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 2+( π / N ) 2 ] /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.