Hellström Lars, Carlsson Linus, Falster Daniel S, Westoby Mark, Brännström Åke
Am Nat. 2018 Jul;192(1):E37-E47. doi: 10.1086/697429. Epub 2018 Apr 10.
Branch formation in trees has an inherent tendency toward exponential growth, but exponential growth in the number of branches cannot continue indefinitely. It has been suggested that trees balance this tendency toward expansion by also losing branches grown in previous growth cycles. Here, we present a model for branch formation and branch loss during ontogeny that builds on the phenomenological assumption of a branch carrying capacity. The model allows us to derive approximate analytical expressions for the number of tips on a branch, the distribution of growth modules within a branch, and the rate and size distribution of tree wood litter produced. Although limited availability of data makes empirical corroboration challenging, we show that our model can fit field observations of red maple (Acer rubrum) and note that the age distribution of discarded branches predicted by our model is qualitatively similar to an empirically observed distribution of dead and abscised branches of balsam poplar (Populus balsamifera). By showing how a simple phenomenological assumption-that the number of branches a tree can maintain is limited-leads directly to predictions on branching structure and the rate and size distribution of branch loss, these results potentially enable more explicit modeling of woody tissues in ecosystems worldwide, with implications for the buildup of flammable fuel, nutrient cycling, and understanding of plant growth.
树木的分支形成具有指数增长的内在趋势，但分支数量的指数增长无法无限持续。有人提出，树木通过同时去除先前生长周期中长出的分支来平衡这种扩张趋势。在此，我们提出了一个在个体发育过程中分支形成和分支损失的模型，该模型基于分支承载能力的现象学假设构建。该模型使我们能够推导出关于分支末梢数量、分支内生长模块分布以及树木枯枝落叶产生速率和大小分布的近似解析表达式。尽管数据可用性有限使得实证验证具有挑战性，但我们表明我们的模型能够拟合红枫（Acer rubrum）的实地观测结果，并指出我们的模型预测的废弃分支年龄分布在定性上与香脂杨（Populus balsamifera）死亡和脱落分支的实证观测分布相似。通过展示一个简单的现象学假设——树木能够维持的分支数量是有限的——如何直接导致对分支结构以及分支损失速率和大小分布的预测，这些结果有可能使全球生态系统中木质组织的建模更加明确，对易燃燃料的积累、养分循环以及植物生长的理解具有重要意义。
