The Uzawa-Lucas Model in Discrete Time with General Population Growth Rate

2017 ◽  
Author(s):  
Emiliano Alvarez ◽  
Juan Gabriel Brida ◽  
Gaston Cayssials ◽  
Pilar Lorenzo ◽  
Mijail Yapor
Keyword(s):  
Growth Rate ◽  
General Population ◽  
Population Growth ◽  
Discrete Time ◽  
Population Growth Rate

scholarly journals Biological scaling in green algae: the role of cell size and geometry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Helena Bestová ◽  
Jules Segrestin ◽  
Klaus von Schwartzenberg ◽  
Pavel Škaloud ◽  
Thomas Lenormand ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Population Growth Rate ◽  
Internal Diffusion ◽  
Scaling Exponent ◽  
Power Scaling ◽  
Nutrient Distribution ◽  
Metabolic Scaling ◽  
Key Factor ◽  
Size And Morphology

AbstractThe 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.

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