  The Gini coefficient of the life table is a concentration index that provides
information on lifespan variation. Originally proposed by economists to measure
income and wealth inequalities, it has been widely used in population studies
to investigate variation in ages at death. We focus on a complementary
indicator, Drewnowski's index, which is as a measure of equality. We study its
mathematical properties and analyze how changes over time relate to changes in
life expectancy. Further, we identify the threshold age below which mortality
improvements are translated into decreasing lifespan variation and above which
these improvements translate into increasing lifespan inequality. We illustrate
our theoretical findings simulating scenarios of mortality improvement in the
Gompertz model. Our experiments demonstrate how Drewnowski's index can serve as
an indicator of the shape of mortality patterns. These properties, along with
our analytical findings, support studying lifespan variation alongside life
expectancy trends in multiple species.
