Modeling individual conifer seed shape as a sum of fused partial ellipsoids

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Because of the importance of seed surface area, volume, and fill to hydraulic and thermal exchanges with the soil, mechanistic simulation of seed physiological processes associated with tree migration dynamics and the spread of invasive species require accurate equations to model seed shape. Seed dimensions have previously been described with measurements of the three principal axes, assuming an implied single ellipsoid. However, conifer seeds often exhibit anisotropy that results from bilaterally symmetric pairing on cone scales. We developed a method for measuring and modeling conifer seed shape as a sum of 2jpartial ellipsoids fused at their equators, where j = 0, …, 3. We demonstrate the use of the methods in the study of shape characteristics of ponderosa pine (Pinus ponderosa P.& C. Lawson) seeds from four families in Montana and among commercial lots of ponderosa pine, lodgepole pine (Pinus contorta Dougl. ex Loud.), and Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco). The shapes of 92%, 73%, and 47% of seeds in commercial lots studied had eight unique ellipsoids when classified with 1%, 5%, and 10% difference classification rules, respectively. Ponderosa pine seeds with longer minor axes were less well filled with storage reserves. Three-dimensional surface areas of lodgepole and ponderosa pine were approximately 2 and 3.4 times larger, respectively, than previously reported one-sided surface areas.