Fig. 4: Phytocentric embedding: function-function networks and multifunctional species keystoneness.

a Function-function network’s weighted adjacency matrix Φ for the Na Redona dataset. b Two examples of conditioned function-function networks Φ∣_i computed by conditioning on the plant species Withania frutescens (bottom) and Heliotropium europaeum (top), showing two cases of plant species with very different multifunctional roles in the ecosystem. Node colors represents each species' relative contribution to the total strength of each function. For a species i, we obtain its contribution to function α relative to that of all species by summing the edge weights (strength) of node i in conditioned function-function network relative to that of all species, which we call multifunctional participation index. Similarly, the color of the edges quantify the weight relative to that of all species along the connections. c Multifunctional species ranking based on enriched metadata of the conditioned function-function networks. In order to rank species, we use the participation indices to obtain its keystone vector (see the text and Methods), which is shown in the figure, color-coded to distinguish contributions from different functions. Species whose score is significantly larger than the respective null model are classified as (multifunctionally) keystone (see the text and Methods). d Pruning analysis of P, plotting the number of secondary function extinctions as a function of the number of perturbed species, performed in the order prescribed by this multifunctional species ranking (c) and the participation strength-based ranking (Fig. 3d), compared to a null model where species are removed at random (see Methods). Both rankings yield very similar extinction curves, which are clearly above the average extinction curve of the null model (see also Supplementary Fig. 7), certifying that the scores on which the rankings predicate to capture a notion of species keystoneness.