  Diversity measurement underpins the study of biological systems, but measures
used vary across disciplines. Despite their common use and broad utility, no
unified framework has emerged for measuring, comparing and partitioning
diversity. The introduction of information theory into diversity measurement
has laid the foundations, but the framework is incomplete without the ability
to partition diversity, which is central to fundamental questions across the
life sciences: How do we prioritise communities for conservation? How do we
identify reservoirs and sources of pathogenic organisms? How do we measure
ecological disturbance arising from climate change?
  The lack of a common framework means that diversity measures from different
fields have conflicting fundamental properties, allowing conclusions reached to
depend on the measure chosen. This conflict is unnecessary and unhelpful. A
mathematically consistent framework would transform disparate fields by
delivering scientific insights in a common language. It would also allow the
transfer of theoretical and practical developments between fields.
  We meet this need, providing a versatile unified framework for partitioning
biological diversity. It encompasses any kind of similarity between
individuals, from functional to genetic, allowing comparisons between
qualitatively different kinds of diversity. Where existing partitioning
measures aggregate information across the whole population, our approach
permits the direct comparison of subcommunities, allowing us to pinpoint
distinct, diverse or representative subcommunities and investigate population
substructure. The framework is provided as a ready-to-use R package to easily
test our approach.
