Lindh Magnus, Johansson Jacob, Bolmgren Kjell, Lundström Niklas L P, Brännström Åke, Jonzén Niclas
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, SE-901 87, Sweden.
Department of Biology, Theoretical Population Ecology and Evolution Group, Lund University, Lund, SE-223 62, Sweden.
New Phytol. 2016 Mar;209(4):1591-9. doi: 10.1111/nph.13706. Epub 2015 Nov 9.
Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.
气候变化导致植物物候变化已有充分记录，但往往难以解读。为了评估观测到的变化的适应价值，我们研究了有无生长限制的一年生植物在生产力和季节长度变化时应如何优化其开花时间。我们考虑了依赖于植物营养质量的生长限制：自遮荫、非光合结构组织的成本和同胞竞争。我们使用最优控制理论从动态能量分配模型中推导出最优开花时间。我们证明，在生长受限和死亡率恒定的情况下，从营养生长到生殖生长的立即切换（砰砰控制）是最优的。在季节长度不变且生长不受限的情况下，平均生产力的提高会延迟最优开花时间。当生长受限且生产力相对较高时，最优开花时间反而提前。当生长季节两端同等延长时，最优开花时间在生长受限时提前，在生长不受限时延迟。我们的结果表明，生长限制是解释物候开花反应时需要考虑的关键因素。它有助于解释沿生产力梯度的物候模式，并将日历尺度上的实证观察与生活史理论联系起来。
