Evolution of virulence:
Why are some pathogens worse and some just bad? This is probably one of the oldest question evolutionary biologists have tried to answer for a long time. To some extent, trade-off hypothesis has been successful in explaining and predicting the evolution of virulence for obligatory pathogens. Opportunistic pathogens, on the other hand, have a complicated life-histories which tend to relax assumed trade-offs of classical virulence evolution model and at the same time there could be other ecological trade-offs that might be important in virulence evolution. I am trying to understand this fascinating question of virulence evolution in the system of opportunistic pathogens. Mathematical modeling is central to my approach.
Evolutionary theories in general:
Modern evolutionary theories are mathematical. Evolution is a multilevel process and there is regular feedbacks between these layers. Different mathematical techniques are utilized to address the problems at each levels but the feedbacks often complicate such endeavors. Recent attempts at unifying different approaches of understanding evolution from theoretical viewpoint (Queller 2017, Lehtonen 2018) are exciting as they could lay some foundational ground for unified framework for evolutionary theory.