Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 98

growing on well-drained to xeric sites. The greatest exception is the tulip poplar site
growing along a stream bottom. Yet, the range of MS is quite large, with PIRI and
BELE having more than twice the MS of QUPR and QUVE. This result suggests
that the expressible range of MS in trees growing in a common macroclimatic envi-
ronment can be highly species dependent, which complicates the use of MS as a
general measure of climate sensitivity.
Some signal strength statistics have been used in the past as qualitative predic-
tors of climate sensitivity of tree-ring chronologies (e.g., MS and RBT). Since they
are based on the same prewhitened tree-ring data as the response functions, the sig-
nal strength statistics can be tested as predictors of the response function modeling
results (cf. Cropper 1982 a ). This was done for response functions based on the EV1
and PVP eigenvector cutoffs, with model selection determined by the minimum
AIC. Those results are provided in Table 4.4 . With respect to calibration R 2 ,allof
the response functions calibrated a significant amount of tree-ring variance, with
PVP always outperforming EV1 because the former resulted in the entry of more
model predictors. This difference ranges from one to five additional predictors and
0.037 to 0.164 in additional fractional variance explained. The verification statistics
(RSQ, RE, CE) tell a more mixed story. As before, the hemlock (TSCA) response
function verifies strongly for all three statistics, with EV1 verifying somewhat better
than PVP. The next best result is for chestnut oak (QUPR), which has a statistically
significant verification RSQ ( p < 0.01) for the PVP model. Tulip poplar (LITU)
and black birch (BELE) also have verification RSQs that are weakly significant
( p < 0.10), again for the PVP model, and pignut hickory (CAGL) performs slightly
better with EV1. None of the other species/models verify in any useful way for either
EV1 or PVP, although the RE and CE tend to be less negative for the EV1 models.
Taken together, these results marginally support PVP over EV1 as an eigenvector
cutoff criterion, but the difference is not large.
Given the way that certain tree-ring statistics have often been used as predictors
of climate sensitivity (e.g., MS; Fritts and Shatz 1975 ) , we have tested that capacity
using the EV1 and PVP response function modeling results. The statistics used as
predictors of response function R 2 are MS, REFF, SNR, and ESR in Table 4.3 . The
other signal strength statistics are either biased by the high within-tree core corre-
lations (RTOT) or are absorbed in the estimate of REFF (RWT, RBT). EPS also
includes REFF in its estimate and asymptotes quickly towards 1.0, making it not
very sensitive for our tests. These comparisons assume that there are no 'species
effects' in our results; i.e., the joint distributions of our predictors of climate sensi-
tivity with the response function results are independent of the species being tested.
This is unlikely to be the case here because of our diverse taxa, but without within-
species replication we have no way of directly testing for 'species effects.' Also,
we have only seven cases to test (5 degrees of freedom), so no claims of statistical
significance will be made. However, the results are interesting enough to warrant
additional study using many more within- and between-species tests.
Figure 4.5 shows the four x-y scatterplots with fitted bivariate regression curves
and simple correlations. REFF correlates with R 2 (Fig. 4.5a ) at levels that suggest
a predictive relationship between them: r equals 0.644 for EV1 and 0.548 for PVP.