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Theoretical aspects of surface-to-volume ratios and water-storage capacities of succulent shoots.

Surface-to-volume (S/V) ratios of drought-adapted plants affect transpiration, photosynthesis, and water-storage capacity. The S/V ratio of cladodes and flat leaves is S/V = 2/T, where T is thickness: even slight thickening greatly reduces S/V. During rain/drought cycles succulent stems swell and shrink without tearing by having flexible ribs, but ribs increase S/V above that of a smooth cylindrical stem with equal volume: the increased surface area is S(ribbed)/S(cylindrical) = N[x + (π/N)]/π(1 + x), where N is number of ribs and x is rib height relative to the radius of the inner stem. Numerous low ribs provide moderate expandability (storage volume) with little increase in S/V and are adaptive where droughts are short. Tall ribs provide greater expandability but greatly increase S/V and probably are adaptive only in mesic habitats. Having ∼8-15 ribs, each about as tall as the inner stem radius, provides large storage capacity and intermediate increase in S/V. By increasing absolute size, S/V is reduced so greatly that even large ribs can have an S/V smaller than that of a narrow cylindrical or spherical stem with less volume.