Optimal allocation patterns and optimal seed mass of a perennial plant.

We present a novel optimal allocation model for perennial plants, in which assimilates are not allocated directly to vegetative or reproductive parts but instead go first to a storage compartment from where they are then optimally redistributed. We do not restrict considerations purely to periods favourable for photosynthesis, as it was done in published models of perennial species, but analyse the whole life period of a perennial plant. As a result, we obtain the general scheme of perennial plant development, for which annual and monocarpic strategies are special cases. We not only re-derive predictions from several previous optimal allocation models, but also obtain more information about plants׳ strategies during transitions between favourable and unfavourable seasons. One of the model׳s predictions is that a plant can begin to re-establish vegetative tissues from storage some time before the beginning of favourable conditions, which in turn allows for better production potential when conditions become better. By means of numerical examples we show that annual plants with single or multiple reproduction periods, monocarps, evergreen perennials and polycarpic perennials can be studied successfully with the help of our unified model. Finally, we build a bridge between optimal allocation models and models describing trade-offs between size and the number of seeds: a modelled plant can control the distribution of not only allocated carbohydrates but also seed size. We provide sufficient conditions for the optimality of producing the smallest and largest seeds possible.