Scaling Laws in Biology and Other Complex Systems
Description
Life is very likely the most complex phenomenon in the Universe manifesting an extraordinary
diversity of form and function over an enormous range. Yet, many of its
most fundamental and complex attributes scale with size in a
surprisingly simple fashion. For example, metabolic rate (the power
required to sustain the system) scales as approximately the 3/4-power
of mass over 27 orders of magnitude from molecular levels up to the
largest multicellular organisms. Similarly, time-scales, such as
lifespans and growth-rates, increase with exponents which are typically
simple powers of 1/4. It will be shown how these universal
quarter-power scaling laws follow from fundamental generic principles
embedded in the dynamics and geometry of underlying networks, leading
to a general quantitative theory that captures essential features of
many diverse biological systems. Examples will include animal and plant
vascular systems, growth, cancer, aging and mortality, sleep, DNA
nucleotide substitution rates. These ideas will be extended to discuss
social organisations such as cities and firms: to what extent, if at
all, can we think of these as very large organisms and therefore as an
extension of biology? Analogues to metabolic rate and behavioral times in cities scale counter to their behaviour in biology.
Driven by innovation and the creation of wealth this has dramatic
implications for their growth, development, sustainability and pace of
life which, left unchecked, potentially sow the seeds for their
collapse.
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