Dear All,

(this msg is a statistics/computing question to the list) 

I'm trying to implement a modern-version of a (classic) "several-step protocol" in Fishery Biology (due to Bhattacharya, 1967): analysis of length-frequency distribution of fish larvae to id cohorts and later estimate growh rates! 

I've trouble with the 1st step: using kernel density estimation (KDE) function to examine size-freq distributions (variable sl):

> density(sl[dofyr==139],bw="nrd0") (dofyr means day of year and refers to a particular sampling date)
> kd139

Call:
        density.default(x = sl[dofyr == 139], bw = "nrd0")

Data: sl[dofyr == 139] (55 obs.);       Bandwidth 'bw' = 0.4234

       x                y            
 Min.   : 4.870   Min.   :0.0001924  
 1st Qu.: 7.207   1st Qu.:0.0120950  
 Median : 9.545   Median :0.0406854  
 Mean   : 9.545   Mean   :0.1068383  
 3rd Qu.:11.883   3rd Qu.:0.1973223  
 Max.   :14.220   Max.   :0.3491222 

Now the question: the densities per x value (obtained using kd139$y) do not sum to one? I expected them to be probabilities and wanted to "extract" the smoothed frequencies for the midpoints of size-intervals (in this example each class is 0.4234 mm wide?!)

Thanks in advance, 
Eduardo Esteves
University of Algarve School of Technology (Portugal)

ps-I'm trying implement the other steps of the procedure, so it's possible that I'll need help (again)!


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