title: Challenges of ecological monitoring: estimating population abundance from sparse trap counts.
abstract: Ecological monitoring aims to provide estimates of pest species abundance-this information being then used for making decisions about means of control. For invertebrate species, population size estimates are often based on trap counts which provide the value of the population density at the traps' location. However, the use of traps in large numbers is problematic as it is costly and may also be disruptive to agricultural procedures. Therefore, the challenge is to obtain a reliable population size estimate from sparse spatial data. The approach we develop in this paper is based on the ideas of numerical integration on a coarse grid. We investigate several methods of numerical integration in order to understand how badly the lack of spatial data can affect the accuracy of results. We first test our approach on simulation data mimicking spatial population distributions of different complexity. We show that, rather counterintuitively, a robust estimate of the population size can be obtained from just a few traps, even when the population distribution has a highly complicated spatial structure. We obtain an estimate of the minimum number of traps required to calculate the population size with good accuracy. We then apply our approach to field data to confirm that the number of trap/sampling locations can be much fewer than has been used in many monitoring programmes. We also show that the accuracy of our approach is greater that that of the statistical method commonly used in field studies. Finally, we discuss the implications of our findings for ecological monitoring practice and show that the use of trap numbers 'smaller than minimum' may still be possible but it would result in a paradigm shift: the population size estimates should be treated probabilistically and the arising uncertainty may introduce additional risk in decision-making.
authors.affiliation: School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK. n.b.petrovskaya@bham.ac.uk
authors.forename: Natalia
authors.initials: N
authors.lastname: Petrovskaya
authors.forename: Sergei
authors.initials: S
authors.lastname: Petrovskii
authors.forename: Archie K
authors.initials: AK
authors.lastname: Murchie
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003625:Data Collection / Q000379:methods*; D003710:Demography / Q000379:methods*; D017753:Ecosystem; D008962:Models, Theoretical; D010571:Pest Control / Q000379:methods*; D011156:Population Density