Defining how aging Pseudotsuga and Abies compensate for multiple stresses through multi-criteria assessment of a functional-structural model

Abstract

Many hypotheses have been advanced about factors that control tree longevity. We use a simulation model with multi-criteria optimization and Pareto optimality to determine branch morphologies in the Pinaceae that minimize the effect of growth limitations due to water stress while simultaneously maximizing carbohydrate gain. Two distinct branch morphologies in the Pareto optimal space resemble Pseudotsuga menziesii (Mirb.) Franco and Abies grandis (Dougl. ex D. Don) Lindl., respectively. These morphologies are distinguished by their performance with respect to two pathways of compensation for hydraulic limitation: 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 between 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. The diverse morphologies that are found in a typical old-growth conifer forest may achieve compensation in different ways. The method of Pareto optimization that we employ preserves all solutions that are successful in achieving different combinations of criteria. The model for branch development that we use simulates the process of delayed adaptive reiteration (DAR), whereby new foliage grows from suppressed buds within the established branch structure. We propose a theoretical synthesis for the role of morphology in the persistence of old Pseudotsuga based on the characteristics of branch morphogenesis found in branches simulated from the optimal set. (i) The primary constraint on branch growth for Pseudotsuga is the mean path length; (ii) as has been previously noted, DAR is an opportunistic architecture; and (iii) DAR is limited by the number of successive reiterations that can form. We show that Pseudotsuga morphology is not the only solution to old-growth constraints, and we suggest how the model results should be used to guide future empirical investigation based on the two contrasting morphologies and how the morphological contrast may relate to physiological processes. Our results show that multi-criteria optimization with Pareto optimality has promise to advance the use of models in theory development and in exploration of functional-structural trade-offs, particularly in complex biological systems with multiple limiting factors.