Cancer growth can be described as a caricature of the renewal process of the tissue of
origin, where the tissue architecture has a strong influence on the evolutionary dynamics …

Natural selection is usually studied between mutants that differ in reproductive rate, but are
subject to the same population structure. Here we explore how natural selection acts on …

Populations evolve in spatially heterogeneous environments. While a certain trait might
bring a fitness advantage in some patch of the environment, a different trait might be …

Spatial heterogeneity plays an important role in the evolution of drug resistance. While
recent studies have indicated that spatial gradients of selection pressure can accelerate …

We present a mathematical study of the emergence of phenotypic heterogeneity in
vascularized tumors. Our study is based on formal asymptotic analysis and numerical …

We consider a mathematical model for the evolutionary dynamics of tumour cells in
vascularised tumours under chemotherapy. The model comprises a system of coupled …

Antibiotic-resistant infections are a growing threat to human health, but basic features of the
eco-evolutionary dynamics remain unexplained. Most prominently, there is no clear …

The signature of early cancer dynamics on the spatial arrangement of tumour cells is poorly
understood, and yet could encode information about how sub-clones grew within the …

The mean conditional fixation time of a mutant is an important measure of stochastic
population dynamics, widely studied in ecology and evolution. Here, we investigate the …

Fixation probability, the probability that the frequency of a newly arising mutation in a
population will eventually reach unity, is a fundamental quantity in evolutionary genetics …