  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.
