The Metabolic Scaling Theory (MST), hypothesizes limitations of resource-transport networks in organisms and predicts their optimization into fractal-like structures. As a result, the relationship between population growth rate and body size should follow a cross-species universal quarter-power scaling. However, the universality of metabolic scaling has been challenged, particularly across transitions from bacteria to protists to multicellulars. The population growth rate of unicellulars should be constrained by external diffusion, ruling nutrient uptake, and internal diffusion, operating nutrient distribution. Both constraints intensify with increasing size possibly leading to shifting in the scaling exponent. We focused on unicellular algae Micrasterias. Large size and fractal-like morphology make this species a transitional group between unicellular and multicellular organisms in the evolution of allometry. We tested MST predictions using measurements of growth rate, size, and morphology-related traits. We showed that growth scaling of Micrasterias follows MST predictions, reflecting constraints by internal diffusion transport. Cell fractality and density decrease led to a proportional increase in surface area with body mass relaxing external constraints. Complex allometric optimization enables to maintain quarter-power scaling of population growth rate even with a large unicellular plan. Overall, our findings support fractality as a key factor in the evolution of biological scaling.

CEFE Univ Montpellier CNRS EPHE IRD 1919 Route de Mende 34293 Montpellier France

Department of Botany Faculty of Science Charles University Benátská 2 Prague Czech Republic

Microalgae and Zygnematophyceae Collection Hamburg Institute of Plant Science and Microbiology Universität Hamburg Ohnhorststr 18 22609 Hamburg Germany

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