Suppose the simplest population model where we track the size $y$ of a population:
$$\frac{dy}{dt} = ry$$
for a positive constant $r$ and some $y$ such that $y(0) > 0$.
For this population model there is a corresponding "replicator dynamic" model defined by
$$x_0 := \frac{1}{1+y}$$
$$x_1 := \frac{y}{1+y}$$
These are supposed to model "frequencies" of different variants in a population,
QUESTION
except its not clear to me what the different variants here. There is only a single species here so of course it is 100% of its own population or 100% of all populations being modeled here, so I feel that I must be misunderstanding what the "frequencies" of the replicator dynamic are. Can someone clarify what $x_0$ and $x_1$ correspond to here? Thank you!