intuitive understanding of (1+parameter)/parameter
I'm not sure, without knowing more, but this is of course equal to $1 + \frac{1}{parameter}$. Out of curiosity I searched for something about fish mortality and growth params and found http://www.fao.org/tempref/docrep/fao/008/a0212e/a0212E08.pdf which sets this up as a log-log regression in terms like a growth param $L_\infty$, which makes sense if there's some power-law distribution.

Maybe the parameter being used is its inverse, and it may be that this is fudged with the +1 just to make sure the value is greater than 1 so that the log is nonnegative. Maybe there's a better domain-specific reason for tweaking it.