Supplement 1. R code for simulation implementation and parameter estimation.

File List EstimationComparison.R (MD5: 5055e25ebc61fe8dbf012b48198eadda) Simulations.R (MD5: 56eef6b34cb59a85d5072b0b20e645ec) CreateFigures.R (MD5: 2c19a14d1ac5887ba544c2937d8639ca) Description EstimationComparison.R - This code was used to simulate time-series of length 30 time-step and either 1, 2, or 3 replicated observations at each time-step. Parameters were then estimated using three different methodologies: restricted maximum likelihood (REML) based on first differences, REML based on second differences and maximum likelihood using the Kalman filter, as implemented in the MARSS R package. Simulations.R - This code was used to simulate time-series of varying length, with varying numbers of replicated observations, under two different rates of decline and several different process and non-process error variances. Estimates of trend, process and non-process error variances were then made with the MARSS R package. CreateFigures.R - This code was used to create the figures that appear in the manuscript and appendices.