slambda3 {lefko3}

Estimate Stochastic Population Growth Rate

Description

Function slambda3() estimates the stochastic population growth rate, a, defined as the long-term arithmetic mean of the log population growth rate estimated per simulated occasion. This function can handle both lefkoMat objects and lists of full A matrices as input.

Usage

slambda3(
  mpm,
  times = 10000L,
  historical = FALSE,
  tweights = NULL,
  force_sparse = NULL
)

Arguments

mpm

A matrix projection model of class lefkoMat, or a list of full matrix projection matrices.

times

Number of occasions to iterate. Defaults to 10000.

historical

An optional logical value only used if object mpm is a list of matrices, rather than a lefkoMat object. Defaults to FALSE for the former case, and overridden by information supplied in the lefkoMat object for the latter case.

tweights

An optional numeric vector or matrix denoting the probabilities of choosing each matrix in a stochastic projection. If a matrix is input, then a first-order Markovian environment is assumed, in which the probability of choosing a specific annual matrix depends on which annual matrix is currently chosen. If a vector is input, then the choice of annual matrix is assumed to be independent of the current matrix. Defaults to equal weighting among matrices.

force_sparse

A text string indicating whether to force sparse matrix encoding ("yes") or not ("no") if the MPM is composed of simple matrices. Defaults to "auto", in which case sparse matrix encoding is used with simple square matrices with at least 50 rows and no more than 50% of elements with values greater than zero.

Value

A data frame with the following variables:

pop

The identity of the population.

patch

The identity of the patch.

a

Estimate of stochastic growth rate, estimated as the arithmetic mean of the log population growth rate across simulated occasions.

var

The estimated variance of a.

sd

The standard deviation of a.

se

The standard error of a.

Notes

The log stochastic population growth rate, a, is as given in equation 2 of Tuljapurkar, Horvitz, and Pascarella 2003. This term is estimated via projection of randomly sampled matrices, similarly to the procedure outlined in Box 7.4 of Morris and Doak (2002).

Stochastic growth rate is estimated both at the patch level and at the population level. Population level estimates will be noted at the end of the data frame with 0 entries for patch designation.

Weightings given in tweights do not need to sum to 1. Final weightings used will be based on the proportion per element of the sum of elements in the user-supplied vector.

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.

Examples

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)

cypsupp3r <- supplemental(stage3 = c("SD", "SD", "P1", "P1", "P2", "P3", "SL",
    "D", "XSm", "Sm", "D", "XSm", "Sm", "mat", "mat", "mat", "SD", "P1"),
  stage2 = c("SD", "SD", "SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL",
    "SL", "SL", "D", "XSm", "Sm", "rep", "rep"),
  stage1 = c("SD", "rep", "SD", "rep", "SD", "P1", "P2", "P3", "P3", "P3",
    "SL", "SL", "SL", "SL", "SL", "SL", "mat", "mat"),
  eststage3 = c(NA, NA, NA, NA, NA, NA, NA, "D", "XSm", "Sm", "D", "XSm", "Sm",
    "mat", "mat", "mat", NA, NA),
  eststage2 = c(NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm", "XSm", "XSm",
    "XSm", "D", "XSm", "Sm", NA, NA),
  eststage1 = c(NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm", "XSm", "XSm",
    "XSm", "XSm", "XSm", "XSm", NA, NA),
  givenrate = c(0.1, 0.1, 0.2, 0.2, 0.2, 0.2, 0.25, NA, NA, NA, NA, NA, NA,
    NA, NA, NA, NA, NA),
  multiplier = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
    NA, 0.5, 0.5),
  type = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3),
  type_t12 = c(1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1),
  stageframe = cypframe_raw, historical = TRUE)

cypmatrix3r <- rlefko3(data = cypraw_v1, stageframe = cypframe_raw, 
  year = "all", patch = "all", stages = c("stage3", "stage2", "stage1"),
  size = c("size3added", "size2added", "size1added"), 
  supplement = cypsupp3r, yearcol = "year2", 
  patchcol = "patchid", indivcol = "individ")

cypstoch <- slambda3(cypmatrix3r)