linear/log relationships of NPP and R_root to latitude

[teixeirak]

@beckybanbury ,

We hypothesize a linear decrease in C flux with latitude, and Fig. 2 seems to support this. However, Table S2 indicates that a lognormal fit was better for NPP and R_root. Is Fig. 2 up to date?

[beckybanbury]

Good catch! Updated is here, and will update in the manuscript next time I knit

[teixeirak]

Hmmm....I actually think the previous version was better in some ways. I think that testing for "closure" works best if we fit the same function shape to each. For just showing the relationships to latitude, we obviously want to show the best-fit function.

Are the log fits significantly better than the linear fits? (That's not just a question for this figure, but for interpretation of the results.)

[beckybanbury]

I agree that the previous version visually reads better for stacking the plots. I didn't test for significant difference between log + linear fits, only relative to the null. I tested for a significant difference between linear and poly fits (as poly builds on the linear fit + so only accept poly if it is significantly better than the linear), but as linear + log aren't nested I didn't do that for them.

I could rewrite the code so that we only accept log as the best model if dAIC > 2 relative to the linear model, which I from an initial look would change at least some of the results - this would be the simplest way of coding it, but is does imply that we are taking a linear model as a sort of second null/base model. Obviously it would be great to have a table which has dAIC values for all models against each other but that's just too much information to really manage I think, especially with so many fluxes/climate variables - if we want to do this perhaps we should just do it for latitude/a couple of key climate variables?

[teixeirak]

I don't think we should recode everything with a linear as a second base model. For this figure (only), I think that if the log fit is significantly better than linear for any of these, then we should just stick with the best fit. However, if the AICs are all close, then its really a tossup which should be used, and my inclination would be to go with the linear fit, just because I see that as more parsimonious.

For latitude, we're inherently asking is there a difference in the shape of the relationships among fluxes?. For this reason, I think that accepting a log fit for a few variables, compared to linear for most, requires a significant difference in AIC. (This is why I said above that it's also a question of interpretation of the results.)

[teixeirak]

If the fits are close and we go with the linear version, we'll obviously need to note it somewhere--perhaps in the figure caption. I agree that we don't want a table with all the models. We do have that in the GitHub repo, right? We can point to that for readers who are interested in the full set of results.

[beckybanbury]

So for latitude the difference between log + linear models for NPP + R root is < 2, so shall I change the figure back to the previous version?

Do you think then that we shouldn't change the methods for generating e.g. table s2, which identifies the log model as the best in several cases, even though dAIC between log + lin models is <2 in some of these cases? I'd be happy to leave it as it is, but noting that the difference between lin and log may not be significant in practice.

In addition, how will this affect how we present the results in the hypothesis table (table 1)?

[teixeirak]

So for latitude the difference between log + linear models for NPP + R root is < 2, so shall I change the figure back to the previous version?

Yes, let's revert to the previous version and note this in the figure caption. I'll do that now.

[teixeirak]

Do you think then that we shouldn't change the methods for generating e.g. table s2, which identifies the log model as the best in several cases, even though dAIC between log + lin models is <2 in some of these cases? I'd be happy to leave it as it is, but noting that the difference between lin and log may not be significant in practice.

I think we can leave it as is.

[beckybanbury]

I agree that we don't want a table with all the models. We do have that in the GitHub repo, right?

We don't currently have a table with all the models, just a more detailed version of table s2, with dAIC values in the table relative to the null. I can easily generate a table with all the models, but again, it would be much easier to just present dAIC values relative to null rather than comparing each model pair (as this would be I think 10 dAIC values per flux/climate combination, rather than just 3)

[teixeirak]

In addition, how will this affect how we present the results in the hypothesis table (table 1)?

I think we should change the hypothesis to "decreases continuously". The real question at stake is whether there's a saturation point as you move into the tropics, and the answer is "no", regardless of whether log or lin model is better.

I'll make that change too.

[teixeirak]

I updated the caption to read " Plotted are linear models, all of which were significant $(p<0.05)$ and within dAIC=2 of the best model (for three fluxes, logarithmic fits were marginally better; Table S2)."

[teixeirak]

We don't currently have a table with all the models, just a more detailed version of table s2, with dAIC values in the table relative to the null. I can easily generate a table with all the models, but again, it would be much easier to just present dAIC values relative to null rather than comparing each model pair (as this would be I think 10 dAIC values per flux/climate combination, rather than just 3)

Could we show all models with AIC within 2 of the top model? I also wouldn't generate dAIC for each model pair.

[teixeirak]

I think we can close this.