The work of John Murra on vertical complementarity has been among the most influential ethnohistoric studies in the Andes. The premise of the vertical archipelagos model is that the rapid altitudinal change along the flanks of the Andes produced a pattern where social groups residing in non-contiguous ecological strata formed distinct communities that developed around intensified production in these strata. Polities and ethnic communities sought to control a variety of these resource pockets following the Andean ideal of self-sufficiency.

Murra's (1972) seminal article distilled observations from ethnohistoric sources, in particular the visitacensus Garci Diez (1964 [1567]) of Chucuito in Puno, conducted only 35 years after the Spanish invasion. Murra showed that late prehispanic altiplano societies obtained direct access to products from a variety of ecological niches through this practice, and that the strategy was a guiding model of organization in some Andean polities (Salomon 1985). According to Murra (1985) the principal characteristics of the vertical archipelago model can be summarized as follows:

1. Ethnic groups aimed to control numerous "floors" or ecological niches in order to exploit the resources that are found there and maintain self-sufficiency. As a consequence, powerful polities residing in the altiplano had considerable wealth in pastoral herds but also controlled land on both the western and eastern flanks of the Andes.
2. The population was concentrated on the altiplano and those living in the peripheral 'islands' maintained continuous social and economic contact with the core region.
3. The institutions of reciprocity and redistribution guaranteed that those living in 'islands' maintained the rights to products available in the center. These rights were defined through kinship ties that were ceremonially reaffirmed in the center.
4. A single 'island' could be shared by different ethnic groups, though the coexistence could be tense.
5. The relationships and functions of these colonies changed through time and may have become more exploitative. They are perhaps an antecedent to the mitimaqstrategy of the Inka empire.

While a chiefdom level of organization and centralized power is a principal characteristic of the Late Intermediate polities that practiced vertical complementarity in the period examined by Murra, the concept was been explored and expanded by archaeologists in the subsequent decades. In Murra's original description, verticality referred explicitly to direct control of a diverse resource base without engaging in trade with other ethnic groups, thereby preserving what Murra (1972) has described as the ancient Andean ideal of economic self-sufficiency that permeated Andean society and ideology far beyond his Lupaca case study. Stanish argues that Murra was explicit about excluding exchange processes, in part, because he perceived "a structural linkage between exchange and markets" (1992: 15). As prehispanic market mechanisms were absent in the south-central it was believed that barter and exchange were also of minimal importance and other means of articulation, such as direct control, were emphasized. Murra, however, later modified the definition to include specialized exchange centers, a change which Browman (1989: 324) argues confuses the issue because it subsumes a variety of processes into a single model.

On a theoretical level a further limitation of the original 'verticality archipelago' model lies in its adaptationalist orientation (Earle 2001).Adaptationist models of exchange and regional control have their basis in Service's (1962) proposal that these arrangements arise from environmental diversity, and then chiefs emerge to administer and redistribute goods produced regularly by their retainers.As observed by Van Buren (1996: 346), the archaeological origins and perpetuation of the archipelago pattern was founded on the assumption that groups benefit, as a whole, from the control of multiple tiers and the ecological resources that are produced in those archipelagos. As mentioned above in the discussion of administered trade, colonial documents emphasize the independence of commoners and the ability of subjects to practice subsistence barter, a pattern that leads authors to suggest that the vertical archipelagos pattern may have had more of a political basis than a foundation in ecological and subsistence practices. The ultimate roots of such a system may lie instead in the capacity of the rulers of such groups to organize larger scale trade and convert the value differential between products in the different ecological zones into political prestige through feasting and ceremony (Stanish 2003: 69-70).