In the original German, 'prevails' is rendered "herrscht." Herrscht shares a common root with the ordinary German word Herr (Mister, or, more evocatively, Master). 'Lordship' (as, in the chapter of Hegel's Phenomenology of Spirit, on 'Lordship and Bondage' is rendered Herrschaft.)
My own reading of Capital tends to center upon the question of domination in capitalist societies, and throughout chapter 1 (in particular, in The Fetishism of Commodities and the Secret Thereof) Marx is especially attuned to the distinguishing how the forms of domination that are prevalent in capitalist societies are distinct from the relations of "personal dependence" that characterize pre-capitalist modes of production.
It seems prudent, therefore, to take note of the way that the seemingly innocuous notion of 'prevalence' is, for Marx, in his original formulation, already evocative of the language of mastery, domination, perhaps even something like 'hegemony'.
Furthermore, the capitalist mode of production prevails--it predominates. Yet, as Louis Althusser observes in his discussion of the concept of the 'mode of production' in On the Reproduction of Capitalism, every concrete social formation can be classified according to the mode of production that is dominant (that prevails--herrscht). In order to dominate, something must implicitly be dominated, or subordinate. "In every social formation," Althusser writes, "there exists more than one mode of production: at least two and often many more." Althusser cites Lenin, who in his analysis of the late 19th c. Russian social formation, observes that four modes of production can be distinguished (Louis Althusser, On the Reproduction of Capitalism, Verso 2014, p. 19.)
In our analysis of social formations, the concrete specificity of each can be articulated by carefully examining the multiplicity of modes of production that coincide within it, and examine the way in which capitalism tends to dominate a multiplicity of subordinate modes of production that, on the one hand, survive from past modes of production but which may also, on the other, be emerging in the present (i.e. communism). Thus even if capitalism tends towards the formation of a contiguous world-system dominated by its particular imperatives, this does not mean that this process is homogenous or unfolds in the same way in each instance.
For some commentators, capitalism is defined by the prevalence of wage labor and the specific dynamics that obtain therefrom. Yet this has often led to confusion over, whether, in analyzing the North American social formation prior to 1865, in which slavery coexists with wage-labor, the mode of production based on slave-labor is pre-capitalist. Yet as we find here in ch. 1, what determines the commodity as a commodity is not that it is the product of wage labor, rather that it is
produced for exchange. As Marx writes on p. 131, "He who satisfies his own need with the product of his own labor admittedly creates use-values, but not commodities.
Insofar as the slave-system in North America produced commodities (cotton, tobacco, etc.) for exchange on the world market, the fact that these commodities were produced under direct conditions of domination does not have any bearing on whether or not we identify this system of production as 'capitalist'. Wage-labor is therefore not likely the determinative factor; the determinative factor is the production of commodities for exchange. It is only insofar as commodities confront one another as exchange-values that the various modes of useful labor appear as expressions of a homogenous common substance, labor in the abstract
It is in this sense that we can observe one of the ways that the capitalist mode of production prevails over other modes of production, as it subordinates these modes of production to production for exchange, and thus the law of value, regardless of whether wage-labor represents the dominant form of this relation.
Moreover, it provides a clue to how we can examine, for example, the persistence of unwaged work within the family, which has important consequences for Social Reproduction Theory.
Nonetheless, we can say that insofar as commodities confront each other on the market in a scene of exchange that they implicitly contain some 'third thing' which enables us to compare them as bearers of a magnitude of value. This 'third thing', as Marx's demonstration shows, is 'socially necessary labour time', which anticipates the way that wage-labor will become a dominant feature of capitalist society.