BALTIMORE — IN Tom Stoppard’s play “Arcadia,” the mathematician Valentine tries to predict how the grouse population on an estate changes from year to year. He does this by using old shooting records as data, under the assumption that the number of grouse killed annually is proportional to the size of that year’s population. His goal is to create a mathematical formula that takes any year’s population as input and gives the next year’s population as output.

Scientists in the Chesapeake Bay area have been playing a real-life version of Valentine’s game, with blue crabs instead of grouse. Each spring, they wait for the results of the baywide Blue Crab Winter Dredge Survey, the most recent of which were announced Monday. The estimate of the crab population gives scientists another data point to work with, and anxious watermen a sense of whether this will be a good or bad year for the most valuable commodity in the Chesapeake.

But how much can formulas tell about these creatures’ unpredictable lives?

Here’s how the math works: One of the simplest population formulas specifies that the output is some number R times the input. So bacteria doubling in a petri dish every hour would have a growth factor of R = 2, while the “population” of money in a bank account earning 12 percent interest compounded annually (one wishes!) would have R = 1.12. For R > 1, this leads to exponential growth. One could also have R < 1, in which case the population would decrease at each step and essentially die out.

Exponential growth, of course, must slow down when resources are limited. By setting R to decrease as population increased, the 19th-century mathematician Pierre-François Verhulst formulated a model in which the population first grew almost exponentially, but eventually stabilized at the maximum carrying capacity of the environment.