title: An Evaluation of the Plant Density Estimator the Point-Centred Quarter Method (PCQM) Using Monte Carlo Simulation.
abstract: BACKGROUND
  In the Point-Centred Quarter Method (PCQM), the mean distance of the first nearest plants in each quadrant of a number of random sample points is converted to plant density. It is a quick method for plant density estimation. In recent publications the estimator equations of simple PCQM (PCQM1) and higher order ones (PCQM2 and PCQM3, which uses the distance of the second and third nearest plants, respectively) show discrepancy. This study attempts to review PCQM estimators in order to find the most accurate equation form. We tested the accuracy of different PCQM equations using Monte Carlo Simulations in simulated (having 'random', 'aggregated' and 'regular' spatial patterns) plant populations and empirical ones.
  
  
  RESULTS
  PCQM requires at least 50 sample points to ensure a desired level of accuracy. PCQM with a corrected estimator is more accurate than with a previously published estimator. The published PCQM versions (PCQM1, PCQM2 and PCQM3) show significant differences in accuracy of density estimation, i.e. the higher order PCQM provides higher accuracy. However, the corrected PCQM versions show no significant differences among them as tested in various spatial patterns except in plant assemblages with a strong repulsion (plant competition). If N is number of sample points and R is distance, the corrected estimator of PCQM1 is 4(4N - 1)/(π ∑ R2) but not 12N/(π ∑ R2), of PCQM2 is 4(8N - 1)/(π ∑ R2) but not 28N/(π ∑ R2) and of PCQM3 is 4(12N - 1)/(π ∑ R2) but not 44N/(π ∑ R2) as published.
  
  
  CONCLUSIONS
  If the spatial pattern of a plant association is random, PCQM1 with a corrected equation estimator and over 50 sample points would be sufficient to provide accurate density estimation. PCQM using just the nearest tree in each quadrant is therefore sufficient, which facilitates sampling of trees, particularly in areas with just a few hundred trees per hectare. PCQM3 provides the best density estimations for all types of plant assemblages including the repulsion process. Since in practice, the spatial pattern of a plant association remains unknown before starting a vegetation survey, for field applications the use of PCQM3 along with the corrected estimator is recommended. However, for sparse plant populations, where the use of PCQM3 may pose practical limitations, the PCQM2 or PCQM1 would be applied. During application of PCQM in the field, care should be taken to summarize the distance data based on 'the inverse summation of squared distances' but not 'the summation of inverse squared distances' as erroneously published.
authors.affiliation: Laboratory of Systems Ecology and Resource Management, Département de Biologie des Organismes, Faculté des Sciences, Université Libre de Bruxelles-ULB, Bruxelles, Belgium.|Institute of Forest Growth and Forest Computer Sciences, TU Dresden, Tharandt, Germany.|Forestry and Wood Technology Discipline, Khulna University, Khulna, Bangladesh.
authors.forename: Md Nabiul Islam
authors.initials: MN
authors.lastname: Khan
authors.affiliation: Biodiversity and Ecology Research Unit, Faculty of Sciences and Bio-engineering Sciences, Vrije Universiteit Brussel-VUB, Brussels, Belgium.|Plant Production Systems, Wageningen University and Research Centre, Wageningen, Netherlands.
authors.forename: Renske
authors.initials: R
authors.lastname: Hijbeek
authors.affiliation: Institute of Forest Growth and Forest Computer Sciences, TU Dresden, Tharandt, Germany.
authors.forename: Uta
authors.initials: U
authors.lastname: Berger
authors.affiliation: Biodiversity and Ecology Research Unit, Faculty of Sciences and Bio-engineering Sciences, Vrije Universiteit Brussel-VUB, Brussels, Belgium.
authors.forename: Nico
authors.initials: N
authors.lastname: Koedam
authors.affiliation: Institute of Forest Growth and Forest Computer Sciences, TU Dresden, Tharandt, Germany.
authors.forename: Uwe
authors.initials: U
authors.lastname: Grueters
authors.affiliation: Forestry and Wood Technology Discipline, Khulna University, Khulna, Bangladesh.
authors.forename: S M Zahirul
authors.initials: SM
authors.lastname: Islam
authors.affiliation: Forestry and Wood Technology Discipline, Khulna University, Khulna, Bangladesh.
authors.forename: Md Asadul
authors.initials: MA
authors.lastname: Hasan
authors.affiliation: Laboratory of Systems Ecology and Resource Management, Département de Biologie des Organismes, Faculté des Sciences, Université Libre de Bruxelles-ULB, Bruxelles, Belgium.|Biodiversity and Ecology Research Unit, Faculty of Sciences and Bio-engineering Sciences, Vrije Universiteit Brussel-VUB, Brussels, Belgium.
authors.forename: Farid
authors.initials: F
authors.lastname: Dahdouh-Guebas
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D009010:Monte Carlo Method; D010944:Plants; D011156:Population Density