Theory of Three Waves
The Theory of Three Waves is a model of human migrations that seeks to explain the distribution and relationships of Akanaran peoples outside of Peilaš. According to this theory, three successive waves of prehistoric migration crossed the island chain from Peilaš to Tuysáfa. The theory is primarily based on archaeological evidence, but has (somewhat speculatively) been used to classify the languages of Tuysáfa into three broad groups, which are theorized to be descended from these three migrations. These linguistic groups are known in Tuysáfan studies as Primundic ('first wave'), Mediundic ('middle wave'), and Ultimundic ('last wave').
First wave
The first wave of migration began with the first foragers to use rafts or simple dugout canoes to leave Peilaš. The first crossing was from the Lotokan coast to the nearest islands of Sumarušuxi; this crossing might date to as early as -40000 YP, though it could be later (as late as -20000, perhaps). The crossings were fairly haphazard, but eventually these people spread over the entire island chain to reach Tuysáfa (by ca. -15000), which they populated. Some scholars have suggested that this was not a single, one-time migration, but rather a gradual trickle of people across the island arc. In any case, members of this population also crossed from Tuysáfa to Zeluzhia, populating that continent as well (possibly as early as -14000).
In Tuysáfa, the languages that are identified as Primundic are mostly isolates or small families that cannot be linked to any of the Mediundic language stocks. Most of them are fairly marginal geographically, and they are especially found in the far east of the continent. In contrast to this, however, almost all important language families in Zeluzhia are thought to belong to the Primundic phylum.
Second wave
The people of the second wave of migration probably descend from a hunting-fishing culture that developed in the coastal regions around Lotoka and Sumarušuxi starting around -15000 to -10000 YP. (This culture may have survived in Sumarušuxi as late as -1500 YP-- that is, until the beginning of the Isles migration.) Something in their subsistence patterns (possibly improved fishing techniques, possibly early small-scale cultivation of food plants, or maybe just the sheer richness of their natural environment) brought this group to unprecedented population densities, especially in eastern Sumarušuxi; this allowed them to expand along coastal areas to Tuysáfa, either absorbing or replacing most of the Primundic groups they encountered. (They may have expanded in Peilaš as well; perhaps some of the east-coast groups there are descended from them.) It's thought that these groups began arriving in Tuysáfa ca -8000 to -7500 and reached the east coast ca -7000 to -6000.
The languages that are identified as Mediundic form a few large stocks or families which dominate most of mainland Tuysáfa.
Third wave
The third wave of migration apparently originated with the Canoe Culture of northeastern Peilaš, a shoreline fishing culture that invented large canoes capable of reliable short-distance ocean travel (around -6000 YP). This culture expanded along all the coastlines available to it, including the island chain to Tuysáfa (which it reached between about -4000 and -3000). Along with the canoe itself, the Canoe Culture introduced new sailing expertise to western Tuysáfa, as well as fishing and trading culture. (It may also be responsible for the adoption of small-scale garden agriculture, though the beginnings of this might actually go back to the second wave expansion.) In any case, this culture expanded rapidly along the coasts of western Tuysáfa, but hardly touched the interior.
The Ultimundic languages are theorized to be descended from the language of migrating Canoe Culture people. Given the relatively shallow time depth (compared to the Primundic and Mediundic groups), they should form a single stock and remain demonstrably related to one another. However, too little is yet known of the languages of western Tuysáfa to identify with certainty the languages that belong to the postulated Ultimundic group. It is widely believed that the Isles languages are part of the Ultimundic stock; however, a competing theory holds that they descend from native Tuysáfan peoples who adopted the Canoe Culture's sailing and fishing technology, and expanded considerably about -3000 YP (the Tuysáfa Fishing Culture). This theory would restrict the Ultimundic group to the northwest coasts, and make the Isles family and its relatives one of the Mediundic stocks. Yet another theory suggests that the spread of the Canoe Culture to Tuysáfa is a case of technological diffusion rather than migration, and the proposed Ultimundic stock is a chimera.