Towards a mechanistic understanding of variation in aquatic food chain length revealed by meta-analysis

Ecologists have long sought to understand the forces determining food chain lengths (FCLs). Multiple hypotheses have proposed a diverse array of potential environmental determinants of FCL, typically including ecosystem size, resource productivity, and disturbance. Yet, many empirical studies have found that FCL responses to these environmental variables can be positive as well as negative. To explain such mixed responses, we develop a simple yet comprehensive, site-occupancy dynamic framework for complex food webs by integrating multiple environmental drivers. With the competition-colonization tradeoff among basal species, our model shows that increasing ecosystem size results in a monotonic increase in FCL as a whole, while FCL displays a non-linear, oscillatory response to resource productivity or disturbance in benign environments. These predictions are generally supported by our meta-analysis of an empirical dataset compiled from diverse aquatic ecosystems. Therefore, this unifying framework offers a novel mechanistic explanation for observed variation in FCLs driven by multiple environmental factors.

Methods
We collected a large empirical dataset of changes in food chain length (FCL) in response to ecosystem size, resource productivity, and disturbance respectively, compiled from 30 published papers (see "References.docx"). This data set includes 36 empirical cases relating to ecosystem size, 36 cases relating to resource productivity, and 16 cases relating to disturbance. We measure the FCL response to these variables using the log response ratio (LRR). All these LRR values are listed in the file "Empirical dataset": namely "LRR_Ecosystem size.xlsx", "LRR_Resource productivity.xlsx" and "LRR_Disturbance.xlsx". 

We also compiled the empirical data (see "Empirical_food_chain_data.csv") for both one- and two-way model analysis, where three variables are included: ecosystem size (size), resource productivity (resource), and distrubance (dist). The units for these variables are listed in "Variable_unit.xlsx".