Optimal Selection of Seed-Trees Using the Multi-Objective NSGA-II Algorithm and a Seed Dispersal Model

Abstract

Optimal seed-tree selection during natural regeneration of shade-intolerant species requires ensuring an ample and uniform seed supply from residual trees with the smallest possible seed-tree density. Here, we propose a novel approach for seed-tree selection using the genetic algorithm. Data are derived from a 3-hectare even-aged stand of Pinus canariensis C.Sm. ex DC, comprising 364 mature trees and 103 seed-traps. Seeds were collected in 2007 and 2008. After constructing a seed-dispersal model for each seed-crop year, we employ the multi-objective non-dominated sorting genetic algorithm to identify the smallest seed-tree set that maximizes post-treatment seed supply and its spatial homogeneity. Optimal solutions range from a maximum of 68.4% to a minimum of 38.1% reduction in stand density, resulting in a 59.5% to 28% reduction in post-felling seed supply. The coefficient of variation of among-site seed-flux varies from 28% to 59.5%. Proposing a treatment involving the removal of 240 trees (65.9% stand-density reduction) and leaving 40 seed-trees per hectare, our findings provide insights into balancing the conflicting objectives of sufficient post-treatment seed supply at a minimum seed-tree density. This approach marks a departure from traditional practices, as the decision about which trees to cut is historically left to the discretion of field managers.