Theory vs. Theory

What does it mean to invoke “evolutionary theory”? Is “neo-Darwinism” (or “Darwinism”) a theory, a school of thought, or something else? What gives a theory structure and meaning?  Can a theory change and, if so, how much?  What is the relationship between mathematical formalisms and other statements of “theory”? Who decides how a theory is defined, or redefined (e.g., is Ohta’s “nearly neutral” theory an alternative to, or a variant of, Kimura’s Neutral Theory of Molecular Evolution)?

For various purposes, it is useful to have a framework for discussing “theory” and “theories”.  Here I begin by identifying two distinct ways that scientists use the word “theory”. 2
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