Speaker
Description
We study the dynamics of a three-trophic level food web model representing a
wasp-waist marine ecosystem, where a single or multiple intermediate consumers
mediate energy flow between primary producers and apex predators. Using a
system of nonlinear ordinary differential equations with ratio-dependent func-
tional responses, we investigate conditions under which the consumer populations
collapse or persist. By analyzing the system near a producer-only boundary equi-
librium, we identify critical thresholds for the initial predator-to-prey biomass
ratio that delineate collapse, escape, and intermediate ("race condition") regimes.
Our analysis employs quasi-stationarity arguments, asymptotic expansions, and
differential inequalities to rigorously characterize the system’s trajectories and
basins of attraction. The results provide a mechanistic understanding of transient
collapse phenomena and offer mathematically tractable early-warning indicators
for instability in structured ecological systems. We propose that the approach can
be extended to analyze output from more complex ecosystem models, enabling
reduced-form interpretations of resilience and early warning indicators in empirical
or high-dimensional simulations of wasp-waist systems
