Backward prediction confirms the conclusion on local plant population viability
aLaboratory of Mathematical Ecology, Institute of Atmospheric Physics, RAS
Pyzhevsky Lane, 3, Moscow, 119017 Russia
bLomonosov Moscow State University, Biological Department, Department of Plant Ecology and Geography
Lenin Hills, 1, Bldg. 12, Moscow, 119234 Russia
*e-mail: danilal@postman.ru
**e-mail: biolenok@mail.ru
***e-mail: iya@ifaran.ru
****e-mail: vonipchenko@mail.ru
One more year of observing the structure of a local Androsace albana population at permanent plots laid in an alpine lichen heath in 2009 added the 10th calibrated matrix to the previous set of 9 annual population projection matrices obtained as an outcome of 10-year observations by means of the matrix model. The original concept of pattern-multiplicative averaging for nonnegative matrices leads to the average of ten matrices, which retains the previous “disappointing survival forecast” of the local population, motivating its confirmation/refutation by the method of backward prediction. We substantiate the technique and present the corresponding computational apparatus of backward prediction in matrix models of discrete-structured populations through reversing the time direction in the observation data. Applied to the A. albana data, the technique gives 10 one-year matrices of the backward prediction, each predicting the increase in local population if its prototype in the direct model prescribes the declined, and vice versa. Similarly, the result of averaging gives the final backward prediction of the population growth in contrast to the direct prediction, thus confirming its adequacy.
