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, but much theory in each discipline has been developed in isolation. While recent work has accomplished eco-evolutionary synthesis, a gap remains between the logical foundations of ecology and evolution. We bridge this gap with a new equation that defines a summed value for a characteristic across individuals in a population, from which the fundamental equations of population ecology and evolutionary biology (the Price equation) are derived. We thereby unify the fundamental equations of population ecology and biological evolution under a general framework. Our unification further demonstrates the equivalence between mean population growth rate and evolutionary fitness, shows how ecological and evolutionary change are reflected in the first and second statistical moments of fitness, respectively, and links this change to ecosystem function.