“Realistic Choice of Annual Matrices Contracts the Range of λ S Estimates” under Reproductive Uncertainty Too

Dmitrii O. Logofet, Leonid L. Golubyatnikov, Elena S. Kazantseva and Nina G. Ulanova
Additional contact information
Dmitrii O. Logofet: Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia
Leonid L. Golubyatnikov: Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia
Elena S. Kazantseva: Biological Department, Moscow State University, 119234 Moscow, Russia
Nina G. Ulanova: Biological Department, Moscow State University, 119234 Moscow, Russia

Mathematics, 2021, vol. 9, issue 23, 1-15

Abstract: Our study is devoted to a subject popular in the field of matrix population models, namely, estimating the stochastic growth rate , λ S , a quantitative measure of long-term population viability, for a discrete-stage-structured population monitored during many years. “ Reproductive uncertainty ” refers to a feature inherent in the data and life cycle graph (LCG) when the LCG has more than one reproductive stage, but when the progeny cannot be associated to a parent stage in a unique way. Reproductive uncertainty complicates the procedure of λ S estimation following the defining of λ S from the limit of a sequence consisting of population projection matrices (PPMs) chosen randomly from a given set of annual PPMs. To construct a Markov chain that governs the choice of PPMs for a local population of Eritrichium caucasicum , an short-lived perennial alpine plant species, we have found a local weather index that is correlated with the variations in the annual PPMs, and we considered its long time series as a realization of the Markov chain that was to be constructed. Reproductive uncertainty has required a proper modification of how to restore the transition matrix from a long realization of the chain, and the restored matrix has been governing random choice in several series of Monte Carlo simulations of long-enough sequences. The resulting ranges of λ S estimates turn out to be more narrow than those obtained by the popular i.i.d. methods of random choice (independent and identically distributed matrices); hence, we receive a more accurate and reliable forecast of population viability.

Keywords: discrete-structured population; matrix population model; population projection matrices; reproductive uncertainty; stochastic growth rate; random choice; weather indices; Markov chain; Monte Carlo simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/23/3007/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/23/3007/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:23:p:3007-:d:686347

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().