The marginal cost of structural diversity of mixed uneven-aged hard maple forests

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Abstract
Theoretical concepts pertaining to the marginal cost (MC) of the structural diversity of a forest stand are developed. A matrix growth model is estimated for mixed uneven-aged forest stands of hard maple (Acer saccharum Marsh.) from southern Ontario. The estimated growth model is used to derive the MC equations for the Shannon and the Simpson indices of total structural diversity (TSD), species diversity (SD), and tree-size diversity (TD). The effects of exclusion and inclusion of the opportunity cost (OC) on the MC of the TSD are compared. The contributions of SD and TD to the MC of the TSD are disaggregated. The MCs of TSD, SD, and TD for the Shannon and the Simpson indices are iso-elastic. The elasticity of the MC of the TSD for the inclusion of OC is greater than the elasticity of MC of the TSD for the exclusion of OC. The elasticities of MC of TSD, SD, and TD for the Shannon index are greater than the elasticities of MC of TSD, SD, and TD, respectively, for the Simpson index. The elasticities of MC of SD are smaller than the elasticities of MC of TD, for both indices. However, these results are specific to the hard maple forests of southern Ontario and cannot be generalized. Some general features of MC equations of structural diversity are discussed.