excluded. During these weeks in 1984 and 1985, daylight samples were not collected because these samples 

 underestimated abundance due to diel behavior of the older larvae, which apparently remained near bottom 

 during the day and were not susceptible to the bongo sampler (NUSCo 1984). 



Typically, the distribution of larval abundance over time is skewed, with a rapid increase to a maximum 

 followed by a slower decline. This skewed density distribution results in a sigmoid-shaped cumulative 

 distribution and the time of peak abundance is the time at which the inflection point occurs in the 

 cumulative distribution. The cumulative Gompertz function (Draper and Smith 1981) was chosen to 

 describe the cumulative distribution data because the inflection point of the Gompertz function is not 

 constrained to the central point of the sigmoid curve. The fonn of the cumulative Gompertz function 

 used was: 



Q = a(exp(-|3e"'^'l) (6) 



where Q = cumulative density at time t 



a = total or asymptotic cumulative density 



P = location parameter 

 k = shape parameter 

 t = time in days from February 15 



The origin of the time scale for our data was set to the 15th of February, which is when winter 

 flounder larvae generally appear in the Niantic River. The parameter a was used as an index to compare 

 annual abundances. 



The derivative of the above cumulative function with respect to time yields a "density" function which 

 directly describes the larval abundance over time. This density function has the form: 



4 = apA:(exp[ - kt{ - pe " '"}]) (7) 



where dt = density at time t 



where all the parameters are the same as in the cumulative function (Equation 6), except for a, which was 



20 



