Many theoretical studies of range expansions focus on the dynamics of species' ranges or on causes and consequences of biological invasions. The similarities between biological range expansions and the dynamics of tumour growth have recently become more obvious, highlighting that tumours can be viewed as a population of abnormal cells expanding its range in the body of its host. Here, we discuss the potential of recent theoretical developments in the context of range expansions to shed light on intra-tumour heterogeneity, and to develop novel computational and statistical methods for studying the increasingly available genomic and phenotypic data from tumour cells. We review two spatial eco-evolutionary processes that could lead to a better understanding of the spatial structure of intra-tumour heterogeneity during the development of solid tumours: (1) the increase in dispersal abilities and (2) the accumulation of deleterious mutations at the front of expanding range edges. We first summarize theoretical and empirical evidences for each of these two phenomena and illustrate the eco-evolutionary dynamics of these processes using mathematical models. Secondly, we review evidences that these phenomena could also occur during the spatial expansion of a tumour within hosts. Finally, we discuss promising avenues for future research with the aim of synthesizing insights from clinical and theoretical studies of tumour development and evolutionary biology.
Keywords: Expansion load; Intra-tumour heterogeneity; Life-history traits; Spread rate.