The philosophically substantive claim about replicator dynamics concerns trajectories from mixed initial conditions, where Weibull's formal results confirm strictly dominated strategies are eliminated with probability one.

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Eliminated with probability one(describing what happens to bad strategies over time): A mathematical way of saying something will definitely disappear or fail—there's essentially no chance it will survive.
Mixed initial conditions(describing what the statement is analyzing): A starting situation where multiple different strategies or types exist together in a population, rather than just one type being present.
Strictly dominated strategies(the type of strategy that gets eliminated in replicator dynamics): A strategy or approach that is worse than another option in every possible situation, so there's no good reason to ever use it.
Weibull(the researcher whose work is being cited): A mathematician (Jörgen Weibull) who developed formal mathematical theorems about how populations behave when different strategies compete with each other.

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