Abstract

The joint dynamics of cowberry (Vaccinium vitis-idaea) and bilberry (V. myrtillus) population occurring after fires in two natural Scots pine forests (wet Polytrichum-type and semi-xeric Vaccinium-type) on poor sandy soils have been studied by means of a mathematical model. The field observations were carried out in the boreo-nemoral zone, the Moscow region, for 25 years (1980–2005). The design of the experiment featured a large sample size on permanent transects, a 5-year reexamination interval, and the use of species rooted frequency on small (20 × 20 cm) quadrats. We propose a discrete Markov chain as a model of how the species replace each other on the quadrats. It has the following four states: both species being absent on the quadrat, one of them being present alone, and both being present jointly. Every 5-year step reveals transitions between any pair of states, and we calibrate the transition matrix of the chain by averaging the transition frequencies over the whole observation period for each forest type. The model predicts, in a standard way, the steady-state distributions of quadrat states in the future and elucidates retrospectively, for the first time, how the post-fire succession in the dwarf shrubs layer had started and been continuing in the past. Identical trends are shown to occur in changes over time in two different communities: the proportion of quadrats only with V. vitis-idaea increases at the early stages of post-fire succession, reaches a local maximum, and decreases after that. On the contrary, the proportions of quadrats with only V. myrtillus and those with both species permanently increase in the course of succession. In both the Polytrichum-type and the Vaccinium-type pine forests, the steady-state distribution of states features the maximum percentage of plots with two species, dominating over those with bilberry alone, which, in turn, dominates over those with cowberry alone. The results confirm that a stable coexistence of bilberry and cowberry is possible at the final stages of succession, with a noticeable predominance of bilberry. The forest types differ mainly in the succession rates: while the model time from the start of post-fire succession in the dwarf shrub layer to reach a stable (final) distribution is 30–45 years in the wet Polytrichum-type pine forest, it is twice as long, 60–90 years, in the semi-xeric Vaccinium-type pine forest. In addition, V. vitis-idaea dominates the early stages of succession in the Vaccinium-type forest. A priori, it is not known at what particular stage of succession the field experiment was started, and the retrospective method we propose allows one to restore nonobvious early phases of succession and link the period of data collection to a certain segment of its course.

中文翻译：

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受保护的火后松林中越橘和越橘种群的联合动态：马尔可夫模型内的回顾性预测

摘要

两片天然樟子松林（湿多毛型和半旱性越橘）火灾后越橘（ Vaccinium v​​itis-idaea ）和越橘（V. myrtillus ）种群的联合动态通过数学模型研究了贫瘠沙质土壤上的（类型）。实地观测在莫斯科地区的北风地带进行了 25 年（1980 年至 2005 年）。实验设计的特点是永久样带上的大样本量、5 年的复查间隔以及在小样方（20 × 20 cm）上使用物种扎根频率。我们提出一个离散马尔可夫链作为物种如何在样方上相互替换的模型。它具有以下四种状态：样方中均不存在两种物种、其中一种单独存在、以及两者共同存在。每 5 年一步都会揭示任何状态对之间的转换，我们通过对每种森林类型的整个观察期内的转换频率进行平均来校准链的转换矩阵。该模型预测，以标准方式计算未来样方状态的稳态分布，并首次回顾性地阐明了矮灌木层的火灾后演替是如何开始并在过去继续进行的。两个不同群落随时间的变化显示出相同的趋势：仅具有V. vitis-idaea在火后演替的早期阶段增加，达到局部最大值，然后减少。相反，仅具有V. myrtillus 的样方的比例以及具有两种物种的样方的比例在演替过程中永久增加。在Polytrichum型和越橘型中型松林中，各州的稳态分布特征是两种树种的地块比例最高，超过了仅种植越橘的地块，而后者又优于仅种植越橘的地块。结果证实，在演替的最后阶段，越橘和越橘可以稳定共存，其中越橘占明显优势。森林类型的差异主要在于演替率：在湿地毛菌型松林中，从矮灌木层火后演替开始到达到稳定（最终）分布的模型时间为 30-45 年，而半干旱越橘型松林的寿命是后者的两倍，为 60-90 年。此外，V. vitis-idaea在越橘型森林的演替早期阶段占主导地位。先验地，我们不知道现场实验是在演替的哪个特定阶段开始的，而我们提出的回顾性方法允许人们恢复演替的非明显早期阶段，并将数据收集时期与其过程的某个部分联系起来。