| density_vr {lefko3} | R Documentation |
Set Density Dependence Relationships in Vital Rates
Description
Function density_vr() provides all necessary data to incorporate
density dependence into the vital rate functions used to create matrices in
function-based projections using function f_projection3(). Four forms
of density dependence are allowed, including the Ricker function, the
Beverton-Holt function, the Usher function, and the logistic function. In
each case, density must have an effect with at least a one time-step delay
(see Notes).
Usage
density_vr(
density_yn = c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
FALSE, FALSE, FALSE, FALSE),
style = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
time_delay = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1),
alpha = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
beta = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
)
Arguments
density_yn |
A 14 element logical vector denoting whether each vital
rate is subject to density dependence. The order of vital rates is: survival
probability, observation probability, primary size transition, secondary size
transition, tertiary size transition, reproductive status probability,
fecundity rate, juvenile survival probability, juvenile observation
probability, juvenile primary size transition, juvenile secondary size
transition, juvenile tertiary size transition, juvenile reproductive status
probability, and juvenile maturity status probability. Defaults to a vector
of 14 |
style |
A 14 element vector coding for the style of density dependence
on each vital rate. Options include |
time_delay |
A 14 element vector indicating the number of occasions back
on which density dependence operates. Defaults to 14 values of |
alpha |
A 14 element vector indicating the numeric values to use as the
alpha term in the two parameter Ricker, Beverton-Holt, or Usher function, or
the value of the carrying capacity K to use in the logistic equation
(see |
beta |
A 14 element vector indicating the numeric values to use as the
beta term in the two parameter Ricker, Beverton-Holt, or Usher function. Used
to indicate whether to use K as a hard limit in the logistic equation
(see |
Value
A data frame of class lefkoDensVR with 14 rows, one for each
vital rate in the order of: survival probability, observation probability,
primary size transition, secondary size transition, tertiary size transition,
reproductive status probability, fecundity rate, juvenile survival
probability, juvenile observation probability, juvenile primary size
transition, juvenile secondary size transition, juvenile tertiary size
transition, juvenile reproductive status probability, and juvenile maturity
status probability. This object can be used as input in function
f_projection3().
Variables in this object include the following:
vital_rate |
The vital rate to be modified. |
density_yn |
Logical value indicating whether vital rate will be subject to density dependence. |
style |
Style of density dependence, coded as |
time_delay |
The time delay on density dependence, in time steps. |
alpha |
The value of alpha in the Ricker, Beverton-Holt, or Usher function, or the value of carrying capacity, K, in the logistic function. |
beta |
The value of beta in the Ricker, Beverton-Holt, or Usher function. |
Notes
This function provides inputs when density dependence is operationalized
directly on vital rates. It can be used only in function
f_projection3(). Users wishing to modify matrix elements directly by
density dependence functions for use in function-based or raw projections
with functions projection3() and f_projection3() should use
function density_input() to provide the correct inputs.
The parameters alpha and beta are applied according to the
two-parameter Ricker function, the two-parameter Beverton-Holt function, the
two-parameter Usher function, or the one-parameter logistic function.
Although the default is that a 1 time step delay is assumed, greater time
delays can be set through the time_delay option.
When using the logistic function, it is possible that the time delay used in
density dependent simulations will cause matrix elements to become negative.
To prevent this behavior, set the associated beta term to 1.0.
Doing so will set K as the hard limit in the logistic equation,
essentially setting a minimum limit at 0 for all matrix elements
modified.
See Also
Examples
data(lathyrus)
sizevector <- c(0, 4.6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8,
9)
stagevector <- c("Sd", "Sdl", "Dorm", "Sz1nr", "Sz2nr", "Sz3nr", "Sz4nr",
"Sz5nr", "Sz6nr", "Sz7nr", "Sz8nr", "Sz9nr", "Sz1r", "Sz2r", "Sz3r",
"Sz4r", "Sz5r", "Sz6r", "Sz7r", "Sz8r", "Sz9r")
repvector <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1)
obsvector <- c(0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
immvector <- c(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0)
indataset <- c(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 4.6, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5)
lathframeln <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
immstatus = immvector, indataset = indataset, binhalfwidth = binvec,
propstatus = propvector)
lathvertln <- verticalize3(lathyrus, noyears = 4, firstyear = 1988,
patchidcol = "SUBPLOT", individcol = "GENET", blocksize = 9,
juvcol = "Seedling1988", sizeacol = "lnVol88", repstracol = "Intactseed88",
fecacol = "Intactseed88", deadacol = "Dead1988",
nonobsacol = "Dormant1988", stageassign = lathframeln, stagesize = "sizea",
censorcol = "Missing1988", censorkeep = NA, NAas0 = TRUE, censor = TRUE)
lathvertln$feca2 <- round(lathvertln$feca2)
lathvertln$feca1 <- round(lathvertln$feca1)
lathvertln$feca3 <- round(lathvertln$feca3)
lathvertln_adults <- subset(lathvertln, stage2index > 2)
surv_model <- glm(alive3 ~ sizea2 + sizea1 + as.factor(patchid) +
as.factor(year2), data = lathvertln_adults, family = "binomial")
obs_data <- subset(lathvertln_adults, alive3 == 1)
obs_model <- glm(obsstatus3 ~ as.factor(patchid), data = obs_data,
family = "binomial")
size_data <- subset(obs_data, obsstatus3 == 1)
siz_model <- lm(sizea3 ~ sizea2 + sizea1 + repstatus1 + as.factor(patchid) +
as.factor(year2), data = size_data)
reps_model <- glm(repstatus3 ~ sizea2 + sizea1 + as.factor(patchid) +
as.factor(year2), data = size_data, family = "binomial")
fec_data <- subset(lathvertln_adults, repstatus2 == 1)
fec_model <- glm(feca2 ~ sizea2 + sizea1 + repstatus1 + as.factor(patchid),
data = fec_data, family = "poisson")
lathvertln_juvs <- subset(lathvertln, stage2index < 3)
jsurv_model <- glm(alive3 ~ as.factor(patchid), data = lathvertln_juvs,
family = "binomial")
jobs_data <- subset(lathvertln_juvs, alive3 == 1)
jobs_model <- glm(obsstatus3 ~ 1, family = "binomial", data = jobs_data)
jsize_data <- subset(jobs_data, obsstatus3 == 1)
jsiz_model <- lm(sizea3 ~ as.factor(year2), data = jsize_data)
jrepst_model <- 0
jmatst_model <- 1
mod_params <- create_pm(name_terms = TRUE)
mod_params$modelparams[3] <- "patchid"
mod_params$modelparams[4] <- "alive3"
mod_params$modelparams[5] <- "obsstatus3"
mod_params$modelparams[6] <- "sizea3"
mod_params$modelparams[9] <- "repstatus3"
mod_params$modelparams[11] <- "feca2"
mod_params$modelparams[12] <- "sizea2"
mod_params$modelparams[13] <- "sizea1"
mod_params$modelparams[18] <- "repstatus2"
mod_params$modelparams[19] <- "repstatus1"
lathsupp3 <- supplemental(stage3 = c("Sd", "Sd", "Sdl", "Sdl", "mat", "Sd", "Sdl"),
stage2 = c("Sd", "Sd", "Sd", "Sd", "Sdl", "rep", "rep"),
stage1 = c("Sd", "rep", "Sd", "rep", "Sd", "mat", "mat"),
eststage3 = c(NA, NA, NA, NA, "mat", NA, NA),
eststage2 = c(NA, NA, NA, NA, "Sdl", NA, NA),
eststage1 = c(NA, NA, NA, NA, "Sdl", NA, NA),
givenrate = c(0.345, 0.345, 0.054, 0.054, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, 0.345, 0.054),
type = c(1, 1, 1, 1, 1, 3, 3), type_t12 = c(1, 2, 1, 2, 1, 1, 1),
stageframe = lathframeln, historical = TRUE)
# While we do not use MPMs to initialize f_projections3(), we do use MPMs to
# initialize functions start_input() and density_input().
lathmat3ln <- flefko3(year = "all", patch = "all", data = lathvertln,
stageframe = lathframeln, supplement = lathsupp3, paramnames = mod_params,
surv_model = surv_model, obs_model = obs_model, size_model = siz_model,
repst_model = reps_model, fec_model = fec_model, jsurv_model = jsurv_model,
jobs_model = jobs_model, jsize_model = jsiz_model,
jrepst_model = jrepst_model, jmatst_model = jmatst_model, reduce = FALSE)
e3m_sv <- start_input(lathmat3ln, stage2 = "Sd", stage1 = "Sd", value = 1000)
dyn7 <- c(TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE,
FALSE, FALSE, FALSE, FALSE, FALSE)
dst7 <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
dal7 <- c(0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
dbe7 <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
e3d_vr <- density_vr(density_yn = dyn7, style = dst7, alpha = dal7,
beta = dbe7)
trial7_dvr_1 <- f_projection3(format = 1, data = lathvertln, supplement = lathsupp3,
paramnames = mod_params, stageframe = lathframeln, nreps = 2,
surv_model = surv_model, obs_model = obs_model, size_model = siz_model,
repst_model = reps_model, fec_model = fec_model, jsurv_model = jsurv_model,
jobs_model = jobs_model, jsize_model = jsiz_model,
jrepst_model = jrepst_model, jmatst_model = jmatst_model,
times = 100, stochastic = TRUE, standardize = FALSE, growthonly = TRUE,
integeronly = FALSE, substoch = 0, sp_density = 0, start_frame = e3m_sv,
density_vr = e3d_vr)