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

Individual-level traits mediate interaction outcomes and community structure. It is important, therefore, to identify the minimum number of traits that characterise ecological networks, that is, their 'minimum dimensionality'. Existing methods for estimating minimum dimensionality often lack three features associated with increased trait numbers: alternative interaction modes (e.g. feeding strategies such as active vs. sit-and-wait feeding), trait-mediated 'forbidden links' and a mechanistic description of interactions. Omitting these features can underestimate the trait numbers involved, and therefore, minimum dimensionality. We develop a 'minimum mechanistic dimensionality' measure, accounting for these three features. The only input our method requires is the network of interaction outcomes. We assume how traits are mechanistically involved in alternative interaction modes. These unidentified traits are contrasted using pairwise performance inequalities between interacting species. For example, if a predator feeds upon a prey species via a typical predation mode, in each step of the predation sequence, the predator's performance must be greater than the prey's. We construct a system of inequalities from all observed outcomes, which we attempt to solve with mixed integer linear programming. The number of traits required for a feasible system of inequalities provides our minimum dimensionality estimate. We applied our method to 658 published empirical ecological networks including primary consumption, predator-prey, parasitism, pollination, seed dispersal and animal dominance networks, to compare with minimum dimensionality estimates when the three focal features are missing. Minimum dimensionality was typically higher when including alternative interaction modes (54% of empirical networks), 'forbidden interactions' as trait-mediated interaction outcomes (92%) or a mechanistic perspective (81%), compared to estimates missing these features. Additionally, we tested minimum dimensionality estimates on simulated networks with known dimensionality. Our method typically estimated a higher minimum dimensionality, closer to the actual dimensionality, while avoiding the overestimation associated with a previous method. Our method can reduce the risk of omitting traits involved in different interaction modes, in failure outcomes or mechanistically. More accurate estimates will allow us to parameterise models of theoretical networks with more realistic structure at the interaction outcome level. Thus, we hope our method can improve predictions of community structure and structure-dependent dynamics.