Define and test hypothesis-driven predictions

[teixeirak]

@mcgregorian1, we're getting a huge number of potential models (#6)! Let's focus our attention by defining hypotheses and associated predictions. Here, I'm focusing on tree-size related aspects. I'm currently thinking it would make sense to keep traits as a separate paper.

Model basics - We're using a mixed effects model with random effects of (1 | sp/tree) + (1 | year). These should be present in all model versions.

Hypotheses (H) and associated predictions (P) (inspired by Bennett et al.) -

H1- Large trees suffer more during drought because of the greater biophysical challenge of lifting water to greater height (see discussion/refs in Bennett), and therefore height itself is a strong predictor. P1-Drought response increases with height at time of drought (derived from dbh). Height will be a significant predictor both alone or in combination with canopy position and elevation. Preliminary results : This is true; inclusion of dbh --and by extension height--strongly improve statistical models (#6). Caveat : Height may also be just a strong co-variate of canopy position or root water access. Support of this prediction doesn't exclusively support H1, but if height itself is less important, the other drivers should come out as significant and potentially stronger predictors. Next step:

• [ ] confirm result holds when using height predicted based on dbh (with bark correction) instead of dbh (see issue #8).

Preliminary conclusion: Taller trees suffer more during drought, and testing of additional hypotheses will identify whether height itself is the most important driver, or whether a correlate of height is more important.

H2- Large trees suffer more during drought because of greater exposure (to radiation, wind, etc.)--either in relation to neighboring trees or because of position on landscape P2a- Trees currently in a canopy position suffered more during drought. If canopy position is more important than height, we'd expect current canopy position to be a better predictor than current height. Preliminary results : This is true; inclusion of canopy position improves statistical model, but the effect is not nearly as strong as height at time of drought (#6). Caveat: canopy position and height are strongly linked, and height at time of drought may be a better descriptor of past canopy position than is current canopy position. Preliminary conclusion: Drought sensitivity differs by canopy position, but this may be just because of its correlation with height. Preliminary conclusion: Height itself is more important than canopy position.

P2b- Current canopy position will improve model over just the effect of height. Better comparison if we use current height. *Preliminary results :

• This is not supported for all 3 droughts combined; inclusion of canopy position along with height increases AIC by ~1.5 (#6).
• Not supported for 1966 drought (see here).
• This is supported for just the most recent drought analyzed (1999; see here)*

Caveat: The study design makes it so that we're prone to type II error (false negative). This is because we're going off of current canopy position. Some trees currently in a dominant/co-dominant position were probably in an intermediate/suppressed position at the time of drought, but the reverse is unlikely to be true. This weakens the separation between canopy and subcanopy individuals Preliminary conclusion: Canopy position is important, but only in the most recent drought-- presumably because current canopy position is not a reliable indicator of canopy position >40-50 years prior.

Next step:

• [ ] try a model with just current height (+ random effects) to see if it is a better predictor than just current canopy position (+ random effects).

P2c-Trees at higher elevations--particularly tall trees--suffer more because they are more exposed. Thus, elevation has additive or interactive effect with that of height (model with height + / elevation better predictor than just height.) Preliminary results : Including elevation in model along with [dbh] or [dbh+canopy] sometimes improves the model (#6, #9). Effect is positive but weak Next step:*

• [ ] try a model with dbh*elev (+ random effects) to see if there is an interaction. Be sure to note direction of interaction, as this will differentiate between H2 and H3 (see below).

H3- Rooting volume/depth relative to water sources are critical in drought response. Effects of drought on larger trees are mediated by the fact that large trees have better access to water. P3a- drought response increases with elevation and/or distance from stream (it would be nice if we knew more about the site hydrology!) Next step:

• [ ] try a model with just elev (+ random effects).
• [ ] check/report direction of elev term in model.
• [ ] consider whether we may have a better option than elev to characterize access to water (e.g., elevation relative to nearest stream)

P3b- There is a dbhelev interaction, elevation (relative to stream?) matters less for big trees with larger (and potentially deeper) root system. Next step:*

• [ ] try a model with dbh*elev (+ random effects) to see if there is an interaction. Be sure to note direction of interaction, as this will differentiate between H2 and H3 (see below).

*H4(?)- Larger trees suffer more because larger trees tend to be species with more drought-sensitive traits.* Note: I'm not sure if we want to get into traits in this paper. I think traits deserve to be a separate, stand-alone paper, both in terms of scientific significance and complexity. However, we could always include TLP (and ring porosity?) here and then dive into traits more thoroughly in anther paper. P4a- TLP predicts drought response Preliminary result : True (#6).

P4b- TLP is lower (larger negative) in smaller/ understory trees Next step:

• [ ] test this.

P4c- Inclusion of TLP in model eliminates (or significantly reduces) effect of height (and elev). Preliminary results : False. Model including TLP + dbh much better than just TLP, and TLP + dbh + elev is slightly better than TLP+dbh (#6)). Next step:

• [ ] test whether strength of height term is reduced by including TLP.

[teixeirak]

Note that it may still make sense to still include the analyses in issue #4 in this paper, although in light of the results we're getting here, it may make sense to also try separating by current dbh.

[teixeirak]

@tepleya, it would be great to get your input when you have a chance. In the meantime, we will keep working on this and contact you if we run into specific questions for you.

[mcgregorian1]

Hi @teixeirak

First of all, this is brilliant, thank you!

Second, I've been reading up more on lmm and I've found that we've been using "year" as the wrong kind of effect. At a minimum, random effects should have at least 5 or 6 different levels, but "year" only has 3. Therefore I corrected it to be a fixed effect and I got the following result. I'll continue working through what you've mentioned using this correction.

Reminder, year is present in all models here because I specifically told R to disregard models without it. If I allow year to not be included, then the best model in this chart is actually the 5th best model.

[teixeirak]

Okay, thanks for fixing that. (We'll still want to include drought year in all models). It looks like this doesn't change anything much, correct?

[mcgregorian1]

Ok. Apparently no, the models are basically in the exact same order as when year was a random effect.

[teixeirak]

@mcgregorian1, could you please work on a comprehensive assessment of the hypotheses / predictions above? I started updating the above, but there are some remaining predictions to test, and enough model versions that this needs to be done systematically.

[mcgregorian1]

For the record I am putting each hypothesis into a different issue, so that way we can follow the progress of each one more easily.

As a reminder, all model runs are being done with removing missing values and removing outliers (resistance values >2).

[teixeirak]

This has been broken up into separate issues; closing this.