Phasic Development of Fagus sylvatica based on 240 Years of Continuous Tree-height Observations

Abstract

Duration of growth is dependent on morphological events or changes in growth rate. It is the latter that is associated with phasic development. The most productive phase of plant growth is the linear or constant rate phase, primarily because it endures longer than the exponential phase. The purpose of our research was to objectively determine the true tree-height growth pattern, the linear and stationary phases of height growth, and to mathematically derive the maximum slope (maximum growth rate) of the growth curve, its location (inflection point), and the maximum slope of the logarithmic form (maximum relative growth rate) of the growth curve. The data were composed of 333 tree-height records covering 240 years from 200 beechwoods in the U.K. Height-age data were fitted using a splined function (S) and the Chapman-Richards function (CR). The growth curve and critical points on the curve were derived from the CR model. The linear phase began when trees were 9 and lasted 43 years. However, the stationary phase did not begin until age 162. Anecdotal evidence suggests that very little fruiting occurs before age 50. Based on derived critical points and anticipated source-sink dynamics, the reproductive stage should have taken place during the progressive “deceleration phase” when trees were between 31 (location of the maximum slope, also inflection point) and 162 (from quadratic root). The linear phase ended at 52 years, (coinciding with minimum acceleration) and may prove a more accurate estimate than 31. Maximum slope was 1.2 m per year occurring at age 31. Maximum slope of the log curve was 0.14 m·m–1 per year. The advantage of the CR function and the importance of the derived quantities and growth phases will be discussed.