## The Lodgepole Pine: A Case Study

Every year, the Statistical Society of Canada has a case study competition for statistics students in Canada. The problem and the data are posted about six months before the annual meeting. Teams of students analyze the problem and then present their results at a poster session at the meetings.

One of the two topics for this year’s competition was “The Effects of Climate on the Growth of Lodgepole Pine”.

The Question of Interest

To what extent do climate, position on the tree bole, and current foliar biomass explain cross-sectional area increment and proportion of early and late wood?

Primary objective

The primary objective is to determine to what extent climate, position on the tree bole (trunk), and current foliar biomass explain cross-sectional area increment and proportion of early and late wood.

Secondary objectives

It is also of interest to learn the following:

1.How have temperature and precipitation affected the annual cross-sectional growth and the proportions of early and late wood in lodgepole pine?

2.Is annual growth best explained by average annual temperature or do monthly maximum and/or minimum values provide a better explanation? Do early and late wood need to be considered separately?

3.Does the use of climate variables to predict the growth and proportions of early and late wood provide more reliable estimates than the use of the growth and density measurements from previous years as measured from the interior rings?

Further information and the data are available on the SSC website here. Data on temperatures and precipitation from the two British Columbia sites are included as well as a variety of variables from the sampled trees.

The winners were two students from the Department of Mathematics and Statistics at University of Victoria in Canada: Eric Cormier and Zheng Sun. Their winning poster does not contain a great deal of details (how much can you fit on a poster?), but it does indicate the models and types of analysis they used. It may be of interest for anyone interested in trees as proxies.

Hey, the stat community is starting to pay some attention to climate science.

1. Posted Aug 28, 2009 at 3:21 PM | Permalink

I was surprised they found better correlation to temp than moisture.

• MrPete
Posted Aug 28, 2009 at 4:26 PM | Permalink

Re: Jeff Id (#1),
If it is located in an area with fully available moisture, or with consistent moisture, you’re not going to see a “moisture” effect.

2. Les Johnson
Posted Aug 28, 2009 at 3:42 PM | Permalink

From our results we see that min temp. and foliar biomass have
a positive effect on CSI while lower trunk position and max temp
have a negative effect.
Annual growth is better explained by monthly max. and min.
temperature than by average annual temperature,

More leafs makes sense. More energy absorption, more growth.

Max temp INHIBITING growth is interesting. As is monthly min/max being a better predictor than average yearly.

The latter makes sense. A warm summer with a cold winter gives an average temperature, but would still have above average growth, as the growth would only occur in the summer.

• Posted Aug 28, 2009 at 7:16 PM | Permalink

Re: Les Johnson (#2),

From our results we see that min temp. and foliar biomass have
a positive effect on CSI while lower trunk position and max temp
have a negative effect.

Annual growth is better explained by monthly max. and min.
temperature than by average annual temperature…

What that means to me is that these trees are poor proxies for annual temperature, and that in the absence of evidence to the contrary, should not be used in reconstructions of past climate.

3. curious
Posted Aug 28, 2009 at 3:44 PM | Permalink

Thanks Roman – good read. Interesting it is negative correlation to max temp and positive to min temp. Is that usual in the dendro world? Haven’t the major reconstruction papers drawn conclusions re: mean temperatures?

Would be nice to see a detailed write up and I didn’t spot references to the source of the temp. data.

Also:

Future Work:
 Use of Skew-elliptical Distribution to model our residuals to
account for both skewness and heavy tails in the error terms
 Incorporate splines to accommodate temporal trend in the ob-
servations

Splines!!?

• romanm
Posted Aug 28, 2009 at 3:52 PM | Permalink

Re: curious (#3),

I didn’t spot references to the source of the temp. data

The data was put together by someone other than the students, but I don’t know what the source of the data was.

4. Calvin Ball
Posted Aug 28, 2009 at 4:25 PM | Permalink

Max temp INHIBITING growth is interesting. As is monthly min/max being a better predictor than average yearly.

In BC, there’s a strong inverse correlation between temperature and moisture. BC (and the American PNW) is a bit unusual in that regard. I’m afraid that the two variables are entangled.

• Posted Aug 28, 2009 at 9:15 PM | Permalink

Re: Calvin Ball (#5),

Very true. In summer it’s very dry here, fall and winter tend to be much wetter.

5. David L. Hagen
Posted Aug 28, 2009 at 9:16 PM | Permalink

CO2 concentrations have a strong impact on growth of pine trees.
See CO2 is green for table and photos.

NIPCC report Ch 7 reviews impacts of CO2 on biological growth

6. AnonyMoose
Posted Aug 28, 2009 at 9:37 PM | Permalink

Higher temperature probably encourages evaporation, which encourages more sap flow, which increases nutrients, which encourages growth. Reports of cool areas under trees suggest cooling evaporation is present; experience indicates water consumption by plants increases with temperature.

7. Nicholas
Posted Aug 28, 2009 at 9:56 PM | Permalink

I’m just guessing here, but isn’t it likely that the reason that overall growth is better correlated to minimum temperature because years with mild winters (i.e. higher average minimum temperatures) mean a longer growing season?

Similarly, wouldn’t the reason for maximum temperatures yielding lower growth be because years with higher average maximums correspond to hot (and possibly dry) summers, and we’re seeing the right side of the inverted U-curve of growth?

The fact that either of these two effects, with opposite outcomes, can lead to the same change in average annual temperature suggests why correlation between growth and average temperature is poor.

• crosspatch
Posted Aug 29, 2009 at 2:56 AM | Permalink

Re: Nicholas (#12),

“wouldn’t the reason for maximum temperatures yielding lower growth be because years with higher average maximums correspond to hot (and possibly dry) summers”

Did you look at the data and see if the hot years were dryer? Just because a year has a higher average doesn’t mean it had a drought. Warmer winters are generally wetter winters than very cold ones and the amount of precipitation over the winter sets the stage for growth conditions in the spring.

8. Geoff Sherrington
Posted Aug 29, 2009 at 5:03 AM | Permalink

This whole topic has been on CA before. It helps to think of a series of inverted U responses relating factors such as moisture, nutrients, sunlight, temperature etc to growth. e.g. too cold and the plant dies, bits of growth in a warmer climate, lots of growth in an optimum temp climate then loss of growth again as the temps get too high until you get desert heat type conditions. The inverted U responses are probably numerous and overlapping and of different scales and impossible to separate except in carefully controlled lab experiments.

Trees might be fine for counting rings as a time base, but the complex non-linear multivariate response to probably about 50 diverse factors makes it rather ambitious to try to link growth with a single factor like temperature, however defined.

• Soronel Haetir
Posted Aug 29, 2009 at 6:22 AM | Permalink

Isn’t that why proxy trees are supposed to be chosen for their location, to maximize the effect of one of the variables?

It would not surprise me at all if just 2 or 3 of the variables could explain most growth for most trees, the obvious pair being temperature and moisture. However as I said some other time, it also wouldn’t surprise me if a perfect graph of growth response has multiple local maxima. That perfect graph is currently unknown of course, and could likely only be obtained by growing trees in BioSphere type greenhouses for long time periods.

• MrPete
Posted Aug 29, 2009 at 8:03 AM | Permalink

Re: Soronel Haetir (#15),
Yes, they’re supposed to be picked that way. Unfortunately,
a) They often are not
b) There’s a huge not-always-valid assumption being made: in a given location, the factors affecting tree growth never change. (That is stated as the Uniformitarian Principle of dendroclimatology.

• Geoff Sherrington
Posted Aug 29, 2009 at 11:03 PM | Permalink

Re: Soronel Haetir (#15),
It is unlikely that growth can be accounted for by a small number of dominant variables. If you see a plant nursery with a few dozen/hundred new plants in pots in a block, you might see considerable size variation from one pot to the next. Distance from the water sprinkler, handful of nutrients thrown over some more than others, differences in potting mix, shading from adjacent objects, pest attack, stronger growth to resist wind bending, the list just goes on.

Besides, if you collect seeds of some species from the wild and then plant them under ideally uniform conditions, you can get enormous variation from plant to plant. There have been past programs to breed from “super trees”. Darwin principles at work, perhaps. BTW, I cannot understand the logic of sampling lone survivor trees. Who knows why others died?

As an aid, think of the size variablilty of people in a like group then apply your deductions to trees.

There is no objection to education in statistics using real life examples. Indeed, it is probably better through providing relevance. But it is not right to pose the exercise using assumptions that might not withstand scrutiny. That starts to become indoctrination.

• Calvin Ball
Posted Aug 29, 2009 at 9:11 AM | Permalink

Re: Geoff Sherrington (#14), Question for the statistical wizards; is there any way to statistically regress a multivalued function (i.e. U-shaped)? Maybe there’s a way of knowing which side of the hump you’re on by estimating the derivative? Otherwise, it seems like this treemometer stuff is fatally flawed.

9. Michael Jankowski
Posted Aug 29, 2009 at 6:57 AM | Permalink

Hey, the stat community is starting to pay some attention to climate science.

If only climate science would involve the stat community.

• RomanM
Posted Aug 29, 2009 at 9:16 AM | Permalink

Some of us are working on it! They can’t ignore that forever.

Re: stan (#17),

The stat competitions have used problem from many different scientific areas over the years. This particular problem involved material which I thought would be of interest to CA.

Winning is determined by the overall quality of the presentation and the correct use of appropriate procedures for the data at hand, not necessarily from “correct conclusions”. The adjudication committee for 2009 consisted of the full membership of the Committee of the Award for Case Studies in Data Analysis of SSC (consisting of 5 statisticians from Statistics Canada and 4 Canadian universities). The data was made available by a Ph.D. research scientist on ecological processes working for the provincial government of British Columbia. It is available from the SSC page detailing the problem. Yes, the competition would indeed work with fabricated data, but I expect that this data is pretty real. I would also expect that what was done was done without major errors, but would not be required to be a completely thorough analysis.

10. stan
Posted Aug 29, 2009 at 8:01 AM | Permalink

Yes, interesting that the stat competition used a climate problem. Conclusions should not be drawn by looking at the winners. One, we don’t know anything about the data. Two, we don’t know anything about who choose what constititutes “winning” or who did the choosing. This type competition could be effective with fabricated data. It isn’t about trying to do accurate science.

11. curious
Posted Aug 29, 2009 at 9:43 AM | Permalink

Stan – From the link in the post my reading of it is that the tree ring data in the study was real and well referenced. The temps are monthly values to 1dp from 1895 onwards but I haven’t seen a source reference. Temps are available as excel files.

12. Kenneth Fritsch
Posted Aug 29, 2009 at 11:12 AM | Permalink

As a layperson, I am impressed with what these students have shown (and in one poster). How would a statistician describe this level/stage of work? It would appear to me to be a preliminary look at the data without hypothesis testing.

In the real world would data be given to statisticians without the close association of and inputs from the science experts? Maybe that would be more proper for the next step in the analysis. Could a model search without some expert a priors be subject to overfitting and data snooping?

Anyway after a preliminary read of this analysis, I am thinking that these students covered some ground that I cannot recall seeing discussed in dendro papers. It is worth a further read in my mind.

• RomanM
Posted Aug 30, 2009 at 9:26 AM | Permalink

The students have done a very creditable job on the data and should rightfully be congratulated on it. They clearly set out a model for the annual growth in terms of other variables, imputed missing values, presented summary plots for some of the variables, transformed the response variable and fitted a mixed model (with random and fixed effects) analysis of covariance . This is the sort of thing that consulting statisticians would do for a client and not what one might consider statistics research since it does not contain innovative methodology in solving a problem.

The problem web page contains links to further information on trees and the analysis of tree data which I would definitely expect that the students would have accessed along with possible further web research and/or contact with people skilled in looking at such data.

Their model contained the ability to estimate the variation in the tree growth due to measuring different positions on the tree and different radii on a disc. The results given for the anacova would be the final run after a sequence of runs identifying and removing factors which did not contribute any effect on the response variable. More was done than appears in the poster.

Re: jae (#23),

I think you are being unreasonably harsh on the student presentation. This not a paper appearing in a climate science journal nor is it intended to be a justification of using trees as treemometers. It addresses and attempts to answer the question of what factors among those given have an effect on the growth and it attempts to do that using viable statistical methods.

As well, the problem web page implies that another question is also behind the reason for the existence of the data:

It is commercially important to be able to predict how lodgepole pine will grow and accumulate wood over time. Using high resolution satellite images of lodgepole pine stands to predict wood attributes is under consideration, but first the relationship of crown properties such as the amount of foliage must be linked to wood properties and growth.

So, no, it is not a “timberline” forest. The tree locations are described as interior (where Quesnel and Kamloops live). I would suspect that the data would be part of a commercially oriented study so it would have been cleaned up somewhat before being given to the students and the quality would likely be pretty good.

I had hoped that readers here might find the questions, the data and the poster informative. Even if this is not the case, no, the poster is not “worthless” and, yes, the “rhetorical” questions are still worth thinking about in their own right.

• Geoff Sherrington
Posted Aug 31, 2009 at 6:51 AM | Permalink

Re: RomanM (#27),

It would be beaut to involve the students here. If I gave an impression of negativity about the students, I did not mean to do that and I apologise if I sounded that way.

I did several years of research on this very subject, one as a new postgrad and one with 25 years of extra age. The extra age failed to reduce my understanding of the complexity of the growth response. In my reading, there has not been much progress towards overall understanding.

Typically, one enters quite difficult ground when moving from physical processes to life processes. That problem can show itself when life-form proxies are used for matters like global temperature.
Why, even our 2 cats are unpredictable and are good at training us.

• RomanM
Posted Sep 1, 2009 at 7:35 AM | Permalink

It would be beaut to involve the students here.

I was of the opinion that curious (#29), invited them to look at the post. They are welcome to post comments and discuss what and why they did the particular analysis in their poster.

In general, from my own experience, I do not think that most students (except for a small number of activists) are cognizant of the details behind AGW and climate change. There is a tendency in the university setting for an unconditional acceptance as fact of the tenets put forward by a subgroup, particularly in situations where a concensus has been declared on something as dramatic as AGW. The students here could be an exception because of whatever research they may have done for the project.

• Kenneth Fritsch
Posted Sep 1, 2009 at 9:07 AM | Permalink

Re: RomanM (#37),

In general, from my own experience, I do not think that most students (except for a small number of activists) are cognizant of the details behind AGW and climate change. There is a tendency in the university setting for an unconditional acceptance as fact of the tenets put forward by a subgroup, particularly in situations where a concensus has been declared on something as dramatic as AGW.

If these students elected to post here, I would hope that the posters here would keep their posts on the topic of what I see as a preliminary analysis of building a model of relating climate to tree ring growth – with all its limitations – and not be tempted to elicit their views on AGW or debate any views that they might volunteer.

As a layperson, I am curious about how original the approach of these students or any part of it is to dendroclimatology and the methodologies used in that science. Perhaps it would be informative to have a dendroclimatologist weigh in here.

• bender
Posted Sep 2, 2009 at 8:43 PM | Permalink

Re: Kenneth Fritsch (#38),
The thing that is unique here is the mixed model, which allows one to estimate random effects and nested effects simultaneously. But look at the conclusions: the nested effect of having two radii per tree is not significant. Duh. This has been shown many many times before and it obviates the need, in this case, for a mixed model. So this is nothing more than a pedagogical exercise. Maybe their method would be more applicable in a different setting, where the nested effects were critical.
.
The authors are, of course, welcome to rebut.

• romanm
Posted Sep 3, 2009 at 9:15 AM | Permalink

Re: bender (#40),

To be accurate, there are more than two radii per tree. Sample discs were taken from ten or more different heights from each tree and two radii were used from each disc

It should also be realized that the trees came from two sites and therefore tree effects are nested within the sites. proper testing for difference between sites requires that the tree effects be treated as random effects as well. You will note that the the coefficients for adjusting for the age in the model are also treated as random.

I don’t understand why you think that the having a non-significant effect due to radii is odd. In fact, this is an indication that the results obtained from two different radii on the same disc are not substantially different. If they were, THAT would create a question about the ability of a particular radius to reasonably measure the amount of growth on a given tree. Checking for this is an integral part of the analysis.

Interaction terms were apparently included in the model, but without seeing the development of the model and the various test statistics, it is not possible to say which terms were included initially.

[self-snip]

• bender
Posted Sep 3, 2009 at 10:16 AM | Permalink

Re: romanm (#43),
Thanks for the correction.

I don’t understand why you think that the having a non-significant effect due to radii is odd.

On the contrary, I said that I, duh, find it totally unsurprising. Hence the triviality of including the nested effect of radii per disc in the model.

Interaction terms were apparently included in the model

Where does the poster say that?

• romanm
Posted Sep 3, 2009 at 10:47 AM | Permalink

Re: bender (#44),

Look at the model statement under figure 2 in the middle column. The formulation includes a term: (interactions). Which interactions this might refer to is unspecified, possibly due to space limitations.

I would think that it would be quite useful and important to evaluate how much of the variation comes from the process of measuring the growth when using different radii. In my opinion, it needs to be done merely to show that it is not having a major effect on the analysis. One of the topics discussed in the past on CA was the fact that cores taken from various sides of the tree can produce drastically inconsistent results.

As used here, the term for radii effect in the model is additive and I am not sure if I would agree with that. Physical considerations would lead me to think that a multiplicative form would be more appropriate, but that would complicate the analysis considerably.

• bender
Posted Sep 3, 2009 at 10:57 AM | Permalink

Re: romanm (#49),

cores taken from various sides of the tree can produce drastically inconsistent results

In even-aged lodgepole pine? Have you looked at the raw data?

Stop generalizing (and extrapolating based on high-elevation brstlecone pine) and start discussing the case study: lodgepole pine in two bug-ridden areas of BC.

Their modeling approach might have merit. I already conceded that from the get-go. But without testing explicitly for temp*precip interactions, nonlinearities, without discussing the effects of insects, I am skeptical this work has any practical merit.

I won’t even go into the issue of using EM to estimate “missing biomass data”.

We need to see the full study. Where’s their turnkey script?

• bender
Posted Sep 3, 2009 at 11:07 AM | Permalink

Re: romanm (#49),

The formulation includes a term: (interactions). Which interactions this might refer to is unspecified

Exactly: unspecified. So were all these “interactions” non-significant? Do they even say? Are the results for the unspecified interactions listed somewhere?

• bender
Posted Sep 3, 2009 at 10:18 AM | Permalink

Re: romanm (#43),

Comment 41 was simply inappropriate and uncalled for.

Fair enough. [snip]

RomanM: I do not think that continuing that sort of baseless speculation serves any useful purpose, here.

• bender
Posted Sep 3, 2009 at 10:19 AM | Permalink

Re: romanm (#43),

[self-snip]

Aha – caught you!

13. jae
Posted Aug 29, 2009 at 9:13 PM | Permalink

There is no way to say anything about this “research” without a great deal more information about the “forest” being studied. It sure as hell was not a “timberline” forest, since lodgepole pines don’t “do that.” Was it coast lodgepole pines, or interior lodgepole pines? Were the trees in a natural stand or a managed stand? Etc., ad infinitum. The “poster session stuff” is absolutely worthless without a great deal more information. But, I guess the rhetorical questions in the post are still worth thinking about???

14. curious
Posted Aug 30, 2009 at 4:54 AM | Permalink

FWIW – The tree data available on the link in romanm’s head post includes location, stand number and tree number. It is presented in such a way as to suggest the details are traceable and verifiable. Credit is given as follows:

Thanks to Roberta Parish of the British Columbia Ministry of Forests and Range for providing this case. Thanks also to Charmaine Dean, Simon Fraser University for her assistance.

Please address queries to Alison Gibbs, Department of Statistics, University of Toronto.

• steven mosher
Posted Aug 30, 2009 at 11:39 AM | Permalink

Re: curious (#25),
Invite the students to come and discuss.

15. Posted Aug 30, 2009 at 7:53 AM | Permalink

As David Hagen has noted in #10, it would have been useful and easy to include CO2 fertilization as a regressor. Also, volcanic or agricultural dust fertilzation might be factor, but one that would be much harder for these stats students to deal with.

Does “monthly Max and Min” mean monthly averages of daily max and min values, or does it mean annual obervations on the max and min over months of monthly averages of daily max/min mean temperatures? These are quite different values. Most have assumed the latter, but the former could be important as well.

Was the net effect of Max and Min (however measured) positive or negative? Ie if both go up or down together, what is the net effect?

RE Calvin Ball #19, it’s easy enough to include quadratic terms in a regression, as long as you don’t try to extrapolate the resulting curve too literally.

16. curious
Posted Aug 30, 2009 at 12:42 PM | Permalink

Yes – nice idea. It would be good to have some enquiring students contributing. I have mailed out of curiousity regarding the temp. data and I gave them a link to the CA article – perhaps they will find their way over!

17. Posted Aug 30, 2009 at 2:07 PM | Permalink

I would love to see a student group seriously interacting with CA.

As a non-professional-scientist who did an independent investigation of the science and story of AGW (click my name) I’m interested to get some idea of the awareness of academic departments whose studies overlap Climate Science – how aware are they of the whole problem of politically-supported alarmism debasing the pure science, how much can they say, are they even aware of the debate being muzzled?

18. Eric Anderson
Posted Aug 30, 2009 at 6:10 PM | Permalink

It has been long enough for some controlled environment (i.e., single-variable control) studies to have been performed on trees over several years. Has anything been done along these lines? My (admittedly limited) observation is that other factors are far more influential than a degree or two of temperature variation. Just by way of analogy, in the non-tree situation of comparing my garden with that of my neighbor the past couple of years I can categorically say that the massive difference in growth and yield between our two gardens has absolutely nothing to do with a temperature differential and, thus, everything to do with better soil, nutrients, water, etc.

There are two large issues. First, without a controlled environment study carried out on trees over several years, it seems impossible to even know how much the various factors contribute to growth. Second, even if we knew how much the various factors contribute to growth, it would be difficult to ascertain which factors contributed to growth in particular years in some historical past.

19. Posted Aug 31, 2009 at 2:40 AM | Permalink

Maybe a good starting point for this type of analysis would be the rich literature on process-based tree growth modelling. I mean, there is no need for reinventing the wheel.

20. Craig Loehle
Posted Aug 31, 2009 at 6:37 AM | Permalink

Lodgepole pine tends to grow where it is either cold or dry (or both). In a cold winter, the snow will stick around longer, shortening the growing season (because cold soil inhibits root activity). Thus a higher minimum will mean a milder winter. This makes sense. A higher max can mean that the available moisture in the soil is used up sooner, and thus again a shorter growing season. This means that if both max and min go up by a comparable degree, there will be no change in growth, which makes this case a terrible tree-mometer and shows why tree growth is not a simple function of temperature.

21. stan
Posted Aug 31, 2009 at 8:43 AM | Permalink

Roman,

I wasn’t denigrating the students’ work. I was merely cautioning commenters here to avoid making any conclusions about what it means in terms of the science. That would be true, even if it was a science competition for grad students in climate science. Actually, that should be true for every science study, especially in climate science.

One of my biggest peeves with climate science is the readiness with which scientists and non-scientists alike automatically treat studies as if the authors’ conclusions constitute proof of something. I think the better approach should be to remember that it may very well be possible that the data used in the study was accurate. It also may be possible that the statistical manipulations of the data actually folded, spindled and mutilated the data in a statistically appropriate manner. And it may be possible that the many assumptions underlying the study (some recognized, some not) may all be appropriate to the physical processes sought to be modelled. Finally, if all those possibilities prove to be true, the study might even help provide a better understanding of how the climate works. Maybe.

In science, step 1 should always be to recognize the limits of what we know and the vastness of our uncertainty. Instead, we get hubris on steroids.

22. Kenneth Fritsch
Posted Aug 31, 2009 at 9:54 AM | Permalink

I would assume that these students were given a limited source of data and general guidelines from the “question of interest”. If the competition is statistics, I would not think that the participants would be judged by how well they knew the science or could a prior come up with any number of potential explanatory variables.

We should be discussing how well they performed in the statistical analysis – and further on whether they have presented any new, or, at least, areas seldom delved into by the dendro literature.

I liked the analysis of maximum, minimum and average temperatures and the significance broken down by months. In the dendro literature I sometimes get the idea that the temperature used (max/min/ave and the months) for reconstructions is determined after that fact and judged by how well those specific temperatures “fit” the model.

The effects of sampling location from individual trees, as I recall, are seldom addressed directly in dendro papers. Maybe that is so basic to the science methods that it is omitted, but then I would thank the students for enlightening me on the matter.

23. bender
Posted Sep 2, 2009 at 8:30 PM | Permalink

This work fails to address two issues raised multiple times in the past at CA: (1) interactions between precip and temp are ignored; (2) the potential effects of insects are not discussed or controlled for. These same shortcomings can be found in some of the paleoclimate reconstructions used by IPCC and The Team. Notable because the effect of insects on lodgepole pine growth has been increasing over time. The pattern is quite HS shaped, in fact.
.
Let the students revise their causal model and then we’ll see how tractable their method is. That is all.

• MrPete
Posted Sep 2, 2009 at 10:13 PM | Permalink

Re: bender (#39),
You could extend “insects” to “other factors”…quite a lot of potential factors, depending on the site(s).

• bender
Posted Sep 3, 2009 at 10:21 AM | Permalink

Re: MrPete (#42),

You could extend “insects” to “other factors”…quite a lot of potential factors, depending on the site(s).

I could. But why should I? In the case of insects on lodgepole pine I think there is a pretty strong case that one should not ignore the effect of mountain pine beetle on tree rings.

• bender
Posted Sep 3, 2009 at 10:26 AM | Permalink

Re: bender (#47),
The two locations studied were Kamloops and Quesnel, both in BC. Nope, no insects there in the last few decades. snark /off

• MrPete
Posted Sep 3, 2009 at 11:05 AM | Permalink

Re: bender (#47),
You are correct. There may even be a similarity to the effect we’ve observed with strip bark.

I live in the midst of a forest (the Black Forest of Colorado), some of which has been affected by Mountain Pine Beetles. Key element: the beetles stress a tree, eventually killing it.

Strip bark also correlates to extreme tree stress, and eventually the tree dies.

I’ve never measured or analyzed growth related to pine beetles. But as a simple hypothesis, does it not make sense that a tree could produce extreme growth response to potentially fatal stress?

If so, then almost by definition, one will tend to find hockey stick data in currently living, highly stressed trees.

Re: romanm (#49),
Interesting thing is that unlike strip bark, which obviously impacts radii differently, beetle attacks are more uniform around the tree circumference.

• bender
Posted Sep 3, 2009 at 11:10 AM | Permalink

Re: MrPete (#52),

the beetles stress a tree, eventually killing it

No, they (or rather, the fungus they carry) kill it rather immediately. Then all that is left for the dendro to sample are the unnattacked living trees that are now surging in growth in response to the space opened up by the beetles.

• Mark T
Posted Sep 3, 2009 at 11:26 AM | Permalink

Re: bender (#54), The fungus kills the tree the summer it becomes infected. It is cyclical, too (a ranger at Long’s Peak told me 400 years, I’ve read 150 years), so stands tend to not be very old.

Mark

• bender
Posted Sep 3, 2009 at 11:29 AM | Permalink

Re: Mark T (#57),
It’s fire (and steep topography) that tends to limit stand age in this system. Beetle-killed timber is highly flammable, especially when flames are buring upslope.

• Mark T
Posted Sep 3, 2009 at 11:54 AM | Permalink

Re: bender (#58), Yes, they are. I suppose the two work in concert, i.e., beetles create the fuel, and fires oblige it.

Mark

• bender
Posted Sep 3, 2009 at 11:57 AM | Permalink

Re: Mark T (#61),
You are wrong. Beetles are not a necessary condition for fire. Fire happens in the absence of beetle kill all the time. Fire limits forest stand age in this region, not beetle attack. Care to war with references?

• Mark T
Posted Sep 3, 2009 at 12:39 PM | Permalink

Re: bender (#62), For gosh sakes bender, chill out. I never said they were a necessary condition, just that the beetles create fuel for fires by killing trees.

Mark

• bender
Posted Sep 3, 2009 at 12:46 PM | Permalink

Re: Mark T (#66),

I never said they were a necessary condition, just that the beetles create fuel for fires by killing trees.

You said:

The fungus kills the tree the summer it becomes infected. It is cyclical, too (a ranger at Long’s Peak told me 400 years, I’ve read 150 years), so stands tend to not be very old.

I disagreed. I said it is fire that keeps the stands young, not a fungus-carrying beetle.

If you accept that I am right and you are wrong, I am prepared to move on.

• Mark T
Posted Sep 3, 2009 at 1:02 PM | Permalink

Re: bender (#68),

I said it is fire that keeps the stands young, not a fungus-carrying beetle.

Nothing in my quote disagrees with your position, bender. I simply pointed out that the beetle problem is cyclical – are you disagreeing with that? Silly, if so. You’re being obtuse for no apparent reason.

Mark

• romanm
Posted Sep 3, 2009 at 11:32 AM | Permalink

Re: MrPete (#52),

The students did not plan the experiment nor did they collect the data. This was done by someone from British Columbia Ministry of Forests and Range. The person listed on the problem site is also the co-author of a paper found at the bottom of the problem page: Dynamics of an old-growth, fire-initiated, subalpine forest in southern interior British Columbia: tree-ring reconstruction of two-year cycle spruce budworm outbreaks.

If I were to hazard a guess, I would assume that this person would be aware of the problems caused by insects. I would also hazard, that for a designed baseline study on the effects of the variables in the study on growth, only trees which had not been seriously damaged by insects would be chosen to be included in the data set. So the potential effect of insects seems like a red herring here.

• bender
Posted Sep 3, 2009 at 11:52 AM | Permalink

Re: romanm (#59),

insects seems like a red herring here

It’s just something that needs to be discussed in the full paper. Maybe these trees are all <30 years old, in which case they were not really vulnerable to attack during the study period, 1975-2004.
.
But you will note that young trees are currently being swallowed up by beetles in places like Quesnel and Kamloops. There goes the conventional wisdom about young trees being invulnerable to beetle attack. And so much for any insights that a mathematician could provide into the dynamics of this system.
.
And so much for your “red herring”. If these stands originated from fires associated with beetle-kill in the 1980s then that would explain the huge bulk of the variation. Not reconstituted “foliar biomass”, but the natural process of decreasing light availability under a closing canopy.

• bender
Posted Sep 3, 2009 at 12:03 PM | Permalink

Re: romanm (#59),

The person listed on the problem site is also the co-author of a paper found at the bottom of the problem page: Dynamics of an old-growth, fire-initiated, subalpine forest in southern interior British Columbia: tree-ring reconstruction of two-year cycle spruce budworm outbreaks.

If I were to hazard a guess, I would assume that this person would be aware of the problems caused by insects.

Roberta Parish is a silviculturist, not an entomologist. And that paper was published in 2002. It wasn’t until the last few years that entomologists began to notice young trees being attacked in large numbers.
.
You are insufficiently critical of the study design. I wouldn’t assume anything about what anybody knows or what was done or why.
.
Shall we talk now about the significant effect of “foliar biomass”, as reconstructed by EM? Whereupon you will begin to realize that the origin of a stand is not unimportant in this case study.

24. bender
Posted Sep 2, 2009 at 9:35 PM | Permalink

[Inappropriate and uncalled for]

25. bender
Posted Sep 3, 2009 at 11:02 AM | Permalink

[C’mon, bender! Inappropriate question. Further comments in this direction will be deleted]

26. bender
Posted Sep 3, 2009 at 11:17 AM | Permalink

I like their Figure 4: future growth is likely to remain at the low levels observed in the later years, but is esentially unpredictable due to the huge uncertainty in model parameter estimates. At least they are honest.

27. bender
Posted Sep 3, 2009 at 11:25 AM | Permalink

The authors, in Fig 4, have ring width taking a dive in 1984. But [a limited sample of] the raw data show this happening in 1985. Wonder what gives.

28. bender
Posted Sep 3, 2009 at 12:09 PM | Permalink

romanm:
Let me know if and when you can find the foliar biomass data used in this analysis. Also: how exactly “inverse regression” was used to replace the missing values.

• romanm
Posted Sep 3, 2009 at 12:31 PM | Permalink

Re: bender (#64),

All of the data which was available to the students can be accessed from the SSC problem page which was linked in my original post. The foliar data is available both as a txt file or an Excel file. I have no idea how the inverse regression was used in this case.

• bender
Posted Sep 3, 2009 at 12:41 PM | Permalink

Re: romanm (#65),

The foliar data is available both as a txt file or an Excel file.

You have verified this?

• bender
Posted Sep 3, 2009 at 12:48 PM | Permalink

Re: bender (#67),
My mistake. The data are in separate files.

• bender
Posted Sep 3, 2009 at 1:16 PM | Permalink

Re: romanm (#65),
That datafile gives foliar biomass of sample branches along the length of the tree crown, i.e. with branches of different ages. It does not given foliar biomass of the whole crown over time. Without a script it is totally unclear what the authors are doing in the analysis.

29. Kenneth Fritsch
Posted Sep 3, 2009 at 1:14 PM | Permalink

Bender, perhaps you could provide your preferred version of the analysis the students used in the competition. A simple outline with comments would, I think, suffice.

• bender
Posted Sep 3, 2009 at 1:19 PM | Permalink

Re: Kenneth Fritsch (#71),
Ken, I can’t do that without understanding what the data actually represent. This branch foliar biomass data has me stumped. (see my #72).
.
But why do this at all? I can’t see why Steve M would be interested in a method that is irrelevant for paleoclimatology, for reasons mentioned in #73.

• romanm
Posted Sep 3, 2009 at 1:39 PM | Permalink

Re: bender (#74),

But why do this at all? I can’t see why Steve M would be interested in a method that is irrelevant for paleoclimatology, for reasons mentioned in #73.

Steve didn’t write this. He was out of town spending quality time in beautifull downtown Italy. I wrote the post because I thought that some people might find it interesting.

• bender
Posted Sep 3, 2009 at 1:56 PM | Permalink

Re: romanm (#76),
I know who the author is. And the study *is* interesting. And I thank you for bringing it to our attention. My point is simply that nothing turns on this. Which is what Ken wanted to know.

30. bender
Posted Sep 3, 2009 at 1:16 PM | Permalink

What relevance would an analysis of very young trees growing in a closed stand have for paleoclimatologists that favor the use of old trees growing in open stands? This statistical method is specially designed for a situation that paleoclimatologists specifically try to avoid.

• romanm
Posted Sep 3, 2009 at 1:36 PM | Permalink

Re: bender (#73),

Probably, not a lot. As I wrote in comment #27,

This not a paper appearing in a climate science journal nor is it intended to be a justification of using trees as treemometers. It addresses and attempts to answer the question of what factors among those given have an effect on the growth and it attempts to do that using viable statistical methods.

As well, the problem web page implies that another question is also behind the reason for the existence of the data:

It is commercially important to be able to predict how lodgepole pine will grow and accumulate wood over time. Using high resolution satellite images of lodgepole pine stands to predict wood attributes is under consideration, but first the relationship of crown properties such as the amount of foliage must be linked to wood properties and growth.

It appears that the reason for the question is to try to estimate the growth of trees in a forest using climate data and satellite photos among other things.

• bender
Posted Sep 3, 2009 at 1:52 PM | Permalink

Re: romanm (#75),
Ok, then. We’re getting somewhere.
.
More generally, then, what do you think is the value of mixed models for paleoclimatology? Are these nested effects really all that important to estimate? Is it really necessary to estimate the random effect of tree, when you could just do what the dendros do and average large samples to statistically iron out the effect of individual trees? Is it really necessary to estimate the effect of radiii within discs or discs witin a tree, when you could do what the dendros do and take a single set of cores at breast height, or average among cores to iron those differences out? Is it really necessary to explicitly estimate the effect of foliar biomass if you can use heuristic methods to remove that trend?
.
This poster thus appears to have little new to offer to dendroclimatology. This directly responds to Ken’s questions in #36, #38.

• Kenneth Fritsch
Posted Sep 3, 2009 at 4:45 PM | Permalink

Re: bender (#73),

What relevance would an analysis of very young trees growing in a closed stand have for paleoclimatologists that favor the use of old trees growing in open stands? This statistical method is specially designed for a situation that paleoclimatologists specifically try to avoid.

Bender, this was the proposition from the introduction to this thread:

To what extent do climate, position on the tree bole, and current foliar biomass explain cross-sectional area increment and proportion of early and late wood?

I would suppose that very old trees were once young and I assume counted in very old proxies. Perhaps you can weigh in on that.

I also am assuming that the reason that Roman chose to post this study was as much or more from the statistical methods used as what from the analysis could specifically be applied to dendrochronology.

I think you need to give more details on what you think could be useful from the students’ analysis to dendrochronoligists from either a statistical perspective or the explanatory variables effecting tree ring growth. The analysis was, after all, presented as an assignment to test the students statistical skills and my point has been what we can we learn from their work – given that I have not been that impressed from the published papers by dendros that I have seen analyzed here at CA and for reasons given above.

• bender
Posted Sep 4, 2009 at 8:48 AM | Permalink

Re: Kenneth Fritsch (#83),

This work has potential importance at three levels: (1) stated objective regarding effects of biomass and climate on young lodgepole pine in fire-origin stands in BC; (2) relevance of results to dendroclimatology; (3) relevance of statistical methods for dendroecology.

(1) IMO we can not assess the validity or significance of the results until we understand how plant biomass was estimated over time.
(2) The results in this paper have no relevance for dendroclimatology because of the types of trees and stands chosen for study. The climatic responses exhibited are not representative of the types of responses you would expect in old, open-grown trees at high elevation. Moreover, the climatic responses are necessarily weak because they are dominated by the up-down pattern of crown expansion and canopy closure over a 30-year period.
(3) The statistical method of mixed models, while applicable, is not likely to overturn any result in dendroclimatology because all of the nested effects estimated are either trivial, or never come into play, or are easy to correct for. Yes, it would be nice to see a side-by-side comparison. That would even be publishable, because it would satisfy curiosities like yours. But the bottom line is that nothing would turn on this. [Ok, well, there is the sad case of the strip-bark bristlecone pines that have inconsistent readings across various radii. There would be some effect in those cases.] Finally, what dendro is going to destructively sample an entire tree so that the needs of this particular model can be satisfied? A practical model has to accomodate non-destructive sampling involving nothing more than a couple of cores. No biomass measures as covariates.

31. bender
Posted Sep 3, 2009 at 2:13 PM | Permalink

Re: foliar biomass as the #1 predictor.
.
Look at the actual pattern being modeled here:
Ring width starts low in the mid- 1970s, when the trees are establishing, goes up, peaks in ~1990 and comes down, troughing in 2004 at the end of the study as the canopy presumably starts to close up. Meanwhile, branch biomass is low for young branches, peaks for medium-aged branches, and drops for the oldest branches. Wait a sec …
.
How did these authors get from branch biomass to whole-crown biomass? Or are they simply, foolishly regressing ring width onto branch foliar biomass? That would certainly help explain why foliar biomass is by far the dominant variable in this analysis.
.
Even if they did the biomass calculation correctly … nuanced climatic fluctuations in the 30 year period from 1975 ot 2004 are not going to explain much for what is essentially a brand new plantation starting from seed. Of course the pattern of radial growth is going to track the process of canopy growth and closure.

32. RomanM
Posted Sep 3, 2009 at 2:47 PM | Permalink

I don’t know the answers to your questions. It appears to me that a study like this would basically be an attempt to get a handle on what factors affect the growth and to roughly what extent. The problem page states

Each year, a tree lays down an annual ring of wood in a layer under the bark. Pressler’s hypothesis states that area of wood laid down annually (measured by the cross-sectional area increment) increases linearly from the top of the tree to the base of the crown (the location of the lowest live branches) with the assumption that it is proportional to the amount of foliage above the point of interest.

This would imply to me that a cumulative value for the foliage variable would be calculated for each level. There is also another statement that I find somewhat confusing in respect of the analysis:

Measurements of the last year of growth and wood density are often unreliable because of proximity to the bark and difficulties of sample preparation. However, it is for this ring only that we have measures of the amount of foliage.

This would mean that “tracking foliage” was apparently not done in the study so I don’t know how it can apply to all of the rings.

• bender
Posted Sep 3, 2009 at 3:06 PM | Permalink

Re: RomanM (#80),

This would mean that “tracking foliage” was apparently not done in the study so I don’t know how it can apply to all of the rings.

Exactly. So here we are at the usual impasse – wondering what exactly was done, wondering why the plotted data don’t line up with the raw data in the source datsets. And so on.

33. curious
Posted Sep 3, 2009 at 4:21 PM | Permalink

For information: the ssc website now includes a source reference for the temperature data.

• romanm
Posted Sep 3, 2009 at 5:08 PM | Permalink

Re: curious (#82),

From near the top of the problem page:

Source of climate data added 2009-09-02

A bit strange for a no-longer-active case study. Statisticians like things to be complete. 😉

34. curious
Posted Sep 4, 2009 at 2:46 AM | Permalink

!! How does FOI work in Canada?? 🙂

35. Kenneth Fritsch
Posted Sep 4, 2009 at 10:42 AM | Permalink

Bender, I guess my curiosities stem from what I do not see in dendroclimatological papers – which does not imply that these matters are not covered elsewhere.

The appearance to a layperson, like me, is that the scientists working in this area write about the specific explanatory variables (months of the year, MXD and TR mix, max, min average temperatures, and even after the fact tree selection) for temperature that they use in their proxies as though these selection criteria are not determined a priori, but merely fitting the selections to provide a model with the highest explanatory power.

How much effort do these scientists put into to determining and understanding the growth factors before undertaking the construction of models relating those factors to temperature (or other climate variables)? How much of this preparatory work can be generalized such that the proxy model does not, or at least not appear to, require “fitting” as though each case and location has very unique properties?

Roman’s thread about these student’s work got me to thinking again about my understanding (or lack thereof) of this situation.

• bender
Posted Sep 4, 2009 at 10:51 AM | Permalink

Re: Kenneth Fritsch (#87),
Your curiosity is understandable and legitimate. The reason the statistical approach used in this paper is not used more broadly is because of the complexity and data-hunger of this model. Why parameterize a full model using masses of data if you can simplify the problem down to essentials and reduce the cost of sampling by orders of magnitude? You will note that these authors STILL have not dealt with the synergies, nonlinearities, disturbances, non-uniformities that other dendros have ignored – so what is gained through the use of this model? Relatively little compared to what could be gained by addressing those other shortcomings.
.
Lastly, These are not “students”. One is a professor.

RomanM: Bender, why do you persist in making this incorrect statement? Eric Cormier was an undergraduate student who graduated this spring and received the UVic Jubilee Medal for Science (for having the top undergraduate GPA). Zheng Sun is listed as a graduate student on the Math and Stat website.

Did you really expect these students to make it their life’s work after the competition was presented in May? Give the undeserved criticism a rest please.