scflowers said: I wonder if they pretty much increase at the same rate each year, given about the same growing conditions, or if they multiply fast, then slow down once established or just continue to multiply until they outcompete themselves.
The fans in a clump will always compete with each other. A daylily grower should expect that they would multiply more quickly when a clump is small and the rate would slow down as the clump becomes larger. Competition for light is something that could only be lessened by dividing a clump. However, competition for water and fertilizer can be reduced if the grower increases the amount of each given to a clump based on the number of fans in the clump; all the fans in a clump share the resources available to the clump.
The rate of increase of fans is quite high in locations such as Florida; Munson considered that the growth and other characteristics were affected if clumps were not divided every year. Presumably he had eight to one increase per year (or better) with his growing conditions and length of growing season.