Temporally autocorrelated populations are correlated in their vital rates (growth, death, etc.) from year to year. It is very common for populations, whether they be bacteria, plants, or humans, to be temporally autocorrelated. This poses a challenge for stochastic population modeling, because a temporally correlated population will behave differently from an uncorrelated one.
This package provides tools for simulating populations with white noise (no temporal autocorrelation), red noise (positive temporal autocorrelation), and blue noise (negative temporal autocorrelation). The algebraic formulation for autocorrelated noise comes from Ruokolainen et al. (2009)

Many populations that change over time are *temporally autocorrelated*,
which means that the random noise in each timestep is correlated to that
of the previous timestep. Instead of uncorrelated white noise, these
populations are governed by blue noise (negatively autocorrelated) or
red noise (positively autocorrelated.)

The colorednoise package allows you to simulate colored noise as well as populations whose behavior is governed by colored noise.

You can install the latest version of colorednoise from github with:

devtools::install_github("japilo/colorednoise")

Here are plots of blue- and red-noise populations generated by the
`matrix_model`

function.

library(colorednoise)set.seed(7927)pop_blue <- matrix_model(data = list(mean = matrix(c(0.6687097, 0.2480645, 0.6687097, 0.4335484), ncol=2),sd = matrix(c(0.34437133, 0.08251947, 0.34437133, 0.10898160), ncol=2),autocorrelation = matrix(rep(-0.4, 4), ncol=2)), timesteps = 100, initialPop = c(100, 100))pop_red <- matrix_model(data = list(mean = matrix(c(0.6687097, 0.2480645, 0.6687097, 0.4335484), ncol=2),sd = matrix(c(0.34437133, 0.08251947, 0.34437133, 0.10898160), ncol=2),autocorrelation = matrix(rep(0.4, 4), ncol=2)), timesteps = 100, initialPop = c(100, 100))ggplot(pop_blue, aes(x = timestep, y = total)) + geom_line(col="blue") + ylim(0, 6000)

ggplot(pop_red, aes(x = timestep, y = total)) + geom_line(col="red") + ylim(0, 6000)

- Updated to be compatible with tibble v2.0.0

`matrix_model`

now has more options for dealing with survival values erroneously set to >1.

- The Makevars have been tweaked so the package runs on more operating systems and compilers.
`colorednoise`

no longer depends on the deprecated package`purrrlyr`

.

`colorednoise`

can now execute matrix population models with the`matrix_model`

function, along with its helper functions`colored_multi_rnorm`

,`multi_rnorm`

, and`cor2cov`

.- Renamed
`raw_noise`

to`colored_noise`

and`timeseries`

to`unstructured_pop`

. - The package now has a more extensive testing suite.

- Recoded the
`raw_noise`

and`timeseries`

functions in Rcpp. - Changed
`timeseries`

to take separate autocorrelation values for survival and fertility. - The output variance of survival probabilities in
`timeseries`

now reliably matches the input variance.