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As an outsider I read some literature on over-fishing (especially in Lake 
Superior) a few years ago and was puzzled by the many uses of the term. Your 
discussion has been very informative.  There is a (too) simple model in which 
equilibrium yield, y, is a function of fishing effort, x:  y = x(1-x).  Based 
on my reading of the literature, three levels of effort have been used to 
define overfishing.  (1) x = 0, any fishing reduces the stock (is 
this “recruitment overfishing”?), (2) x = ½, the maximum sustainable yield, (3) 
x = 1, produces extinction.  It seems to me that there are two other 
interesting levels:  (4) some value between x = 0 and x = ½, which maximizes 
the overall social gain, and unfortunately, (5) some value between x = ½ and x 
= 1, at which it is no longer profitable for anyone new to enter the fishery.  
This simple logistic model is not realistic, but it does serve to illustrate 
different levels of fishing that people might not want to exceed.  Textbooks 
may, quite sensibly, choose one of these levels (x = ½), but this does not 
prevent writers of scientific papers from using different levels and confusing 
naïve readers like me.

Dick Green
Department of Mathematics and Statistics
University of Minnesota-Duluth
Duluth, MN 55812

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