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We consider a model for the dynamics of growing cell populations withheterogeneous mobility and proliferation rate. The cell phenotypic state isdescribed by a continuous structuring variable and the evolution of the localcell population density function (i.e. the cell phenotypic distribution at eachspatial position) is governed by a non-local advection-reaction-diffusionequation. We report on the results of numerical simulations showing that, inthe case where the cell mobility is bounded, compactly supported travellingfronts emerge. More mobile phenotypic variants occupy the front edge, whereasmore proliferative phenotypic variants are selected at the back of the front.In order to explain such numerical results, we carry out formal asymptoticanalysis of the model equation using a Hamilton-Jacobi approach. In summary, weshow that the locally dominant phenotypic trait (i.e. the maximum point of thelocal cell population density function along the phenotypic dimension)satisfies a generalised Burgers' equation with source term, we constructtravelling-front solutions of such transport equation and characterise thecorresponding minimal speed. Moreover, we show that, when the cell mobility isunbounded, front edge acceleration and formation of stretching fronts mayoccur. We briefly discuss the implications of our results in the context ofglioma growth.

Invasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobility