Models of knot and stem development in black spruce trees indicate a shift in allocation priority to branches when growth is limited.

The branch autonomy principle, which states that the growth of individual branches can be predicted from their morphology and position in the forest canopy irrespective of the characteristics of the tree, has been used to simplify models of branch growth in trees. However, observed changes in allocation priority within trees towards branches growing in light-favoured conditions, referred to as 'Milton's Law of resource availability and allocation,' have raised questions about the applicability of the branch autonomy principle. We present models linking knot ontogeny to the secondary growth of the main stem in black spruce (Picea mariana (Mill.) B.S.P.), which were used to assess the patterns of assimilate allocation over time, both within and between trees. Data describing the annual radial growth of 445 stem rings and the three-dimensional shape of 5,377 knots were extracted from optical scans and X-ray computed tomography images taken along the stems of 10 trees. Total knot to stem area increment ratios (KSR) were calculated for each year of growth, and statistical models were developed to describe the annual development of knot diameter and curvature as a function of stem radial increment, total tree height, stem diameter, and the position of knots along an annual growth unit. KSR varied as a function of tree age and of the height to diameter ratio of the stem, a variable indicative of the competitive status of the tree. Simulations of the development of an individual knot showed that an increase in the stem radial growth rate was associated with an increase in the initial growth of the knot, but also with a shorter lifespan. Our results provide support for 'Milton's Law,' since they indicate that allocation priority is given to locations where the potential return is the highest. The developed models provided realistic simulations of knot morphology within trees, which could be integrated into a functional-structural model of tree growth and above-ground resource partitioning.