Interactions between climate change, competition, dispersal, and disturbances in a tree migration model

Potentially significant shifts in the geographical patterns of vegetation are an expected result of climate change. However, the importance of local processes (e.g., dispersal, competition, or disturbance) has been often ignored in climate change modeling. We develop an individual-based simulation approach to assess how these mechanisms affect migration rate. We simulate the northward progression of a theoretical tree species when climate change makes northern habitat suitable. We test how the rate of progression is affected by (1) competition with a resident species, (2) interactions with disturbance regimes, (3) species dispersal kernel, and (4) the intensity of climate change over time. Results reveal a strong response of species’ expansion rate to the presence of a local competitor, as well as nonlinear effects of disturbance. We discuss these results in light of current knowledge of northern forest dynamics and results found in the climatic research literature. © Springer

Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods

This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips