Thanks very much indeed Carsten and Philippe!
Lots to consider.  I should have specified this before, but the  
variable with zero values that I would like to log (ln) transform does  
consist of many small values.  The range is between 0.00 and 0.35,  
since this variable is the percentage abundance of bipedal rodents  
captured on a given night of trapping:

Y <- c(0.040, 0.040, 0.030, 0.000, 0.030, 0.055, 0.120, 0.050, 0.160,  
0.130, 0.150, 0.040, 0.080, 0.130, 0.150, 0.110, 0.280, 0.170, 0.000,  
0.230, 0.140, 0.340, 0.000, 0.000, 0.000, 0.150, 0.020, 0.093, 0.065,  
0.043, 0.030, 0.030, 0.055, 0.100, 0.007, 0.010, 0.030, 0.000, 0.140,  
0.025, 0.090, 0.015, 0.078, 0.160, 0.010, 0.100, 0.000, 0.010, 0.050,  
0.010, 0.000, 0.043, 0.087, 0.040, 0.020, 0.057, 0.107, 0.110, 0.190,  
0.110, 0.055, 0.030, 0.091, 0.090, 0.020, 0.350, 0.200, 0.177, 0.350)

 From your "rules of thumb" advice, it sounds like adding 1 to this  
data through log1p() might be quite distorting to the analyses.  This  
would deal with the issue of zero values (log(0+1)=0), but small  
positive values such as 0.01 would go from -4.605 to 0.00995 by log(x 
+1).  Adding 0.5 is only slightly better (log(0.01+0.5)= -0.6733).   
Should I assume that this effect will "even out" over all values since  
the log(x+1) transformation is applied to the entire variable?

Or, is it best to go with one of these alternatives for the c in log(x 
+c):
1.  c <- signif(0.5*sort(unique(Y))[2], 2)   #c=0.0035
2.  c <- (quantile(Y)[2]^2)/quantile(Y)[4]   #c=0.0048

Does anyone have English references for alternatives 1 or 2?
This is super helpful, many thanks!
--Nate


On Jun 24, 2009, at 6:59 AM, Matthew Landis wrote:

> Many thanks to Carsten, Philippe, and Nate for a very informative  
> and entertaining discussion of something I have always wondered  
> about, having heard suggestions for both approaches.  At least now I  
> have a better understanding of the rationale for each!
>
> Matt
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Matthew Landis
> Dept. Biology
> Middlebury College
> Middlebury VT 05753
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_________________________________
Nathan S. Upham
Ph.D. student
Committee on Evolutionary Biology
University of Chicago
1025 E. 57th St., Culver 402
Chicago, IL 60637
nsupham@uchicago.edu
_________________________________





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