Shota Shibasaki , Akira Terui

1. Food chain length (FCL), roughly defined by the number of trophic links, is one important aspect of biodiversity. However, studies on FCL are limited to simple food webs (e.g., only three or four species in a community) or simple hypotheses (i.e., what is a determinant of FCL?)

2. In this review, we propose research directions to comprehensively understand how multiple environmental factors affect FCL using food webs as complex as natural ones. To facilitate these research directions, we first introduce basic ideas of graph theory. Graph theory clarifies the requirements of food webs in the analysis of FCL and methods to calculate FCL.

3. We recommend using only directed acyclic graphs in studies of FCL because some definitions of FCL cannot be used in cyclic food webs. Within more than ten models that generate food webs as complex as in nature, a part of them generates only acyclic food webs. Such models include the (generalized) cascade model and the preferential prey model. In contrast, the (generalized) niche model and the nested hierarchy model can generate cyclic food webs, and they are not appropriate in the studies of FCL.

4. We then discuss how we can study the interdependent effects of the multiple environmental factors on FCL while using models that generate complex acyclic food webs. In addition, we propose research questions that would enrich our understanding of FCL.