  This paper presents a mathematical framework for modeling the dynamics of
heterogeneous populations. Models describing local and non-local growth and
transport processes, dependent on dynamically changing population structures,
appear in a variety of applications such as crowd dynamics, tissue
regeneration, cancer development, and coagulation-fragmentation processes. The
current body of literature regarding mathematical modeling presents common
challenges to mathematicians due to the multiscale nature of the structures
that underlie self-organisation and control within complex, heterogeneous
systems. In various applications, similar, abstract mathematical concepts arise
through problem formulation and the assimilation of mathematical depictions
into the language of measure evolution on a multi-faceted state space. In view
of the above observations, we propose an overarching mathematical framework for
nonlinear structured population models on abstract metric spaces, which are
only assumed to be separable and complete.
  To achieve this, we exploit the structure of the space of non-negative Radon
measures under the dual bounded Lipschitz distance (flat metric), a
generalization of the Wasserstein distance that is capable of addressing
non-conservative problems. The formulation of models on generic metric spaces
facilitates the study on infinite-dimensional state spaces or graphs with a
combination of discrete and continuous structures. This opens up exciting
possibilities for modeling single cell data, crowd dynamics or
coagulation-fragmentation processes.
