Using strong inference to falsify differential equation models of sugar maple height growth

Platt’s research strategy called ‘strong inference’ is often studied, but is difficult to apply. Here strong inference is applied in selecting differential equation models of sugar maple, Acer saccharum M., height growth. Two model groups proposed by Zeide (1993; Zeide, B. 1993. Analysis of growth equations. For. Sci. 39(3):594-616.) are supplemented with two additional groups, 1) size decline and 2) second order differential equations, nearly exhausting the possible height growth models currently in the literature. A ‘crucial experiment’ was to fit a simultaneous system of equations to height age data collected from a cohort of trees felled years earlier for stem analysis. Models for cohort members are identical in right-hand-sides, have common parameters, but have tree-specific initial heights. Common parameters and tree-specific initial heights are estimated during fitting. Results, based on stem analysis data for a cohorts of from three to five sugar maple growing on 54 plots in the Lake States, showed that all cohort members were predicted by logarithm of time decline (LTD) models to have extremely similar initial heights (< 0.01 m range), which contradicts experience and leads to their falsification. Three of four models in the time decline (TD) class predict a very small range in final heights, but a large range in initial heights (from 6.4 to 2.9m), hence can also be considered falsified. Size decline and second order models could not be falsified using the height age cohort data available.