Species are being lost from ecosystems, and for more than 20 years, ecologists have sought to understand the extent to which these species losses trigger secondary extinctions—i.e., the additional loss of species following lost resources or key interactions—measured as robustness. In particular, ecologists aim to identify generalizable rules that explain which types of food webs are more or less robust to secondary extinctions. Food web structure, or the patterns formed by species and their interactions, has been extensively studied as a potential factor that influences robustness. However, there has not yet been a review of our understanding of the relationships between food web structure and robustness. We systematically reviewed 28 studies to identify the relationships between food web structures and robustness, and how the conclusions depend on methodological differences. More than 20 food web structures were reported to determine robustness, but the shape and direction of these relationships varied based on methodology. While there are not yet generalizable patterns in structure-robustness relationships, we find that methodological differences across studies underscored conflicting results, impeding the potential for generality. Based on our findings, we propose recommendations to improve these methods and identify future research questions.

We conducted a systematic literature review following the Reporting standards for Systematic Evidence Synthesis (ROSES) protocol from Haddaway et al. (2017), we described our process in full in Supporting Fig.1. This review involved two stages: 1. abstract screening, and 2. full paper review. We queried the Web of Science Core Collection on April 22, 2021, using the search string: TS= (((“food web” OR food-web) AND (robustness OR persistence OR fragility OR “cascad* extinction*” OR “second* extinction*”))), which yielded 1,107 papers. Our choice of search terms is likely biased towards English language studies, which we acknowledge as an important caveat. Our search terms intentionally do not include network structure or properties given the diverse vocabulary used to describe these ideas (e.g., complexity, structure, properties, attributes). Instead, we queried for all papers that considered the interactions we were interested in (i.e., trophic interactions in food webs) and the simulation of species losses that result in secondary, or cascading species losses (“robustness”). While there is interest in the relationship between structure and secondary extinctions associated with invasive species, we narrowed our review to consider secondary extinctions that result from species removals/losses (i.e., actively performed extinctions, Dominguez-Garcia et al. 2019), as opposed to from the addition of species (e.g., of invasive species as in Romanuk et al. (2017)). Finally, we acknowledge that robustness is only one of many ways to examine the stability of a community (Donohue et al. 2016; Kefi et al. 2019; Landi et al. 2018); food webs are one of many possible types of ecological networks (e.g., mutualistic networks, competition networks); and many factors could influence the stability of a network other than network structure (e.g., regional species pool, invasive species, anthropogenic disturbance, environmental constraints; Doré et al. 2021). However, our search terms still provided a large pool of papers that we then screened to determine if the papers connected consequences of species losses (i.e., secondary extinctions) to aspects of network structure, properties, and characteristics. Further, even within this narrower search, we find substantial methodological differences.

1.1 Abstract Screening

Keyes screened abstracts from the initial 1,107 papers to exclude papers that did not meet the following criteria: 1. authors studied food webs, 2. authors simulated species losses and tracked secondary losses (i.e., calculated robustness), and 3. authors studied at least one food web property or structure in relation to robustness. We did not constrain the properties or structures to a pre-defined list and considered a broad definition of food web structure, including any food web property or network attributes that result from patterns in species that are present (i.e., nodes) and their interactions (i.e., links). Note that we excluded studies that may have simulated species removal if they did not explicitly quantify food web robustness.

1.2 Full-paper review

Of the original 1,107 papers, 28 papers met all three criteria (inclusion rate=2.5%). We reviewed all papers using a combination of free and fixed response questions on Google Forms. If one author was uncertain about a question, another author also reviewed the paper and the question was discussed. For each paper, we collected data on food web properties or structures studied, structure-robustness relationships, and methodology.