name of the function to calculate the effect of external modifiers, can be NULLfn.prep.common.vars the name of the function to calculate auxiliary variables, such as basal area of the stand (see ‘The fn.prep.common.vars’ subsection above) .Further details on the requirements of the functions listed above can be found under the section “The user-defined functions”.
The sitree() function is a flexible framework for forest growth simulations. Any growth sub-model, mortality sub-model, management, etc. can be used. Some examples are provided in SiTree and in SiTreeE, but generally, the submodels functions need to be provided by the user. The examples provided in SiTree and in SiTreeE can be used as a template. To debug the user-defined functions we suggest to use the provided example as a starting point, set print.comments = TRUE and switch the submodels functions one by one to test them.
An example of how the list provided in the functions argument of sitree should look like is given below, and further details on each of the functions are provided next.
The fn.growth function should return a data frame with two columns giving diameter increment (dbh.inc.mm) and height increment (hgt.inc.dm) of all live trees. This data frame should only contain numerical data (no missing data allowed). Care must be taken to ensure that the order matches that of the tree list. Examples of the growth functions are provided as grow.dbhinc.hgtinc, dbhi.BN2009, and height.korf.
The fn.mort function should return a TRUE/FALSE vector of same length as the number of trees in the tree list. TRUE indicates a tree that will die before the next period, and FALSE indicates a tree that will stay alive. An example of a fn.mort function is provided in mort.B2007.
The fn.recr function is the function that estimates recruitment, the new trees for the next period. This function should return a list of new trees (or an empty list if there are no new trees) with elements plot.id, treeid, dbh.mm, height.dm, yrs.sim (indicates when are the trees incorporated to the plot, for example, in the middle of the period), and tree.sp.An example of a fn.recr function is provided in recr.BBG2008.
fn.management is optional. It should return a list, with at least one element called management which should be a vector with length equal to the number of plots in stand.df. The example we provide uses a simple code to define management (a five characters string indicating with a binary code (1 = present, 0 = absent) the treatments to be executed: harvest-thinning-fertilization-pruning-other), but any other way to code management can be used, as far as fn.management returns a vector. When no management will take place during the simulation fn.management can be set to NULL. An example of a fn.management function is provided in management.prob.
fn.tree.removal is optional. It should return a TRUE/FALSE vector indicating which trees are to be removed. The vector should have the same length as the number of trees alive at the current period. When no tree removal will take place during the simulation (no harvest is allowed) fn.tree.removal can be set to NULL. An example of a fn.tree.removal function is provided in mng.tree.removal.
fn.modif is a function that can be used to modify characteristics of the plot or stand, such as site index. This function is optional, and no example is provided in the current version of the package. It should return a list with names matching some of those in the stand.df data frame. After the external modifiers are calculated with the function defined as fn.modif, the elements in the plot data that matches those of the results of fn.modif are replaced before the rest of the simulation continues. For example, if the plot has been fertilized and we can assume that SI has increased by 2 meters, the fn.modif function needs to return a list with a SI element with all SI as in the plot data frame except for those that have changed.
fn.prep.common.vars is the function used to calculate everything needed for the fn.growth, fn.mort, etc to be calculated. For example, the fn.prep.common.vars function is the place to calculate stand competition indices, volume, stand age, etc. An example is given in the function prep.common.vars.fn.