Fig. 2

Enhanced prediction accuracy in the kNN method with increasing training samples. We used the GLV model to generate abundance profiles as a training set and 20 test samples, whose abundance profiles were predicted based on their species assemblages. The prediction error is calculated as the rJSD between the predicted and real abundance profiles. Symbols and shaded areas represent the average over 100 realizations and the standard deviation, respectively. a Prediction error of the kNN (circles) and the null model (squares) versus the number of training samples, for a system of 10 interacting species. b and c same as a for 20 and 40 species, respectively. The kNN predictions improve for a larger number of training samples, in marked contrast with the null model which is effectively independent of the number of training samples. d same as a for 100 species, here we set \(\sigma =0.4\). e Results of predictions of a neural network model trained and tested with similar conditions as in a–c. Compared with the kNN, the neural network model yields a higher prediction error for a small number of training samples (\(<500\))