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Size and Scaling

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lightbulbAbout this topic
Size and scaling is the study of how physical properties and biological functions of organisms or systems change with size. It examines the relationships between dimensions, mass, and other characteristics, often employing mathematical models to understand the implications of size variations across different contexts in biology, physics, and engineering.
lightbulbAbout this topic
Size and scaling is the study of how physical properties and biological functions of organisms or systems change with size. It examines the relationships between dimensions, mass, and other characteristics, often employing mathematical models to understand the implications of size variations across different contexts in biology, physics, and engineering.

Key research themes

1. How does size and scaling affect nutrient uptake and growth dynamics in phytoplankton communities?

This research theme investigates the mechanistic and physiological effects of phytoplankton cell size on nutrient uptake kinetics, growth rates, and carbon fixation, incorporating physiological trade-offs and environmental resource availability. It aims to understand how size-dependent traits influence ecological community structure and biogeochemical function, especially under varying light and nutrient conditions in marine ecosystems.

Key finding: This paper presents a novel model that integrates a size-based framework accounting for extracellular diffusive limitation with an optimal resource allocation trade-off to explain the half-saturation constant for nitrate... Read more
Key finding: Using physiological models, this study shows that phytoplankton growth rate scaling exponents vary from about 3/4 under resource saturation to between 1/3 and 2/3 under nutrient or light limitation, reflecting the shifting... Read more
Key finding: Empirical analysis reveals near-isometric scaling of carbon fixation rates with cell size across oceanic ecosystems, with biomass-specific photosynthesis rates largely independent of size. Contrasting size-abundance scaling... Read more

2. How can scaling principles elucidate the growth and structure of complex networked systems?

This theme centers on the origins and mechanisms underlying observed super-linear and sub-linear scaling behaviors in the growth of complex, spatially embedded networks, including online communities, urban systems, citation networks, and ecological webs. The focus is on unified geometric network models that capture how spatial constraints and node interactions produce characteristic scaling laws, offering analytical insight into network dynamics and aggregation.

Key finding: The proposed Spatial-Constrained Attachment (SCA) geometric network model, parameter-free and embedded in Euclidean space of arbitrary dimension, simultaneously reproduces super-linear scaling of links/activities and... Read more

3. How do concepts of scale and scaling influence the implementation of innovations in mathematics education research?

This research area addresses the conceptual clarity and operational definitions of scale and scaling in the context of large-scale implementation of educational innovations, especially in mathematics education. It explores dimensions such as spread, sustainability, depth, and ownership shifts, and distinguishes small, medium, and large-scale implementations based on organizational, material, and contact factors to better characterize and guide scaling efforts.

Key finding: Using a Delphi-inspired method combined with literature review, this study elucidates varying expert understandings of scale and scaling, moving beyond simplistic notions of expansion in participant numbers. It... Read more

4. What are the risks and limitations inherent in scaling big capital investments and infrastructure projects?

This theme investigates the fragility associated with large-scale capital investments, challenging the assumption that bigger projects inherently yield better economies of scale and scope. It highlights how scaling increases non-linear exposure to uncertainties leading to poor financial and operational outcomes. The work emphasizes a critical assessment of where scaling adds value versus where it leads to disproportionate risks, with implications for project leadership and management.

Key finding: This paper theorizes the systematic fragility of large capital investments, showing that despite economies of scale, big projects incur disproportionate uncertainty exposures that lead to frequent negative net present values... Read more

All papers in Size and Scaling

We present a new model for the kinetics of nutrient uptake by phytoplankton, which we derive by combining existing models: (1) a size-based modeling framework that accounts for the effects of extra-cellular diffusive limitation, and (2) a... more
The problem considered in this work is formation control for non-identical linear multi-agent systems (MASs) under a time-varying communication network. The size of the formation is scalable via a scaling factor determined by a leader... more
The problem considered in this work is formation control for non-identical linear multi-agent systems (MASs) under a time-varying communication network. The size of the formation is scalable via a scaling factor determined by a leader... more
This study was aimed at identifying macroecological patterns in the relationship between phytoplankton cell size, abundance and metabolism in 2 marine ecosystems characterised by marked differences in resource availability and... more
The size of an organism matters for its metabolic, growth, mortality, and other vital rates. Scale-free community size spectra (i.e., size distributions regardless of species) are routinely observed in natural ecosystems and are the... more
by S. Lan Smith and 
1 more
We present a new model for the kinetics of nutrient uptake by phytoplankton, which we derive by combining existing models: (1) a size-based modeling framework that accounts for the effects of extra-cellular diffusive limitation, and (2)... more
On the basis of the assumption that natural selection should tend to produce organisms optimally adapted to their environments, we consider optimality as a guiding concept for abstracting the behavior of aquatic microorganisms (plankton)... more
Microalgal photosynthesis can be predicted using empirical allometric or mechanistic bio-optic models. These two descriptions are usually considered independently. We compare the size scaling of photosynthesis predicted by these two... more
On the basis of the assumption that natural selection should tend to produce organisms optimally adapted to their environments, we consider optimality as a guiding concept for abstracting the behavior of aquatic microorganisms (plankton)... more
A primary goal of macroecology is to identify principles that apply across varied ecosystems and taxonomic groups. Here we show that the allometric relationship observed between maximum abundance and body size for terrestrial plants can... more
Communities of marine phytoplankton consist of cells of many different sizes. The size-structure of these communities often varies predictably with environmental conditions in aquatic systems. It has been hypothesized that physiological... more
Size scaling of phytoplankton growth rates and size-dependent carbon to nitrogen (C:N) stoichiometry determine phytoplankton size structure and coupling of carbon and nitrogen cycling of marine ecosystems. They are critical in predicting... more
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