There has been much interest in understanding the factors that control tree longevity, including those that limit growth in large trees and how trees are able to persist despite growth limitations. As with many problems in complex ecological systems, there is a paucity of tools that enable effective evaluation of the many factors that are likely acting simultaneously to inform system behavior. We present a novel application of multi-criteria optimization and Pareto optimality, coupled with a simulation model, to determine branch morphologies in the Pinacea that minimize the effect of growth limitations due to water stress, while simultaneously maximizing carbohydrate gain. The Pareto optimal frontier is the set of all mutually co-dominant solutions not dominated by any other solution. Two solutions are considered to be mutually co-dominant if performance with respect to one criterion is to the detriment of another criterion. This method enables one to explore the full range of tradeoffs among multiple criteria, and to evaluate the possibility of multiple optimal solutions. The model for branch development that we use is a functional-structural model (FSM) that simulates the process of delayed adaptive reiteration (DAR), whereby new foliage grows from suppressed buds within the established branch structure. 

Results/Conclusions

We find two distinct morphologies in the Pareto optimal solution set, and these resemble Pseudotsuga menziesii and Abies grandis, respectively. These two morphologies are distinguished by their performance with respect to minimizing the mean path length to terminal foliage (Pseudotsuga), and minimizing the mean number of junction constrictions to terminal foliage (Abies). Within these two groups we find trade-offs among the criteria for foliage display and the criteria for hydraulic functioning, which shows that an appropriate framework for considering tree longevity is how trees compensate, simultaneously, for multiple stresses. We use the optimization results to propose a theoretical synthesis for how Pseudotsuga morphology may compensate for size-related limitations. 1) The primary constraint on branch growth for Pseudotsuga is the mean path length; 2) As has been previously noted, DAR is an opportunistic architecture; 3) DAR is limited by the number of successive reiterations that can form; and 4) Pseudotsuga morphology is not the only solution. Our results show that multi-criteria optimization with Pareto optimality has promise to advance the use of models in theory development.