Fig. 5.

Comparison of causal assessment in ecosystem data with existing methods. The ecosystem data include Lotka Volterra predator–prey model^21,22 (first row), Didinium and Paramecium data⁴⁵ (second row), wolf and moose data from the United States Isle Royale National Park²³ (third row), and lynx and hare data from trading records obtained from Hudson’s Bay Company²⁴ (fourth row). The results were derived from convergent cross mapping (CCM) (embedding dimension = 3), Granger’s and mutual information from mixed embedding (MIME) methods. The colour of lines and bars indicate the causal strength of a given predator (blue) or prey (red). In CCM, the difference in correlation values between predator and prey indicates the direction of causal direction. In Granger causality, the F-test was used to assess the causal strength and the vertical dashed line denotes the significance threshold with P < 0.05. In MIME method, the relative causal strength was represented by difference in mutual information