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Faster Growth in Warmer Winters for Large Trees in a Mediterranean-Climate Ecosystem
Competition Assessment. Distance from target tree and dbh was measured for trees within 10 m of the
target tree. Hegyi's competition index (Mailly et al. 2003) was calculated for each tree but the relationship
with the mean growth rate over the 15 years preceding core extraction was not significant so we
concluded that competition with neighbors was not strongly influencing ring widths, and do not present
these results herein.
Core preparation and standardization. Stem cores were removed using a 5.15 mm diameter, 70 cm
long increment borer (Haglöf, Sweden). Cores were mounted on grooved boards then sanded to a high
gloss using successively finer sand paper to 400x grit. Ring widths back to 1895 were measured with a
computer-interfaced microscope stage. Growth series from cores were cross-dated to annual resolution
using the visual and statistical utilities of the Dendrological Program Library (Bunn, 2010); procedures
included comparison to species-specific standard chronologies (URL: www.ncdc.noaa.gov/ paleo/
treering.html). Several series from each species were discarded because they correlated poorly with the
population, and chronologies ultimately retained series from ≥15 trees per species. Ring-widths were
standardized by fitting a cubic spline which removed 50% of variance at 2/3 of the series length, i.e., 73
years . A cubic spline was used because variation in tree age meant that many series did not exhibit the
geometric decline in ring width that is most suitable for detrending with a negative exponential equation.
The conservative 73-year variance-removal parameter meant that resulting models were unimodal and did
not remove high-frequency variation. Detrending was accomplished by dividing observed by predicted
values and the resulting ratio is the ring width index. Species' chronologies were created by averaging
ring-width indices for each year with Tukey's biweight robust mean after removing one-year autocorrelation from the series; removing of auto-correlation improves the independence among data points
that is an underlying assumption of regression analysis The expressed population signal was ≥0.86 for all
species, indicating good cross-dating and synchronous response to external factors.
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Gap-filling of Meteorological Data. Available data differed among the four stations: Canyon Dam,
precipitation and temperature 1914-2010; Chester, precipitation 1909-2011, temperature 1958-2011;
Greenville, precipitation 1894-1914 and 1944-2008, temperature 1895-1914); and Quincy, precipitation
and temperature, 1895-2010. Only data from months missing ≤ 3 d of data were used. Precipitation data
were available from 3-4 sites for >75% of the 1320-month record. Variance decreased strongly as
monthly precipitation increased; the coefficient of variation was 1.02 for precipitation <10 mm and 0.23
for precipitation ≥ 10 mm. Because months with high variance contribute little to annual precipitation, a
composite record was obtained by taking the simple monthly average of available precipitation data. and a
linear regression of mean monthly precipitation as a function of year was used to fill 13 points missing
monthly data. Precipitation was summed by cool season (November through April) and warm season
(May to October) for initial analyses, but these showed that warm season precipitation accounted for a
small but statistically non-significant portion of growth. Therefore cool season and warm season
precipitation were added together to create a single hydrological year; precipitation for a given calendar
begins in November of the previous calendar year.
Temperature data were sparser and more variable than precipitation data; fewer than 1/3 of the
months had data from ≥3 sites and there was a strong seasonal pattern to temperature differences between
stations. Therefore, gaps in the data record for each station were filled using non-parametric regression on
data from other stations. The regression equation included a linear term for temperature of the predictor
station, a smoothing-spline-based term for month, and a linear term for year (Wood 2006). The coefficient
of determination (r2) for equations varied from 0.87 to 0.98; a station's gaps were filled in with available
data from surrounding stations starting with the predictive equation with highest r2. Data for all but 5
months were filled in this way, and the remaining months were filled using data and equations from a
nearby station (Portola, CA). Monthly averages (maximum and minimum) from the completed record
were adjusted to the mean elevation of the sample trees (1400 m) using lapse rates calculated from the
data; lapse rates were -0.01 ºC m-1 for maximum temperatures (consistent with the dry adiabatic lapse
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rate: Monteith and Unsworth 1990), and -0.04 ºC m-1 for minimum temperatures. For analysis monthly
maximum and minimum temperature were averaged by season, where winter was December to February,
spring was March to May, summer was June to August, and autumn was September to November.
Figure S1. At right, technician preparing to extract core from incense cedar. At lower left, technician
mounting core on grooved board.
References Cited
Bunn AG (2008) A dendrochronology program library in R (dplR) Dendrochronologia 26:115-124.
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Bunn AG (2010) Statistical and visual crossdating in R using the dplR library Dendrochronologia 28:251258.
Mailly D, Turbis S, Pothier D (2003) Predicting basal area increment in a spatially explicit, individual
tree model: a test of competition measures with black spruce. Can J For Res 33:435-443.
Monteith JB, Unsworth MH (1990) Principles of Environmental Physics. Edward Arnold, London.
Wood SN (2006) Generalized Additive Models: an Introduction with R. Chapman & Hall/CRC Boca
Raton, FL.