The weight share method in forest inventories: refining the relation between points and trees

The population of forest trees having no sampling frame, forest inventories have relied on indirect sampling methods. This indirect sampling uses two populations: the discrete populations of trees and the continuous population of points, from which trees are being sampled. Important works such as Mandallaz (1991), Eriksson (1995) and Stevens and Urquhart (2000) brought the fundamental elements in the formalization of the sampling of trees, by defining the duality principle that relates both populations. They led to the so-called continuous population approach where trees attributes are transformed into attribute density values. However, in these approaches, the trees quickly fade away despite being the target population while their weight is calculated as the inverse of their inclusion probability. We explain how the Generalized Weight Share Method (GWSM) can be used to formalize the link between the two populations. GWSM allows to revisit previous concepts proposed to solve the question of how to produce estimations from tree-level attributes, under uniform random or more complex sampling designs. The principles of the method are explained, and its functioning is illustrated under a variety of points and trees sampling designs, including fixed-area, Bitterlich and cluster sampling.