A three year record of daily fecal coliform counts in a Massachusetts water
reservoir has the appearance of an irregular time series punctuated by out
bursts of varying duration. The pattern is described in terms of a probabil
istic model where the fluctuations in the 'regular' and 'explosive' regimes
are governed by two sets of probabilities. It has been assumed that the ra
ndom oscillations has a lognormal distribution, and that once an explosion
threshold has been exceeded the increments or decrements in the population
size have fixed probability distributions. The threshold for triggering an
outburst was estimated by examining the randomness of the autocorrelation f
unction of the record after it is filtered to eliminate peaks of progressiv
ely increasing magnitude. Once the threshold has been identified, the mean
and standard deviation of the underlying lognormal distribution could be es
timated directly from remains found in the record after all the peaks were
removed. The probabilities of an increment and decrement during the outburs
ts and their relative magnitudes could also be estimated using simple formu
las. These estimated parameter values were then used to generate realistic
records with known threshold levels, which were subsequently used to assess
the procedure's feasibility and sensitivity. (C) 2001 Society for Mathemat
ical Biology.