Function aflefko2() returns ahistorical age x stage MPMs corresponding
to the patches and occasions given, including the associated component
transition and fecundity matrices, data frames detailing the characteristics
of ahistorical stages and the exact age-stage combinations corresponding to
rows and columns in estimated matrices, and a data frame characterizing the
patch and occasion combinations corresponding to these matrices.
aflefko2(
year = "all",
patch = "all",
stageframe,
supplement = NULL,
repmatrix = NULL,
overwrite = NULL,
data = NULL,
modelsuite = NULL,
surv_model = NULL,
obs_model = NULL,
size_model = NULL,
sizeb_model = NULL,
sizec_model = NULL,
repst_model = NULL,
fec_model = NULL,
jsurv_model = NULL,
jobs_model = NULL,
jsize_model = NULL,
jsizeb_model = NULL,
jsizec_model = NULL,
jrepst_model = NULL,
jmatst_model = NULL,
paramnames = NULL,
inda = NULL,
indb = NULL,
indc = NULL,
surv_dev = 0,
obs_dev = 0,
size_dev = 0,
sizeb_dev = 0,
sizec_dev = 0,
repst_dev = 0,
fec_dev = 0,
jsurv_dev = 0,
jobs_dev = 0,
jsize_dev = 0,
jsizeb_dev = 0,
jsizec_dev = 0,
jrepst_dev = 0,
jmatst_dev = 0,
density = NA,
fecmod = 1,
random.inda = FALSE,
random.indb = FALSE,
random.indc = FALSE,
final_age = NA,
continue = TRUE,
prebreeding = TRUE,
negfec = FALSE,
ipm_method = "CDF",
reduce = FALSE,
simple = FALSE,
err_check = FALSE,
exp_tol = 700,
theta_tol = 1e+08,
sparse_output = FALSE
)If all inputs are properly formatted, then this function will return
an object of class lefkoMat, which is a list that holds the matrix
projection model and all of its metadata. The structure has the following
elements:
A list of full projection matrices in order of sorted patches and
occasions. All matrices output in R's matrix class, or in
the dgCMatrix class from the Matrix package if sparse.
A list of survival transition matrices sorted as in A. All
matrices output in R's matrix class, or in the dgCMatrix class
from the Matrix package if sparse.
A list of fecundity matrices sorted as in A. All matrices
output in R's matrix class, or in the dgCMatrix class from the
Matrix package if sparse.
A data frame matrix showing the pairing of ahistorical stages
used to create historical stage pairs. Set to NA for age-by-stage
MPMs.
A data frame showing the stage number and stage name
corresponding to ahstages, as well as the associated age, of each
row in each age-by-stage matrix.
A data frame detailing the characteristics of associated ahistorical stages, in the form of a modified stageframe that includes status as an entry stage through reproduction.
A data frame giving the patch and year of each matrix in order.
In aflefko2(), only one population may be analyzed at once.
A vector showing the numbers of individuals and rows in the vertical dataset used as input.
A short vector describing the number of non-zero elements in
U and F matrices, and the number of annual matrices.
This is the qc portion of the modelsuite input.
An optional element only added if err_check = TRUE.
This is a list of vital rate probability matrices, with 7 columns in the
order of survival, observation probability, reproduction probability, primary
size transition probability, secondary size transition probability, tertiary
size transition probability, and probability of juvenile transition to
maturity.
An optional element only added if err_check = TRUE.
This is a data frame giving the values used to determine each matrix element
capable of being estimated.
A variable corresponding to the observation occasion, or a set
of such values, given in values associated with the year term used in linear
model development. Defaults to "all", in which case matrices will be
estimated for all occasions.
A variable designating which patches or subpopulations will have
matrices estimated. Defaults to "all", but can also be set to specific
patch names or a vector thereof.
An object of class stageframe. These objects are
generated by function sf_create(), and include information on
the size, observation status, propagule status, reproduction status,
immaturity status, maturity status, stage group, size bin widths, and other
key characteristics of each ahistorical stage.
An optional data frame of class lefkoSD that
provides supplemental data that should be incorporated into the MPM. Three
kinds of data may be integrated this way: transitions to be estimated via the
use of proxy transitions, transition overwrites from the literature or
supplemental studies, and transition multipliers for survival and fecundity.
This data frame should be produced using the supplemental()
function. Can be used in place of or in addition to an overwrite table (see
overwrite below) and a reproduction matrix (see repmatrix
below).
An optional reproduction matrix. This matrix is composed
mostly of 0s, with non-zero entries acting as element identifiers and
multipliers for fecundity (with 1 equaling full fecundity). If left
blank, and no supplement is provided, then aflefko2() will
assume that all stages marked as reproductive produce offspring at 1x that of
estimated fecundity, and that offspring production will yield the first stage
noted as propagule or immature. Must be the dimensions of an ahistorical
stage-based matrix.
An optional data frame developed with the
overwrite() function describing transitions to be overwritten
either with given values or with other estimated transitions. Note that this
function supplements overwrite data provided in supplement.
The historical vertical demographic data frame used to estimate
vital rates (class hfvdata), which is required to initialize times and
patches properly. Variable names should correspond to the naming conventions
in verticalize3() and historicalize3(). Not
required if option modelsuite is set to a vrm_input object.
One of two kinds of lists. The first is a lefkoMod
object holding the vital rate models and associated metadata. Alternatively,
an object of class vrm_input may be provided. If given, then
surv_model, obs_model, size_model, sizeb_model,
sizec_model, repst_model, fec_model, jsurv_model,
jobs_model, jsize_model, jsizeb_model,
jsizec_model, jrepst_model, jmatst_model, and
paramnames are not required. No models should include size or
reproductive status in occasion t-1. Although this is optional input,
it is recommended, and without it all vital rate model inputs (named
XX_model) are required.
A linear model predicting survival probability. This can
be a model of class glm or glmer, and requires a predicted
binomial variable under a logit link. Ignored if modelsuite is
provided. This model must have been developed in a modeling exercise testing
only the impacts of occasion t.
A linear model predicting sprouting or observation
probability. This can be a model of class glm or glmer, and
requires a predicted binomial variable under a logit link. Ignored if
modelsuite is provided. This model must have been developed in a
modeling exercise testing only the impacts of occasion t.
A linear model predicting primary size. This can be a model
of class glm, glmer, glmmTMB, zeroinfl,
vglm, lm, or lmer. Ignored if modelsuite is
provided. This model must have been developed in a modeling exercise testing
only the impacts of occasion t.
A linear model predicting secondary size. This can be a
model of class glm, glmer, glmmTMB, zeroinfl,
vglm, lm, or lmer. Ignored if modelsuite is
provided. This model must have been developed in a modeling exercise testing
only the impacts of occasion t.
A linear model predicting tertiary size. This can be a
model of class glm, glmer, glmmTMB, zeroinfl,
vglm, lm, or lmer. Ignored if modelsuite is
provided. This model must have been developed in a modeling exercise testing
only the impacts of occasion t.
A linear model predicting reproduction probability. This
can be a model of class glm or glmer, and requires a predicted
binomial variable under a logit link. Ignored if modelsuite is
provided. This model must have been developed in a modeling exercise testing
only the impacts of occasion t.
A linear model predicting fecundity. This can be a model of
class glm, glmer, glmmTMB, zeroinfl, vglm,
lm, or lmer. Ignored if modelsuite is provided. This
model must have been developed in a modeling exercise testing only the
impacts of occasion t.
A linear model predicting juvenile survival probability.
This can be a model of class glm or glmer, and requires a
predicted binomial variable under a logit link. Ignored if modelsuite
is provided. This model must have been developed in a modeling exercise
testing only the impacts of occasion t.
A linear model predicting juvenile sprouting or observation
probability. This can be a model of class glm or glmer, and
requires a predicted binomial variable under a logit link. Ignored if
modelsuite is provided. This model must have been developed in a
modeling exercise testing only the impacts of occasion t.
A linear model predicting juvenile primary size. This
can be a model of class glm, glmer, glmmTMB,
zeroinfl, vglm, lm, or lmer. Ignored if
modelsuite is provided. This model must have been developed in a
modeling exercise testing only the impacts of occasion t.
A linear model predicting juvenile secondary size. This
can be a model of class glm, glmer, glmmTMB,
zeroinfl, vglm, lm, or lmer. Ignored if
modelsuite is provided. This model must have been developed in a
modeling exercise testing only the impacts of occasion t.
A linear model predicting juvenile tertiary size. This
can be a model of class glm, glmer, glmmTMB,
zeroinfl, vglm, lm, or lmer. Ignored if
modelsuite is provided. This model must have been developed in a
modeling exercise testing only the impacts of occasion t.
A linear model predicting reproduction probability of a
mature individual that was immature in time t. This can be a model
of class glm or glmer, and requires a predicted binomial
variable under a logit link. Ignored if modelsuite is provided. This
model must have been developed in a modeling exercise testing only the
impacts of occasion t.
A linear model predicting maturity probability of an
individual that was immature in time t. This can be a model of class
glm or glmer, and requires a predicted binomial variable under
a logit link. Ignored if modelsuite is provided. This model must have
been developed in a modeling exercise testing only the impacts of occasion
t.
A data frame with three columns, the first describing all
terms used in linear modeling, the second (must be called mainparams)
giving the general model terms that will be used in matrix creation, and the
third showing the equivalent terms used in modeling (must be named
modelparams). Function create_pm() can be used to
create a skeleton paramnames object, which can then be edited. Only
required if modelsuite is not supplied.
Can be a single value to use for individual covariate a
in all matrices, a pair of values to use for times t and t-1 in
historical matrices, or a vector of such values corresponding to each
occasion in the dataset. Defaults to NULL.
Can be a single value to use for individual covariate b
in all matrices, a pair of values to use for times t and t-1 in
historical matrices, or a vector of such values corresponding to each
occasion in the dataset. Defaults to NULL.
Can be a single value to use for individual covariate c
in all matrices, a pair of values to use for times t and t-1 in
historical matrices, or a vector of such values corresponding to each
occasion in the dataset. Defaults to NULL.
A numeric value to be added to the y-intercept in the linear
model for survival probability. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for observation probability. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for primary size. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for secondary size. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for tertiary size. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for probability of reproduction. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for fecundity. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for juvenile survival probability. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for juvenile observation probability. Defaults to 0.
A numeric value to be added to the y-intercept in the linear
model for juvenile primary size. Defaults to 0.
A numeric value to be added to the y-intercept in the
linear model for juvenile secondary size. Defaults to 0.
A numeric value to be added to the y-intercept in the
linear model for juvenile tertiary size. Defaults to 0.
A numeric value to be added to the y-intercept in the
linear model for juvenile reproduction probability. Defaults to 0.
A numeric value to be added to the y-intercept in the
linear model for juvenile maturity probability. Defaults to 0.
A numeric value indicating density value to use to propagate
matrices. Only needed if density is an explanatory term used in one or more
vital rate models. Defaults to NA.
A scalar multiplier of fecundity. Defaults to 1.0.
A logical value denoting whether to treat individual
covariate a as a random, categorical variable. Otherwise is treated as
a fixed, numeric variable. Defaults to FALSE.
A logical value denoting whether to treat individual
covariate b as a random, categorical variable. Otherwise is treated as
a fixed, numeric variable. Defaults to FALSE.
A logical value denoting whether to treat individual
covariate c as a random, categorical variable. Otherwise is treated as
a fixed, numeric variable. Defaults to FALSE.
The final age to model in the matrix, where the first age will be age 0. Defaults to the maximum age in the dataset.
A logical value designating whether to allow continued
survival of individuals past the final age noted in the stageframe, using the
demographic characteristics of the final age. Defaults to TRUE.
A logical value indicating whether the life history model
is a pre-breeding model. Defaults to TRUE.
A logical value denoting whether fecundity values estimated to
be negative should be reset to 0. Defaults to FALSE.
A string indicating what method to use to estimate size
transition probabilities, if size is treated as continuous. Options include:
"midpoint", which utilizes the midpoint method; and "CDF",
which uses the cumulative distribution function. Defaults to "CDF".
A logical value denoting whether to remove age-stages
associated solely with 0 transitions. These are only removed in cases
where the associated row and column sums in ALL matrices estimated equal 0.
Defaults to FALSE.
A logical value indicating whether to produce A,
U, and F matrices, or only the latter two. Defaults to
FALSE, in which case all three are output.
A logical value indicating whether to append extra
information used in matrix calculation within the output list. Defaults to
FALSE.
A numeric value used to indicate a maximum value to set
exponents to in the core kernel to prevent numerical overflow. Defaults to
700.
A numeric value used to indicate a maximum value to theta as
used in the negative binomial probability density kernel. Defaults to
100000000, but can be reset to other values during error checking.
A logical value indicating whether to output matrices
in sparse format. Defaults to FALSE, in which case all matrices are
output in standard matrix format.
Unlike rlefko2(), rlefko3(),
arlefko2(), and rleslie(), this function does not
currently distinguish populations. Users wishing to use the same vital rate
models across populations should label them as patches (though we do not
advise this approach, as populations should typically be treated as
statistically independent).
This function will yield incorrect estimates if the models utilized incorporate state in occasion t-1. Only use models developed testing for ahistorical effects.
The default behavior of this function is to estimate fecundity with regards
to transitions specified via associated fecundity multipliers in either
supplement or repmatrix. If both of these fields are left
empty, then fecundity will be estimated at full for all transitions leading
from reproductive stages to immature and propagule stages. However, if a
supplement is provided and a repmatrix is not, or if
repmatrix is set to 0, then only fecundity transitions noted in the
supplement will be set to non-zero values. To use the default behavior of
setting all reproductive stages to reproduce at full fecundity into immature
and propagule stages but also incorporate given or proxy
survival transitions, input those given and proxy transitions through the
overwrite option.
The reproduction matrix (field repmatrix) may only be supplied as
ahistorical. If provided as historical, then aflefko2() will fail and
produce an error.
Stageframes used in this function should include ages for minimum and maximum
age for each stage. NAs are treated as 0s in minimum age, and
as final_age for maximum age.
Users may at times wish to estimate MPMs using a dataset incorporating
multiple patches or subpopulations, but without discriminating between those
patches or subpopulations. Should the aim of analysis be a general MPM that
does not distinguish these patches or subpopulations, the
modelsearch() run should not include patch terms.
Input options including multiple variable names must be entered in the order of variables in occasion t+1 and t. Rearranging the order will lead to erroneous calculations, and may lead to fatal errors.
Care should be taken to match the random status of year and patch to the
states of those variables within the modelsuite. If they do not match,
then they will be treated as zeroes in vital rate estimation.
The ipm_method function gives the option of using two different means
of estimating the probability of size transition. The midpoint method
("midpoint") refers to the method in which the probability is
estimated by first estimating the probability associated with transition from
the exact size at the midpoint of the size class using the corresponding
probability density function, and then multiplying that value by the bin
width of the size class. Doak et al. 2021 (Ecological Monographs) noted that
this method can produce biased results, with total size transitions
associated with a specific size not totaling to 1.0 and even specific size
transition probabilities capable of being estimated at values greater than
1.0. The alternative and default method, "CDF", uses the corresponding
cumulative density function to estimate the probability of size transition as
the cumulative probability of size transition at the greater limit of the
size class minus the cumulative probability of size transition at the lower
limit of the size class. The latter method avoids this bias. Note, however,
that both methods are exact and unbiased for the Poisson and negative
binomial distributions.
Under the Gaussian and gamma size distributions, the number of estimated
parameters may differ between the two ipm_method settings. Because
the midpoint method has a tendency to incorporate upward bias in the
estimation of size transition probabilities, it is more likely to yield non-
zero values when the true probability is extremely close to 0. This will
result in the summary.lefkoMat function yielding higher numbers of
estimated parameters than the ipm_method = "CDF" yields in some cases.
Using the err_check option will produce a matrix of 7 columns, each
characterizing a different vital rate. The product of each row yields an
element in the associated U matrix. The number and order of elements
in each column of this matrix matches the associated matrix in column vector
format. Use of this option is generally for the purposes of debugging code.
Individual covariates are treated as categorical only if they are set as
random terms. Fixed categorical individual covariates are currently not
allowed. However, such terms may be supplied if the modelsuite option
is set to a vrm_input object. In that case, the user should also set
the logical random switch for the individual covariate to be used to
TRUE (e.g., random.inda = TRUE).
mpm_create()
flefko3()
flefko2()
fleslie()
arlefko2()
rlefko3()
rlefko2()
rleslie()
# \donttest{
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)
minima <- c(1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)
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, minage = minima)
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)
lathmodelsln2 <- modelsearch(lathvertln, historical = FALSE,
approach = "mixed", suite = "main",
vitalrates = c("surv", "obs", "size", "repst", "fec"), juvestimate = "Sdl",
bestfit = "AICc&k", sizedist = "gaussian", fecdist = "poisson",
indiv = "individ", patch = "patchid", year = "year2", age = "obsage",
year.as.random = TRUE, patch.as.random = TRUE, show.model.tables = TRUE,
quiet = "partial")
# Here we use supplemental() to provide overwrite and reproductive info
lathsupp2 <- supplemental(stage3 = c("Sd", "Sdl", "mat", "Sd", "Sdl"),
stage2 = c("Sd", "Sd", "Sdl", "rep", "rep"),
eststage3 = c(NA, NA, "mat", NA, NA),
eststage2 = c(NA, NA, "Dorm", NA, NA),
givenrate = c(0.345, 0.054, NA, NA, NA),
multiplier = c(NA, NA, 0.8, 0.345, 0.054), type = c(1, 1, 1, 3, 3),
stageframe = lathframeln, historical = FALSE, agebased = TRUE)
lathmat2age <- aflefko2(year = "all", patch = "all",
stageframe = lathframeln, modelsuite = lathmodelsln2, data = lathvertln,
supplement = lathsupp2, final_age = 3, continue = TRUE, reduce = FALSE)
# }
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