Is it possible to come up with a macroscopic, mathematical, general model for how the audience of a blog or a twitter account, or the size of a web community evolves over time? How accurate can a simple model be?

To start with something simple, one may take a demographic view of the group under consideration. At birth, the audience is zero. Then, hopefully, content is added and it starts gaining followers at a certain rate. Some people unsubscribe, at a different rate, and the difference between the two is the growth rate of the audience.

Picture the audience as a small puddle of water at the bottom of a container, and potential audience as water vapor above the surface. The individual water molecules are people. When they hit the surface of the water they may stick (subscribe) and join the liquid; conversely some of the molecules in the liquid may evaporate (unsubscribe). A successfully growing audience is an expanding pool of liquid. A dried-out puddle is a shipment of fail.

Thinking out loud


Let's start with the simplest possible system: an inactive Twitter account without a single posted item, without followers. How will people discover and subscribe? The only sources for growth will be:
  • search engines, which may get people to land on the account profile page;
  • inbound links to the account.

Now, suppose the account is followed by a number of other users. We have to add a source for growth:
  • the people landing on the account page while exploring friends of friends,

Now, throw in a user that doesn't update but actively seeks out other users and follows them. We add one source for growth:
  • people checking out the account page because the owner has followed their own Twitter account.

Moving on, we might have an inactive Twitter account with, say, a stock of 100 past updates. All things being equal, one might expect faster growth here, because people may find the account through searches (from within or without Twitter) that land them on update pages.

Now, what about an active Twitter account (say, 5 updates a day), but in the absence of retweets or outside links? Here, the situation is the same as in the previous example, except that with each new update the stock grows, which increases the "surface area" of the account.

Governing factors


So, which factors might govern growth? Can they be measured in some way?
  • Output flow (items per day)
  • Archive size (items)
  • Audience size
  • Content quality (hard to quantify) - influences # of backlinks or retweets


Conjectures


Could it be that:
  • The growth rate rises with output flow, but only up to a certain limit?


All this has obvious ties to innovation diffusion thermodynamics - the modeling of how innovations get adopted.