As I discuss in this question, the Sri Vaishnava sect (of which I'm a member) is divided into two sub-sects, Thenkalai and Vadakalai. Now each of these sub-sects has a bunch of Mathams belonging to it, and each Matham is headed by a Sri Vaishnava Acharya, just like the four Shankaracharya Mathams in Advaita. Most Sri Vaishnavas belong to one of these Mathams; for instance my Dad's family belongs to Vanamamalai Matham and my Mom's family belongs to Ahobilam Matham. But there are some Sri Vaishnavas who don't belong to any Matham at all, known as Swayamacharya people. For them their father functions as their Acharya. Swayamacharya people are rare; usually only the families descended from famous Sri Vaishnava Acharyas are Swayamacharya people. For instance my maternal grandmother comes from the Swayamacharya family of Agnihotram Tathachariar, a descendant of Nathamuni, the founder of Sri Vaishnavism.
Now I have noticed a pattern among Swayamacharya people, or at least among Vadakalai Swayamacharya people. Most of them seem to belong to Munitrayam. For those who don't know, the term Munitrayam, which means "the three sages", refers to three Vadakalai Acharyas who were all disciples of Gopala Desikan, an 18th century Vadakalai Acharya. The most prominent of the three is Ranga Ramanuja, the Sri Vaishnava commentator on the Upanishads. In any case, two Vadakalai Mathams, Sri Rangam Andavan Ashram and Poundarikapuram Andavan Ashram, trace their Guru Parampara to Munitrayam. But my question is, what is the connection between Swayamacharyas and Munitrayam?
Most Vadakalai Swayamacharya people I know belong to Munitrayam, and it's not just anecdotal evidence; this Wikipedia article says the same thing:
Munitraya – Followers of Srimad Andavan of Andavan Ashramams, and Swayamacharyas.The Srirangam Srimad Andavan Ashramam, Poundarikapuram Andavan Ashramam, and most of the present-day Vadagalai 'svayam-acharya purusha' families are directly connected to this acharya parampara, and follow the worship and ritual patterns outlined by Sri Gopalarya Mahadesikan.
But how can Swayamacharyas be connected to the Munitraya Parampara? By definition the Guru Parampara of a Swayamacharya is just his line of biological ancestors. For instance if you look at my maternal grandmother's relative Agnihotram Tathachariar, his guru was his father, whose guru was his father, etc., all the way back to Nathamuni. So where would Munitrayam enter the picture? Or is it that Swayamacharya people don't trace their Guru Parampara to Munitrayam, but rather they just "follow the worship and ritual patterns" of Munitrayam as Wikipedia suggests? I'm not even sure what these worship and ritual patterns are, but if that's the case what is the reason why so many Swayamacharya people follow Munitrayam? Is there some historical event or circumstance which led to this?