Coral reefs with connectivity to mangrove nurseries exhibit increased parrotfish grazing, but the relative magnitude of the enhancement differs among habitats; shallow reefs receive a greater boost to grazing than those at mid-depth. Model simulations found that the consequences of increased grazing on coral population dynamics exhibited a surprising, non-intuitive pattern such that coral populations in shallow reefs were unaffected, whereas those at greater depth responded dramatically to a relatively weak rise in grazing. Therefore, the observed effects of ontogenetic dispersal can diverge dramatically from their ecosystem-level consequences, which implies that caution must be exercised when inferring the consequences of observed patterns of species abundance for ecosystem processes and stability.
The sudden phase shift exhibited by mid-shelf reefs in response to a slight increase in coral mortality implies strongly that the system can exhibit multiple stable states and unstable equilibria (May 1977; Scheffer & Carpenter 2003). Indeed, an analysis of equilibrial coral cover for various levels of grazing revealed two stable community states (one coral-dominated, one macroalgal-dominated) and a region of unstable equilibria defined by an upper and lower bifurcation point (Fig. 2 in Mumby, Hastings & Edwards 2007). At an unstable equilibrium, corals and macroalgae can coexist only under very restricted circumstances. Slight shifts in favour of either competitor result in successful exclusion of the competitor. These mechanisms occur because of feedbacks reinforcing the direction of community shift. For example, a reduction in coral cover permits an increase in macroalgae because grazing becomes dispersed more widely over the benthos and individual patches of algae are regrazed less often. An increase in macroalgal cover not only reduces settlement space for corals, but it increases the mortality rate of coral recruits (Bak & Engel 1979; Box & Mumby 2007). A reduction in recruitment may reduce the replenishment of juvenile and adult corals, therefore causing a further decrease in coral cover. This process is reinforced as further reductions in coral cover allow macroalgae to increase, thereby reducing the survival of coral recruits still further and generating a bottleneck in the coral population. This is an emergent property of the model because the mortality rates simulated did not affect coral recruits. Importantly, the kind of phenomena we observe are generic, and do not depend critically upon the specific details of the model (Mumby, Hastings & Edwards 2007). The bifurcation structure, and the dependence on the control parameters, are well-known mathematical phenomena in ecological models with similar overall structure (Angeli, Ferrell & Sontag 2004). In ecological systems, the kind of behaviour we model is similar to that used to explain outbreaks of insects in a generic model (Ludwig, Jones & Holling 1978). The key ingredients are a separation of time-scales combined with density dependence to create the non-linearity.
Grazing determined the vulnerability of the reef ecosystem to sudden phase changes. Mangrove impacts on grazing were significant in mid-shelf reefs because their magnitude coincided with the zone of system instability (Fig. 5). A modest change in grazing was able to shift the reef state beyond its upper bifurcation point, resulting in radical differences in system dynamics. System instability was absent from shallow reefs because grazing impacts of 49% 6 months−1 (to 57% with mangroves) exceeded the upper bifurcation point for unstable equilibria, which occurred at a grazing impact of around 24% 6 months−1 (Fig. 5). Once grazing levels are high enough to surpass the upper bifurcation point reefs move towards a coral state, although acute disturbances deplete coral cover in the short term. Interestingly, the model predicted that shallow reefs have greater overall resilience than mid-shelf reefs (i.e. the threshold bifurcation of grazing for coral-dominance was lower in shallow reefs). This result could not have been predicted without the model because the parameterization for shallow reefs included both positive and negative implications for resilience; the increase in coral growth rate would tend to enhance resilience, whereas the increase in macroalgal growth rate would tend to decrease resilience. Clearly, the consequences of increasing coral growth rate outweighed those of allowing faster algal growth.
implications for ecology and conservation
This study provides an important new insight into ecosystem connectivity. By translating demographic consequences of connectivity (increases in fish density) explicitly into an ecosystem process (grazing) and investigating the impact of that process on ecosystem dynamics (resilience), we can contrast the magnitude of demographic effects and ecosystem consequences. Clearly, the observed effects of ontogenetic migration can diverge dramatically from their ecosystem-level consequences (i.e. demographic effects were weakest in mid-shelf reefs but had the greatest impacts on resilience). Therefore, caution must be exercised when inferring the ecosystem-level consequences of observed patterns of species abundance.
The emergence of bistability in mid-shelf reefs strongly reinforces speculation about the permanency of coral degradation (Done 1992; McManus & Polsenberg 2004; Hughes et al. 2005) and poses a challenge to coral reef managers. In order to prevent reefs shifting to a macroalgal state, managers must strive to keep grazing levels high and coral mortality rates low. Of course, this is no easy task, given widespread exploitation of grazing fishes (Bellwood et al. 2004), continued paucity of the urchin D. antillarum in much of the Caribbean (despite recovery in some areas: Carpenter & Edmunds 2006), rising levels of coral disease (Harvell et al. 1999) and accelerating climate-driven disturbance (Hoegh-Guldberg 2004). Indeed, rates of coral recovery after disturbance are already low in many parts of the Caribbean (Connell 1997; Cote et al. 2005; Gardner et al. 2005). Although several of these disturbances, such as coral bleaching, were not included in the simulations, this will not influence our conclusions qualitatively because we contrasted whether the mangrove influence on grazing occurred within a zone of system instability (as was the case for mid-depth reefs) or beyond the zone of instability (as was the case in shallow reefs), such that the trajectory of coral cover between successive impacts will always be one of recovery. Increasing disturbance does not affect the relationship between mangrove impact on grazing and the grazing levels at which bifurcation occurs. Of course, a propensity for recovery between disturbances does not imply that the reef will always appear to be ‘healthy’ with high coral cover, because levels of disturbance could become sufficiently intense to maintain the reef in a state of low cover.
Our conclusions are drawn from a model ecosystem and this naturally raises the question of field testing. Some of the model predictions, such as threshold effects on equilibrial dynamics (Fig. 3), are impossible to test because they simulate reefs for long periods in the absence of acute disturbance phenomena. Even the overall conclusion that mangroves will confer a disproportionately large increase on the resilience of mid-shelf reefs will be difficult to test empirically. This is because individual reef trajectories are subject to the vagaries of many local processes and patchy disturbance. It would be challenging to isolate mangrove-based impacts on reef dynamics without the study being confounded by one of many other factors such as fishing pressure, nutrient supply, bleaching impacts or hurricane impacts. While this does not discount the importance of field testing, our present alternative is to consider the efficacy of the model. All parameters were fitted from empirical studies and while no model can represent the full complexity of the ecosystem, model predictions were found to emulate an independent 20-year record of coral dynamics even when key parameters, such as the ability of algae to overgrow coral tissue, were varied to extreme, albeit published, values (Mumby, Hastings & Edwards 2007). Moreover, recent studies of mid-shelf reefs in the Bahamas found that high levels of parrotfish grazing led to a twofold increase in coral recruitment (Mumby et al. 2007), which fits previous model predictions (Mumby 2006).
Although general limitations and sensitivities of the model have been discussed in previous papers, several considerations should be raised. First, the impacts of mangroves on adjacent reefs were confined to the elevation of fish grazing. In some environments, efflux of decomposed organic matter from mangroves may elevate levels of organic nutrients which potentially favours macroalgal growth on reefs. However, most studies have found weak evidence for such nutrient enrichment (Lapointe, Littler & Littler 1987; Ogden 1997), and a previous study found the model to be insensitive to even major changes in macroalgal growth rate (Mumby et al. 2006b). Secondly, the parameterization of fish grazing in shallow reefs did not explicitly include species in the family Acanthuridae. Acanthurids comprise around 9% of the grazer biomass in mid-shelf reefs but up to 20% in shallow reefs (Mumby, unpublished data from Belize and the Bahamas). By ignoring the greater contribution of these fishes in shallow reefs, the model may have underestimated actual levels of grazing. However, an underestimation of grazing has little impact on the conclusions because even 49–57% grazing appeared to prevent unstable equilibria. Thirdly, hurricane impacts parameterized for mid-depth reefs were assumed to be identical to those in the shallower zone. In general, hurricane effects would be expected to be greater in shallower water because wave-power, which can dislodge and shatter corals, declines with increasing depth (Massel & Gourlay 2000). In the case of this model, however, it seems unlikely that such impacts would have been underestimated heavily for shallow water. This is because the parameterization for mid-depth reefs was generated from two of the most severe events in the 20th century, in which corals were scoured intensively by entrained sand (i.e. by using severe hurricanes, the parameterization will tend to over-estimate the impact of average hurricanes). Lastly, it should be borne in mind that the model did not include corals with a branching morphology and a later study will incorporate the effects of disturbance on A. palmata in shallow water and A. cervicornis on mid-depth reefs.
Mangroves in the Americas are currently being deforested at a faster rate than rainforest (Valiela, Bowen & York 2001), yet they appear to play a pivotal role in coastal and fisheries dynamics (Manson et al. 2005). Mangroves are often cited as protecting coral reefs from the efflux of sediment from estuaries (Ogden 1997). Here, we show that mangrove-based ontogenetic migrations of parrotfish may, through a trophic cascade on macroalgae, enhance the recovery rate of mid-shelf reefs from hurricanes. This conclusion is particularly significant given concerns about rising frequencies of intense hurricanes that may be linked to climate change (Knutson et al. 2001; Webster et al. 2005).