Coral and crustose coralline algae (CCA) are important reef builders that compete for space on tropical reefs.  While some species of CCA provide settlement cues to coral and other invertebrates, others overgrow juvenile corals and employ antifouling defenses to prevent other species from settling on or overgrowing them.  Many types of coral and CCA compete for space in areas that have sufficient light for long term survival and growth, and coexist in these habitats despite the overgrowth of coral by CCA.  Some current theory suggests that species competing in homogeneous habitats against an overgrowing competitor can escape exclusion by occupying open space more effectively.  However, compelling evidence for such a life history tradeoff does not exist for many corals, which may not have advantages in growth rates or colonization ability.  An alternative mechanism for coexistence is that the competitive ability of a coral colony increases with colony size, to the extent that overgrowth by CCA is slowed or halted once the colony achieves sufficient biomass.  We employ three models of increasing complexity to ask whether a size refuge from competition could allow coral with a vulnerable early life stage to compete successfully through an invulnerable mature stage.   

Results/Conclusions

Ordinary differential equation (ODE) models containing a simple mechanism for size dependent competition suggest that a size refuge can indeed allow corals to persist with or exclude CCA, in agreement with earlier studies.  However, ODE models overlook two crucial aspects of the system: the time required to reach larger sizes, and the contiguous free space needed for colonies to grow.  We use delay differential equations and spatially explicit simulations that account for these factors to show that size dependent competition cannot alone guarantee the persistence of corals that are vulnerable to overgrowth from CCA when small.  Using growth and overgrowth parameters derived from field studies, we find that only a very small proportion of corals survives long enough to outgrow the vulnerable stage.  Simulation models demonstrate that the lack of contiguous unoccupied substrate when CCA is established can further hinder coral growth and prevent re-invasion in the absence of extensive disturbance.  We then extend the simulations to include spatial heterogeneity and demonstrate how protected microhabitats for coral settlement, in conjunction with size-dependent competition, can enable coexistence of coral with CCA in well-lit habitats.