  Aging is a fundamental aspect of living systems that undergo a progressive
deterioration of physiological function with age and an increase of
vulnerability to disease and death. Living systems, known as complex systems,
require complexity in interactions among molecules, cells, organs, and
individuals or regulatory mechanisms to perform a variety of activities for
survival. On this basis, aging can be understood in terms of a progressive loss
of complexity with age; this suggests that complexity in living systems would
evolve with age. In general, aging dynamics is mathematically depicted by a
survival function, which monotonically changes from 1 to 0 with age. It would
be then useful to find an adequate survival function to link aging dynamics and
complexity evolution. Here we describe a flexible survival function, which is
derived from the stretched exponential function by adopting an age-dependent
exponent. We note that the exponent is associated with evolving complexity,
i.e., a fractal-like scaling in cumulative mortality. The survival function
well depicts a general feature in survival curves; healthy populations show a
tendency to evolve towards rectangular-like survival curves, as examples in
humans or laboratory animals. This tendency suggests that both aging and
complexity would evolve towards healthy survival in living systems. Our
function to link aging with complexity may contribute to better understanding
of biological aging in terms of complexity evolution.
