Figure S1. Scaling coefficients of flux (J), surface area (A), thickness (x), diffusion (Dc), capacitance (β), and the oxygen gradient (ΔPO2). from Upper limits to body size imposed by respiratory-structural trade-offs in Antarctic pycnogonids

Scaling coefficients of flux (J), surface area (A), thickness (x), diffusion (Dc), capacitance (β), and the oxygen gradient (ΔPO2). Coloured lines correspond to coloured variables within Fick's law (eq. 3 and displayed on each graph). The exponents within the equation are equal to the scaling coefficient from the associated figure. A) Fick's law described in terms of scaling coefficients from Gillooly et al. (2016). In vertebrates, Dc, β, and ΔPO2 do not scale with body size and changes in A and x are sufficient to meet oxygen demands (i.e., 0.89 – 0.1 = 0.79). B-D) Hypothesized scaling coefficients of animals relying on cutaneous respiration. Slopes of all Fick variables, when added up following Fick's equation, should be equivalent to scaling of MR (null expectation, b = 0.75). A and x are hypothesized to scale with geometric isometry (b = 0.66 and 0.33, respectively), because cuticle provides structural support. In contrast to vertebrates, either Dc (B), ΔPO2 (C), or both (D) must scale positively to meet the increased oxygen demands of larger animals. Capacitance (β) is not expected to vary with body size as it is only dependent on the temperature and type of medium.