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 ∑ 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. 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.
Subject(s)
Computer Simulation , Monte Carlo Method , Plants , Population Density , AlgorithmsABSTRACT
In vegetation science and forest management, tree density is often used as a variable. To determine the value of this variable, reliable field methods are necessary. When vegetation is sparse or not easily accessible, the use of sample plots is not feasible in the field. Therefore, plotless methods, like the Point Centred Quarter Method, are often used as an alternative. In this study we investigate the accuracy of different plotless sampling methods. To this end, tree densities of a mangrove forest were determined and compared with estimates provided by several plotless methods. None of these methods proved accurate across all field sites with mean underestimations up to 97% and mean overestimations up to 53% in the field. Applying the methods to different vegetation patterns shows that when random spatial distributions were used the true density was included within the 95% confidence limits of all the plotless methods tested. It was also found that, besides aggregation and regularity, density trends often found in mangroves contribute to the unreliability. This outcome raises questions about the use of plotless sampling in forest monitoring and management, as well as for estimates of density-based carbon sequestration. We give recommendations to minimize errors in vegetation surveys and recommendations for further in-depth research.
