# stablestage3.lefkoMat: Estimate Stable Stage Distribution of Matrices in lefkoMat... In lefko3: Historical and Ahistorical Population Projection Matrix Analysis

 stablestage3.lefkoMat R Documentation

## Estimate Stable Stage Distribution of Matrices in lefkoMat Object

### Description

stablestage3.lefkoMat() returns the deterministic stable stage distributions of all A matrices in an object of class lefkoMat, as well as the long-run projected mean stage distribution in stochastic analysis. This function can handle large and sparse matrices, and so can be used with large historical matrices, IPMs, age x stage matrices, as well as ahistorical matrices.

### Usage

## S3 method for class 'lefkoMat'
stablestage3(
mats,
stochastic = FALSE,
times = 10000,
tweights = NA,
seed = NA,
force_sparse = "auto",
...
)

### Arguments

 mats An object of class lefkoMat. stochastic A logical value indicating whether to use deterministic (FALSE) or stochastic (TRUE) analysis. Defaults to FALSE. times An integer variable indicating number of occasions to project if using stochastic analysis. Defaults to 10000. tweights An optional vector indicating the probability weighting to use for each matrix in stochastic simulations. If not given, then defaults to equal weighting. seed A number to use as a random number seed. force_sparse A text string indicating whether to use sparse matrix encoding ("yes") if standard matrices are provided. Defaults to "auto", in which case sparse matrix encoding is used with square matrices with at least 50 rows and no more than 50% of elements with values greater than zero. ... Other parameters.

### Value

This function returns the stable stage distributions (and long-run mean stage distributions in stochastic analysis) corresponding to the matrices in a lefkoMat object.

The output depends on whether the lefkoMat object used as input is ahistorical or historical, and whether the analysis is deterministic or stochastic. If deterministic and ahistorical, then a single data frame is output, which includes the number of the matrix within the A element of the input lefkoMat object, followed by the stage id (numeric and assigned through sf_create()), the stage name, and the estimated proportion of the stable stage distribution (ss_prop). If stochastic and ahistorical, then a single data frame is output starting with the number of the population-patch (matrix_set), a string concatenating the names of the population and the patch (poppatch), the assigned stage id number (stage_id), and the stage name (stage), and the long-run average stage distribution (ss_prop).

If a historical matrix is used as input, then two data frames are output into a list object. The hist element describes the historical stage-pair distribution, while the ahist element describes the stage distribution. If deterministic, then hist contains a data frame including the matrix number (matrix), the numeric stage designations for stages in occasions t and t-1, (stage_id_2 and stage_id_1, respectively), followed by the respective stage names ( stage_2 and stage_1), and ending with the estimated stable stage-pair distribution. The associated ahist element is as before. If stochastic, then the hist element contains a single data frame with the number of the population-patch (matrix_set), a string concatenating the names of the population and the patch (poppatch), the assigned stage id numbers in times t and t-1 ( stage_id_2 and stage_id_2, respectively), and the associated stage names (stage_2 and stage_1, respectively), and the long-run average stage distribution (ss_prop). The associated ahist element is as before in the ahistorical, stochastic case.

In addition to the data frames noted above, stochastic analysis will result in the additional output of a list of matrices containing the actual projected stage distributions across all projected occasions, in the order of population-patch combinations in the lefkoMat input.

### Notes

In stochastic analysis, the projected mean distribution is the arithmetic mean across the final 1000 projected occasions if the simulation is at least 2000 projected occasions long. If between 500 and 2000 projected occasions long, then only the final 200 are used, and if fewer than 500 occasions are used, then all are used. Note that because stage distributions in stochastic simulations can change greatly in the initial portion of the run, we encourage a minimum of 2000 projected occasions per simulation, with 10000 preferred.

Speed can sometimes be increased by shifting from automatic sparse matrix determination to forced dense or sparse matrix projection. This will most likely occur when matrices have between 30 and 300 rows and columns. Defaults work best when matrices are very small and dense, or very large and sparse.

stablestage3()

stablestage3.list()

stablestage3.matrix()

stablestage3.dgCMatrix()

### Examples

# Lathyrus deterministic example
data(lathyrus)

sizevector <- c(0, 100, 13, 127, 3730, 3800, 0)
stagevector <- c("Sd", "Sdl", "VSm", "Sm", "VLa", "Flo", "Dorm")
repvector <- c(0, 0, 0, 0, 0, 1, 0)
obsvector <- c(0, 1, 1, 1, 1, 1, 0)
matvector <- c(0, 0, 1, 1, 1, 1, 1)
immvector <- c(1, 1, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 100, 11, 103, 3500, 3800, 0.5)

lathframe <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
immstatus = immvector, indataset = indataset, binhalfwidth = binvec,
propstatus = propvector)

lathvert <- verticalize3(lathyrus, noyears = 4, firstyear = 1988,
patchidcol = "SUBPLOT", individcol = "GENET", blocksize = 9,
juvcol = "Seedling1988", sizeacol = "Volume88", repstracol = "FCODE88",
nonobsacol = "Dormant1988", stageassign = lathframe, stagesize = "sizea",
censorcol = "Missing1988", censorkeep = NA, censor = TRUE)

lathsupp3 <- supplemental(stage3 = c("Sd", "Sd", "Sdl", "Sdl", "Sd", "Sdl", "mat"),
stage2 = c("Sd", "Sd", "Sd", "Sd", "rep", "rep", "Sdl"),
stage1 = c("Sd", "rep", "Sd", "rep", "npr", "npr", "Sd"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "mat"),
eststage2 = c(NA, NA, NA, NA, NA, NA, "Sdl"),
eststage1 = c(NA, NA, NA, NA, NA, NA, "NotAlive"),
givenrate = c(0.345, 0.345, 0.054, 0.054, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, 0.345, 0.054, NA),
type = c(1, 1, 1, 1, 3, 3, 1), type_t12 = c(1, 2, 1, 2, 1, 1, 1),
stageframe = lathframe, historical = TRUE)

ehrlen3 <- rlefko3(data = lathvert, stageframe = lathframe, year = "all",
stages = c("stage3", "stage2", "stage1"), supplement = lathsupp3,
yearcol = "year2", indivcol = "individ")

ehrlen3mean <- lmean(ehrlen3)
stablestage3(ehrlen3mean)

# Cypripedium stochastic example
data(cypdata)

sizevector <- c(0, 0, 0, 0, 0, 0, 1, 2.5, 4.5, 8, 17.5)
stagevector <- c("SD", "P1", "P2", "P3", "SL", "D", "XSm", "Sm", "Md", "Lg",
"XLg")
repvector <- c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 0, 0, 0, 0, 0.5, 0.5, 1, 1, 2.5, 7)

cypframe_raw <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
propstatus = propvector, immstatus = immvector, indataset = indataset,
binhalfwidth = binvec)

cypraw_v1 <- verticalize3(data = cypdata, noyears = 6, firstyear = 2004,
patchidcol = "patch", individcol = "plantid", blocksize = 4,
sizeacol = "Inf2.04", sizebcol = "Inf.04", sizeccol = "Veg.04",
repstracol = "Inf.04", repstrbcol = "Inf2.04", fecacol = "Pod.04",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)

# Here we use supplemental() to provide overwrite and reproductive info
cypsupp2r <- supplemental(stage3 = c("SD", "P1", "P2", "P3", "SL", "D",
"XSm", "Sm", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "rep",
"rep"),
eststage3 = c(NA, NA, NA, NA, NA, "D", "XSm", "Sm", NA, NA),
eststage2 = c(NA, NA, NA, NA, NA, "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.10, 0.20, 0.20, 0.20, 0.25, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, NA, NA, 0.5, 0.5),
type =c(1, 1, 1, 1, 1, 1, 1, 1, 3, 3),
stageframe = cypframe_raw, historical = FALSE)

cypmatrix2r <- rlefko2(data = cypraw_v1, stageframe = cypframe_raw,
year = "all", patch = "all", stages = c("stage3", "stage2", "stage1"),