An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation

M.N.I. Khan, Renske Hijbeek, Uta Berger, Nico Koedam, Uwe Grueters, S.M.Z. Islam, M.A. Hasan, Farid Dahdouh-Guebas

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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. Principal Findings 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 Σ R2) but not 12N/(π Σ R2), of PCQM2 is 4(8N - 1)/(π Σ R2) but not 28N/(π Σ R2) and of PCQM3 is 4(12N - 1)/(π Σ R2) but not 44N/(π Σ R2) as published. Significance 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.

Original languageEnglish
Article numbere0157985
JournalPLoS ONE
Volume11
Issue number6
DOIs
Publication statusPublished - 2016

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Monte Carlo Method
Monte Carlo method
plant density
methodology
Sampling
Monte Carlo simulation
sampling
plant competition
Population

Cite this

Khan, M. N. I., Hijbeek, R., Berger, U., Koedam, N., Grueters, U., Islam, S. M. Z., ... Dahdouh-Guebas, F. (2016). An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation. PLoS ONE, 11(6), [e0157985]. https://doi.org/10.1371/journal.pone.0157985
Khan, M.N.I. ; Hijbeek, Renske ; Berger, Uta ; Koedam, Nico ; Grueters, Uwe ; Islam, S.M.Z. ; Hasan, M.A. ; Dahdouh-Guebas, Farid. / An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation. In: PLoS ONE. 2016 ; Vol. 11, No. 6.
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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. Principal Findings 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 Σ R2) but not 12N/(π Σ R2), of PCQM2 is 4(8N - 1)/(π Σ R2) but not 28N/(π Σ R2) and of PCQM3 is 4(12N - 1)/(π Σ R2) but not 44N/(π Σ R2) as published. Significance 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.",
author = "M.N.I. Khan and Renske Hijbeek and Uta Berger and Nico Koedam and Uwe Grueters and S.M.Z. Islam and M.A. Hasan and Farid Dahdouh-Guebas",
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Khan, MNI, Hijbeek, R, Berger, U, Koedam, N, Grueters, U, Islam, SMZ, Hasan, MA & Dahdouh-Guebas, F 2016, 'An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation', PLoS ONE, vol. 11, no. 6, e0157985. https://doi.org/10.1371/journal.pone.0157985

An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation. / Khan, M.N.I.; Hijbeek, Renske; Berger, Uta; Koedam, Nico; Grueters, Uwe; Islam, S.M.Z.; Hasan, M.A.; Dahdouh-Guebas, Farid.

In: PLoS ONE, Vol. 11, No. 6, e0157985, 2016.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - An evaluation of the plant density estimator the point-centred quarter method (PCQM) using monte carlo simulation

AU - Khan, M.N.I.

AU - Hijbeek, Renske

AU - Berger, Uta

AU - Koedam, Nico

AU - Grueters, Uwe

AU - Islam, S.M.Z.

AU - Hasan, M.A.

AU - Dahdouh-Guebas, Farid

PY - 2016

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N2 - 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. Principal Findings 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 Σ R2) but not 12N/(π Σ R2), of PCQM2 is 4(8N - 1)/(π Σ R2) but not 28N/(π Σ R2) and of PCQM3 is 4(12N - 1)/(π Σ R2) but not 44N/(π Σ R2) as published. Significance 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.

AB - 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. Principal Findings 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 Σ R2) but not 12N/(π Σ R2), of PCQM2 is 4(8N - 1)/(π Σ R2) but not 28N/(π Σ R2) and of PCQM3 is 4(12N - 1)/(π Σ R2) but not 44N/(π Σ R2) as published. Significance 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.

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