judging polynomial models based on their making "biological sense"

[teixeirak]

@beckybanbury, we currently state:

"If the shape of the relationship made biological sense, and was a significant improvement on the linear relationship ($\delta$AIC >2), we accepted the polynomial as the best model."

We need to revisit this criteria, as it's bound to run into trouble in peer review. We need objective criteria here.

Which were the instances where a polynomial term came out significantly better? I think one was an exponential increase in GPP with latitude. Others?

We have two options: 1- accept the polynomial fits, present these 2- if we feel that the polynomial fits are truly inappropriate, we could adjust criteria.

[beckybanbury]

@teixeirak yes - I've been thinking about how to approach this, but wasn't sure in the end. It's really just latitude and I think tempseasonality/temp range annual where they were coming in with an exponential increase. I don't know if we could specify that we were testing for a specific shape of polynomial (saturating) as one way round it?

[teixeirak]

That would work, and would be the easiest solution (just require tweaking a bit of language in the document)

[beckybanbury]

I've just noticed that we actually have temperature seasonality graphed with an exponential increase in the manuscript draft, which I think we don't want?

[teixeirak]

Actually, on second thought I'd allow the exponential increase there and with GPP-MAT (or any others). In the case of GPP, it's probably driven by the MAT*MAP interaction in Fig. 4.

[teixeirak]

@beckybanbury, next step here is to redo figures, allowing for an exponential increase of GPP with MAT:

• [x] Fig. 4a
• [x] Fig. S4
• [x] Table S2
• [x] Table S4
• [x] text

[beckybanbury]

@teixeirak do you mean that we allow an exponential increase for GPP with all climate variables, but not for any of the other fluxes? Or just allow an exponential increase for everything?

[teixeirak]

I think for consistency we need to allow it for everything.

[beckybanbury]

Okay! I just want to clarify how we are deciding on the best model for each. Currently, I run a null model, a model with a linear term, and a model with a polynomial term for each flux + climate variable combination. We use AIC values to select the best model. However, in some cases, there is a deltaAIC <2 for the best and second best model (i.e. no real difference between polynomial and linear). What do you think we should do in these cases?

In addition, when I report the deltaAIC value for the model, I'm unsure about whether I report it for the best model and the second best model, or for the best model and the null model.

[teixeirak]

Let's go with the linear model unless the polynomial model is significantly better (deltaAIC <2). Let's report the dAIC relative to the null (although looking at the manuscript and SI now, I don't see where those are reported).

[beckybanbury]

You're right - they aren't reported (I was getting confused with table S4). For our reference though, the dAIC values in the unweighted model raw data table are now comparing the best model and the null model. Some of the models have changed now that the criteria have been refined - tables and figures are now mostly updated (just working on S4)

[beckybanbury]

Table S4 doesn't change, as the best model for all fluxes for MAT and length growing season is still the linear model

[beckybanbury]

text in methods section updated