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Random walk and mean-field models to estimate insect population density from trap counts

Grant number: 13/07476-0
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): October 01, 2013
Effective date (End): September 30, 2014
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:José Fernando Fontanari
Grantee:Paulo Fernando Coimbra Tilles
Supervisor abroad: Sergei V. Petrovskii
Home Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Local de pesquisa : University of Leicester, England  
Associated to the scholarship:11/11386-1 - Analysis of the bonequilibrium phase transition of Axelrods model for cultural dissemination, BP.PD


Trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. Despite this, the interpretation of trap counts is challenging. Traps are effective at providing relative counts that enable comparisons but are poor at delivering information on the absolute population size. Making better use of trap data is impeded by the lack of a consistent underlying theoretical model. In this project we aim to overcome current limitations of trapping methods used in ecological studies by extending the novel theoretical approach by Petrovskii et. al to account for more practical applications: we will seek exact solutions in compact form of the diffusion equation in 2 and 3 dimensions to describe trapping by crawling (or walking) and flying insects as well as the cases of non-isotropic Brownian motion, that describes the biased random walk towards attracting traps as of light bulbs, and Levy flights, whose heavy-tailed probability distribution may also describe insects' movement. (AU)

Scientific publications (5)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
AHMED, DANISH A.; PETROVSKII, SERGEI V.; TILLES, PAULO F. C. The ``Levy or Diffusion{''} Controversy: How Important Is the Movement Pattern in the Context of Trapping?. MATHEMATICS, v. 6, n. 5 MAY 2018. Web of Science Citations: 2.
TILLES, PAULO F. C.; PETROVSKII, SERGEI V.; NATTI, PAULO L. A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes. SCIENTIFIC REPORTS, v. 7, OCT 30 2017. Web of Science Citations: 0.
TILLES, PAULO F. C.; PETROVSKII, SERGEI V.; NATTI, PAULO L. A random walk description of individual animal movement accounting for periods of rest. ROYAL SOCIETY OPEN SCIENCE, v. 3, n. 11 NOV 2016. Web of Science Citations: 4.
TILLES, PAULO F. C.; PETROVSKII, SERGEI V. How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making. Journal of Mathematical Biology, v. 73, n. 1, p. 227-255, JUL 2016. Web of Science Citations: 6.
TILLES, PAULO F. C.; PETROVSKII, SERGEI V. Statistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spread. ECOLOGICAL COMPLEXITY, v. 22, p. 86-92, JUN 2015. Web of Science Citations: 6.

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