The “Public Goods Problem” has confounded biologists (and social scientists) for generations. In the cancer biology context, it can be posed as follows: how does a new clone that produces diffusible factors (e.g. paracrine growth signal, cytokine, or angiogenic factor) benefiting a whole tumor microenvironment invade and persist in the tumor population? Previously, it has been shown that subclone coexistence can persist indefinitely in a population under certain conditions, but, at the same time, it has been hypothesized that ‘invasion’, i.e. clonal expansion from a single cell, is not possible. Generally speaking, invasion is more complicated than subclone coexistence because invader numbers are extremely low and stochasticity plays an important role. We performed numerical simulations using square lattice with Von Neumann neighborhood, introducing a single invader that secretes diffusible public goods that diffuse by random walk through the lattice probabilistically binding to cells located at lattice nodes. We find that invasion of public good producers is indeed possible (i) across a wide range of biologically-relevant parameters, (ii) regardless of whether the population is expanding or not, and (iii) robust to moderate fitness costs associated with production. In addition, we built an analytical model, results of which agreed well with the numerical simulation approach and identified a dimensionless parameter that describes the regions of parameter space where invasion is common.
© 2026 - The Mathematical Oncology Blog
© 2026 - The Mathematical Oncology Blog