Socio-ecological dynamics of Caribbean coral reef ecosystems and conservation opinion propagation

Abstract

The Caribbean coral reef ecosystem has experienced a long history of deterioration due to various stressors. For instance, over-fishing of parrotfish - an important grazer of macroalgae that can prevent destructive overgrowth of macroalgae - has threatened reef ecosystems in recent decades and stimulated conservation efforts such as the formation of marine protected areas. Here we develop a mathematical model of coupled socio-ecological interactions between reef dynamics and conservation opinion dynamics to better understand how natural and human factors interact individually and in combination to determine coral reef cover. We find that the coupling opinion and reef systems generates complex dynamics that are difficult to anticipate without use of a model. For instance, instead of converging to a stable state of constant coral cover and conservationist opinion, the system can oscillate between low and high live coral cover as human opinion oscillates in a boom-bust cycle between complacency and concern. Out of various possible parameter manipulations, we also find that raising awareness of coral reef endangerment best avoids counter-productive nonlinear feedbacks and always increases and stabilizes live coral reef cover. In conclusion, an improved understanding of coupled opinion-reef dynamics under anthrogenic stressors is possible using coupled socio-ecological models, and such models should be further researched.

Figure 1

Flowchart illustrating the basic dynamics of the coral reef ecosystem.

Figure 2

Time series of reef-opinion dynamics at baseline parameter values, showing response of the human population to declining coral reef cover. Baseline parameter values are κ = 1.014 yr⁻¹, J = 1.68, ϕ = 0.2. Initial conditions are M(0) = 0.3, C(0) = 0.6, P(0) = 0.2, x(0) = 0.1.

Figure 3

Time series depicting: (a) The catastrophic equilibrium with complete parrotfish eradication, where s = 0 yr⁻¹, and σ = 0.1 yr⁻¹. (b) The catastrophic equilibrium with parrotfish survival, where s = 0 yr⁻¹, and σ = 0.15 yr⁻¹. (c) The unassisted macroalgae-free equilibrium, where s = 0.3 yr⁻¹, and σ = 0.05 yr⁻¹. (d) Oscillatory behaviour, where s = 0.2 yr⁻¹, and σ = 0.5 yr⁻¹. (e) Oscillatory behaviour which eventually converges to the assisted macroalgae-free equilibrium, where s = σ = 0.4 yr⁻¹. (f) The assisted macroalgae-free equilibrium, s = 0.35 yr⁻¹, and σ = 0.5 yr⁻¹. All other parameters remain at baseline values.

Figure 4

Parameter planes depicting the model dynamical regimes under parameter variations in, (a) the parrotfish growth rate s and the maximal fishing rate σ, with all other parameters held at baseline values, (b) the social learning rate κ and the parrotfish growth rate s, with all other parameters held at baseline values, (c) the social learning rate κ and the maximal fishing rate σ, with all other parameters held at baseline values, (d) the effect of social pressure ϕ and the maximal fishing rate σ, with all other parameters held at baseline values, (e) the effect of social pressure ϕ and the parrotfish growth rate s, with all other parameters held at baseline values, and (f) the coral density sensitivity J and the maximal fishing rate σ, with all other parameters held at baseline values. *Denotes the baseline value of the parameter. See Tables 1 and 2 for the interpretation of the dynamical regimes.