The coarse-grid problem in ecological monitoring

Natalia Petrovskaya, SV Petrovskii

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


Obtaining information about pest-insect population size is an important problem of pest monitoring and control. Usually, this problem has to be solved based on scarce spatial data about the population density. The problem of monitoring can thus be linked to a more general mathematical problem of numerical integration on a coarse grid. Numerical integration on coarse grids has rarely been considered in literature as it is usually assumed that the grid can be refined. However, this is not the case in ecological monitoring where fine grids are not available. In this paper, we introduce a method of numerical integration that allows one to accurately evaluate an integral on a coarse grid. The method is tested on several functions with different properties to show its effectiveness. We then use the method to obtain an estimate of the population size for different population distributions and show that an ecologically reasonable accuracy can be achieved on a very coarse grid consisting of just a few points. Finally, we summarize our mathematical findings as a protocol of ecological monitoring, thus sending a clear and practically important message to ecologists and pest-control specialists.
Original languageEnglish
Pages (from-to)2933-2953
Number of pages21
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Publication statusPublished - 1 Oct 2010


  • pest control
  • numerical integration
  • coarse grid
  • ecological monitoring


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