Incorporating trait-based mechanisms, alternative interaction modes and forbidden links increases the minimum dimensionality of ecological networks

Multiple traits are involved in intra- and interspecific interactions, influencing interaction outcomes and community structure. Knowing the minimum number of traits required to explain observed network structures, i.e. the ‘minimum dimensionality’, can help us to focus on key biological questions. Existing theoretical methods for estimating minimum dimensionality are often simplified in three ways: (i) they are phenomenological, (ii) they lack the ubiquitous feature of alternative interaction (e.g. feeding) modes, (iii) they do not consider phenological and/or phenotypic mismatches, known as ‘forbidden links’. Here we develop a method to estimate the ‘minimum mechanistic dimensionality’ of ecological networks, which can assume alternative interaction modes and account for forbidden links. Our method compares the performance of traits, e.g. predator mouth gape versus prey body size. A system of linear inequalities—making assumptions of how traits are involved in alternative interaction modes—is constructed to explain the observed interaction outcomes. We attempt to solve these inequalities with mixed integer linear programming. Minimum mechanistic dimensionality is the minimum number of traits required for a feasible system of inequalities. We illustrate how the inclusion of alternative interaction modes alters the explanation of an intransitive ‘rock–paper–scissors’ system of competing marine invertebrates. We apply our method to 658 published empirical ecological networks— including animal dominance, predator–prey, primary consumption, pollination, parasitism and seed dispersal networks—to determine whether minimum dimensionality estimates change following the inclusion of concepts emerging from our framework, i.e., alternative interaction modes, trait-mediated ‘forbidden links’ and a mechanistic approach to describing trait-based interactions. The minimum mechanistic dimensionality was typically higher in ecological networks when including alternative interaction modes (54% of empirical networks), ‘forbidden interactions’ as trait-mediated interaction outcomes (92%), or a mechanistic perspective (81%), compared to dimensionality estimates in the absence of these features. Our method can inform us about how many traits are mechanistically involved in pairwise interactions, to generate theoretical networks of more accurate structure at the interaction outcome level. In general, it can reduce the risk of omitting essential traits, for improved understanding, explanation, and prediction of community structures, and structure-dependent community, ecosystem, and evolutionary processes.