Appendix A. Supporting descriptions of methods and results.
Proxy development from wood anatomical data
Vessel formation would clearly be inhibited at 0°C or at some level above 0°C, but the linear relationships predict negative temperature values for lower end vessel sizes sampled (Fig. 5, Table A3). Similarly, spring temperatures occurring during EW formation should have some upper bound. To address this we modified the linear relationships to follow asymptotic trends such that anatomical proxies were restricted to estimating maximum temperature of about 17°C and minimum temperatures of either 2°C or 6°C (Fig. A2). For reference, the maximum and minimum spring temperatures occurring across all sites from 1895–2008 were 14.5°C and 7.0°C (Table 1). In a strict sense these threshold values were arbitrary, but our goal was to allow temperature estimates to approach and occasionally exceed the modern range of temperature values (Tables 1, A1, A2). The 2° minimum value was included largely for reference as we consider the 6° minimum more biologically reasonable. The 6° C minimum for average spring temperature is 1°C lower than that which has been observed at any of the three sites (Table 1) and corresponds to the average temperature associated with treeline limitation of growth whether there are strong or weak seasonal dynamics (Hoch and Körner 2009).
EWA_{s} of modern wood decreased during cold springs and had a strong relationship to temperature (Fig. 5, Table 2). However, the greater EWF_{S} of subfossil wood (Fig. 3) and the resulting increases in EWA and EWA_{s} compared to modern wood (Table 3) would predict implausibly warmer temperatures for subfossil wood for the entire late Quaternary period. To address this issue, we standardized each EWF_{S} measurement of subfossil wood to correspond to the modern wood value for the same EWD (i.e., each EWD measurement was multiplied by the ratio of the modern regression predicted EWF_{S} / subfossil regression predicted EWF_{S} for a given EWD; these regression lines werevery nearly the same as the relationships of EWF_{S} vs. EWD shown in Fig. 3). Atmospheric CO_{2} concentrations are likely the only consistent difference between the modern oaks and the Late Quaternary environmental conditions. By standardizing each EWF_{S} measurement of subfossil wood to correspond to the modern wood EWF_{S} for the same EWD we were able to take advantage of the strong temperature signal incorporated by EWA_{S} (Fig. 5), while accounting for the putative CO_{2} effects on EWF_{S}.
TABLE A1. Temperature estimates for subfossil wood using different functions for earlywood diameter (EWD) earlywood hydraulic diameter (EWD_{h}), modal EWD and earlywood specific lumen area (EWA_{s}). The range and means represent values calculated for each cambial ages and tree combination. Values for EWA_{s} were corrected to the modern earlywood specific vessel frequency for a given EWD_{a}.
Anatomical variable 
Function 
Minimum 
Mean 
Maximum 
EWD 
Linear 
0.5 
6.6 
12.5 
Sigmoid: 17° max, 2° min 
2.0 
6.1 
12.8 

Sigmoid: 17° max, 6° min 
6.0 
7.8 
12.7 

EWD_{h} 
Linear 
13.2 
4.1 
14.5 
Sigmoid: 17° max, 2° min 
2.0 
5.0 
14.2 

Sigmoid: 17° max, 6° min 
6.0 
7.2 
14.2 

Modal EWD 
Linear 
0.4 
12.3 
22.9 
Sigmoid: 17° max, 2° min 
2.3 
12.0 
16.5 

Sigmoid: 17° max, 6° min 
6.0 
11.6 
16.8 

EWA_{s} 
Linear 
4.7 
8.8 
15.4 
TABLE A2. Equations used for linear and sigmoidal temperature estimates.
Anatomical variable 
Equation form for 
a 
b 
x0 
y0 
EWD 
T = ax+b 
0.0464 
5.1731 

EWD_{h} 
T = ax+b 
0.1086 
20.547 

Modal EWD 
T = ax+b 
0.0834 
8.7502 

EWA_{s} Linear 
T = ax+b 
41.322 
2.2727 

EWD, 2° min 
T = y0+a/(1+((x/x0)^b)) 
15.1515 
5.092 
318.0105 
2 
EWD_{h}, 2° min 
T = y0+a/(1+((x/x0)^b)) 
14.9303 
9.3561 
275.7743 
2 
Modal EWD, 2° min 
T = y0+a/(1+((x/x0)^b)) 
15.7254 
4.7545 
224.2319 
2 
EWD, 6° min 
T = y0+a/(1+((x/x0)^b)) 
11.3981 
5.8523 
357.9158 
6 
EWD_{h}, 6° min 
T = y0+a/(1+((x/x0)^b)) 
11.019 
11.0428 
293.4685 
6 
Modal EWD 6° min 
T = y0+a/(1+((x/x0)^b)) 
11.6014 
6.6674 
255.4677 
6 
TABLE A3. Results of pairwise comparisons using SMATR software to test scaling relationships of EWF_{s} and EWD_{a}. Significance is indicated by * = p < 0.05, ** = P < 0.01, *** = P < 0.001. Other results abbreviations: NS = nonsignificant, NT = comparison not tested, NCS = no common slope among pairs necessary for test. Category abbreviations: MO = Missouri, WI = Wisconsin, SD = South Dakota, PB = PreBoreal, YD = YoungerDryas, BA = BollingAllerod, SF = all subfossil wood, MOD = all modern wood.
MO 
WI 
SD 
PB 
YD 
BA 
SF 
MOD 

Elevation 
MO 
 







WI 
** 
 







SD 
* 
NS 
 






PB 
NCS 
NCS 
NCS 
 





YD 
NCS 
NCS 
NCS 
NS 
 




BA 
NCS 
NCS 
NCS 
* 
NS 
 



SF 
*** 
*** 
*** 
NT 
NT 
NT 
 


MOD 
NT 
NT 
NT 
*** 
*** 
*** 
*** 
 

Shift 
MO 
 







WI 
*** 
 







SD 
*** 
*** 
 






PB 
NCS 
NCS 
NCS 
 





YD 
NCS 
NCS 
NCS 
NS 
 




BA 
NCS 
NCS 
NCS 
NS 
NS 
 



SF 
*** 
*** 
NS 
NT 
NT 
NT 
 


MOD 
NT 
NT 
NT 
NS 
NS 
NS 
NS 
 
FIG. A1. Light microscopy images of transverse sections of subfossil bur oak wood, containing of normalshaped vessels, moderately collapsed wood, and severely collapsed wood. Image (a) is sample MED 681: cambial age = 111 years, EW diameter estimate = 238.9 um, EW diameter corrected for collapse = 226.5 um. Image (b) is the same image as (a), highlighting examples of measurements conducted on a single treering. The earlywood (EW) and latewood (LW) areas outlined, labeled and highlighted and separated by a dashed line. Examples of EW vessels areas measured are filled black. Note that small vessels, of approximately 70 µm diameter or less that were within the EW area were not measured on any sample. Image (c) shows MED 257: cambial age: 91 years, EW diameter estimate = 196.1 um, diameter corrected for collapse = 214.4 um. Image (d) shows MED 634: cambial age = 44 years, EW diameter estimate = 177.5 um, diameter corrected for collapse = 227.5 um. 
FIG. A2. Examples of sigmoidal transfer functions used to estimate spring temperature from earlywood vessel diameter (EWD) modal EWD, and earlywood vessel hydraulic diameter (EWD_{h}). The sigmoidal relationships approximate the linear trends (Fig. 6) across the temperature range covered by our sampling (shaded gray area) while constraining the maximum and minimum spring temperatures that might be recorded by earlywood vessel sizes. 