Scaling analyses and morphometrics of <i>Ginkgo biloba</i> seeds

This study establishes the scaling relationships of the Ginkgo biloba sclerotesta and its contents (denoted henceforth as “seed”) using 1,225 samples from four trees. The scaling exponent of seed volume (V) vs. the volume of a hypothetical triaxial ellipsoid (defined by semi-axes equivalent to half the seed length, width, and thickness; denoted as VE) was 1.0028 (95% confidence interval: 0.9837 − 1.0220), indicating isometric scaling. In contrast, the scaling exponent of V vs. seed fresh mass (M) was 1.0455 (95% confidence interval: 1.0294 − 1.0626), indicating allometric scaling. When seeds were grouped by the ellipsoid index (EI = V/VE), the scaling exponent of V vs. M decreased from values significantly greater than one to values less than one as EI increased. This progression indicated that increases in V slightly outpace increases in M associated with small EI values, whereas increases in V do not keep pace with increases in M across large EI values. Seeds exhibited consistent geometric asymmetry, with a mean thickness-to-width ratio of 0.82, indicating that they are not solids of revolution. The isometry in V vs. VE and the systematic shift in V vs. M scaling across shape groups indicate a coordinated system for physical space and biomass allocation. Significant morphometric differences were found among seeds when they were grouped by their EI values. This work provides a quantitative framework for understanding resource partitioning in an ancient gymnosperm, applicable to other seeds with approximately ellipsoidal or non-rotational symmetry.