density_input: Set Density Dependence Relationships in Matrix Elements
In lefko3: Historical and Ahistorical Population Projection Matrix Analysis
density_input R Documentation
Set Density Dependence Relationships in Matrix Elements
Description
Function density_input() provides all necessary data to incorporate
density dependence into a lefkoMat object, a list of matrices, or a
single matrix. 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 a delay of
at least one time-step (see Notes). The resulting data frame provides a
guide for other lefko3 functions to modify matrix elements by
density.
Usage
density_input(
mpm,
stage3 = NULL,
stage2 = NULL,
stage1 = NULL,
age2 = NULL,
style = NULL,
time_delay = NULL,
alpha = NULL,
beta = NULL,
type = NULL,
type_t12 = NULL
)
Arguments
mpm
The lefkoMat object that will be subject to density
dependent projection.
stage3
A vector showing the name or number of the stage in occasion
t+1 in the transitions to be affected by density. Abbreviations for
groups of stages are also usable (see Notes).
stage2
A vector showing the name or number of the stage in occasion
t in the transition to be affected by density. Abbreviations for
groups of stages are also usable (see Notes).
stage1
A vector showing the name or number of the stage in occasion
t-1 in the transition to be affected by density. Only needed if a
historical MPM is used. Abbreviations for groups of stages are also usable
(see Notes).
age2
A vector showing the age of the stage in occasion t in the
transition to be affected by density. Only needed if an age-by-stage MPM is
used.
style
A vector coding for the style of density dependence on each
transition subject to density dependence. Options include 1,
ricker, ric, or r for the Ricker function; 2,
beverton, bev, and b for the Beverton-Holt function;
3, usher, ush, and u for the Usher function; and
4, logistic, log, and l for the logistic
function. If only a single code is provided, then all noted transitions are
assumed to be subject to this style of density dependence. Defaults to
ricker.
time_delay
An integer vector indicating the number of occasions back
on which density dependence operates. Defaults to 1, and may not equal
any integer less than 1. If a single number is input, then all noted
transitions are assumed to be subject to this time delay. Defaults to
1.
alpha
A 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 Notes section for more on this term). If a single number is
provided, then all noted transitions are assumed to be subject to this value
of alpha. Defaults to 1.
beta
A 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 section
Notes below). If a single number is provided, then all noted
transitions are assumed to be subject to this value of beta. Defaults
to 1.
type
A vector denoting the kind of transition between occasions
t and t+1 to be replaced. This should be entered as 1,
S, or s for the replacement of a survival transition; or
2, F, or f for the replacement of a fecundity
transition. If empty or not provided, then defaults to 1 for survival
transition.
type_t12
An optional vector denoting the kind of transition between
occasions t-1 and t. Only necessary if a historical MPM in
deVries format is desired. This should be entered as 1, S, or
s for a survival transition; or 2, F, or f for a
fecundity transitions. Defaults to 1 for survival transition, with
impacts only on the construction of deVries-format hMPMs.
Value
A data frame of class lefkoDens. This object can be used as
input in function projection3().
Variables in this object include the following:
stage3
Stage at occasion t+1 in the transition to be replaced.
stage2
Stage at occasion t in the transition to be replaced.
stage1
Stage at occasion t-1 in the transition to be replaced,
if applicable.
age2
Age at occasion t in the transition to be replaced, if
applicable.
style
Style of density dependence, coded as 1, 2, 3, or 4 for the
Ricker, Beverton-Holt, Usher, or logistic function, respectively.
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.
type
Designates whether the transition from occasion t to
occasion t+1 is a survival transition probability (1), or a fecundity
rate (2).
type_t12
Designates whether the transition from occasion t-1 to
occasion t is a survival transition probability (1), a fecundity rate
(2).
Notes
This function provides inputs when density dependence is operationalized
directly on matrix elements. It can be used in both projection3() and
f_projection3(). Users wishing to modify vital rate functions by
density dependence functions for use in function-based projections with
function f_projection3() should use function density_vr() 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.
Entries in stage3, stage2, and stage1 can include
abbreviations for groups of stages. Use rep if all reproductive stages
are to be used, nrep if all mature but non-reproductive stages are to
be used, mat if all mature stages are to be used, immat if all
immature stages are to be used, prop if all propagule stages are to be
used, npr if all non-propagule stages are to be used, obs if
all observable stages are to be used, nobs if all unobservable stages
are to be used, and leave empty or use all if all stages in stageframe
are to be used.
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
start_input()
projection3()
Examples
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",
fecacol = "Intactseed88", deadacol = "Dead1988",
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)
e3d <- density_input(ehrlen3mean, stage3 = c("Sd", "Sdl"),
stage2 = c("rep", "rep"), stage1 = c("all", "all"), style = 1,
time_delay = 1, alpha = 1, beta = 0, type = c(2, 2), type_t12 = c(1, 1))
lathproj <- projection3(ehrlen3, nreps = 5, stochastic = TRUE, substoch = 2,
density = e3d)
lefko3 documentation built on Oct. 14, 2023, 1:07 a.m.
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| density_input | R Documentation |
Set Density Dependence Relationships in Matrix Elements
Description
Function density_input() provides all necessary data to incorporate
density dependence into a lefkoMat object, a list of matrices, or a
single matrix. 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 a delay of
at least one time-step (see Notes). The resulting data frame provides a
guide for other lefko3 functions to modify matrix elements by
density.
Usage
density_input(
mpm,
stage3 = NULL,
stage2 = NULL,
stage1 = NULL,
age2 = NULL,
style = NULL,
time_delay = NULL,
alpha = NULL,
beta = NULL,
type = NULL,
type_t12 = NULL
)
Arguments
mpm |
The |
stage3 |
A vector showing the name or number of the stage in occasion t+1 in the transitions to be affected by density. Abbreviations for groups of stages are also usable (see Notes). |
stage2 |
A vector showing the name or number of the stage in occasion t in the transition to be affected by density. Abbreviations for groups of stages are also usable (see Notes). |
stage1 |
A vector showing the name or number of the stage in occasion t-1 in the transition to be affected by density. Only needed if a historical MPM is used. Abbreviations for groups of stages are also usable (see Notes). |
age2 |
A vector showing the age of the stage in occasion t in the transition to be affected by density. Only needed if an age-by-stage MPM is used. |
style |
A vector coding for the style of density dependence on each
transition subject to density dependence. Options include |
time_delay |
An integer vector indicating the number of occasions back
on which density dependence operates. Defaults to |
alpha |
A 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 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 section
|
type |
A vector denoting the kind of transition between occasions
t and t+1 to be replaced. This should be entered as |
type_t12 |
An optional vector denoting the kind of transition between
occasions t-1 and t. Only necessary if a historical MPM in
deVries format is desired. This should be entered as |
Value
A data frame of class lefkoDens. This object can be used as
input in function projection3().
Variables in this object include the following:
stage3 |
Stage at occasion t+1 in the transition to be replaced. |
stage2 |
Stage at occasion t in the transition to be replaced. |
stage1 |
Stage at occasion t-1 in the transition to be replaced, if applicable. |
age2 |
Age at occasion t in the transition to be replaced, if applicable. |
style |
Style of density dependence, coded as 1, 2, 3, or 4 for the Ricker, Beverton-Holt, Usher, or logistic function, respectively. |
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. |
type |
Designates whether the transition from occasion t to occasion t+1 is a survival transition probability (1), or a fecundity rate (2). |
type_t12 |
Designates whether the transition from occasion t-1 to occasion t is a survival transition probability (1), a fecundity rate (2). |
Notes
This function provides inputs when density dependence is operationalized
directly on matrix elements. It can be used in both projection3() and
f_projection3(). Users wishing to modify vital rate functions by
density dependence functions for use in function-based projections with
function f_projection3() should use function density_vr() 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.
Entries in stage3, stage2, and stage1 can include
abbreviations for groups of stages. Use rep if all reproductive stages
are to be used, nrep if all mature but non-reproductive stages are to
be used, mat if all mature stages are to be used, immat if all
immature stages are to be used, prop if all propagule stages are to be
used, npr if all non-propagule stages are to be used, obs if
all observable stages are to be used, nobs if all unobservable stages
are to be used, and leave empty or use all if all stages in stageframe
are to be used.
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
start_input()
projection3()
Examples
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",
fecacol = "Intactseed88", deadacol = "Dead1988",
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)
e3d <- density_input(ehrlen3mean, stage3 = c("Sd", "Sdl"),
stage2 = c("rep", "rep"), stage1 = c("all", "all"), style = 1,
time_delay = 1, alpha = 1, beta = 0, type = c(2, 2), type_t12 = c(1, 1))
lathproj <- projection3(ehrlen3, nreps = 5, stochastic = TRUE, substoch = 2,
density = e3d)
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