Appendix C. Test of model assumptions.
We made many simplifying assumptions in the construction of the model presented here. In this supplement, we test the importance of two key simplifying assumptions: closed symbiont dynamics and complete coral phototrophy.
Experimental evidence suggests that, after bleaching events, previously unobserved symbionts may infect corals (Lewis and Coffroth 2004), which we do not account for when assuming closed symbiont dynamics in the original model. To explore the impact of open symbiont dynamics on the model outcome, we replace Eq. (1) with:
where is the rate of symbiont infection from populations outside the coral, and all other terms are as before. Using cells cm yr based on Lewis and Coffroth (2004), we test the impact of open symbiont dynamics on model predictions with multiple symbiont types (and without evolution because the selection pressures on symbiont thermal tolerance outside the coral are unknown). Preliminary results indicate that open symbiont dynamics do not alter qualitative model trends under the parameter values used (Fig. C1).
|FIG. C1. Simulation predictions with one thermal-stress-susceptible, slow-growing coral and open symbiont dynamics. ISST is the past temperature data; SRES A1b and SRES B1 are the future temperature data with greater or less greenhouse gas emissions, respectively. Simulations with one symbiont are in red with circles, with two symbionts with a C difference in thermal tolerance in gray with diamonds (solid lines for the first symbiont dynamics and broken lines for the second, more thermally tolerant symbiont dynamics), and with two symbionts with a C difference in thermal tolerance in magenta with down-facing triangles; no simulations include evolution. In the coral population size plot with past temperature (ISST) data, filled and open up-facing triangles indicate observed major and minor bleaching events, respectively (Noordeloos et al. 2007). For comparison to closed symbiont dynamics, see lines with the same colors and symbols in Figs. 2–3.|
Furthermore, corals may be able to obtain energy from sources outside symbionts, such as through heterotrophic feeding (Grottoli et al. 2006), which we ignore when assuming that coral growth and mortality depend directly on symbiont population sizes. To explore the impact of heterotrophic coral energy acquisition on the model outcome, we replace Eq. (2) with:
where is the heterotrophic coral growth rate from energy gained independent of symbionts, and all other terms are as before. Using yr assuming that the 21–35% percentage of the daily animal respiration from heterotrophy reported in Grottoli et al. (2006) resembles the percent contribution of heterotrophy to net coral growth when zooxanthellae are at carrying capacity, we test the impact of coral heterotrophy on model predictions. Preliminary results indicate that coral heterotrophy also does not alter qualitative model trends under the parameter values used (Fig. C2). However, note that these results assume constant coral heterotrophy; any potential for corals to up-regulate heterotrophy during bleaching events, as may occur for some species, may increase the potential for such corals to survive bleaching events and future climate change (Grottoli et al. 2006).
|FIG. C2. Simulation predictions with one thermal-stress-susceptible, slow-growing coral and coral heterotrophy. ISST is the past temperature data; SRES A1b and SRES B1 are the future temperature data with greater or less greenhouse gas emissions, respectively. Simulations with one non-evolving symbiont are in red (circles). Simulations with one evolving symbiont are in blue (squares); genetic distribution 95% confidence intervals are shown in the genotype plots. Simulations with two non-evolving symbiont types are in gray (diamonds); solid and broken lines indicate the less and more thermally tolerant symbiont, respectively. For comparison to closed symbiont dynamics, see lines with the same colors and symbols in Fig. 2.|
Grottoli, A. G., L. J. Rodrigues, and J. E. Palardy. 2006. Heterotrophic plasticity and resilience in bleached corals. Nature 440:1186–1189.
Lewis, C. L., and M. A. Coffroth. 2004. The acquisition of exogenous algal symbionts by an octocoral after bleaching. Science 304:1490–1492.
Noordeloos, M., M. Tupper, Y. Yusuf, M. Tan, S. Tan, S. Teoh, and S. Ikbal. 2007. ReefBase: A global information system on coral reefs. Online. Available from: http://www.reefbase.org.