Analysed non-linear data with GAM regression, but reviewer has suggested fitting exponential or logarithmic curves instead. Which to use? I am trying to publish my Masters thesis which looked at elephant impacts on vegetation, with a focus on the effect of artificial waterholes. I have made my initial submission and am now performing major revision, which involves some questioning of my statistical approaches.
Some of the elephant impact measures I looked at showed a non-linear relationship with distance to water which led me to use GAMs. However, a reviewer has said that they feel this is statistical overkill and achieves little more than "fitting complicated nonlinear functions that demonstrate that distance matters". They suggest I should rather describe non-linear relationships between elephant impacts and distance to water by fitting simple functions which others can use (e.g. exponential decay curves). I think the point being made is that these simpler functions would allow me to say something more generalisable about the elephant impacts (e.g. they resemble a logarithmic curve), while the GAMs are only useful for describing the impacts I found in my particular study area and is thus of less general usefulness.
I'm still a novice at statistics so I would appreciate some thoughts on which approach seems more sensible. I have included some examples from my data below.
The top graph shows canopy volume/ha in one vegetation type at different distances from water(the circles represent individual sampling plots). The line shows the predicted relationship from the GAM regression. This sort of relationship appears to resemble a logarithmic curve so the reviewer would perhaps recommend I fit that instead in a case like this.


The second graph shows canopy volume/ha in relation to distance to water, but in a second vegetation type. This vegetation type was more heavily impacted by elephants. Again the line on the graph is derived from the GAM prediction, but this could be one where I could look to fit an exponential curve?
I'd appreciate any thoughts on the merits of my use of GAMs versus the reviewer's recommendation to use simpler functions. As an aside, I also have not really explored fitting logarithmic or exponential curves to data in R, so I would also much appreciate any pointers in that regard.

In addition to Demetri's answer (+1):

*

*The use of GAM is well-established in the field of Ecology so I would add certain books/influential articles. Show you are not reinventing the wheel rather that you are abreast with modern modelling approaches.

*You do not describe your sample size but you might want to try a validation schema to show that through the use of GAMs you get better goodness-of-fit. While hand-wavy if something like an AIC/BIC shows a clear preference for a particular model this can pacify some (not too sophisticated) criticism...

*I would emphasise how the GAM fitting procedure looks into shrinkage. It is plausible that someone oversimplified GAMs in his/her head as "a polynomial basis of sorts" and therefore prone to overfit.

*Take their view-point for a moment: are there any established studies suggesting logarithmic, or exponential decay curves already? The reviewer might be satisfied that you acknowledge them as a possibility. Maybe you can make a critical assessment of that prior work and show how your work is a step forward.

*As Dimitri mentioned, specifying a functional form without prior knowledge can induce strong bias. You can politely double-down on the fact you are using a non-parametric approach. Maybe even try a different basis functions (e.g.  cubic regression splines and thin-plate splines) and show how the results are (hopefully) very similar and thus not dependant on the choice of basis functions.

Just to be clear: In my opinion, using GAMs is the correct approach here; the criticism of "why not X-functional form" is weak. Such criticism might be warranted if prior research suggested robust evidence for a particular modelling assumption but even then it would not be a particularly strong position to take. That said, try to see where they are come from too, criticism can be helpful strength your manuscript and/or alleviate worries of future readers too.
