Add sampling error to matrix population models (MPMs) based on expected values of transition rates and sample sizes
Source:R/add_mpm_error.R
add_mpm_error.RdProduces a list of matrix population models based on expected values in the
transition matrix and sample size. The expected values are provided in lists
of two submatrices: mat_U for the growth/development and survival
transitions and mat_F for the reproductive transitions. The output mat_U
values are simulated based on expected probabilities, assuming a binomial
process with a sample size defined by sample_size. The output mat_F
values are simulated using a Poisson process with a sample size defined by
sample_size.Thus users can expect that large sample sizes will result in
simulated matrices that match closely with the expectations, while simulated
matrices with small sample sizes will be more variable.
Arguments
- mat_U
A list of U submatrices, or a single U submatrix.
- mat_F
A list of F submatrices, or a single F submatrix.
- sample_size
either (1) a single matrix of sample sizes for each element of every MPM, (2) a list of two named matrices ("
mat_F_ss", "mat_U_ss") containing sample sizes for the survival and reproductive output submatrices of every MPM or (3) a single value applied to the every element of every matrix.- split
logical, whether to split the output into survival and reproductive output matrices or not. Defaults to
TRUE.- by_type
A logical indicating whether the matrices should be returned in a list by type (A, U, F, C). If split is
FALSE, thenby_typemust also beFALSE. Defaults toTRUE.
Value
list of matrices of survival and reproductive output if split = TRUE, otherwise a single matrix of the sum of survival and reproductive
output.
Details
if any sample_size input is 0, it is assumed that the estimate for
the element(s) concerned is known without error.
See also
Other errors:
calculate_errors(),
compute_ci(),
compute_ci_U()
Other errors:
calculate_errors(),
compute_ci(),
compute_ci_U()
Author
Owen Jones jones@biology.sdu.dk
Examples
set.seed(42) # set seed for repeatability
# First generate a set of MPMs
mpm_set <- rand_lefko_set(n = 5, n_stages = 5, fecundity = c(
0, 0, 4, 8, 10
), archetype = 4, output = "Type4")
# Now apply sampling error to this set
add_mpm_error(
mat_U = mpm_set$U_list, mat_F = mpm_set$F_list, sample_size =
50
)
#> $A_list
#> $A_list[[1]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.04 0.00 4.16 7.36 9.92
#> [2,] 0.40 0.38 0.00 0.00 0.00
#> [3,] 0.00 0.00 0.20 0.00 0.00
#> [4,] 0.00 0.00 0.44 0.42 0.00
#> [5,] 0.00 0.00 0.00 0.32 0.94
#>
#> $A_list[[2]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.02 0.00 3.88 8.14 11.38
#> [2,] 0.32 0.38 0.00 0.00 0.00
#> [3,] 0.00 0.02 0.64 0.00 0.00
#> [4,] 0.00 0.00 0.04 0.38 0.00
#> [5,] 0.00 0.00 0.00 0.32 0.76
#>
#> $A_list[[3]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5 0.00 4.34 8.06 9.58
#> [2,] 0.0 0.56 0.00 0.00 0.00
#> [3,] 0.0 0.20 0.38 0.00 0.00
#> [4,] 0.0 0.00 0.38 0.20 0.00
#> [5,] 0.0 0.00 0.00 0.68 1.00
#>
#> $A_list[[4]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.26 0.00 3.66 8.24 9.34
#> [2,] 0.00 0.00 0.00 0.00 0.00
#> [3,] 0.00 0.38 0.06 0.00 0.00
#> [4,] 0.00 0.00 0.36 0.14 0.00
#> [5,] 0.00 0.00 0.00 0.58 0.88
#>
#> $A_list[[5]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.20 0.00 4.24 7.44 9.80
#> [2,] 0.26 0.46 0.00 0.00 0.00
#> [3,] 0.00 0.08 0.70 0.00 0.00
#> [4,] 0.00 0.00 0.04 0.10 0.00
#> [5,] 0.00 0.00 0.00 0.58 0.78
#>
#>
#> $U_list
#> $U_list[[1]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.04 0.00 0.00 0.00 0.00
#> [2,] 0.40 0.38 0.00 0.00 0.00
#> [3,] 0.00 0.00 0.20 0.00 0.00
#> [4,] 0.00 0.00 0.44 0.42 0.00
#> [5,] 0.00 0.00 0.00 0.32 0.94
#>
#> $U_list[[2]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.02 0.00 0.00 0.00 0.00
#> [2,] 0.32 0.38 0.00 0.00 0.00
#> [3,] 0.00 0.02 0.64 0.00 0.00
#> [4,] 0.00 0.00 0.04 0.38 0.00
#> [5,] 0.00 0.00 0.00 0.32 0.76
#>
#> $U_list[[3]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5 0.00 0.00 0.00 0
#> [2,] 0.0 0.56 0.00 0.00 0
#> [3,] 0.0 0.20 0.38 0.00 0
#> [4,] 0.0 0.00 0.38 0.20 0
#> [5,] 0.0 0.00 0.00 0.68 1
#>
#> $U_list[[4]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.26 0.00 0.00 0.00 0.00
#> [2,] 0.00 0.00 0.00 0.00 0.00
#> [3,] 0.00 0.38 0.06 0.00 0.00
#> [4,] 0.00 0.00 0.36 0.14 0.00
#> [5,] 0.00 0.00 0.00 0.58 0.88
#>
#> $U_list[[5]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.20 0.00 0.00 0.00 0.00
#> [2,] 0.26 0.46 0.00 0.00 0.00
#> [3,] 0.00 0.08 0.70 0.00 0.00
#> [4,] 0.00 0.00 0.04 0.10 0.00
#> [5,] 0.00 0.00 0.00 0.58 0.78
#>
#>
#> $F_list
#> $F_list[[1]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 4.16 7.36 9.92
#> [2,] 0 0 0.00 0.00 0.00
#> [3,] 0 0 0.00 0.00 0.00
#> [4,] 0 0 0.00 0.00 0.00
#> [5,] 0 0 0.00 0.00 0.00
#>
#> $F_list[[2]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 3.88 8.14 11.38
#> [2,] 0 0 0.00 0.00 0.00
#> [3,] 0 0 0.00 0.00 0.00
#> [4,] 0 0 0.00 0.00 0.00
#> [5,] 0 0 0.00 0.00 0.00
#>
#> $F_list[[3]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 4.34 8.06 9.58
#> [2,] 0 0 0.00 0.00 0.00
#> [3,] 0 0 0.00 0.00 0.00
#> [4,] 0 0 0.00 0.00 0.00
#> [5,] 0 0 0.00 0.00 0.00
#>
#> $F_list[[4]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 3.66 8.24 9.34
#> [2,] 0 0 0.00 0.00 0.00
#> [3,] 0 0 0.00 0.00 0.00
#> [4,] 0 0 0.00 0.00 0.00
#> [5,] 0 0 0.00 0.00 0.00
#>
#> $F_list[[5]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 4.24 7.44 9.8
#> [2,] 0 0 0.00 0.00 0.0
#> [3,] 0 0 0.00 0.00 0.0
#> [4,] 0 0 0.00 0.00 0.0
#> [5,] 0 0 0.00 0.00 0.0
#>
#>
# Also works with a single matrix.
mats <- make_leslie_mpm(
survival = c(0.1, 0.2, 0.5),
fecundity = c(0, 1.2, 2.4),
n_stages = 3, split = TRUE
)
# Sample size is a single value
add_mpm_error(mat_U = mats$mat_U, mat_F = mats$mat_F, sample_size = 20)
#> $mat_A
#> [,1] [,2] [,3]
#> [1,] 0.0 1.0 2.50
#> [2,] 0.1 0.0 0.00
#> [3,] 0.0 0.2 0.45
#>
#> $mat_U
#> [,1] [,2] [,3]
#> [1,] 0.0 0.0 0.00
#> [2,] 0.1 0.0 0.00
#> [3,] 0.0 0.2 0.45
#>
#> $mat_F
#> [,1] [,2] [,3]
#> [1,] 0 1 2.5
#> [2,] 0 0 0.0
#> [3,] 0 0 0.0
#>
# Sample size is a list of two matrices
# here with a sample size of 20 for fecundity and 10 for growth/survival.
mpm_set <- rand_lefko_set(
n = 5, n_stages = 3, fecundity = c(0, 2, 4),
archetype = 4, output = "Type4"
)
ssMats <- list(
"mat_F_ss" = matrix(20, nrow = 3, ncol = 3),
"mat_U_ss" = matrix(10, nrow = 3, ncol = 3)
)
# Add sampling error to the matrix models
output <- add_mpm_error(
mat_U = mpm_set$U_list, mat_F = mpm_set$F_list,
sample_size = ssMats
)
# Examine the outputs
names(output)
#> [1] "A_list" "U_list" "F_list"
output
#> $A_list
#> $A_list[[1]]
#> [,1] [,2] [,3]
#> [1,] 0.3 1.5 4.1
#> [2,] 0.1 0.3 0.0
#> [3,] 0.0 0.5 1.0
#>
#> $A_list[[2]]
#> [,1] [,2] [,3]
#> [1,] 0.5 2.2 4.25
#> [2,] 0.2 0.5 0.00
#> [3,] 0.0 0.3 0.70
#>
#> $A_list[[3]]
#> [,1] [,2] [,3]
#> [1,] 0.0 1.9 4.15
#> [2,] 0.9 0.7 0.00
#> [3,] 0.0 0.0 1.00
#>
#> $A_list[[4]]
#> [,1] [,2] [,3]
#> [1,] 0.5 1.45 3.7
#> [2,] 0.2 0.40 0.0
#> [3,] 0.0 0.40 1.0
#>
#> $A_list[[5]]
#> [,1] [,2] [,3]
#> [1,] 0.7 1.9 3.8
#> [2,] 0.1 0.6 0.0
#> [3,] 0.0 0.4 1.0
#>
#>
#> $U_list
#> $U_list[[1]]
#> [,1] [,2] [,3]
#> [1,] 0.3 0.0 0
#> [2,] 0.1 0.3 0
#> [3,] 0.0 0.5 1
#>
#> $U_list[[2]]
#> [,1] [,2] [,3]
#> [1,] 0.5 0.0 0.0
#> [2,] 0.2 0.5 0.0
#> [3,] 0.0 0.3 0.7
#>
#> $U_list[[3]]
#> [,1] [,2] [,3]
#> [1,] 0.0 0.0 0
#> [2,] 0.9 0.7 0
#> [3,] 0.0 0.0 1
#>
#> $U_list[[4]]
#> [,1] [,2] [,3]
#> [1,] 0.5 0.0 0
#> [2,] 0.2 0.4 0
#> [3,] 0.0 0.4 1
#>
#> $U_list[[5]]
#> [,1] [,2] [,3]
#> [1,] 0.7 0.0 0
#> [2,] 0.1 0.6 0
#> [3,] 0.0 0.4 1
#>
#>
#> $F_list
#> $F_list[[1]]
#> [,1] [,2] [,3]
#> [1,] 0 1.5 4.1
#> [2,] 0 0.0 0.0
#> [3,] 0 0.0 0.0
#>
#> $F_list[[2]]
#> [,1] [,2] [,3]
#> [1,] 0 2.2 4.25
#> [2,] 0 0.0 0.00
#> [3,] 0 0.0 0.00
#>
#> $F_list[[3]]
#> [,1] [,2] [,3]
#> [1,] 0 1.9 4.15
#> [2,] 0 0.0 0.00
#> [3,] 0 0.0 0.00
#>
#> $F_list[[4]]
#> [,1] [,2] [,3]
#> [1,] 0 1.45 3.7
#> [2,] 0 0.00 0.0
#> [3,] 0 0.00 0.0
#>
#> $F_list[[5]]
#> [,1] [,2] [,3]
#> [1,] 0 1.9 3.8
#> [2,] 0 0.0 0.0
#> [3,] 0 0.0 0.0
#>
#>