A homoclinic route to chaos in omnivore communities

TL;DR

This work addresses how omnivory via intraguild predation can generate intrinsic, self-organized population fluctuations in ecological communities. It introduces a minimal three-species IGP model with a Holling type-II response and analyzes stability of the coexistence equilibrium E^*, revealing it as a saddle-focus that can undergo a Shilnikov homoclinic bifurcation, leading to chaos. Numerical simulations and Lyapunov-spectrum analysis show a progression from regular oscillations to Shilnikov-type chaos, with a Smale-horseshoe–style attractor near the saddle-focus; the model reproduces field-like patterns and matches observed host-parasite community data with Bray-Curtis similarities exceeding 0.9 across productivity levels. Collectively, the results provide a mechanistic, intrinsic route to complex dynamics in omnivorous networks and highlight Shilnikov chaos as a plausible driver of irregular population fluctuations in natural ecosystems.

Abstract

Omnivory, where species feed across multiple trophic levels, is a widespread feature of ecological networks. A key mechanism underlying such complexity is intraguild predation (IGP), in which a top predator consumes both an intermediate predator and a shared resource. Here, we show that Shilnikov homoclinic orbits emerge in a minimal intraguild predation model, triggering a cascade of homoclinic bifurcations near a saddle-focus equilibrium that culminates in chaos. Numerical simulations and Lyapunov spectrum analysis reveal multiple coexistence modes, ranging from regular oscillations to Shilnikov homoclinic orbits and chaos. Our model quantitatively reproduces patterns observed in natural omnivore networks, providing mechanistic insights into complex population fluctuations in ecological systems.

Figures (5)

• Figure 1: Schematic of a minimal intraguild predation model. An intermediate predator $C_1$ feeds on the basal resource $R$, while the top predator $C_2$ preys upon both $R$ and $C_1$, generating a dual interaction of competition and predation. Arrows indicate the direction of biomass flow.
• Figure 2: Emergence of Shilnikov homoclinic attractors in a minimal intraguild predation model as resource productivity $r$ increases across different ecosystems. (a-b) Time series of population abundances, showing the transition from regular oscillations to Shilnikov homoclinic oscillations. (c-d) The corresponding 3D phase-space trajectories associated with panel (a-b), demonstrating the transition from a stable limit cycle to a homoclinic orbit. See SM Sec. III for simulation details of Figs. \ref{['HomoclinicChaos']}-\ref{['CompareExp']}.
• Figure 3: Chaotic dynamics in a minimal intraguild predation model. (a) Time series of predator and prey abundances showing irregular, aperiodic oscillations. (b) Divergence of trajectories under small perturbations ($\Delta C_{1}=10^{-4}$), demonstrating sensitivity to initial conditions. (c) Chaotic attractor in the $\left(R,C_1,C_2\right)$ phase space, showing horseshoe-type strange attractor. (d) Temporal evolution of the Lyapunov exponents computed by the Benettin algorithm; the positive $\lambda_{1}$ and negative sum of exponents confirm chaos.
• Figure 4: Comparison of model results with field data from a host-parasite community Borer2003. (a-c) Simulated time series of species abundances under increasing resource productivity (modeled via parameter $r$). Markers indicate time-averaged abundances, and error bars represent oscillation amplitudes. (d) Comparison of model results and experimental data Borer2003 based on time-averaged relative abundances across productivity gradients (grapefruit: low; citrus: medium; lemon: high). Model-experiment correspondence is quantified using Bray-Curtis similarity, with values of 0.93 (low), 0.97 (medium) and 0.97 (high). Species are color-coded as follows: $R$ in orange, $C_1$ in blue, and $C_2$ in green.
• Figure S1: Disruption of omnivory in the minimal intraguild predation model (\ref{['P-Psystem2']}) leads to predator extinction. (a-b) Time courses of species abundances showing the extinction of $C_{2}$, simulated from Eq. (\ref{['P-Psystem2']}) with omnivory disrupted $\left( \omega_{3}=0, \alpha_{4}=0 \right)$. (a): $\alpha_1 = 0.5, \alpha_2 = 2.5, \alpha_3 = 1.6, \omega_1 = 2.3, \omega_2 = 0.032, m_1 = 0.3, m_2 = 0.2, r = 2.5$. (b) : $\alpha_1 = 2.0, \alpha_2 = 1.6, \alpha_3 = 1.005, \omega_1 = 1.95, \omega_2 = 0.038, m_1 = 0.25, m_2 = 0.55, r = 6.6$.