Because the Bahamas was severely disturbed by the 1998 coral bleaching event 
, and later by hurricane Frances in the summer of 2004, coral cover was low at the beginning of the study, averaging only 7% at reserve and non-reserve sites (Supporting Information Table S1
). The proportional increase in coral cover after 2.5 years was fairly high at reserve sites (mean of 19% per site) and significantly greater (one-tailed t-test P
0.004) than that in non-reserve sites which, on average, exhibited no net recovery. A mechanistic insight into the change in coral cover was sought using regression onto the cover of macroalgae at the start of the study (). Macroalgal cover explained 43% of the variance in the change in total coral cover over time (P
0.041). Coral cover increased at sites with relatively low macroalgal cover but declined at sites with higher cover. The change in cover was mostly driven by two diminutive brooding species of coral (Porites astreoides
and Agaricia agaricites
) and one framework-building species, Montastraea annularis
. In each of these species, the overall pattern of recovery contrasted across park boundaries, showing net recovery (increase in percentage cover) inside the park but net mortality outside (one-tailed Mann-Whitney U-test, P<0.05 for the brooders though only marginally significant for M. annularis
0.068). The change in cover of Agaricia
was moderately-strongly and negatively related to macroalgal cover (r2
0.46, P<0.03 in both species) but a relationship with macroalgal cover was not evident for the trajectory of M. annularis
Effect of macroalgal cover on the absolute change in total coral cover at survey sites.
Although trajectories of coral cover were positive inside reserves and generally negative outside reserves, our results were potentially biased by differences in the initial size-distribution of corals which varied significantly among sites in several species, including A. agaricites
and M. annularis
(Kolmogorov-Smirnoff test, P<0.05). Bias is possible because coral populations of equivalent cover but different size distributions have strikingly different scope for recovery. Imagine a series of reefs, each with identical coral cover, but some comprise a few large corals whereas others comprise many small corals. As encrusting corals grow in a linear, radial fashion 
the final coral cover after, say, 1 year of growth is substantially greater in the community dominated by many small colonies (e.g., if the initial cover comprised 20 small colonies then the absolute increase of cover would be six times greater than a community of identical initial cover that comprised a single large colony). To address this problem we developed an abstract alternative measure using Monte Carlo simulation that took the initial size distribution of each species at each site and found the radial growth rate that most closely accounted for the difference in total cover between sampling intervals. The process was repeated at each site giving an overall ‘size-adjusted rate of change of cover’ (SARCC) for each coral species based on the size distribution and observed change in coral cover at that site. Although SARCC is calculated as a linear extension rate of coral it does not directly represent a radial growth rate because it is a population-level property that subsumes coral colonisation, growth, shrinkage and mortality. However, basing its calculation on the radial growth of individual corals has the desirable property of explicitly incorporating the initial size distribution of corals. It is not intended to offer any demographic insight other than if the value is positive then recruitment and growth outweigh mortality and vice versa
(the properties of SARCC are discussed further in the Materials and Methods
Repeating our analyses with SARCC instead of absolute or proportional change in coral cover did not alter our conclusions ( and ). However, the difference in SARCC between reserve and non-reserve sites for M. annularis
moved from marginal (P
0.068) to clear significance (P
0.018), and macroalgal cover explained a greater proportion of the variance in SARCC of A. agaricites
Size-adjusted rate of change of cover (SARCC) of dominant coral species at survey sites.
Effect of macroalgal cover on the size-adjusted rate of change of cover (SARCC).
We also subjected our analysis to one further refinement in light of the coral bleaching event of 2005 
. Although coral bleaching was not severe in the Bahamas 
(also confirmed by in situ
observations at the study sites, Mumby pers. obs.), we calculated the accumulated thermal stress in 2005 above that of the climatological maximum monthly mean 
. We then asked whether differences in thermal stress constituted a plausible alternative explanation of our results to that of macroalgal cover. Adding accumulated thermal stress in a linear model against either absolute change in coral cover, proportional change in cover or SARCC did not result in a significant coefficient. In fact, the most severe thermal stress was encountered at one site in the ECLSP and no significant differences were found between the stress experienced at reserve and non-reserve sites.
Some of the most abundant macroalgae on Caribbean reefs, such as Lobophora variegata
and Dictyota pulchella
, compete with corals through a variety of mechanisms including direct overgrowth 
, pre-emption of settlement space and reduced colony growth rate 
. Our data do not allow us to disentangle the detailed way in which macroalgae influence coral recruitment, growth and mortality because there are many ways in which demographic processes can generate the observed size distributions 
and additional data on demographic rates would be required. However, our results do provide some insight into macroalgal impacts at population scales. Comparing the size structure of coral populations from 2004 to 2007 reveals a striking difference between reserve and non-reserve sites (), that complements the analyses of coral cover trajectories (–). Coral populations exhibited a healthy demographic flux inside reserves with colonies growing from smaller size classes to larger classes (). In the case of Porites
, the increase in smaller size classes in 2007 was partly due to continued recruitment between census dates but successful somatic growth of established colonies also took place because new recruits could not have grown large enough to reach the fifth and fourth size classes (for Porites
respectively) in the time elapsed between census dates. In contrast, coral populations outside the reserve lacked the demographic succession among size classes that was observed inside the reserve, implying that populations were, on average, not recovering (). Relatively little recruitment was observed in Porites
outside reserves and the density of colonies in larger size classes either remained stable or declined over time (), strongly implying that a macroalgal-induced population bottleneck restricts the supply of smaller corals to larger size classes. The degree to which this bottleneck is caused by macroalgal impacts on colony somatic growth or mortality cannot be determined definitively from our data though the identification of a population bottleneck is consistent with small-scale field experiments 
and predictions from ecological models 
. The bottleneck appeared to be even more extreme in Agaricia
where there was no sign of net recruitment or growth outside the reserve, a pattern in stark contrast to that observed within the reserve ().
Size distributions of coral density in three coral species.
The mechanisms driving change in the recovery of M. annularis
are more difficult to identify. Recruitment occurs rarely in this species and the increased densities found in the smaller size classes outside the reserve were almost entirely attributable to fission of established colonies rather than recruitment. Colony somatic growth appears to have occurred across a range of size classes inside the reserve but not so outside its boundaries; indeed a significant decline occurred in the largest size class (). The role of macroalgae in arresting recovery outside the reserve is unclear given the lack of a simple linear relationship. Contact with macroalgae certainly has energetic costs for M. annularis 
but if algae are a cause of diminished recovery, the relationship may either be complex or simply difficult to measure, possibly because of the high susceptibility of M. annularis
to disease 
which may obscure the effects of processes like algal competition.
Most studies of macroalgal impacts on coral have taken place in small experimental plots and our results provide new insight into the scalability of such studies from individual to population scales. Experimental manipulations have found that A. agaricites
is highly susceptible to macroalgal overgrowth 
, and our study suggests that this conclusion is borne out at ecosystem scales. Experimental studies of macroalgal impacts on P. astreoides
led us to expect a weaker impact than that found for A. agaricites
because P. astreoides
has been found to be relatively resistant to Lobophora
and contact with Dictyota
has reduced coral growth rate but not led to mortality 
. Again, this a priori
expectation was generally supported because, despite some inter-site variation (), mean Porites
SARCC outside the reserve appeared to be in near-stasis () whereas Agaricia
exhibited a sharp contraction (negative SARCC; ). Further, comparing the relative magnitudes of contraction outside the reserve and expansion inside the reserve () shows that the proportional level of contraction is tenfold weaker in Porites
(contraction/expansion 0.05/0.5 vs. 0.16/0.16 respectively, ).
The response of large spawning corals to a gradient of macroalgal cover exhibited a variable fit to experimental predictions. Previous studies have found Siderastrea siderea
to be unaffected by Dictyota
which is consistent with the absence of a significant effect in our study (). In contrast, Montastraea faveolata
has been found to be highly susceptible to algal overgrowth 
whereas we found no effect () despite Lobophora
being common in our study area 
. Our finding of mixed levels of scalability from experimental outcomes to ecosystem-level effects in the Bahamas in no way implies criticism of the original experiments. However, it does reinforce the need to repeat experiments in different biophysical environments and test their scalability under a variety of conditions; a process that is rarely attempted.
Marine reserves cannot protect corals from direct climate-induced disturbance 
, but they can increase the post-disturbance recovery rate of some corals providing that macroalgae have been depleted by more abundant communities of grazers that benefit from reduced fishing pressure. Such trophic cascades are most likely in the Caribbean because of the depauperate herbivore community and increased functional importance of parrotfishes following a disease-induced mortality event that significantly reduced densities of a major herbivore taxon, the urchin Diadema antillarum 
. The only other study that has attempted to quantify trajectories of coral populations inside and outside of reserves was conducted in the Indian Ocean, and found insignificant differences in coral cover growth rates 
. The higher diversity of herbivores compared to Caribbean reefs, and therefore smaller differences in trophic cascades between fished and unfished reefs, is likely to have been an important factor limiting the effect of the reserves on coral recovery rates.
While the absolute rate of coral recovery in the ECLSP was low, it must be borne in mind that these reefs had little coral to start with and that recovery trajectories would normally accelerate as corals recover 
. The degree to which reserve-driven rates of recovery will buffer the anticipated rise in rate of coral bleaching, disease, and severe hurricanes is currently unclear and will undoubtedly vary regionally 
. Indeed, coral cover does not appear to be increasing in some Caribbean reserves 
and the causation might include overwhelming coral mortality, a lack of reserve impacts on fish, or a lack of herbivore impacts on the benthos if other processes, such as nutrification or sedimentation, were to dominate the response of algae. Nonetheless, it is perhaps significant that the first documentation of net recovery from a heavily-depleted Caribbean coral community (<10% cover) stems from one of the region's most successful marine reserves. The need to take local action to reduce anthropogenic stress on reefs is both warranted and urgent.