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Existing studies comparing individual-based models of growing cellpopulations and their continuum counterparts have mainly focused on homogeneouspopulations, in which all cells have the same phenotypic characteristics.However, significant intercellular phenotypic variability is commonly observedin cellular systems. Therefore, we develop here an individual-based model forthe growth of phenotypically heterogeneous cell populations. In this model, thephenotypic state of each cell is described by a structuring variable thatcaptures intercellular variability in cell proliferation and migration rates.The model tracks the spatial evolutionary dynamics of single cells, whichundergo pressure-dependent proliferation, heritable phenotypic changes anddirectional movement in response to pressure differentials. We formally showthat the continuum limit of this model comprises a non-local partialdifferential equation for the cell population density, which generalisesearlier models of growing cell populations. Results of the individual-basedmodel illustrate how proliferation-migration tradeoffs shaping the evolution ofsingle cells can lead to the formation of travelling waves at the populationlevel where highly-mobile cells locally dominate at the invasive front, whilemore-proliferative cells are found at the rear. We demonstrate that there is anexcellent quantitative agreement between these results and the results ofnumerical simulations and formal travelling-wave analysis of the continuummodel, when sufficiently large cell numbers are considered. We providenumerical evidence of scenarios in which the predictions of the two models maydiffer due to demographic stochasticity, which cannot be captured by thecontinuum model. This indicates the importance of integrating individual-basedand continuum approaches when modelling the growth of phenotypicallyheterogeneous cell populations.

Individual-based and continuum models of phenotypically heterogeneous growing cell populations