Evolution

Intra-tumor heterogeneity is a hallmark of nearly all cancers. Populations of tumor cells show remarkable heterogeneity in almost all phenotypic attributes, including clinically important features such as treatment resistance and metastatic potential. Intra-tumor heterogeneity (ITH) represents a major challenge for effective cancer treatment and precision medicine. However, the patterns of ITH and aspects of underlying modes of tumor evolution are poorly understood for most cancer types.

During his upcoming Public Lecture, evolutionary biologist Martin Nowak, author of the best-selling book SuperCooperators, will share his cutting-edge research on the mysteries of cooperation. According to Nowak, many problems that challenge us today can be traced back to a tension between what is good and desirable for society as a whole and what is good and desirable for an individual. This conflict is illustrated by global problems such as climate change, pollution, hunger, and overpopulation.

We consider a class of models that generalizes the Bak Sneppen model
that can be used to study evolution.
Agents with random fitnesses are located at the vertices of a graph $G$.
At every time-step the agent with the worst fitness emph{and its neighbors on $G$} are
replaced by new agents with random fitnesses.

By using Order Statistics
and Dynamical Systems, we succeeded in solving a number of questions
about how the distribution of the fitnesses evolves under this process.