Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems

Real food chains are very rarely investigated since long data sequences are required. Typically, if we consider that an ecosystem evolves with a period corresponding to the time for maturation, possessing few dozen of cycles would require to count species over few centuries. One well known example of a long data set is the number of Canadian lynx furs caught by the Hudson Bay company between 1821 and 1935 as reported by Elton and Nicholson in 1942. In spite of the relative quality of the data set (10 undersampled cycles), two low-dimensional global models that settle to chaotic attractors were obtained. They are compared with an ad hoc 3D model which was proposed as a possible model for this data set. The two global models, which were estimated with no prior knowledge about the dynamics, can be considered as direct evidences of chaos in real ecosystems.