General models for the spectra of surface area scaling strategies of cells and organisms: fractality, geometric dissimilitude, and internalization

Surface areas and volumes of biological systems—from molecules to organelles, cells, and organisms—affect their biological rates and kinetics. Therefore, surface-area-to-volume ratios and the scaling of surface area with volume profoundly influences ecology, physiology, and evolution. The zeroth-order geometric expectation is that surface area scales with body mass or volume as a power law with an exponent of two-thirds, with consequences for surface-area-to-volume (SA:V) ratios and constraints on size; however, organisms have adaptations for altering the surface area scaling and SA:V ratios of their bodies and structures. The strategies fall into three groups: (i) fractal-like surface convolutions and crinkles; (ii) classic geometric dissimilitude through elongating, flattening, fattening, and hollowing; and (iii) internalization of surfaces. Here I develop general quantitative theory to model the spectra of effects of these strategies on SA:V ratios and surface area scaling, from expo...