Abstract—

In the former two parts (Logofet et al., 2017, 2018), we reported on a matrix model for a local population of Eritrichium caucasicum, a herbaceous short-lived perennial, at high altitudes of north-western Caucasus. The model was constructed and calibrated in accordance with the observations on permanent plots in the period 2009–2014. The temporal variability of the data predetermined the temporal variations among the vital rates of the local population, too,—the elements of the “annual” matrices that project the vector, x(t), of the stage structure observed at the year t to the similar vector observed at the year t + 1. Quantitative measure of the local population fitness was calculated as the dominant eigenvalue, λ₁(G), of the matrix G—the pattern-geometric average of five annual matrices—and it turned out to be greater than 1, i.e., gave a positive forecast of the population viability. After the expansion of the time series with the 2015–2017 data (presented in this article), the forecast has reversed, although the corresponding offset in λ₁(G) has not been more than 16%. An alternative mode of prediction is based on the (upper and lower) estimates of the stochastic growth rate (λ_S) of the population in a random environment, which has been formed in the model by a random choice from 8 annual matrices distributed equally probable and independent of the choice made at the previous step. All the estimates of λ_S turn out to be lower than λ₁(G), hereby confirming the negative viability prediction; however, a too simple model of the random environment needs further development and links to potential changes in the local habitat.

中文翻译：

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作为数学建模对象的高产Eritrichium caucasicum。三，随机环境下的人口增长

摘要—

在前两个部分（Logofet等人，2017,2018）中，我们报告了西北高加索高原高海拔埃特里希姆（Eritrichium caucasicum）本地种群的矩阵模型。该模型是根据2009-2014年期间对永久地块的观测结果构建和校准的。数据的时间变化性也预先确定了当地人口的生命率之间的时间变化，即投影在t到t年观察到的阶段结构的向量x（t）的“年度”矩阵的元素。在t年观察到的相似向量1. +当地居民健身的定量度量计算为主导本征值，λ ₁（g ^），矩阵的ģ五个年度-the图案几何平均矩阵和它原来是大于1，即对人口生存率给出了积极的预测。与2015-2017的数据（本文中给出）的时间序列的膨胀之后，预测已经反转，虽然相应的λ偏移₁（g ^）一直没有超过16％。预测的替代方式是基于（上部和下部）的随机生长速率的估计值（λ_小号）随机环境中的总体人口），该随机环境是在模型中由8个年度概率矩阵中的随机选择形成的，这些矩阵均等概率分布且独立于上一步所做的选择。λ的所有的估计_š变成为比λ下₁（g ^），在此确认负存活率预测; 但是，过于简单的随机环境模型需要进一步发展，并与当地栖息地的潜在变化联系在一起。