## Supplement 1. R scripts for calculating maximum likelihood estimates, restricted maximum likelihood estimates, and parametric bootstrap likelihood ratio tests of density dependence, for the Ornstein-Uhlenbeck state-space model, using population-abundance data having possibly unequal observation time intervals.

## File List

RUNNING-ROUSS.R (MD5: c07b061d09a71a54d0a0f70844ef9d77)

RUNNING-PBLRT.R (MD5: f786fefc7684bd3bd099a1f682babaa5)

ROUSSE-1.0.R (MD5: d3ced6b948020ce1231da2262e3f0648)

## Description

This supplement contains three R scripts: (1) RUNNING-ROUSS.R calculates maximum likelihood and restricted maximum likelihood estimates for the Ornstein Uhlenbeck state space model (stationary and non-stationary), using population-abundance data having possibly unequal observation time intervals. (2) RUNNING-PBLRT.R performs parametric bootstrap likelihood ratio test of exponential growth state space model vs. Ornstein-Uhlenbeck state space model. (3) ROUSSE-1.0.R contains the functions used in statistical inferences for the Ornstein-Uhlenbeck state space model. ROUSSE-1.0.R is called by both RUNNING-ROUSS.R and RUNNING-PBLRT.R and must be present (as a file by that name) in the working directory of R.