Symbolic dynamics for identifying similarity between rhythms of ecological time series

Explaining the associations between animal populations or between population and environmental signals is an important challenge. The time series that quantify animal populations are often complex, nonlinear, noisy and non-stationary. These characteristics may make it inappropriate to use traditional techniques when analysing these time series and their mutual dependencies. Here I propose to use symbolic dynamics and techniques from Information Theory to evaluate the degree of dynamic cohesion between time series fluctuations. The main idea is to check whether two (or more) signals tend to oscillate simultaneously, rising and falling together with the same rhythm. Based on synthetic and real time series, I demonstrate that this method is robust to the presence of noise and to the short length of the analysed time series and gives relevant information about the weak relationships between different series. Furthermore, this method appears as simple as classical cross-correlation and outperforms it in the analysed examples.