Modelling coral reef biodiversity and habitat destruction

Abstract

World wide coral reef decline has now been well nities, species have been understood to interact in a documented, but the actual dynamics of this disturbing phehierarchical web of competitive interactions, In all of nomenon are still far from understood. In t h~s note we the above models, a set of N species colonize and com- Coral reefs, the most complex and diverse of all aquatic ecosystems, are currently facing widespread devastation. Wilkinson (1993) warned that some 70% of the world's reefs will be completely destroyed over the next 40 yr and massive species extinctions are to be expected if the process is not soon reversed. The recent model of Tilman et al. (1994) (henceforth referred to as TMLN) becomes of particular relevance, for it predicts the species extinction debt in ecosystems as habitat destruction (D) increases. Here we modify TMLN and test it with field data from the reef flats in Eilat, Israel. The following note is intended to focus more on the ecological implications of our findings. Complete details concerning the more technical theoretical and mathematical aspects of our work will be presented in a companion paper (Stone 1995).The spatial model described by TMLN and also used here, was originally designed by Hastings (1980) for application to coral reef communities. In such commuthe good colonizers are weak competitors. Because individuals are mortal, species are constantly losing patches by the usual death process. This in turn provides a continuous source of newly opened patches for which species compete. On average, the weaker competitors are able to colonize vacant patches more rapidly. This is how the trade-off between competition and colonization helps prevent the best competitor from eventually taking over all possible space.In the terminology of the present note, we let p, denote the proportion of the total number of patches on which species i resides, which is also loosely referred to here as the species' abundance. The colonization potential of the ith species is taken to be c;, while its mortality rate is m,. Following TMLN, we assume that a proportion D of sites, where 0 6 D 5 1, are permanently destroyed and can never be colonized. Ultimately we seek to determine the effects of habitat destruction on a model coral reef system..The spatial growth of the ith species is modelled by the differential equation (Hastings 1980, TMLN):

The future of coral reefs

“…Stone (99,100) analyzed a Red Sea reef flat and concluded that numbers of species extinctions associated with habitat reduction would be especially catastrophic because competitively dominant corals were already rare. However, this result reflects the fact that reef flats are regularly disturbed and, thus, always dominated by weedy corals.…”

“…The models (97,98), as they have been applied to reefs to date (99,100), assume that each patch is occupied by a single species. In this sense, the analyses describe the dynamics on single reefs, with patches being de facto the spaces occupied by individual colonies.…”

Can Caribbean coral populations be modelled at metapopulation scales?

“…Caswell & Cohen 1993, Tilman et al 1994, Man et al 1995, Stone et al 1996 assume th.at disturba.nce leads to complete extinction of species on a patch but, during ecological time scales, such severe effects of disturbance are not appropriate for open populations of marine organisms which may show greater resistance to extinction (Caley et al 1996, Connell et al 1997. A more suitable model would allow local populations to be depressed but rarely driven to extinction.…”

“…Iwasa . Man et al 1995, Stone et al 1996). An appropriate model of larval dispersal needs 2 principal components: (1) the geographic transport of larvae between reefs, which depends on the velocity and vertical stratification of oceanic and coastal currents, and the motility of larvae, and (2) the survivorship of larvae over time.…”

“…Possingham & Roughgarden 1990, Stone et al 1996 and mobile (Man et al 1995) marine organisms, but, as I will show later, none are su~table for modelling fish or invertebrate metapopulations distributed across reefs of the Caribbean. hletapopulation models were originally conceived by Levins (1970) to describe a structureless network of conspecific populations whose dynamics were dominated by extinction and colonisation.…”