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:
Here are plots of blue- and red-noise populations generated by the
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)
matrix_modelnow has more options for dealing with survival values erroneously set to >1.
colorednoiseno longer depends on the deprecated package
colorednoisecan now execute matrix population models with the
matrix_modelfunction, along with its helper functions
timeseriesfunctions in Rcpp.
timeseriesto take separate autocorrelation values for survival and fertility.
timeseriesnow reliably matches the input variance.