Characteristic length scales of spatial models in ecology via fluctuation analysis

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Abstract
To examine algal (= zooxanthellae) regulation and control, and the factors determining algal densities in hard corals, the zooxanthellae mitotic index and release rates were regularly determined in branch tips from a colony of a staghorn coral, Acropora formosa, recovering from a coral ‘bleaching’ event (the stress–related dissociation of the coral–algal symbiosis). Mathematical models based upon density–dependent decreases in the algal division frequency and increases in algal release rates during the post–bleaching recovery period accurately predict the observed recovery period (≈ 20 weeks). The models suggest that (i) the colony recovered its algal population from the division of the remaining zooxanthellae, and (ii) the continual loss of zooxanthellae significantly slowed the recovery of the coral. Possible reasons for the ‘paradoxical’ loss of healthy zooxanthellae from the bleached coral are discussed in terms of endodermal processes occurring in the recovering coral and the redistribution of newly formed zooxanthellae to aposymbiotic host cells. At a steady–state algal density of 2.1 × 106 zooxanthellae cm−2 at the end of the recovery period, the zooxanthellae would have to form a double layer of cells in the coral tissues, consistent with microscopic observations. Neighbouring colonies of A. formosa with inherently higher algal densities possess proportionately smaller zooxanthellae. Results suggest that space availability and the size of the algal symbionts determines the algal densities in the coral colonies. The large increases in the algal densities reported in corals exposed to elevated nutrient concentrations (i.e between a two– and five–fold increase in the algal standing stock) are not consistent with this theory. We suggest that increases of this magnitude are a product of the experimental conditions: reasons for this statement are discussed. We propose that the stability of the coral–algal symbiosis under non–stress conditions, and the constancy of zooxanthellae densities in corals reported across growth form, depth and geographic range, are related to space availability limiting algal densities. However, at these densities, zooxanthellae have attributes consistent with nutrient limitation.

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