3 years ago

Local Population of Eritrichium caucasicum as an Object of Mathematical Modelling. II. How Short Does the Short-Lived Perennial Live?

D. O. Logofet, E. S. Kazantseva, I. N. Belova, V. G. Onipchenko

Abstract

In the previous publication (Logofet et al., 2017), we reported on constructing a matrix model for a local population of Eritrichium caucasicum at high altitudes of north-western Caucasus. The model described the population structure according to the stages of ontogeny and field data for 6 years of observation. Calibrated from the data, the matrices, L(t), of stage-specific vital rates, which projected the population vector at time t (t = 2009, 2010, …, 2013) to the next year, were dependent on t and naturally different, reflecting indirectly the temporal differences in habitat conditions that occurred during the observations. Therefore, the model turned out to be non-autonomous. In addition to the range of variations in the adaptation measure λ1(L), we also obtained certain “age traits from a stage-structured model,” such as the average stage duration and the life expectancy for each stage. Those traits were uniquely determined for each given matrix L by a known (from the English literature) VAMC (virtual absorbing Markov chain) technique, while their variations for different years t pointed out the need to solve a mathematical problem of finding the geometric mean (G) of five matrices L(t) with a fixed pattern. The problem has no exact solution, whereas the best approximate one (presented here) results in the estimate of life expectancy as 3.5 years and that of the mean age at first flowering as 12 years. Given the data of 6-year observations, the forecast of whether the local population increases/declines in the long term draws on the range of possible variations in the measure λ1(G) under reproductive uncertainty, and this range localizes entirely to the right of 1, though very close to λ1 = 1 meaning a stable population.

Publisher URL: https://link.springer.com/article/10.1134/S2079086418030076

DOI: 10.1134/S2079086418030076

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.