Foundations of ecological and evolutionary change

Biological evolution is realised through the same mechanisms of birth and death that underlie change in population density. The deep interdependence between ecology and evolution is well-established, and recent models focus on integrating eco-evolutionary dynamics to demonstrate how ecological and evolutionary processes interact and feed back upon each other. Nevertheless, a gap remains between the logical foundations of ecology and evolution. Population ecology and evolution have fundamental equations that define how the size of a population (ecology) and the average characteristic within a population (evolution) change over time. These fundamental equations are a complete and exact description of change for any closed population, but how they are formally linked remains unclear. We link the fundamental equations of population ecology and evolution with an equation that sums how individual characteristics interact with individual fitness in a population. From this equation, we derive the fundamental equations of population ecology and evolutionary biology (the Price equation). We thereby identify an overlooked bridge between ecology and biological evolution. Our unification formally recovers the equivalence between mean population growth rate and evolutionary fitness and links this change to ecosystem function. We outline how our framework can be used to further develop eco-evolutionary theory.