# Foundations of Ecological and Evolutionary Change

## TL;DR

This paper bridges population ecology and evolution by unifying their fundamental equations, revealing how individual traits and fitness drive population and ecosystem changes.

## Contribution

The paper establishes a formal link between population ecology and evolution using the Price equation, revealing a new bridge between these fields.

## Key findings

- The fundamental equations of ecology and evolution are unified through an equation linking individual traits to fitness.
- The Price equation is derived to show how ecological and evolutionary changes are interconnected.
- The equivalence between mean population growth rate and evolutionary fitness is formally recovered and linked to ecosystem function.

## Abstract

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.

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). Our unification formally recovers the equivalence between mean population growth rate and evolutionary fitness and links this change to ecosystem function.