Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 106

phylogenetically related species (e.g., Cook and Cole 1991 ; Graumlich 1993 ; Cook
et al. 2001 ) are two recommended approaches.
Biological uncertainty is a more difficult problem to deal with because it can
be due to emergent properties of tree growth that are essentially unpredictable from
lower-level processes. For this reason, process-based mechanistic models may never
be sufficiently complete to model the finer details of tree radial growth due to climate
over a broad range of tree species and environmental conditions. Even so, simplified
mechanistic models can work quite well in modeling the essentials of ring width
variation due to climate for a variety of tree species (Anchukaitis et al. 2006 ; Evans
et al. 2006 ; Vaganov et al. Chapter 3 , this volume). Therefore, to deal with the
possibility of emergent properties of tree growth that might be missed by a process-
based model, we suggest that mechanistic and statistical models be used jointly
to model the response of trees to climate and to test each other, because neither
approach is likely to provide all the answers.
Finally, tree-ring analysis should also always contain a significant amount of data
exploration, because the inherent biological uncertainty of tree growth in uncon-
trolled natural environments will never be eliminated. This, in our opinion, is good
because it means that there will be a lot of interesting discoveries to make in the
future! In turn, the results of exploratory data analysis can—and should—lead to
numerous confirmatory tests of newly revealed associations that would have been
otherwise missed if only a previously planned analysis were conducted. This does
not eliminate the need or desire for a good a priori experimental design. Rather,
it expands the scope of statistical analyses to allow for the unforeseen. As the
father of exploratory data analysis, John Tukey, put it, 'restricting one's self to the
planned analysis—failing to accompany it with exploration—loses sight of the most
interesting results too frequently to be comfortable' (Tukey 1977 , p.3).

Acknowledgements This chapter is a contribution to the meeting 'Tree Rings and Climate:
Sharpening the Focus,' held at the University of Arizona, Tucson, on April 6-9, 2004. We thank
the organizing committee members (Malcolm Hughes, Henry Diaz, and Tom Swetnam) for their
kind support and encouragement. This chapter is based the generous long-term support of the
Lamont-Doherty Tree-Ring Laboratory (TRL)by the National Science Foundation and the National
Oceanic and Atmospheric Administration Office of Global Programs. The U.S. Department of
Energy Global Change Education Program also supported N. Pederson in his PhD dissertation
research at the Lamont TRL that contributed to this chapter. We also thank the Mohonk Preserve
(Paul Huth and John Thompson) for permission to sample trees used in this study and for access to
the Mohonk Lake meteorological data, and to the remarkable naturalist Daniel Smiley of Mohonk
who made all of this possible. Lamont-Doherty Earth Observatory Contribution No. 7205.

Appendix

Basic chronology statistics for tree-ring series of length n :
Arithmetic Mean:

n

1
n

x

= x i

i = 1