Modeling the continua in the outcomes of biotic interactions

The outcome of many ecological interactions lies somewhere along a continuum between pure positive and pure negative effects. Although the popularity of this idea has notoriously risen in the last decades, with the occurrence of continua in interaction outcomes invoked for a wide variety of interactions, the absence of a precise theoretical treatment has led to considerable inaccuracy and ambiguity in its treatment. We develop here a consumer-resource model to explore the occurrence of continua. This model is based on the assumption that the distribution of individual interaction events includes both negative and positive immediate outcomes, with variable frequencies, for at least one of the interacting species. Our study shows that continua in interaction outcomes happen just by varying the sign and impact of individual events. The exact shape of the continua depends on the proportion of positive versus negative events and the relative magnitude of per-capita interaction strengths. Our model shows that continua in interaction outcomes are a key property of most pairwise interactions and are originated from the variable roles played by the interacting partners. It constitutes a step forward in the paradigm change from discrete categorization of ecological interactions to a new perspective over a continuous space.