Bark beetle larval dynamics carved in the egg gallery: a study of mathematically reconstructing bark beetle tunnel maps

• Published in: Advances in difference equations Vol. 2019; no. 1; pp. 1 - 16
• Main Authors: Li, Hui, Li, Tianwei
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 11.12.2019; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Bark; Bark beetle; Curve fitting; Difference and Functional Equations; Dynamics; Egg gallery; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Scolytinae; Bark beetle; Scolytinae; Egg gallery; Dynamics; Curve fitting
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-019-2452-2

Scolytinae (bark beetle) is one of the most detrimental pests on the Chongming Island. It is desirable to understand the behaviour of the Scolytinae throughout its life cycle. Behaviour studies regarding mass attacks, mating behaviour and chemical control have been frequently reported in literature. However, little research could be found regarding the life of Scolytinae in the larval stage, especially for beetles in the field. In this paper, we analyse the tunnel map beneath the tree bark, since it is a potential source of information on the population size, egg gallery and larval development. We propose four hypotheses including synchronous larval growth (SLG), outward normal direction (OND), communication and repulsion (CR) and individual differences(ID), then employ the methods of curve fitting and differential equation modelling to mathematically reconstruct the tunnel map. Furthermore, we introduce the Frechet distance to measure the similarity of curves. Numerical simulation shows that the reconstructed tunnel map closely matches the collected sample.