Ecological Archives A21-064-A3

Jessica Melbourne-Thomas, Craig R. Johnson, Tak Fung, Robert M. Seymour, Laurent M. Chérubin, J. Ernesto Arias-González, and Elizabeth A. Fulton. 2011. Regional-scale scenario modeling for coral reefs: a decision support tool to inform management of a complex system. Ecological Applications 21:1380–1398.

Appendix C. Summary of results from sensitivity analysis for CORSET.

Table C1 summarizes results from a detailed sensitivity analysis for CORSET (Melbourne-Thomas et al. unpublished manuscript). This analysis examined four categories of sensitivity, or sources of uncertainty, using multivariate coral community state as the response variable. Multivariate techniques were used to group ‘modes’ of model behavior under different parameter conditions and spatio-temporal resolutions, and hence to evaluate sensitivity responses (as described by Klepper 1997). Sensitivity to initial conditions was assessed by determining whether model trajectories converged to steady-state conditions over a range of different initial values for benthic and consumer state variables. Two complementary approaches were used to examine parameter sensitivity in CORSET. The first used principal components analysis (PCA; Chatfield and Collins 1980) to visualize modeled community state under the minimum and maximum values for each parameter (as in Mumby 2006), and hence to identify parameters that have a strong influence on model outcomes. The second introduced a perturbation event (i.e. a 60% decline in proportional coral cover) and compared the recovery capacity of the modeled reef system under different parameter scenarios (following Preece and Johnson 1993).

Model sensitivity to spatial resolution was assessed by comparing the portion of multivariate space occupied by model outputs under different base map resolutions (i.e. cell sizes of 0.5 km × 0.5 km, 1 km × 1 km and 2 km × 2 km). Finally, sensitivity to temporal resolution was evaluated by comparing model behavior under daily, weekly, fortnightly, monthly and yearly updating intervals. Behavior was characterized by (a) the proportion of model runs for which dynamics went outside the biological domain (i.e. outside the range 0 – 100% for benthic covers and < 0 or tending to infinity for consumer biomasses), which indicates dynamic instability and (b) differences in steady-state community composition under different updating intervals.

In two additional analyses not summarized in Table C1 we examined (a) changes in patterns of connectivity resulting from the inclusion or exclusion of some Mexican reefs as larval sources (as described in the main text), and (b) the effects of assumptions regarding parameter variability over time on modeled community composition. In (a), the exclusion of source reefs had no detectable effect on connectivity patterns for spawning corals, fish and urchins. In (b), there was greater variability in modeled community composition when parameters were fixed between years, than when parameter values were selected randomly for each simulation year. However, mean model behavior under both conditions was equivalent.

TABLE C1. Summary of results from sensitivity analysis for CORSET (from Melbourne-Thomas et al. unpublished manuscript). The perturbation used in testing model sensitivity to parameter values was a severe coral mortality event (a 60% decline in proportional coral cover).

Source of uncertainty Sensitivity response
Initial conditions* In the absence of external forcings, model trajectories converge to steady-state conditions regardless of initial conditions for benthic and consumer groups.
Parameter values (i) Local-scale model parameters
Modeled community composition is most sensitive to coral growth rate (), coral mortality rate (), and the mortality rates of piscivorous fish (,) under steady-state and perturbed conditions.
(ii) Reproduction and recruitment parameters
Modeled community composition is most sensitive to coral fecundity (i.e. brooding and spawning coral larval production; Appendix A: Table A2) under steady-state and perturbed conditions.
Spatial resolution Differences in modeled community composition at different spatial resolutions (cell size = 0.5 km × 0.5 km, 1 km × 1 km, 2 km × 2 km) are ecologically non-significant.
Temporal resolution Steady-state community composition is equivalent under daily, weekly and fortnightly updating intervals. Dynamic instabilities exist only for updating intervals greater than a fortnight, i.e. monthly and yearly intervals.

* Initial values tested for coral cover, macroalgal cover and macroturf cover were 1%, 30%, 60% and 90%, and for herbivorous fish, piscivorous fish (small-to-intermediate and large piscivores combined) and sea urchins the initial biomass values used were 5g/m2, 20g/m2, 40g/m2 (the maximum of reported values for piscivorous fish and sea urchin biomass for the Meso-American region; Arias-González 1998, Newman et al. 2006) and 60g/m2 (the maximum reported herbivorous fish biomass for the Meso-American region; Arias-González 1998).


Arias-González, J. E. 1998. Trophic models of protected and unprotected coral reef ecosystems in the south of the Mexican Caribbean. Journal Of Fish Biology 53:236–255.

Chatfield, C., and A. J. Collins. 1980. Introduction to Multivariate Analysis. Chapman and Hall, London, UK.

Klepper, O. 1997. Multivariate aspects of model uncertainty analysis: tools for sensitivity analysis and calibration. Ecological Modelling 101:1–13.

Mumby, P. J. 2006. The impact of exploiting grazers (Scaridae) on the dynamics of Caribbean coral reefs. Ecological Applications 16:747–769.

Newman, M. J. H., G. A. Paredes, E. Sala, and J. B. C. Jackson. 2006. Structure of Caribbean coral reef communities across a large gradient of fish biomass. Ecology Letters 9:1216–1227.

Preece, A. L., and C. R. Johnson. 1993. Recovery of model coral communities: complex behaviours from interaction of parameters operating at different spatial scales. Pages 69–81 in D. G. Green and T. Bossomaier, editors. Complex systems: from biology to computation. IOS Press, Amsterdam, The Netherlands.

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