The reprex below simplifies the code and explains what it does.
library(popdemo)
#> Welcome to popdemo! This is version 1.3-0
#> Use ?popdemo for an intro, or browseVignettes('popdemo') for vignettes
#> Citation for popdemo is here: doi.org/10.1111/j.2041-210X.2012.00222.x
#> Development and legacy versions are here: github.com/iainmstott/popdemo
dat <- data.frame(
row.names = c("N1", "N2", "N3", "N4", "N5", "N6"),
N1 = c(0, 0.369, 0, 0, 0, 0),
N2 = c(0, 0, 0.232, 0, 0, 0),
N3 = c(0, 0, 0, 0.207, 0, 0),
N4 = c(0, 0, 0, 0, 0.047, 0),
N5 = c(0, 0, 0, 0, 0, 0.042),
N6 = c(2082, 0, 0, 0, 0, 0.32)
)
delta <- seq(0, 4*dat[1, 6], 0.1)
data_delta <- dat
lambda_delta <- numeric(length(delta))
for(i in 1:length(delta)){
data_delta[1, 6] <- dat[1, 6] + delta[i]
lambda_delta[i] <- eigs(data_delta, "lambda")
}
plot(delta, lambda_delta, type = "l")

This reflects the fecundity value at N1,N6 multiplied by 4 and incremented by 0.1 to show and increase of \lambda as the eigenvectors climb.
§6.1 of the vignette shows how to do a sensitivity analysis of the same data
library(popdemo)
#> Welcome to popdemo! This is version 1.3-0
#> Use ?popdemo for an intro, or browseVignettes('popdemo') for vignettes
#> Citation for popdemo is here: doi.org/10.1111/j.2041-210X.2012.00222.x
#> Development and legacy versions are here: github.com/iainmstott/popdemo
dat <- data.frame(
row.names = c("N1", "N2", "N3", "N4", "N5", "N6"),
N1 = c(0, 0.369, 0, 0, 0, 0),
N2 = c(0, 0, 0.232, 0, 0, 0),
N3 = c(0, 0, 0, 0.207, 0, 0),
N4 = c(0, 0, 0, 0, 0.047, 0),
N5 = c(0, 0, 0, 0, 0, 0.042),
N6 = c(2082, 0, 0, 0, 0, 0.32)
)
tfsm_inertia(as.matrix(dat), bound = "lower", tolerance = 1e-6)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.0000000 0.00000000 0.00000000 0.0000000 0.0000000 -6.573952e-06
#> [2,] 0.2560898 0.00000000 0.00000000 0.0000000 0.0000000 0.000000e+00
#> [3,] 0.0000000 0.08016566 0.00000000 0.0000000 0.0000000 0.000000e+00
#> [4,] 0.0000000 0.00000000 -0.02935737 0.0000000 0.0000000 0.000000e+00
#> [5,] 0.0000000 0.00000000 0.00000000 -0.2815965 0.0000000 0.000000e+00
#> [6,] 0.0000000 0.00000000 0.00000000 0.0000000 -0.3263449 -2.072519e-01