## Notational Conventions

The need to keep track of many different mathematical objects could lead to a notational explosion. Adherence to strict mathematical consistency throughout the entry would have necessitated writing eqn [1] as, for example,

with '|' to be read as 'for the given', Xm and Xr the mutant and resident trait vectors, respectively, Eattr(Xr) the environment produced by Xr, and Eattr(Xr)(t) the corresponding environmental condition at t. This notational explosion is prevented by only displaying the symbols figuring in the specific argument at hand. For example, A(Xm|Eattr(Xr)(t)) is written as just A(t) when the argument is only about temporal fluctuations.

Vectors are assumed to be written as columns, with the transposition operator T transforming columns into rows. Differentiating a scalar for a column produces a row. In products, row vectors will be treated on equal footing with matrices. 1T denotes (1, ...,1) and n = 1TN (expected) total population size or density. Angular brackets, ( ), denote averaging.

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