Supplement 1. R program to calculate maximum-likelihood or restricted maximum-likelihood estimates of model parameters, as well as to calculate and plot profile log-likelihoods, for the Gompertz state-space models with replicated sampling.
The computer program, in the open-source R language (R Core Development Team. 2006. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria), uses numerical maximization of a multivariate-normal log-likelihood to compute maximum-likelihood and restricted maximum-likelihood parameter estimates for the Gompertz state-space model of density dependent population growth, for time series abundance data with replicated samples at each observation time. The program also computes and plots profile log-likelihoods for the four model parameters. The data included in the program as an example are the simulated observations appearing in the top panel of Fig. 1 of the main article, and the program was used to produce Fig. 2 in the same paper.
Dennis_etal_Gompertz_state_space_model_with_replicated_sampling.R contains annotated code for fitting a stochastic, density-dependent population growth model to time series abundance data in which samples have been replicated at each sampling time.