[Paper Review] Persistence of complex food webs in metacommunities

Gesa A. Böhme, Thilo Groß|arXiv (Cornell University)|Dec 20, 2012

Plant and animal studies16 references3 citations

TL;DR

This paper develops a general analytical framework to compute persistence conditions for complex food webs in metacommunities, where local patches support only simple food chains but landscape-scale connectivity enables omnivory and coexistence. The key finding is that omnivore persistence is most likely when feeding on prey from low or similar trophic levels, with persistence ranges determined by patch network connectivity and interaction network structure.

ABSTRACT

Metacommunity theory is considered a promising approach for explaining species diversity and food web complexity. Recently Pillai et al. proposed a simple modeling framework for the dynamics of food webs at the metacommunity level. Here, we employ this framework to compute general conditions for the persistence of complex food webs in metacommunities. The persistence conditions found depend on the connectivity of the resource patches and the structure of the assembled food web, thus linking the underlying spatial patch-network and the species interaction network. We find that the persistence of omnivores is more likely when it is feeding on (a) prey on low trophic levels, and (b) prey on similar trophic levels.

Motivation & Objective

• To identify general conditions under which complex food webs persist in metacommunities despite local food chains being simple.
• To investigate how spatial network structure (geographical network) and species interaction networks jointly influence food web persistence.
• To determine the role of omnivory in stabilizing complex food webs across patch networks.
• To develop a scalable mathematical formalism for computing persistence ranges of arbitrary food web configurations in metacommunities.

Proposed method

• Uses a binary state model where each patch is either occupied or vacant by species, with dynamics governed by local extinction and colonization.
• Models extinction rates as cumulative sums based on trophic position: higher trophic species go extinct when their prey do.
• Applies a colonization rule requiring suitable patches to be reachable, unoccupied by stronger competitors, and containing prey.
• Introduces a transition matrix formalism (S*) to describe patch dynamics in the absence of a focal omnivore.
• Adapts the transition matrix (Sx) to account for patch availability when the omnivore is present, using a modified matrix subtraction.
• Employs eigenvalue analysis of derived matrices (M̂ and M̂) to compute persistence thresholds based on the largest eigenvalues.

Experimental results

Research questions

• RQ1 Under what conditions can omnivores persist in a metacommunity when local patches support only simple food chains?
• RQ2 How does the trophic level difference between omnivore prey species affect the size and location of the coexistence range?
• RQ3 How does the connectivity of the geographical network (mean degree ⟨k⟩) influence the persistence of omnivores and specialist predators?
• RQ4 What is the relationship between the structure of the interaction network and the stability of complex food webs at the metacommunity scale?

Key findings

• Omnivores feeding on prey from low trophic levels (e.g., trophic levels 1 and 3) have a larger coexistence range than those feeding on distant levels.
• The persistence range for an omnivore feeding on species from non-adjacent trophic levels is smaller and shifted to lower values of the colonization rate z compared to omnivores on adjacent levels.
• For a 4-trophic chain with omnivory on levels 1 and 3, the analytical coexistence range is 2/(13+√97) < z < 1/(5+√13), which matches simulation results.
• The largest eigenvalue of the matrix M̂ = s₂ · (−s₁⁻¹) determines the upper persistence threshold, while M̂ determines the lower threshold.
• Simulation results confirm that analytical thresholds accurately predict the appearance and disappearance of species in the metacommunity.
• The method successfully predicts the emergence of maximal food webs in metacommunities, as demonstrated in the 4-trophic chain example with non-adjacent omnivory.