A comparison of statistical methods for detecting species interactions from short, noisy time series data
Understanding species interactions is critically important in ecological research and population management. However, it is extreme hard to determine species interactions from population time series data. In this paper, we describe four different methods to detect species interactions from time series data, and evaluate their performance on short and noisy data, a common situation in ecology, from a predator-prey model. For the data generating model, it had a nonlinear predation process and compensatory density dependence on the prey survival. In addition, process error was added by letting population parameters of either the prey or predator to fluctuate. The fluctuation in population density resulting from the process error is stationary, but it may display apparent nonstationarity because of the short observation period. Three levels of zero-mean Gaussian observation errors (noise) were also added to all of the simulated time series data. Four methods being evaluated are simple linear regression (SLR), modified Shelton correlation coefficient (CC), multivariate autoregressive (MAR) and a newly proposed integration-cointegration robust (ICR) models. None of these models correspond to the data generating model.
Through simulation, we found that methods that account for autocorrelation (CC, MAR and ICR) had better performance in terms of type I error rates across all noise levels. Among these three methods, only the ICR method produced consistent type I error rates at all of the commonly used 1%, 5% and 10% α values. The CC method was conservative at the 1% value, but had inflated error rates at the 5% and 10% values. The VAR method had inflated type I error rates at all three α values. For the power analysis, the CC procedure had the highest percentage of correctly identifying bottom up and top down controls. Among SLR, MAR and ICR methods, SLR procedure had higher power in detecting three types of interactions than the ICR and MAR. In conclusion, we found that both the CC and the MAR methods could not adequately control type I error rate when time series exhibited nonstationry fluctuation, the newly proposed method had the best control over the type I error rate. However, the power of the new method suffered due to uncertainty about the dynamics of the underlying process. In practice, researchers should choose the method to balance these two types of statistical errors based on both the property of the time series and the ecology of the system.