Capturing complex interactions in disease ecology with simplicial sets

Abstract

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher‐order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Not your private tête-à-tête: leveraging the power of higher-order networks to study animal communication

“…Simplicial sets (not illustrated) are broadly equivalent to hyperedges and represent an alternative mathematical framework to represent higher-order interactions [27]. For example, 0-simplex is the same as a node in a network, 1-simplex is the same as an edge, 2-simplex is an interaction involving three individuals and so on.…”

“…We use this total dose to calculate the transition probability of an individual from non-calling to calling. The transmission model is equivalent to the one described in [27]. We model the behavioural contagion for 1000 timesteps (timesteps are arbitrary).…”

“…Accessible software tools are not as well developed for higher-order network approaches as they are for dyadic networks, although this is changing rapidly. There are recent broad overviews of higher-order methods [12,13] and Silk et al [27] provide an overview of the main tools available to ecologists, so here we focus on the most relevant tools available. The XGI Python library [72] provides a comprehensive toolkit for working with higher-order networks.…”

Comparative approaches in social network ecology

“…Another source of lost information in all comparative social network studies conducted so far—and existing data repositories—is that data is stored as dyadic networks, even when this is a simplification (e.g., group‐based data). This loses information on interaction size that can be captured using higher‐order network approaches (Silk et al., 2022). While these have only rarely been used in behavioural ecology (Musciotto et al., 2022), they are gaining popularity as a tool in network science (Battiston et al., 2021).…”

Comparative approaches in social network ecology

“…group-based networks). This loses information on the size of social interactions that can be captured using higher-order network approaches (Silk et al 2022). While these have only rarely been used in behavioural ecology thus far (Musciotto et al 2022), they are gaining popularity as a tool in broader network science (Battiston et al 2021).…”