This model of tribal behavior was produced by E.E. Evans-Pritchard in the 1930's during his study of the Nuer in what is now Sudan. As seen in the common saying, "It involves a series of genealogically identified nested groups, and is explained reasonably well by Wright:
"But the unusual feature of tribalism, as anthropologists have noted for at least the last century or so, is that loyalties and customary obligations are 'segmentised' - in other words, tribes can easily split at a large number of different levels, based on perceptions, often mythical, of a person's genealogical origin. In theory, the more recent the common ancestor between X and Y (in the male line in the Arab context), the tighter the bonds of solidarity between them should be. That means that, even in a theoretically 'perfect' model, tribes need not always act as a coherent unit, unless they are in direct conflict with another tribe of equal size and coherence."
Evans-Pritchard did not elaborate this system strictly off observation, however, but was influenced by W. Robertson Smith's 1885 work Kinship and Marriage in Early Arabia. Robertson Smith was not an anthropologist, but an orientalist, and here I do not use that term pejoratively, who was working with written Arabic sources from the 8th century which had been heavily influenced by the administrative organization of tribal identity in the early caliphate. Since the 1980's, Evans-Pritchard's segmentation theory has been steadily questioned by anthropologists working on modern Bedouins societies for many reasons: It ignores links forged through women, it assumes wrongly that parallel segments will have similar sizes, it has little to say about the development and influence of tribal leadership, it does not account for genealogical changes, and tribal alliances seldom seen to actually follow it despite the fact they they accept it as a theory of their actions. At the very least, it probably has much more to do with very small, immediately related groups than it does broader tribal confederations.
Here I wish I did have detailed knowledge of Libyan tribal politics, but I can raise some points to consider. First, even independent of settlement and the like, tribespeople are not socially programmed automatons. A team of anthropologists whose work I admire, William and Fidelity Lancaster, have emphasized the way tribespeople perceive their tribal identities as assets, options, and obligations, and make a series of rational calculations about whether and how to activate or follow them. Second, the role of leaders must be considered in a case like Libya. What relationship might they have to the state? What is their source of influence? Do they control agricultural resources, or channels of patronage? The Libyan state has to be the main economic power in most people's lives, and the intersection of this with tribal networks (my own preferred term to just "tribes") colors how people see their assets and obligations. In fact, states often use tribal leaders to incorporate tribespeople into their web, as happened with Jordan during the British Mandate, and given that I'm more interested in the actions of "tribal leaders" as a group than I am individual tribes.
To conclude, though, I want to emphasize that Libya is very definitely not one of my strong points, though I hope to know a bit more by Saturday than I do now.