Mark R. Lesser and Stephen T. Jackson. 2012. Making a stand: five centuries of population growth in colonizing populations of Pinus ponderosa. Ecology 93:1071–1081.

Appendix B. Age–height offset analysis.

To correct tree ages to a germination age we used a subset of 80 trees, selected across all four of the study populations that were cored twice on the same side, but at different heights. We developed a regression equation to explain the difference in height based on age. To account for heteroscedasticity the data was transformed as follows:

	(B.1)
	(B.2)

and entered into the equation:

(B.3)

Based on this model we used the fitted equation to solve for age. For every 10 cm of height difference between cores the model predicted that 5 years be added to the age of a tree.

FIG. B1. Height regressed against age for 80 ponderosa pine. Fitted regression line is shown along with 50 and 95% confidence intervals. Transformed, observed data are shown with open circles.