| Type: | Package |
| Title: | Adaptive Dynamics and Community Matrix Model Projections |
| Version: | 1.0.1 |
| Date: | 2025-07-11 |
| Description: | Runs projections of groups of matrix projection models (MPMs), allowing density dependence mechanisms to work across MPMs. This package was developed to run both adaptive dynamics simulations such as pairwise and multiple invasibility analyses, and community projections in which species are represented by MPMs. All forms of MPMs are allowed, including integral projection models (IPMs). Also includes individual-based modeling (IBM) versions of these. |
| Encoding: | UTF-8 |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://github.com/dormancy1/adapt3 |
| Imports: | Rcpp (≥ 1.0.12), lefko3, methods, rlang, grDevices |
| LinkingTo: | Rcpp, RcppArmadillo, BH, lefko3 |
| LazyData: | true |
| BugReports: | https://github.com/dormancy1/adapt3/issues |
| RoxygenNote: | 7.3.2 |
| Suggests: | knitr, rmarkdown |
| VignetteBuilder: | knitr, rmarkdown |
| NeedsCompilation: | yes |
| Packaged: | 2025-07-12 01:02:14 UTC; richpshefferson |
| Author: | Richard P. Shefferson
 [aut, cre] |
| Maintainer: | Richard P. Shefferson <cdorm@g.ecc.u-tokyo.ac.jp> |
| Depends: | R (≥ 3.5.0) |
| Repository: | CRAN |
| Date/Publication: | 2025-07-16 15:40:08 UTC |
Adaptive Dynamics and Community Matrix Model Projections
Description
Runs projections of groups of matrix projection models (MPMs), allowing density dependence mechanisms to work across MPMs. This package was developed to run both adaptive dynamics simulations such as pairwise and multiple invasion analysis, and community projections in which species are represented by MPMs. All forms of MPMs are allowed, including integral projection models (IPMs).
Details
The adapt3 package provides three categories of functions:
1. Core projection
2. Function characterizing relationships among MPMs
3. Functions describing, summarizing, or visualizing results
adapt3 also includes example datasets complete with sample code.
Author(s)
Maintainer: Richard P. Shefferson cdorm@g.ecc.u-tokyo.ac.jp (ORCID)
Richard P. Shefferson <cdorm@g.ecc.u-tokyo.ac.jp>
References
Pending
See Also
Useful links:
Demographic Dataset of Cypripedium parviflorum Population, in Horizontal Format
Description
A dataset containing the states and fates of Cypripedium parviflorum (small yellow lady's slipper orchids), family Orchidaceae, from a population in Illinois, USA, resulting from monitoring that occurred annually between 1994 and 2011.
Usage
data(cypa_data)
Format
A data frame with 1119 individuals and 37 variables. Each row
corresponds to an unique individual, and each variable from Inf.94
on refers to the state of the individual in a particular year.
- plant_id
A numeric variable giving a unique number to each individual.
- Inf.94
Number of inflorescences in 1994.
- Veg.94
Number of stems without inflorescences in 1994.
- Inf.95
Number of inflorescences in 1995.
- Veg.95
Number of stems without inflorescences in 1995.
- Inf.96
Number of inflorescences in 1996.
- Veg.96
Number of stems without inflorescences in 1996.
- Inf.97
Number of inflorescences in 1997.
- Veg.97
Number of stems without inflorescences in 1997.
- Inf.98
Number of inflorescences in 1998.
- Veg.98
Number of stems without inflorescences in 1998.
- Inf.99
Number of inflorescences in 1999.
- Veg.99
Number of stems without inflorescences in 1999.
- Inf.00
Number of inflorescences in 2000.
- Veg.00
Number of stems without inflorescences in 2000.
- Inf.01
Number of inflorescences in 2001.
- Veg.01
Number of stems without inflorescences in 2001.
- Inf.02
Number of inflorescences in 2002.
- Veg.02
Number of stems without inflorescences in 2002.
- Inf.03
Number of inflorescences in 2003.
- Veg.03
Number of stems without inflorescences in 2003.
- Inf.04
Number of inflorescences in 2004.
- Veg.04
Number of stems without inflorescences in 2004.
- Inf.05
Number of inflorescences in 2005.
- Veg.05
Number of stems without inflorescences in 2005.
- Inf.06
Number of inflorescences in 2006.
- Veg.06
Number of stems without inflorescences in 2006.
- Inf.07
Number of inflorescences in 2007.
- Veg.07
Number of stems without inflorescences in 2007.
- Inf.08
Number of inflorescences in 2008.
- Veg.08
Number of stems without inflorescences in 2008.
- Inf.09
Number of inflorescences in 2009.
- Veg.09
Number of stems without inflorescences in 2009.
- Inf.10
Number of inflorescences in 2010.
- Veg.10
Number of stems without inflorescences in 2010.
- Inf.11
Number of inflorescences in 2011.
- Veg.11
Number of stems without inflorescences in 2011.
Source
Shefferson, R.P., R. Mizuta, and M.J. Hutchings. 2017. Predicting evolution in response to climate change: the example of sprouting probability in three dormancy-prone orchid species. Royal Society Open Science 4(1):160647.
Examples
library(lefko3)
data(cypa_data)
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 = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", indivcol = "individ")
lambda3(cypmatrix2r)
Create an Equivalence Vector for Each Population
Description
Function equiv_input() creates a data frame summarizing the degree to
which an individual in each stage of a life history is equivalent to a
standard individual.
Usage
equiv_input(mpm, stage2 = NA, stage1 = NA, age2 = NA, value = 1)
Arguments
mpm |
The lefkoMat object to be used in projection. Can be an example MPM if function-based projection is planned. |
stage2 |
A vector showing the name or number of a stage in occasion
t that should be set to a positive number of individuals in the start
vector. Abbreviations for groups of stages are also usable (see Notes).
This input is required for all stage-based and age-by-stage MPMs. Defaults to
|
stage1 |
A vector showing the name or number of a stage in occasion t-1 that should be set to a positive number of individuals in the start vector. Abbreviations for groups of stages are also usable (see Notes). This is only used for historical MPMs, since the rows of hMPMs correspond to stage-pairs in times t and t-1 together. Only required for historical MPMs, and will result in errors if otherwise used. |
age2 |
A vector showing the age of each respective stage in occasion
t that should be set to a positive number of individuals in the start
vector. Only used for Leslie and age-by-stage MPMs. Defaults to |
value |
A vector showing the values, in order, of the number of
individuals set for the stage or stage-pair in question. Defaults to
|
Value
A list of class adaptEq, with four objects, which can be
used as input in function project3(). The last three include
the ahstages, hstages, and agestages objects from the
lefkoMat object supplied in mpm. The first element in the list
is a data frame with the following variables:
stage2 |
Stage at occasion t. |
stage_id_2 |
The stage number associated with |
stage1 |
Stage at occasion t-1, if historical. Otherwise NA. |
stage_id_1 |
The stage number associated with |
age2 |
The age of individuals in |
row_num |
A number indicating the respective starting vector element. |
value |
Number of individuals in corresponding stage or stage-pair. |
Notes
Entries in 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.
Examples
library(lefko3)
data(cypdata)
data(cypa_data)
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)
cycaraw_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)
cyparaw_v1 <- verticalize3(data = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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)
cyp_supp_list1 <- list(cypsupp2r, cypsupp2r)
cycamatrix2r <- rlefko2(data = cycaraw_v1, stageframe = cypframe_raw,
year = "all", patch = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cypamatrix2r <- rlefko2(data = cyparaw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cyp_mpm_list <- list(cycamatrix2r, cypamatrix2r)
cyca2_start <- start_input(cycamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(500, 100, 200))
cypa2_start <- start_input(cypamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(5000, 1000, 2000))
cyp_start_list <- list(cyca2_start, cypa2_start)
cyp2_dv <- density_input(cypamatrix2r, stage3 = c("SD", "P1"),
stage2 = c("rep", "rep"), style = c(1, 1), alpha = c(0.5, 1.2),
beta = c(1.0, 2.0), type = c(2, 1))
cyp_dv_list <- list(cyp2_dv, cyp2_dv)
cyp_eq <- equiv_input(cycamatrix2r,
stage2 = c("SD", "P1", "SL", "D", "XSm", "Sm", "Md", "Lg", "XLg"),
value = c(0, 1, 1, 1, 1, 1, 1, 1, 1))
eq_list <- list(cyp_eq, cyp_eq)
cyp_comm_proj <- project3(mpms = cyp_mpm_list, starts = cyp_start_list,
density = cyp_dv_list, times = 10)
summary(cyp_comm_proj)
Run Pairwise and Multiple Invasion Analysis
Description
Function invade3 runs pairwise and multiple invasion analyses.
Usage
invade3(
axis = NULL,
mpm = NULL,
vrm = NULL,
stageframe = NULL,
supplement = NULL,
equivalence = NULL,
starts = NULL,
years = NULL,
patches = NULL,
tweights = NULL,
format = NULL,
entry_time = NULL,
sp_density = NULL,
ind_terms = NULL,
dev_terms = NULL,
fb_sparse = NULL,
firstage = NULL,
finalage = NULL,
fecage_min = NULL,
fecage_max = NULL,
cont = NULL,
prebreeding = NULL,
fecmod = NULL,
density = NULL,
density_vr = NULL,
stochastic = NULL,
A_only = NULL,
integeronly = NULL,
fitness_table = NULL,
trait_optima = NULL,
zap_min = NULL,
converged_only = NULL,
err_check = NULL,
var_per_run = 2L,
substoch = 0L,
elast_mult = 0.995,
nreps = 1L,
times = 10000L,
fitness_times = 100L,
exp_tol = 700,
theta_tol = 1e+08,
threshold = 1e-08,
loop_max = 150L
)
Arguments
axis |
The |
mpm |
An MPM of class |
vrm |
A |
stageframe |
A stageframe defining stages and the life cycle for the
entered object in argument |
supplement |
An optional data frame of class |
equivalence |
An optional object of class |
starts |
An optional |
years |
An optional term corresponding to a single integer vector of
time |
patches |
An optional single string giving a single pop-patch to be used during invasion analysis. Defaults to the population-level set or the first patch, depending on whether the former exists. |
tweights |
An optional numeric vector or matrice denoting the probabilities of choosing each matrix in each MPM in a stochastic projection. If a matrix, 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 an element of the list is a vector, then the choice of annual matrix is assumed to be independent of the current matrix. Defaults to equal weighting among matrices. |
format |
An optional integer indicating the kind of function-based MPM
to create, if argument |
entry_time |
An optional integer vector giving the entry time for each
variant into each simulation. Defaults to a zero vector with length equal to
the number of variants to run concurrently in each simulation, as given by
argument |
sp_density |
An optional argument for use with argument |
ind_terms |
An optional argument providing values of individual or
environmental covariate values for argument |
dev_terms |
An optional data frame including 14 columns and up to
|
fb_sparse |
A logical value indicating whether function-based MPMs
should be produced in sparse matrix format. Defaults to |
firstage |
An optional integer used for function-based Leslie and
age-by-stage MPMs giving the starting age in such MPMs. Use only if the MPM
is both function-based and has age structure. Typically, the starting age in
such MPMs should be set to |
finalage |
An optional integer used for function-based Leslie and age-by-stage MPMs giving the final age in such MPMs. Use only if the MPM is both function-based and has age structure. |
fecage_min |
An optional integer used for function-based Leslie MPMs
giving the first age at which organisms can reproduce. Use only if the MPM
is both function-based and has age structure. Defaults to the value given in
|
fecage_max |
An optional integer used for function-based Leslie MPMs
giving the final age at which organisms can reproduce. Use only if the MPM
is both function-based and has age structure. Defaults to the value given in
|
cont |
An optional logical value for function-based Leslie and age-by-stage MPMs stating whether the MPM should should include a stasis transition within the final age. This should be used only when an organism can maintain the demographic characteristics of the final described age after reaching that age. |
prebreeding |
An optional logical value indicating whether the life
cycle is prebreeding ( |
fecmod |
An optional numeric value for function-based MPMs giving scalar multipliers for fecundity terms, when two fecundity variables are used for a collective fecundity per individual. |
density |
An optional data frames of class |
density_vr |
An optional data frame of class |
stochastic |
A logical value indicating whether the projection will be
run as a temporally stochastic projection. Defaults to |
A_only |
A logical value indicating whether to alter survival and
fecundity matrix elements separately prior to creating the overall |
integeronly |
A logical value indicating whether to round the number of
individuals projected in each stage at each occasion down to the next lower
integer. Defaults to |
fitness_table |
A logical value dictating whether to include a data
frame giving Lyapunov coefficients for all combinations of variants tested.
Necessary for the creation of pairwise invasibility plots (PIPs). Defaults
to |
trait_optima |
A logical value indicating whether to assess the optimal
values of traits, generally as kinds of evolutionary stage equilibrium (ESS)
points. Trait optimization is conducted via elasticity analysis of traits
that are variable within the |
zap_min |
A logical value indicating whether to treat traits and
fitness as 0 when their absolute values are less than the value given in
argument |
converged_only |
A logical value indicating whether to show predicted
trait optima only in cases where the Lyapunov coefficient in elasticity
analysis has converged to 0. Defaults to |
err_check |
A logical value indicating whether to include an extra list
of output objects for error checking. Can also be set to the text value
|
var_per_run |
The number of variants to run in each simulation.
Defaults to |
substoch |
An integer value indicating whether to force survival-
transition matrices to be substochastic in density dependent and density
independent simulations. Defaults to |
elast_mult |
A multiplier for traits to assess the elasticity of
fitness in trait optimization. Defaults to |
nreps |
The number of replicate projections. Defaults to |
times |
Number of occasions to iterate per replicate. Defaults to
|
fitness_times |
An integer giving the number of time steps at the end
of each run to use to estimate the fitness of the respective genotype.
Defaults to |
exp_tol |
A numeric value used to indicate a maximum value to set
exponents to in the core kernel to prevent numerical overflow. Defaults to
|
theta_tol |
A numeric value used to indicate a maximum value to theta as
used in the negative binomial probability density kernel. Defaults to
|
threshold |
The lower limit for the absolute value of fitness, below which fitness is rounded to 0. Defaults to 0.00000001. |
loop_max |
An integer value denoting the number of search cycles allowed per ESS during ESS optimization. Defaults to 150. |
Value
A list of class adaptInv, with the following elements:
fitness |
A data frame giving the Lyapunov coefficients estimated for each variant, per replicate. |
variants_out |
A two-level list with the top level list having number of elements equal to the number of variants, and the lower level corresponding to the number of replicates. Each element of the lower level list is a matrix showing the number of individuals in each stage (row) at each time (column). |
N_out |
A list with the number of elements equal to the number of replicates. Each element within this list is data frame showing the number of individuals of each species or genotype alive at each time. The number of rows are equal to the number of MPMs used, and the columns correspond to the time steps. |
stageframe_list |
A list in which each element is the stageframe for each MPM used. |
hstages_list |
A list giving the used |
agestages_list |
A list giving the used |
labels |
A small data frame giving the the population and patch identities for each MPM entered. |
err_check |
An optional list composed of an additional six lists, each
of which has the number of elements equal to the number of MPMs utilized.
List output include |
Notes
The argument var_per_run establishes the style of simulation to run.
Entering var_per_run = 1 runs each variant singly. Entering
var_per_run = 2 runs pairwise invasibility analysis, trying each pair
permutation of variants. Greater values will lead to multiple invasibility
analysis with different permutations of groups. For example,
var_per_run = 3 runs each permutation of groups of three. The integer
set must be positive, and must not be larger than the number of variants.
When optima = TRUE, ESS values for traits that vary in the input
adaptAxis data frame are evaluated. The methodology is that
originally developed in Benton and Grant (1999, Evolution 53:677-688), as
communicated in Roff (2010, Modeling evolution: an introduction to numerical
methods, Oxford University Press). In essence, function invade3
determines which traits vary among all traits noted in the input trait axis.
A new trait axis is then created with values of variable traits multiplied
by 0.995, and this new trait axis is composed entirely of invaders that will
be paired against each respective row in the original trait axis. These two
trait axis frames are then used to conduct pairwise invasibility elasticity
analyses, particularly noting where fitness values and trends invert. Note
that this optimization approach really only works with one variable trait.
Examples
library(lefko3)
data(cypdata)
sizevector <- c(0, 0, 0, 0, 1, 2.5, 4.5, 8, 17.5)
stagevector <- c("SD", "P1", "SL", "D", "XSm", "Sm", "Md", "Lg", "XLg")
repvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
binvec <- c(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)
cypsupp2r <- supplemental(stage3 = c("SD", "P1", "SL", "D",
"XSm", "Sm", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "SL", "SL", "SL", "rep",
"rep"),
eststage3 = c(NA, NA, NA, "D", "XSm", "Sm", NA, NA),
eststage2 = c(NA, NA, NA, "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.10, 0.40, 0.25, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, 1000, 1000),
type =c(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"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cypmean <- lmean(cypmatrix2r)
cyp_start <- start_input(cypmean, stage2 = c("SD", "P1", "D"),
value = c(1000, 200, 4))
c2d_4 <- density_input(cypmean, stage3 = c("P1", "P1"), stage2= c("SD", "rep"),
style = 2, time_delay = 1, alpha = 0.005, beta = 0.000005, type = c(2, 2))
# A simple projection allows us to find a combination of density dependence
# and running time that produces a stable quasi-equilibrium
cyp_proj <- projection3(cypmean, times = 250, start_frame = cyp_start,
density = c2d_4, integeronly = TRUE)
plot(cyp_proj)
cyp_ta <- trait_axis(stageframe = cypframe_raw,
stage3 = rep("P1", 15),
stage2 = rep("rep", 15),
multiplier = seq(from = 0.1, to = 10.0, length.out = 15),
type = rep(2, 15))
cyp_inv <- invade3(axis = cyp_ta, mpm = cypmean, density = c2d_4, times = 350,
starts = cyp_start, entry_time = c(0, 250), fitness_times = 30,
var_per_run = 2)
plot(cyp_inv)
Create Contour Plot of Pairwise Invasibility Analysis Results
Description
Function plot.adaptInv plots pairwise invasibility contour plots. This
function is based on code derived from Roff's Modeling Evolution: An
Introduction to Numerical Methods (2010, Oxford University Press).
Usage
## S3 method for class 'adaptInv'
plot(
x,
xlab = "Resident",
ylab = "Invader",
res_variant = 1,
inv_variant = 2,
repl = 1,
pip = TRUE,
elast = FALSE,
run = 1,
filled = TRUE,
plot.title,
plot.axes,
axes = TRUE,
frame.plot = TRUE,
auto_ylim = TRUE,
auto_col = TRUE,
auto_lty = TRUE,
auto_title = FALSE,
...
)
Arguments
x |
An |
xlab |
The x axis label forthe contour plot. Defaults to
|
ylab |
The y axis label forthe contour plot. Defaults to
|
res_variant |
The number of the variant representing the resident subpopulation. |
inv_variant |
The number of the variant representing the mutant subpopulation. |
repl |
The replicate number to plot, in the |
pip |
A logical value indicating whether to produce a pairwise
invasibility plot. If |
elast |
A logical value indicating whether to produce an elasticity
plot. Such plots can only be produced when trait optimization is performed
during invasibility analysis. Defaults to |
run |
An integer giving the run to plot if |
filled |
A logical value indicating whether to produce a filled contour
plot, or a standard contour plot. Defaults to |
plot.title |
A title for the plot. |
plot.axes |
A generic parameter providing axis information for pairwise invasibility plots. |
axes |
A logical value indicating whether to include axis lines.
Defaults to |
frame.plot |
A logical value indicating whether to frame the plot. |
auto_ylim |
A logical value indicating whether the maximum of the y axis
should be determined automatically. Defaults to |
auto_col |
A logical value indicating whether to shift the color of
lines associated with each patch automatically. Defaults to |
auto_lty |
A logical value indicating whether to shift the line type
associated with each replicate automatically. Defaults to |
auto_title |
A logical value indicating whether to add a title to each
plot. The plot is composed of the concatenated population and patch names.
Defaults to |
... |
Other parameters used by functions |
Value
A contour plot showing the overall fitness dynamics of the invader variant, assuming a pairwise invasibility analysis.
Notes
By default, function plot.adaptInv produces a filled contour plot in
which grey regions show where the invader has positive fitness relative to
the resident, and white regions show where the invader has negative fitness
relative to the resident. Fitness here refers to the Lyapunov coefficient,
calculated over the final fitness_times in the original call to
function invade3().
Examples
library(lefko3)
data(cypdata)
sizevector <- c(0, 0, 0, 0, 1, 2.5, 4.5, 8, 17.5)
stagevector <- c("SD", "P1", "SL", "D", "XSm", "Sm", "Md", "Lg", "XLg")
repvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
binvec <- c(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)
cypsupp2r <- supplemental(stage3 = c("SD", "P1", "SL", "D",
"XSm", "Sm", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "SL", "SL", "SL", "rep",
"rep"),
eststage3 = c(NA, NA, NA, "D", "XSm", "Sm", NA, NA),
eststage2 = c(NA, NA, NA, "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.10, 0.40, 0.25, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, 1000, 1000),
type =c(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"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cypmean <- lmean(cypmatrix2r)
cyp_start <- start_input(cypmean, stage2 = c("SD", "P1", "D"),
value = c(1000, 200, 4))
c2d_4 <- density_input(cypmean, stage3 = c("P1", "P1"), stage2= c("SD", "rep"),
style = 2, time_delay = 1, alpha = 0.005, beta = 0.000005, type = c(2, 2))
# A simple projection allows us to find a combination of density dependence
# and running time that produces a stable quasi-equilibrium
cyp_proj <- projection3(cypmean, times = 250, start_frame = cyp_start,
density = c2d_4, integeronly = TRUE)
plot(cyp_proj)
cyp_ta <- trait_axis(stageframe = cypframe_raw,
stage3 = rep("P1", 15),
stage2 = rep("rep", 15),
multiplier = seq(from = 0.1, to = 10.0, length.out = 15),
type = rep(2, 15))
cyp_inv <- invade3(axis = cyp_ta, mpm = cypmean, density = c2d_4, times = 350,
starts = cyp_start, entry_time = c(0, 250), fitness_times = 30,
var_per_run = 2)
plot(cyp_inv)
Create Plot of Community Projection
Description
Function plot.adaptProj plots community projections.
Usage
## S3 method for class 'adaptProj'
plot(
x,
repl = 1,
auto_ylim = TRUE,
auto_col = TRUE,
auto_lty = TRUE,
auto_title = FALSE,
...
)
Arguments
x |
An |
repl |
The replicate to plot. Defaults to |
auto_ylim |
A logical value indicating whether the maximum of the y axis
should be determined automatically. Defaults to |
auto_col |
A logical value indicating whether to shift the color of
lines associated with each patch automatically. Defaults to |
auto_lty |
A logical value indicating whether to shift the line type
associated with each replicate automatically. Defaults to |
auto_title |
A logical value indicating whether to add a title to each
plot. The plot is composed of the concatenated population and patch names.
Defaults to |
... |
Other parameters used by functions |
Value
A plot of the results of a project3() run.
Notes
Output plots are currently limited to time series of population size.
Examples
library(lefko3)
data(cypdata)
data(cypa_data)
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)
cycaraw_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)
cyparaw_v1 <- verticalize3(data = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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)
cyp_supp_list1 <- list(cypsupp2r, cypsupp2r)
cycamatrix2r <- rlefko2(data = cycaraw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", indivcol = "individ")
cypamatrix2r <- rlefko2(data = cyparaw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", indivcol = "individ")
cyp_mpm_list <- list(cycamatrix2r, cypamatrix2r)
cyca2_start <- start_input(cycamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(500, 100, 200))
cypa2_start <- start_input(cypamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(5000, 1000, 2000))
cyp_start_list <- list(cyca2_start, cypa2_start)
cyp2_dv <- density_input(cypamatrix2r, stage3 = c("SD", "P1"),
stage2 = c("rep", "rep"), style = c(1, 1), alpha = c(0.5, 1.2),
beta = c(1.0, 2.0), type = c(2, 1))
cyp_dv_list <- list(cyp2_dv, cyp2_dv)
cyp_comm_proj <- project3(mpms = cyp_mpm_list, starts = cyp_start_list,
density = cyp_dv_list, times = 10)
plot(cyp_comm_proj, lwd = 2, bty = "n")
Project Multiple MPMs With or Without Density Dependence
Description
Function project3 uses pre-existing or function-based MPMs to run
community projection simulations, in which different populations are run as
separate MPMs. Density dependence can be used with individual equivalence
vectors specifying Lotka-Volterra coefficients to adjust overall population
sizes to make them comparable.
Usage
project3(
mpms = NULL,
vrms = NULL,
stageframes = NULL,
supplements = NULL,
equivalence = NULL,
starts = NULL,
years = NULL,
patches = NULL,
tweights = NULL,
format = NULL,
entry_time = NULL,
sp_density = NULL,
ind_terms = NULL,
dev_terms = NULL,
fb_sparse = NULL,
firstage = NULL,
finalage = NULL,
fecage_min = NULL,
fecage_max = NULL,
cont = NULL,
fecmod = NULL,
density = NULL,
density_vr = NULL,
err_check = NULL,
stochastic = FALSE,
integeronly = FALSE,
substoch = 0L,
nreps = 1L,
times = 10000L,
prep_mats = 20L,
force_fb = FALSE,
exp_tol = 700,
theta_tol = 1e+08
)
Arguments
mpms |
An optional list of MPMs. Each MPM must be of class
|
vrms |
An optional list of |
stageframes |
An optional list of stageframes, corresponding in number
and order to the MPMs in argument |
supplements |
An optional list of data frames of class |
equivalence |
An optional numeric vector, list of numeric vectors,
data frame of class |
starts |
An optional list of |
years |
An optional term corresponding either to a single integer vector
of time |
patches |
An optional string vector with length equal to the number of
MPMs, detailing the name of each patch to project for each MPM, in order.
Only a single pop-patch may be projected for each MPM given. A value of
|
tweights |
An optional list composed of numeric vectors or matrices
denoting the probabilities of choosing each matrix in each MPM in a
stochastic projection. If an element of the list is a matrix, 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 an element of the list is a vector, then the choice of
annual matrix is assumed to be independent of the current matrix. Defaults
to equal weighting among matrices. If used, then one element per MPM is
required, with equal weighting assumed for any element set to |
format |
An optional integer vector indicating the kind of
function-based MPM to create for each |
entry_time |
An optional integer vector giving the entry time for each
MPM into the projection. Defaults to a zero vector with the length of the
number of MPMs, as given either by argument |
sp_density |
An optional argument for use with |
ind_terms |
An optional argument providing values of individual or
environmental covariate values for |
dev_terms |
An optional list of data frames, one for each
|
fb_sparse |
A logical vector indicating whether function-based MPMs
should be produced in sparse matrix format. Defaults to |
firstage |
An optional integer vector used for function-based Leslie
and age-by-stage MPMs giving the starting ages in such MPMs. Use only if at
least one MPM is both function-based and has age structure. Typically,
the starting age in such MPMs should be set to |
finalage |
An optional integer vector used for function-based Leslie and age-by-stage MPMs giving the final ages in such MPMs. Use only if at least one MPM is both function-based and has age structure. Do not use if no MPM has age structure. |
fecage_min |
An optional integer vector used for function-based Leslie
MPMs giving the first age at which organisms can be reproductive in such
MPMs. Use only if at least one MPM is a function-based Leslie MPM. Defaults
to the values given in |
fecage_max |
An optional integer vector used for function-based Leslie
MPMs giving the final age at which organisms can be reproductive in such
MPMs. Use only if at least one MPM is a function-based Leslie MPM. Defaults
to the values given in |
cont |
An optional vector used for function-based Leslie and
age-by-stage MPMs stating whether the MPM should should include a stasis
transition within the final age. This should be used only when an organism
can maintain the demographic characteristics of the final described age
after reaching that age. Can be entered as a logical vector or an integer
vector. MPMs without age structure should be entered as |
fecmod |
An optional vector used for function-based MPMs giving scalar
multipliers for fecundity terms, when two fecundity variables are used for a
collective fecundity per individual. Each entry refers to each
|
density |
An optional list of data frames of class |
density_vr |
An optional list of data frames of class
|
err_check |
A logical value indicating whether to include an extra list
of output objects for error checking. Can also be set to the text value
|
stochastic |
A logical value indicating whether the projection will be
run as a temporally stochastic projection. Defaults to |
integeronly |
A logical value indicating whether to round the number of
individuals projected in each stage at each occasion in each MPM to the
nearest integer. Defaults to |
substoch |
An integer value indicating whether to force survival-
transition matrices to be substochastic in density dependent and density
independent simulations. Defaults to |
nreps |
The number of replicate projections. Defaults to |
times |
Number of occasions to iterate per replicate. Defaults to
|
prep_mats |
An integer value for use when creating function-based MPM
projections. If using |
force_fb |
A logical value indicating whether to force function-based
MPMs to be developed at each time step even if fewer than |
exp_tol |
A numeric value used to indicate a maximum value to set
exponents to in the core kernel to prevent numerical overflow. Defaults to
|
theta_tol |
A numeric value used to indicate a maximum value to theta as
used in the negative binomial probability density kernel. Defaults to
|
Value
A list of class adaptProj, with the following elements:
comm_out |
A two-level list with the top level list having number of elements equal to the number of MPMs used as input, and the lower level corresponding to the number of replicates. Each element of the lower level list is a data frame showing the number of individuals in each stage at each time. Rows and columns in the data frames correspond to stages and time steps, respectively. |
N_out |
A list with the number of elements equal to the number of replicates. Each element within this list is data frame showing the number of individuals of each species or genotype alive at each time. The number of rows are equal to the number of MPMs used, and the columns correspond to the time steps. |
stageframe_list |
A list in which each element is the stageframe for each MPM used. |
hstages_list |
A list giving the used |
agestages_list |
A list giving the used |
labels |
A small data frame giving the the population and patch identities for each MPM entered. |
err_check |
An optional list composed of an additional six lists, each
of which has the number of elements equal to the number of MPMs utilized.
List output include |
Notes
This function has been optimized in the function-based approach such that
if there are relatively few matrices required per MPM to run the projection
forward, then these matrices will be made prior to running the projection.
This approach saves time, but only if there are relatively few unique
matrices required for each MPM. If many or only unique MPMs are required at
each time step, then the matrices will be made on the fly during the
projection itself. Such a situation will most likely occur if each time
step requires a new matrix resulting from a unique individual covariate
value, or if the density_vr argument is used. The key argument
determining this behavior is prep_mats, which provides the maximum
limit for the number of matrices required per MPM in order to create
matrices prior to projection.
Examples
library(lefko3)
data(cypdata)
data(cypa_data)
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)
cycaraw_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)
cyparaw_v1 <- verticalize3(data = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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)
cyp_supp_list1 <- list(cypsupp2r, cypsupp2r)
cycamatrix2r <- rlefko2(data = cycaraw_v1, stageframe = cypframe_raw,
year = "all", patch = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cypamatrix2r <- rlefko2(data = cyparaw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cyp_mpm_list <- list(cycamatrix2r, cypamatrix2r)
cyca2_start <- start_input(cycamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(500, 100, 200))
cypa2_start <- start_input(cypamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(5000, 1000, 2000))
cyp_start_list <- list(cyca2_start, cypa2_start)
cyp2_dv <- density_input(cypamatrix2r, stage3 = c("SD", "P1"),
stage2 = c("rep", "rep"), style = c(1, 1), alpha = c(0.5, 1.2),
beta = c(1.0, 2.0), type = c(2, 1))
cyp_dv_list <- list(cyp2_dv, cyp2_dv)
cyp_comm_proj <- project3(mpms = cyp_mpm_list, starts = cyp_start_list,
density = cyp_dv_list, times = 10)
summary(cyp_comm_proj)
Summarize adaptInv Objects
Description
Function summary.adaptInv() summarizes adaptInv objects.
Usage
## S3 method for class 'adaptInv'
summary(object, ...)
Arguments
object |
An |
... |
Other parameters currently not utilized. |
Value
This function only produces text summarizing the numbers of variants, time steps, replicates, ESS optima, etc.
Examples
library(lefko3)
data(cypdata)
sizevector <- c(0, 0, 0, 0, 1, 2.5, 4.5, 8, 17.5)
stagevector <- c("SD", "P1", "SL", "D", "XSm", "Sm", "Md", "Lg", "XLg")
repvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 1, 1, 1, 1, 1, 1)
binvec <- c(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)
cypsupp2r <- supplemental(stage3 = c("SD", "P1", "SL", "D",
"XSm", "Sm", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "SL", "SL", "SL", "rep",
"rep"),
eststage3 = c(NA, NA, NA, "D", "XSm", "Sm", NA, NA),
eststage2 = c(NA, NA, NA, "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.10, 0.40, 0.25, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, 1000, 1000),
type =c(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"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
cypmean <- lmean(cypmatrix2r)
cyp_start <- start_input(cypmean, stage2 = c("SD", "P1", "D"),
value = c(1000, 200, 4))
c2d_4 <- density_input(cypmean, stage3 = c("P1", "P1"), stage2= c("SD", "rep"),
style = 2, time_delay = 1, alpha = 0.005, beta = 0.000005, type = c(2, 2))
# A simple projection allows us to find a combination of density dependence
# and running time that produces a stable quasi-equilibrium
cyp_proj <- projection3(cypmean, times = 250, start_frame = cyp_start,
density = c2d_4, integeronly = TRUE)
plot(cyp_proj)
cyp_ta <- trait_axis(stageframe = cypframe_raw,
stage3 = rep("P1", 15),
stage2 = rep("rep", 15),
multiplier = seq(from = 0.1, to = 10.0, length.out = 15),
type = rep(2, 15))
cyp_inv <- invade3(axis = cyp_ta, mpm = cypmean, density = c2d_4, times = 350,
starts = cyp_start, entry_time = c(0, 250), fitness_times = 30,
var_per_run = 2)
summary(cyp_inv)
Summarize adaptProj Objects
Description
Function summary.adaptProj() summarizes adaptProj objects.
Usage
## S3 method for class 'adaptProj'
summary(
object,
threshold = 1,
inf_alive = TRUE,
milepost = c(0, 0.25, 0.5, 0.75, 1),
ext_time = FALSE,
...
)
Arguments
object |
An |
threshold |
A threshold population size to be searched for in projections. Defaults to 1. |
inf_alive |
A logical value indicating whether to treat infinitely
large population size as indicating that the population is still extant.
If |
milepost |
A numeric vector indicating at which points in the projection
to assess detailed results. Can be input as integer values, in which case
each number must be between 1 and the total number of occasions projected in
each projection, or decimals between 0 and 1, which would then be translated
into the corresponding projection steps of the total. Defaults to
|
ext_time |
A logical value indicating whether to output extinction times
per population-patch. Defaults to |
... |
Other parameters currently not utilized. |
Value
Apart from a statement of the results, this function outputs a list with the following elements:
milepost_sums |
A data frame showing the number of replicates at each of the milepost times that is above the threshold population/patch size. |
extinction_times |
A dataframe showing the numbers of replicates going
extinct ( |
Notes
The inf_alive and ext_time options both assess whether
replicates have reached a value of NaN or Inf. If
inf_alive = TRUE or ext_time = TRUE and one of these values is
found, then the replicate is counted in the milepost_sums object if
the last numeric value in the replicate is above the threshold value,
and is counted as extant and not extinct if the last numeric value in the
replicate is above the extinction threshold of a single individual.
Extinction time is calculated on the basis of whether the replicate ever falls below a single individual. A replicate with a positive population size below 0.0 that manages to rise above 1.0 individual is still considered to have gone extinct the first time it crossed below 1.0.
If the input lefkoProj object is a mixture of two or more other
lefkoProj objects, then mileposts will be given relative to the
maximum number of time steps noted.
Examples
library(lefko3)
data(cypdata)
data(cypa_data)
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)
cycaraw_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)
cyparaw_v1 <- verticalize3(data = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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)
cyp_supp_list1 <- list(cypsupp2r, cypsupp2r)
cycamatrix2r <- rlefko2(data = cycaraw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", indivcol = "individ")
cypamatrix2r <- rlefko2(data = cyparaw_v1, stageframe = cypframe_raw,
year = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", indivcol = "individ")
cyp_mpm_list <- list(cycamatrix2r, cypamatrix2r)
cyca2_start <- start_input(cycamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(500, 100, 200))
cypa2_start <- start_input(cypamatrix2r, stage2 = c("SD", "P1", "P2"),
value = c(5000, 1000, 2000))
cyp_start_list <- list(cyca2_start, cypa2_start)
cyp2_dv <- density_input(cypamatrix2r, stage3 = c("SD", "P1"),
stage2 = c("rep", "rep"), style = c(1, 1), alpha = c(0.5, 1.2),
beta = c(1.0, 2.0), type = c(2, 1))
cyp_dv_list <- list(cyp2_dv, cyp2_dv)
cyp_comm_proj <- project3(mpms = cyp_mpm_list, starts = cyp_start_list,
density = cyp_dv_list, times = 10)
summary(cyp_comm_proj)
Create Skeleton Data Frame for Trait Variation for Invasion Analysis
Description
Function ta_skeleton() creates a core data frame that can be modified
by users to provide the core variation in transition elements and vital
rates to use in invasion analysis. The resulting data frame should be used
as input in function invade3().
Usage
ta_skeleton(rows = 10L)
Arguments
rows |
The number of rows needed in the data frame. Defaults to 10. |
Value
A data frame of class adaptAxis, with the following columns:
variant |
Denotes each variant in order, with each row corresponding to a novel variant. |
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. |
age3 |
Age at occasion t+1 in the transition to be replaced. |
age2 |
Age at occasion t in the transition to be replaced. |
eststage3 |
Stage at occasion t+1 in the transition to replace
the transition designated by |
eststage2 |
Stage at occasion t in the transition to replace the
transition designated by |
eststage1 |
Stage at occasion t-1 in the transition to replace
the transition designated by |
estage3 |
Age at occasion t+1 in the transition to replace the
transition designated by |
estage2 |
Age at occasion t in the transition to replace the
transition designated by |
givenrate |
A constant to be used as the value of the transition. |
offset |
A constant value to be added to the transition or proxy transition. |
multiplier |
A multiplier for proxy transitions or for fecundity. |
convtype |
Designates whether the transition from occasion t to occasion t+1 is a survival transition probability (1), a fecundity rate (2), or a fecundity multiplier (3). |
convtype_t12 |
Designates whether the transition from occasion t-1 to occasion t is a survival transition probability (1), a fecundity rate (2). |
surv_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for survival probability. |
obs_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for observation probability. |
size_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for primary size transition. |
sizeb_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for secondary size transition. |
sizec_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for tertiary size transition. |
repst_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for reproduction probability. |
fec_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for fecundity. |
jsurv_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile survival probability. |
jobs_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile observation probability. |
jsize_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile primary size transition. |
jsizeb_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile secondary size transition. |
jsizec_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile tertiary size transition. |
jrepst_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for juvenile reproduction probability. |
jmatst_dev |
A numeric vector giving the deviations to the y-intercept of the vital rate model for maturity status. |
Examples
current_traits <- ta_skeleton(4)
current_traits$stage3 <- c("Dorm", "Dorm", "Sdl1", NA)
current_traits$stage2 <- c("cut", "V0r", "rep", NA)
current_traits$convtype <- c(1, 1, 2, NA)
current_traits$offset <- c(0.1, 0.2, 0.3, NA)
current_traits$surv_dev <- c(NA, NA, NA, 0.1)
Create a Data Frame of Trait Data for Invasion Analysis
Description
Function trait_axis() provides all necessary data for invasion
analysis. It lists the specific variations to MPMs for each variant run.
Variants can be given via overwritten matrix elements, proxy matrix
elements, additive offsets on matrix elements, matrix element multipliers,
and additive offsets to y-intercepts in vital rate models.
Usage
trait_axis(
historical = NULL,
stagebased = NULL,
agebased = NULL,
stageframe = NULL,
stage3 = NULL,
stage2 = NULL,
stage1 = NULL,
age3 = NULL,
age2 = NULL,
eststage3 = NULL,
eststage2 = NULL,
eststage1 = NULL,
estage3 = NULL,
estage2 = NULL,
givenrate = NULL,
offset = NULL,
multiplier = NULL,
type = NULL,
type_t12 = NULL,
surv_dev = NULL,
obs_dev = NULL,
size_dev = NULL,
sizeb_dev = NULL,
sizec_dev = NULL,
repst_dev = NULL,
fec_dev = NULL,
jsurv_dev = NULL,
jobs_dev = NULL,
jsize_dev = NULL,
jsizeb_dev = NULL,
jsizec_dev = NULL,
jrepst_dev = NULL,
jmatst_dev = NULL
)
Arguments
historical |
A single logical value indicating whether the MPMs
intended will be historical or ahistorical. Defaults to |
stagebased |
A single logical value indicating whether the MPM will be
stage-based or age-by-stage. Defaults to |
agebased |
A single logical value indicating whether the MPM will be
age-based or age-by-stage. Defaults to |
stageframe |
The stageframe used to produce the MPM. Required if producing any stage-based or age-by-stage MPM. Must be omitted for purely age-based MPMs. |
stage3 |
String vector of stage names in occasion t+1 in the
transition to be affected. Abbreviations for groups of stages are also
usable (see |
stage2 |
String vector of stage names in occasion t in the
transition to be affected. Abbreviations for groups of stages are also
usable (see |
stage1 |
String vector of stage names in occasion t-1 in the
transition to be affected. Only needed if a historical matrix is to be
produced. Abbreviations for groups of stages are also usable (see
|
age3 |
An integer vector of the ages in occasion t+1 to use in transitions to be affected. Required for all age- and age-by-stage MPMs. |
age2 |
An integer vector of the ages in occasion t to use in transitions to be affected. Required for all age- and age-by-stage MPMs. |
eststage3 |
String vector of stage names to replace |
eststage2 |
String vector of stage names to replace |
eststage1 |
String vector of stage names to replace |
estage3 |
Integer vector of age at time t+1 to replace
|
estage2 |
Integer vector of age at time t to replace |
givenrate |
A numeric vector of fixed rates or probabilities to replace
for the transition described by |
offset |
A numeric vector of fixed numeric values to add to the
transitions described by |
multiplier |
A numeric vector of multipliers for the transition
described by |
type |
Integer vector denoting the kind of transition between occasions
t and t+1 to be replaced. This should be entered as |
type_t12 |
An optional integer 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 |
surv_dev |
An optional vector of numeric deviations to the y-intercept
of the survival model used in function-based MPM creation. Defaults to
|
obs_dev |
An optional vector of numeric deviations to the y-intercept
of the observation model used in function-based MPM creation. Defaults to
|
size_dev |
An optional vector of numeric deviations to the y-intercept
of the primary size model used in function-based MPM creation. Defaults to
|
sizeb_dev |
An optional vector of numeric deviations to the y-intercept
of the secondary size model used in function-based MPM creation. Defaults to
|
sizec_dev |
An optional vector of numeric deviations to the y-intercept
of the tertiary size model used in function-based MPM creation. Defaults to
|
repst_dev |
An optional vector of numeric deviations to the y-intercept
of the reproduction model used in function-based MPM creation. Defaults to
|
fec_dev |
An optional vector of numeric deviations to the y-intercept
of the fecundity model used in function-based MPM creation. Defaults to
|
jsurv_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile survival model used in function-based MPM creation. Defaults
to |
jobs_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile observation model used in function-based MPM creation.
Defaults to |
jsize_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile primary size model used in function-based MPM creation.
Defaults to |
jsizeb_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile secondary size model used in function-based MPM creation.
Defaults to |
jsizec_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile tertiary size model used in function-based MPM creation.
Defaults to |
jrepst_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile reproduction model used in function-based MPM creation.
Defaults to |
jmatst_dev |
An optional vector of numeric deviations to the y-intercept
of the juvenile maturity model used in function-based MPM creation.
Defaults to |
Value
A data frame of class adaptAxis. This object can be used as
input in function invade3().
Variables in this object include the following:
variant |
Denotes each variant in order, with each row corresponding to a novel variant. |
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. |
age3 |
Age at occasion t+1 in the transition to be replaced. |
age2 |
Age at occasion t in the transition to be replaced. |
eststage3 |
Stage at occasion t+1 in the transition to replace
the transition designated by |
eststage2 |
Stage at occasion t in the transition to replace the
transition designated by |
eststage1 |
Stage at occasion t-1 in the transition to replace
the transition designated by |
estage3 |
Age at occasion t+1 in the transition to replace the
transition designated by |
estage2 |
Age at occasion t in the transition to replace the
transition designated by |
givenrate |
A constant to be used as the value of the transition. |
offset |
A constant value to be added to the transition or proxy transition. |
multiplier |
A multiplier for proxy transitions or for fecundity. |
convtype |
Designates whether the transition from occasion t to occasion t+1 is a survival transition probability (1), a fecundity rate (2), or a fecundity multiplier (3). |
convtype_t12 |
Designates whether the transition from occasion t-1 to occasion t is a survival transition probability (1), a fecundity rate (2). |
surv_dev |
Numeric deviations to the y-intercept of the vital rate model of survival. |
obs_dev |
Numeric deviations to the y-intercept of the vital rate model of observation. |
size_dev |
Numeric deviations to the y-intercept of the vital rate model of primary size. |
sizeb_dev |
Numeric deviations to the y-intercept of the vital rate model of secondary size. |
sizec_dev |
Numeric deviations to the y-intercept of the vital rate model of tertiary size. |
repst_dev |
Numeric deviations to the y-intercept of the vital rate model of reproduction. |
fec_dev |
Numeric deviations to the y-intercept of the vital rate model of fecundity. |
jsurv_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile survival. |
jobs_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile observation. |
jsize_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile primary size. |
jsizeb_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile secondary size. |
jsizec_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile tertiary size. |
jrepst_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile reproduction. |
jmatst_dev |
Numeric deviations to the y-intercept of the vital rate model of juvenile maturity. |
Notes
Negative values are not allowed in givenrate and multiplier
input, but are allowed in offset, if values are to be subtracted from
specific estimated transitions. Stage entries should not be used for purely
age-based MPMs, and age entries should not be used for purely stage-based
MPMs.
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. Also use groupX to denote all
stages in group X (e.g. group1 will use all stages in the respective
stageframe's group 1).
Type 3 conversions are referred to as fecundity set values, or general
fecundity multipliers. These set the transitions to be used as fecundity
transitions. Transitions set here will be interpreted as being generally
reproductive, meaning that the from and to stages will be used to determine
the general fecundity transitions to incorporate into stage-based MPMs,
while the age portion of the input will be used to incorporate the actual
multiplier(s) specified. If only stage transitions at certain ages are
expected to be the sole contributors to fecundity, then type 2 conversions
should also be included in the supplement (Type 1 and 2 conversions can be
purely age-specific, and do not set reproductive transitions in MPM
creation). For example, if all stage 2 to stage 3 transitions above age 2
yield fecundity, then stage 2 to stage 3 can be set to
multiplier = 1.0 with convtype = 3, and the same transition
for age2 = c(1, 2) can be set to multiplier = c(0, 0).
Several operations may be included per transition. Operations on the same row of the resulting data frame are generally handled with given rate substitutions first, then with proxy transitions, then by additive offsets, and finally by multipliers. This order can be manipulated by ordering operations across rows, with higher numbered rows in the data frame being performed later.
See Also
Examples
library(lefko3)
data(cypa_data)
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 = cypa_data, noyears = 18, firstyear = 1994,
individcol = "plant_id", blocksize = 2, sizeacol = "Inf.94",
sizebcol = "Veg.94", repstracol = "Inf.94", fecacol = "Inf.94",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
cypa_ta <- trait_axis(stageframe = cypframe_raw,
stage3 = c("P1", "P1", "P1", NA, NA, NA),
stage2 = c("rep", "rep", "rep", NA, NA, NA),
multiplier = c(0.5, 2.0, 10., NA, NA, NA), type = c(2, 2, 2, NA, NA, NA),
obs_dev = c(NA, NA, NA, 0.5, 2.0, 50), fec_dev = c(NA, NA, NA, -1000, 0, 1000))