How to replace a complex term in an equation using a function? I have recently been working on a few models that look at mosquito predation. Now one of the peers wants me to add the complete equation of my model in the manuscript. I previously had the equation broken down in several parts but the reviewer was not happy with that. So I decided to add the full equations, here is an example:
$$N_{e}=N{}_{0}-\frac{W\left(\frac{a}{1+c(P-1)+abcN_{0}(P-1)}bN_{0}\exp\left(-\frac{a}{1+c(P-1)+abcN_{0}(P-1)}(PT-bN_{0})\right)\right)}{\frac{a}{1+c(P-1)+abcN_{0}(P-1)}b}$$
The editor of the journal now told me to break it down again. This are his exact words: "...there is one complex term that occurs three times. This term could be replaced by a function name, e.g. F(x, y, z, …), and then F(x, y, z, ..) defined in the following line."
I'm not really sure how to write this because I am not very good with mathematical notations, symbols and all that. Is the editor basically asking my to do the following?:
$$N_{e}=N{}_{0}-\frac{W(F(x,y,z)bN_{0}\exp(-(F(x,y,z)(PT-bN_{0})))}{(F(x,y,z)b}$$
and then:
$$F(x,y,z)=\frac{a}{1+c(P-1)+abcN_{0}(P-1)}$$
If this is what he is asking I don't see how this differs with my first version in which I had the following:
$$N_{e}=N{}_{0}-\frac{W\alpha bN_{0}\exp(-(\alpha(PT-bN_{0})))}{\alpha b}$$
combined with:
$$\alpha=\frac{a}{1+c(P-1)+abcN_{0}(P-1)}$$
 A: Say something like this:
For notational convenience, let
$$F:=\frac{a}{1+c(P-1)+abcN_{0}(P-1)}.$$
Then our model is
$$N_{e}=N{}_{0}-\frac{W(F\,bN_{0}\exp(-(F\,(PT-bN_{0})))}{F\,b}.$$
Here, the $:=$ means "is equal to be definition".
It's not clear to me if variables on the right-hand side of $F$ are indeed independent variables or parameters. If variables, I'd say $$F(a,b,c,P,N_0):=$$ instead of $$F:=$$ but they feel like parameters to me. And if they are indeed parameters, I'd probably choose a different letter than $F$ to represent that quantity.
You're right, this isn't any different than what you had using $\alpha$ unless the point of this is to treat $\alpha$ as a function of those variables on the right-hand side of the defining expression for $\alpha$ (or $F$).
A: You have same things written three times : it s a function F 
the function depends on a,b,c,$N_{0}$, and P so your function can be written $F(a,b,c,N_{0},P)$
$N_{e}=N{}_{0}-\frac{W(F(a,b,c,N_{0},P)bN_{0}exp(-F(a,b,c,N_{0},P)(PT-bN_{0}))}{F(a,b,c,N_{0},P)b}$
or 
$N_{e}=N{}_{0}-\frac{W(FbN_{0}exp(-F(PT-bN_{0}))}{Fb}$ where $F=\frac{a}{1+c(P-1)+abcN_{0}(P-1)}$
Note you have on extra ')' at the end 
