  Lexicase selection is a successful parent selection method in genetic
programming that has outperformed other methods across multiple benchmark
suites. Unlike other selection methods that require explicit parameters to
function, such as tournament size in tournament selection, lexicase selection
does not. However, if evolutionary parameters like population size and number
of generations affect the effectiveness of a selection method, then lexicase's
performance may also be impacted by these `hidden' parameters. Here, we study
how these hidden parameters affect lexicase's ability to exploit gradients and
maintain specialists using diagnostic metrics. By varying the population size
with a fixed evaluation budget, we show that smaller populations tend to have
greater exploitation capabilities, whereas larger populations tend to maintain
more specialists. We also consider the effect redundant test cases have on
specialist maintenance, and find that high redundancy may hinder the ability to
optimize and maintain specialists, even for larger populations. Ultimately, we
highlight that population size, evaluation budget, and test cases must be
carefully considered for the characteristics of the problem being solved.
