  Measures of biodiversity change such as the Living Planet Index describe
proportional change in the abundance of a typical species, which can be thought
of as change in the size of a community. Here, I discuss the orthogonal concept
of change in relative abundances, which I refer to as shape change. To be
logically consistent, a measure of the rate of shape change should be scaling
invariant (have the same value for all data with the same vector of
proportional change over a given time interval), but existing measures do not
have this property. I derive a new, scaling invariant measure. I show that this
new measure and existing measures of biodiversity change such as the Living
Planet Index describe different aspects of dynamics. I show that neither body
size nor environmental variability need affect the rate of shape change. I
extend the measure to deal with colonizations and extinctions, using the
surreal number system. I give examples using data on hoverflies in a garden in
Leicester, UK, and the higher plant community of Surtsey. I hypothesize that
phylogenetically-restricted assemblages will show a higher proportion of size
change than diverse communities.
