Taking one step back from the math, this is true on inspection. The total number of members can only grow. The number of active members, however, is limited by enviromental factors (bandwidth and computing power)
Let’s say, for purposes of argument, that board performance begins to significantly degrade at 4000 active members and grinds to a complete hault at 8000 active members. Population pressure, therefore, begins to impact survival rates at 4000 members because the less fit i.e., people without huge amounts of time on their hands, will stop posting. As the active membership increases, this population pressure increases until an equilibrium is reached.
In other words, there is a fixed number of active members that can be supported by the SDMB ecosystem but an ever increasing number of posters who could not successfully compete for resources and “died out.”
Now I’m wondering if we can figure out a model (based on the number of views) to estimate the number of lurkers . . .
One small adjustment first: it struck me last night that including an adjustment to make the thing fit with the most recent data point is absurd. Instead, I should just be picking the exponential factor from the most recent data point in the first place. D’oh! That’s what comes of working with dodgy insurance data for too long.
Revising, we get:
10,000 x (exp(0.0374.t) - 0.85 x exp(0.0395.t)}
This gives about 38,500 members when we would have expected 40k, 28,000 when we sould have expected 30k and 19,250 when we would have expected 20k (all correct to nearest 0.25k) A pretty good fit (if systematically too low, though the nature of an exponential growth is that it is memoryless so once you drop below expected, it tends to stay there). Call it 0.038 on pure judgement. An average between the two.
I also have to revise my predictions. In one year, I would actually expect 72,800 members (rather than 71,500), of whjich 5,800 would be active. Note that the active membership is the difference between two large numbers by this point, making it very sensitive to changes in the assumptions of either.
So, revised hypothesis: P(A) = 10,000 x (exp(0.0380.t) - 0.85 x exp(0.0395.t)}
Truth Seeker: the model you seek is the logistic model, which includes an assumption of competition for natural resources and a built-in maximum point. Maybe I’ll repeat an analysis on active membership only using this model, rather than as the difference betwee the members and the dormants and see what happens.
LC, an “active member” is a member who we completely arbitrarily decide is active. Algernon has chosen to use a population capture technique to get this. It seems reasonable but it’s still arbitrary.
Very interesting analyses. It’s particularly interesting to see the logisitic equation invoked, which classically has been used to determine the carrying capacity of an environment for organisms. I would agree that competion for bandwidth may in part determine population size, but this has to be considered not just in terms of the number of posters, but the posting rate of individuals. It would be interesting to have data on how both poster population, plus total posting rate, increased during periods just after additional bandwidth (additional resources) were made available.
Regarding the information on the distribution of post counts per poster, such data in principle can be used to estimate the total species richness (total number of posters), including “rare” species (infrequent posters). Ranked species abundances classically have been found to obey a log-normal curve, although this may not hold at the rare tail end of the distribution.
This site discusses EstimateS, one species-richness estimator, as well as some others.
Of course, post counts are not really analogous to population sizes, since posts never die (with the exception of the rare few that are deleted). Instead post counts are more analogous to the distribution of tree diameters in a forest, since the diameter is dependent on both age of the tree and its growth rate.
In the interest of completeness, I wanted to throw this site, big-boards, into the mix. It automatically gathers board data and has some stats regarding what has happened since the announcement. It looks like there has been a significant drop off in new memberships since 3/18. Not too surpising, I suppose.
Rank Board name and description Posts Members
83 vBulletin The Straight Dope 4593607 45079
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