title: Size change, shape change, and the growth space of a community.
abstract: 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.
authors.affiliation: School of Environmental Sciences, University of Liverpool, Liverpool L69 3GP, UK. Electronic address: m.spencer@liverpool.ac.uk.
authors.forename: Matthew
authors.initials: M
authors.lastname: Spencer
mesh_terms: D000818:Animals; D044822:Biodiversity; D049628:Body Size; D004175:Diptera; D017753:Ecosystem; D063245:Plant Development; D011157:Population Dynamics; D013045:Species Specificity; D013997:Time Factors; D006113:United Kingdom
keywords: Aitchison distance; Community dynamics; Per capita growth; Succession; Surreal numbers