Disappointing survival forecast for a local population of Androsace albanain a random environment
A local population of Androsace albana, a short-lived perennial plant, has been monitored during 10 years on permanent plots laid down in an alpine lichen heath in 2009. We summarize the outcome of monitoring as a non-autonomous matrix model of stage-structured population dynamics. The model originates from a life cycle graph constructed earlier for the stages of ontogenesis and consists of 9 annual “projection” matrices that are calibrated in a unique way from the observation data. Five of the 9 matrices have their dominant eigenvalues greater than 1, i.e., give favorable forecasts for the local population survival, while the rest four have those values less than 1, i.e., give the negative forecasts. To make the resulting prediction, we apply an original concept of the pattern-geometric averaging of given nonnegative matrices and obtain the dominant eigenvalue, λ<sub>1</sub>(G<sub>9</sub>), of the average matrix G<sub>9</sub> markedly less than 1, indicating the population decline in the long term. The traditional method to forecast the local population is to estimate λ<sub>S</sub>, the stochastic growth rate of the population in a random environment formed by a random choice from the same 9 annual matrices. Assuming the choice to be independent and equiprobable, we obtain the negative result as well, yet with higher quantitative values of λ<sub>S</sub>. We associate these higher values with the artificial assumption of equal choice probability when forming the random sequence of annual matrices, each of which is indirectly reflecting the habitat conditions that influenced the growth and development of plants during the year prior to the calibration moment. This motivates the task to construct a more adequate model for choosing annual matrices, in which the probability of choice would be related to the dynamics of the real habitat factors for a given local population.