elasticity3.lefkoMat | R Documentation |

`elasticity3.lefkoMat()`

returns the elasticities of population growth
rate to elements of all `$A`

matrices in an object of class
`lefkoMat`

. If deterministic, then `\lambda`

is taken as the
population growth rate. If stochastic, then stochastic `\lambda`

, or
the stochastic growth rate, is taken as the population growth rate. This
function can handle large and sparse matrices, and so can be used with large
historical matrices, IPMs, age x stage matrices, as well as smaller
ahistorical matrices.

```
## S3 method for class 'lefkoMat'
elasticity3(
mats,
stochastic = FALSE,
steps = 10000,
time_weights = NA,
force_sparse = "auto",
append_mats = FALSE,
...
)
```

`mats` |
An object of class |

`stochastic` |
A logical value determining whether to conduct a deterministic (FALSE) or stochastic (TRUE) elasticity analysis. Defaults to FALSE. |

`steps` |
The number of occasions to project forward in stochastic simulation. Defaults to 10,000. |

`time_weights` |
Numeric vector denoting the probabilistic weightings of annual matrices. Defaults to equal weighting among occasions. |

`force_sparse` |
A text string indicating whether to use sparse matrix
encoding ( |

`append_mats` |
A logical value indicating whether to include the original
A, U, and F matrices in the output |

`...` |
Other parameters. |

This function returns an object of class `lefkoElas`

, which is a
list with 8 elements. The first, `h_elasmats`

, is a list of historical
elasticity matrices (`NULL`

if an ahMPM is used as input). The second,
`ah_elasmats`

, is a list of either ahistorical elasticity matrices if an
ahMPM is used as input, or, if an hMPM is used as input, then the result is a
list of elasticity matrices in which historical elasticities have been summed
by the stage in occasions *t* and *t*+1 to produce
historically-corrected elasticity matrices, which are equivalent in dimension
to ahistorical elasticity matrices but reflect the effects of stage in
occasion *t*-1. The third element, `hstages`

, is a data frame
showing historical stage pairs (NULL if ahMPM used as input). The fourth
element, `agestages`

, shows age-stage combinations in the order used in
age-by-stage MPMs, if suppled. The fifth element, `ahstages`

, is a data
frame showing the order of ahistorical stages. The last 3 elements are the A,
U, and F portions of the input.

Deterministic elasticities are estimated as eqn. 9.72 in Caswell (2001,
Matrix Population Models). Stochastic elasticities are estimated as eqn.
14.99 in Caswell (2001). Note that stochastic elasticities are of the
stochastic `\lambda`

, while stochastic sensitivities are with regard to
the log of the stochastic `\lambda`

.

Speed can sometimes be increased by shifting from automatic sparse matrix determination to forced dense or sparse matrix projection. This will most likely occur when matrices have between 30 and 300 rows and columns. Defaults work best when matrices are very small and dense, or very large and sparse.

`elasticity3()`

`elasticity3.dgCMatrix()`

`elasticity3.matrix()`

`elasticity3.list()`

`summary.lefkoElas()`

```
# Lathyrus example
data(lathyrus)
sizevector <- c(0, 100, 13, 127, 3730, 3800, 0)
stagevector <- c("Sd", "Sdl", "VSm", "Sm", "VLa", "Flo", "Dorm")
repvector <- c(0, 0, 0, 0, 0, 1, 0)
obsvector <- c(0, 1, 1, 1, 1, 1, 0)
matvector <- c(0, 0, 1, 1, 1, 1, 1)
immvector <- c(1, 1, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 100, 11, 103, 3500, 3800, 0.5)
lathframe <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
immstatus = immvector, indataset = indataset, binhalfwidth = binvec,
propstatus = propvector)
lathvert <- verticalize3(lathyrus, noyears = 4, firstyear = 1988,
patchidcol = "SUBPLOT", individcol = "GENET", blocksize = 9,
juvcol = "Seedling1988", sizeacol = "Volume88", repstracol = "FCODE88",
fecacol = "Intactseed88", deadacol = "Dead1988",
nonobsacol = "Dormant1988", stageassign = lathframe, stagesize = "sizea",
censorcol = "Missing1988", censorkeep = NA, censor = TRUE)
lathsupp3 <- supplemental(stage3 = c("Sd", "Sd", "Sdl", "Sdl", "Sd", "Sdl", "mat"),
stage2 = c("Sd", "Sd", "Sd", "Sd", "rep", "rep", "Sdl"),
stage1 = c("Sd", "rep", "Sd", "rep", "npr", "npr", "Sd"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "mat"),
eststage2 = c(NA, NA, NA, NA, NA, NA, "Sdl"),
eststage1 = c(NA, NA, NA, NA, NA, NA, "NotAlive"),
givenrate = c(0.345, 0.345, 0.054, 0.054, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, 0.345, 0.054, NA),
type = c(1, 1, 1, 1, 3, 3, 1), type_t12 = c(1, 2, 1, 2, 1, 1, 1),
stageframe = lathframe, historical = TRUE)
ehrlen3 <- rlefko3(data = lathvert, stageframe = lathframe, year = "all",
stages = c("stage3", "stage2", "stage1"), supplement = lathsupp3,
yearcol = "year2", indivcol = "individ")
elasticity3(ehrlen3, stochastic = TRUE)
# Cypripedium example
data(cypdata)
sizevector <- c(0, 0, 0, 0, 0, 0, 1, 2.5, 4.5, 8, 17.5)
stagevector <- c("SD", "P1", "P2", "P3", "SL", "D", "XSm", "Sm", "Md", "Lg",
"XLg")
repvector <- c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 0, 0, 0, 0, 0.5, 0.5, 1, 1, 2.5, 7)
cypframe_raw <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
propstatus = propvector, immstatus = immvector, indataset = indataset,
binhalfwidth = binvec)
cypraw_v1 <- verticalize3(data = cypdata, noyears = 6, firstyear = 2004,
patchidcol = "patch", individcol = "plantid", blocksize = 4,
sizeacol = "Inf2.04", sizebcol = "Inf.04", sizeccol = "Veg.04",
repstracol = "Inf.04", repstrbcol = "Inf2.04", fecacol = "Pod.04",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE)
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", patch = "all", stages = c("stage3", "stage2", "stage1"),
size = c("size3added", "size2added"), supplement = cypsupp2r,
yearcol = "year2", patchcol = "patchid", indivcol = "individ")
elasticity3(cypmatrix2r)
```

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