I have 30 years of research experience in nonlinear dynamics. With initial interests in the abstraction of symmetries governing pattern formation in natural and experimental systems, in the last 20 years my research activity has primarily involved mathematical modelling of infectious disease dynamics and epidemiology. Over the last 10 years, I became increasingly appreciative of the need to build and promote new infectious disease epidemiology theory to account for individual variation in characteristics that are under selection, especially when selection forces are dynamic. These characteristics may not be heritable, in which case selection affects each generation while being invisible to current evolutionary theory, which to some extent also needs to be re-examined. More generally, whether we refer to populations of humans, animals, microbes, or cells, the idea that in every observational or experimental study there is always a degree of unobserved heterogeneity that can reverse the direction of our conclusions is unsettling, but the issue can be tackled by general mathematical formalisms that account for it combined with study designs that enable its estimation.

Ten years ago, I encountered a concept that transformed the way I think about populations. The idea of frailty variation was introduced in demography 40 years ago to describe variation in individual longevity. As the frailest individuals are removed earlier from a heterogeneous cohort, death rates decline over time creating an impression that individual longevity is increasing even when it is not. This is the simplest realisation of a phenomenon that has manifold manifestations in any study that involves counting the individuals that constitute a population over time, across environments or experimental conditions. It appears to explain a wide range of reported discrepancies between studies and contribute to resolve decade-long debates, such as why vaccines appear less efficacious where disease burdens are high, why mathematical models tend to overpredict the impact of disease control measures and whether niche mechanisms need to be invoked to explain the levels of biodiversity observed in nature. I have reformulated these and other problems and have been privileged to collaborate with colleagues around the world.