Local Population of Eritrichium caucasicum as an Object of Mathematical Modelling. III. Population Growth in the Random Environment

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 (λS) 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 λS 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.