Family trees are familiar and similarly dissatisfying models in historical linguistics and in the history of religion. In linguistic pedigrees, proto-languages give way to language families that are in turn replaced by modern descendants, so that proto-Indo-European begat Germanic and her sisters; Germanic begat West, East, and North Germanic; and West Germanic begat English, Dutch, German, and Frisian. A similar diagram might illustrate how an original Christian unity was divided by schism into Catholic and Protestant, from which developed the related sects of contemporary Christianity. The problems with family trees in religious history are well known to Mormons: we are emphatically Christian, but we disavow any place in the offshoots of Catholicism that have appeared since 1517. What may be less well known is that family trees are just as unsatisfactory models in historical linguistics as well.
The more you know about a language’s history, the less family trees can describe it adequately. It seems clear enough now that there never was a cohesive speech community that spoke “West Germanic,” for example, but instead a fairly wide range of related dialects whose speakers regularly shifted in their allegiance to each other. A unified “Germanic” or “Indo-European” is similarly unlikely. It still makes sense to discuss and reconstruct features of proto-languages, but you have to assume considerable diversity in these prehistorical language communities.
Family trees are also inadequate for describing dialects and their relations to each other. It’s said that you can start walking in Portugal and continue your trip through Spain and France to the toe of Italy without ever finding a distinct linguistic border. To the extent that people speak their local dialect, they can understand speakers of the dialect across the valley without difficulty, who in turn can understand the people in the next valley over, and so on from the Atlantic to the Mediterranean. And yet someone from the middle of Spain will not understand someone from the middle of France or Italy.
One attempt to deal with the inadequacies of family trees in the late nineteenth century was the wave theory. It proposed that language change emanated from centers of innovation, more or less like ripples in a pond. In some cases, one can even find documentary evidence of a linguistic feature spreading slowly up the Rhine over centuries as people adapted their speech habits to those of their neighbors. The isoglosses that define the borders of a linguistic feature extend and decline over time, sometimes joining with and reinforcing other isoglosses, even splitting one language continuum into speech communities that are not mutually intelligible. The wave theory is not perfect, and certainly not the last word in language change, but it has been a useful and stable model in dialect geography.
It seems to me that something like wave theory is necessary to account for Church history. Such a theory of Church history in a nutshell might note that the religious landscape of the Restoration in nineteenth-century New England was marked by disagreement and strife–but argument is also a form of communication, and the obstacles to shifting allegiance from one Christian sect to another seem to have been quite low. Joseph Smith appeared on the scene as a highly productive center of innovation from whom many new religious features emanated, although into an existing American Protestant environment rather than writing on a blank slate, and in competition with other voices. The isoglosses that defined Mormonism rendered it fairly impervious to influences from outside, changing it from a dialect of the second Great Awakening to a separate religion in its own right, and then the trek westward substantially isolated the new faith for nearly a century. The Church continues to be vigilant against unsanctioned innovations or relic-area conservatism that might lead to the development of schisms or differentiation into religious orders. One nice feature of the wave model is that it acknowledges the religious heritage of the first Mormon converts without requiring us to view ourselves as an offshoot of the Methodists, or something equally nonsensical.