Innovation rather than improvement: a solvable high-dimensional model highlights the limitations of scalar fitness

TL;DR

This paper explores the limitations of scalar fitness in high-dimensional ecological models, revealing that traditional low-dimensional intuition can be misleading in complex, diverse ecosystems.

Contribution

It introduces an analytical framework for studying high-dimensional eco-evolutionary dynamics, highlighting how scalar fitness notions break down in such settings.

Findings

Scalar fitness can be irrelevant for survival in high dimensions

High-dimensional geometry explains the breakdown of low-dimensional intuition

Resource competition models can be extended to evolutionary questions

Abstract

Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived from low-dimensional models applies to the complex, high-dimensional reality. For instance, most naturally occurring microbial communities are strikingly diverse, harboring a large number of coexisting species, each of which contributes to shaping the environment of others. Understanding the eco-evolutionary interplay in these systems is an important challenge, and an exciting new domain for statistical physics. Recent work identified a promising new platform for investigating highly diverse ecosystems, based on the classic resource competition model of MacArthur. Here, we describe how the same analytical framework can be used to study evolutionary questions. Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading. Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.