Understanding Growth Response Modeling
Posted by Jeff Id on May 25, 2012
As we have continued to argue on the last thread about whether it makes sense to sort trees by ‘sensitivity’ to temperature (it doesn’t), we left off one of the most important critiques of dendroclimatology. This has been discussed here before in the context of Dr. Craig Loehle’s publication on non-linear tree growth, but it is important that we not forget how critical this issue is in the context of linear regressions. I am glad to have experts around to keep us on track – Jeff Id
Guest Post by John F. Pittman.
Below is a response from a temperature sensitive species that has been well documented. Different authors were able to control the nutrition, conductivity, spacing, etc, because these are unicellular plants. Actually it is two genera and multiple species. The curve represents an idealized single organism. This particular organism has a peak about 91% of maximum growth response and a peak response at about 28 C. So, now we can discuss the errors and incorrect modeling.
The first constraint of a correct statistically correct biological model is to consider what happens as more individuals are added. The first part we will look at is the area from 5C to 10C. As one adds more and more specimens, the curve will flatten towards the 0% line. The next area is the area above 80% that between 25C and 33C will tend to flatten towards the 80% line. The last is that as one adds more and more specimens the curve tends to go asymptotic to 40C. The reasons have to do with the temperature response of proteins and enzymes, and adaptation of the species wrt time, and acclimation of an individual wrt time, and of course, measurement variance.
Now, we can discuss what has been missed, by some, in JeffID’s “Sometimes They Forget” post. First there is no linear response. Second, any growth measurement has two answers. This was one of the points of Dr. Loehle’s paper. Also, those not familiar with the creation of a skewed bell curve for biological study; the range of temperature can be larger or much smaller. Examples of this are fish that live in extremely hot trapped water systems in deserts, and fish that live in special niches in the arctic.
We are going to assume that the sorting that went on and goes on is close to being correct. One can assume the 6 sigma response of certain trees to be correct, but if you understand the model, it means it is worse than what we will discuss for being close to correct. The first point is JeffID’s comments about the de-amplification or amplification of the signal. In his red noise examples it can be either. In the biological case it can only be one direction, de-amplification when a positive linear assumption is made. The linear model will not detect the temperature going down, since it will be below the threshold of the method’s detection limits at the low end. It will not be able to the temperature change at the top of the bell for the same reason. Finally, by not using the correct curve, there will be the higher temperatures, that will be read as lower temperatures further compacting the response. This is why the handle of the “Hockey Stick” is broken. The red noise series of JeffID and Steve McIntyre will not have the compaction of the series if these trees really are temperature sensitive. Also, where as Steve and Jeff’s results are a probability, using the linear assumption is a guarantee of compaction of the signal in the handle.
The proof lies in believe it or not, in the first email of the original Climategate. In this email, Hantemirov, IIRC, stated that sub fossil trees indicated that the tree line was some distance away and was some thousands of years ago, generally known to be warmer that the current warm period. This tells us that the area of interest is somewhere, in our example, in the 0C to 15C region. The other part of the proof is the disbelief by one of the responders in Climategate II, questioning the use of the linear assumption. This indicates that the authors knew or should have known that linear assumption should not be used. Finally, the sad or joyful part is that the divergence actually could be proof that one can use trees as a decent temperature proxy. There will still be de-amplification problems. However, a good decompression routine could be used to great effect on the initial results to obtain a more realistic temperature change profile. Finally, if you want to really understand why it matters and scientists should be skeptical of attribution, you need to read and understand the posts I wrote for JeffID when the first Climategate occurred.
John F. Pittman