Backward Prediction Confirms the Conclusion on Local Plant Population Viability

摘要

Another year of observing the structure of the local Androsace albana population at the permanent plots laid in an alpine lichen heath in 2009 added a tenth calibrated matrix to the previous set of nine annual population projection matrices obtained from 10 observation years by means of a matrix model a year before. In the present study, the original concept of pattern-multiplicative averaging for nonnegative matrices leads to the average of ten matrices that retains the previous “disappointing survival forecast” of the local population, thus motivating its confirmation or refutation by the method of backward prediction. The technique is substantiated, and the corresponding computational apparatus is presented for backward prediction in matrix models of discrete-structured populations via reversing the time direction in the observation data. Applied to the A. albana data, the technique gives ten 1-year matrices of backward prediction; each predicts the increase in the local population if its prototype in the direct model prescribes the decline, and vice versa. Similarly, in contrast to the direct prediction, the final result of averaging backwardly predicts a population increase, thus confirming the consistency of the direct method.