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2023 | OriginalPaper | Chapter

6. Closest Distance and Nearest Neighbor Methods

Authors : George A. F. Seber, Matthew R. Schofield

Published in: Estimating Presence and Abundance of Closed Populations

Publisher: Springer International Publishing

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Abstract

This is a specialized and short chapter that deals with stationary populations of objects such as plants and trees and gives many methods currently used for estimating population density and related parameters. There are two basic methods. The first uses the distance of the closest or rth closest object from a chosen point, and the second uses the closest (nearest neighbor) or rth nearest neighbor to a chosen object.
The estimators, which are extensively reviewed, have been referred to as plotless density estimators. Sometimes the two methods have been combined to test for population randomness. Estimators and some variances are given for objects that have a spatial Poisson, negative-binomial, and general nonrandom distributions.
Trees are given a prominent place, where the previous methods are also compared with other population methods such as plot sampling and distance sampling from points and transects. Several studies comparing various methods are described and conclude with three shortcomings of the closest distance method.

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Literature
go back to reference Basiri, R., Moradi, M., Kiani, B., & Maasumi Babaarabi, M. (2018). Evaluation of distance methods for estimating population density in Populus euphratica Olivier natural stands (case study: Maroon riparian forests Iran). Journal of Forest Science, 64(5), 230–244.CrossRef Basiri, R., Moradi, M., Kiani, B., & Maasumi Babaarabi, M. (2018). Evaluation of distance methods for estimating population density in Populus euphratica Olivier natural stands (case study: Maroon riparian forests Iran). Journal of Forest Science, 64(5), 230–244.CrossRef
go back to reference Besag, J. E., & Gleaves, J. T. (1973). On the detection of spatial pattern in plant communities. Bulletin of the International Statistical Institute, 45, 153–158. Besag, J. E., & Gleaves, J. T. (1973). On the detection of spatial pattern in plant communities. Bulletin of the International Statistical Institute, 45, 153–158.
go back to reference Buckland, S. T., Rexstad, E. A., Marques, T. A., & Oedekoven, C. S. (2015). Distance sampling: Methods and applications. Springer International Publishing: Switzerland.CrossRef Buckland, S. T., Rexstad, E. A., Marques, T. A., & Oedekoven, C. S. (2015). Distance sampling: Methods and applications. Springer International Publishing: Switzerland.CrossRef
go back to reference Burch, B. D., & Sánchez Meador, A. J. (2018). Comparison of forest age estimators using k-tree, fixed-radius, and variable-radius plot sampling. Canadian Journal of Forest Research, 48(8), 942–951.CrossRef Burch, B. D., & Sánchez Meador, A. J. (2018). Comparison of forest age estimators using k-tree, fixed-radius, and variable-radius plot sampling. Canadian Journal of Forest Research, 48(8), 942–951.CrossRef
go back to reference Clark, P. J., & Evans, F. C. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology, 35(4), 445–453.CrossRef Clark, P. J., & Evans, F. C. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology, 35(4), 445–453.CrossRef
go back to reference Cogbill, C. V., Thurman, A. L., Williams, J. W., Zhu, J., Mladenoff, D. J., & Goring, S. J. (2018). A retrospective on the accuracy and precision of plotless forest density estimators in ecological studies. Ecosphere, 9(4), e02187.CrossRef Cogbill, C. V., Thurman, A. L., Williams, J. W., Zhu, J., Mladenoff, D. J., & Goring, S. J. (2018). A retrospective on the accuracy and precision of plotless forest density estimators in ecological studies. Ecosphere, 9(4), e02187.CrossRef
go back to reference Cottam, G, Curtis, B. W., & Hale, B. (1953). Some sampling characteristics of a population of randomly dispersed individuals. Ecology, 34(4), 741–757.CrossRef Cottam, G, Curtis, B. W., & Hale, B. (1953). Some sampling characteristics of a population of randomly dispersed individuals. Ecology, 34(4), 741–757.CrossRef
go back to reference Dacey, M. F. (1963). Order neighbor statistics for a class of random patterns in multidimensional space. Annals of the Association of American Geographers, 53(4), 505–515.CrossRef Dacey, M. F. (1963). Order neighbor statistics for a class of random patterns in multidimensional space. Annals of the Association of American Geographers, 53(4), 505–515.CrossRef
go back to reference Dacey, M. F. (1964). Modified poisson probability law for point pattern more regular than random. Annals of the Association of American Geographers, 54(4), 559–565.CrossRef Dacey, M. F. (1964). Modified poisson probability law for point pattern more regular than random. Annals of the Association of American Geographers, 54(4), 559–565.CrossRef
go back to reference Dacey, M. F. (1965). Order distance in an inhomogeneous random point pattern. Canadian Geographer, 9(3), 144–153.CrossRef Dacey, M. F. (1965). Order distance in an inhomogeneous random point pattern. Canadian Geographer, 9(3), 144–153.CrossRef
go back to reference Dacey, M. F. (1966). A compound probability law for a pattern more dispersed than random and with areal inhomogeneity. Economic Geography, 42(2), 172–179.CrossRef Dacey, M. F. (1966). A compound probability law for a pattern more dispersed than random and with areal inhomogeneity. Economic Geography, 42(2), 172–179.CrossRef
go back to reference Diggle, P. J. (1975). Robust density estimation using distance methods. Biometrika, 62(1), 39–48.CrossRef Diggle, P. J. (1975). Robust density estimation using distance methods. Biometrika, 62(1), 39–48.CrossRef
go back to reference Diggle, P. J. (1977). A note on robust density estimation for spatial point patterns. Biometrika, 64(1), 91–95.CrossRef Diggle, P. J. (1977). A note on robust density estimation for spatial point patterns. Biometrika, 64(1), 91–95.CrossRef
go back to reference Eberhardt, L. L. (1967) Some developments in ‘distance sampling’. Biometrics, 23(2), 207–216.PubMedCrossRef Eberhardt, L. L. (1967) Some developments in ‘distance sampling’. Biometrics, 23(2), 207–216.PubMedCrossRef
go back to reference Fehrmann, L., Gregoire, T. G., & Kleinn, C. (2012). Triangulation based inclusion probabilities: A design-unbiased sampling approach. Environmental and Ecological Statistics, 19(1), 107–123.CrossRef Fehrmann, L., Gregoire, T. G., & Kleinn, C. (2012). Triangulation based inclusion probabilities: A design-unbiased sampling approach. Environmental and Ecological Statistics, 19(1), 107–123.CrossRef
go back to reference Gao, M. (2013). Detecting spatial aggregation from distance sampling: A probability distribution model of nearest neighbor distance. Ecological Research, 28(3), 397–405.CrossRef Gao, M. (2013). Detecting spatial aggregation from distance sampling: A probability distribution model of nearest neighbor distance. Ecological Research, 28(3), 397–405.CrossRef
go back to reference Gregoire, T. G. (1982). The unbiasedness of the mirage correction procedure for boundary overlap. Forest Science, 28(3), 504–508. Gregoire, T. G. (1982). The unbiasedness of the mirage correction procedure for boundary overlap. Forest Science, 28(3), 504–508.
go back to reference Gregoire, T. G. & Scott, C. T. (1990). Sampling at the stand boundary: A comparison of the statistical performance among eight Methods. Research in Forest Inventory, Monitoring, Growth and Yield. Proceedings of the International Union of Forest Research Organizations XIX World Congress, Montreal, Canada, 5–11 August, 1990, eds. H. E. Burkhart, G. M. Bonnor, and J. J. Lowe, Publ. FWS-3-90, School of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, pp. 78–85. Gregoire, T. G. & Scott, C. T. (1990). Sampling at the stand boundary: A comparison of the statistical performance among eight Methods. Research in Forest Inventory, Monitoring, Growth and Yield. Proceedings of the International Union of Forest Research Organizations XIX World Congress, Montreal, Canada, 5–11 August, 1990, eds. H. E. Burkhart, G. M. Bonnor, and J. J. Lowe, Publ. FWS-3-90, School of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, pp. 78–85.
go back to reference Gregoire, T. G., & Valentine, H. T. (2008). Sampling strategies for natural resources and the environment. New York: Chapman and Hall/CRC. Gregoire, T. G., & Valentine, H. T. (2008). Sampling strategies for natural resources and the environment. New York: Chapman and Hall/CRC.
go back to reference Grosenbaugh, L. R. (1952). Plotless timber estimates—new, fast, easy. Journal of Forestry, 50, 32–37. Grosenbaugh, L. R. (1952). Plotless timber estimates—new, fast, easy. Journal of Forestry, 50, 32–37.
go back to reference Grosenbaugh, L. R. (1958). Point-sampling and line-intercept sampling: Probability theory, geometric implications, synthesis. In Southern Forest Experiment Station Occasional Paper SO-160. Washington, D.C.: USDA Forest Service. Grosenbaugh, L. R. (1958). Point-sampling and line-intercept sampling: Probability theory, geometric implications, synthesis. In Southern Forest Experiment Station Occasional Paper SO-160. Washington, D.C.: USDA Forest Service.
go back to reference Haxtema, Z., Temesgen, H., & Marquardt, T. (2012). Evaluation of n-tree distance sampling for inventory of headwater riparian forests of western Oregon. Western Journal of Applied Forestry, 27(3), 109–117.CrossRef Haxtema, Z., Temesgen, H., & Marquardt, T. (2012). Evaluation of n-tree distance sampling for inventory of headwater riparian forests of western Oregon. Western Journal of Applied Forestry, 27(3), 109–117.CrossRef
go back to reference Hsu,, Y.-H., Chen, Y., Yang, T. R., Kershaw, Jr., J. A., & Ducey, M. J. (2020). Sample strategies for bias correction of regional LiDAR-assisted forest inventory: Estimates on small woodlots. Annals of Forest Science, 77, 75.CrossRef Hsu,, Y.-H., Chen, Y., Yang, T. R., Kershaw, Jr., J. A., & Ducey, M. J. (2020). Sample strategies for bias correction of regional LiDAR-assisted forest inventory: Estimates on small woodlots. Annals of Forest Science, 77, 75.CrossRef
go back to reference Khan, M. N. I., Hijbeek, R., & et al. (2016). An evaluation of the plant density estimator the point-centred quarter method (PCQM) using Monte Carlo simulation. PLoS One, 11(6), e0157985. Khan, M. N. I., Hijbeek, R., & et al. (2016). An evaluation of the plant density estimator the point-centred quarter method (PCQM) using Monte Carlo simulation. PLoS One, 11(6), e0157985.
go back to reference Kleinn, C., & Vilc̆ko, F. (2006a). A new empirical approach for estimation in k-tree sampling. Forest Ecology and Management, 237(1), 522–533. Kleinn, C., & Vilc̆ko, F. (2006a). A new empirical approach for estimation in k-tree sampling. Forest Ecology and Management, 237(1), 522–533.
go back to reference Kleinn, C., & Vilc̆ko, F. (2006b). Design-unbiased estimation for point-to-tree distance sampling. Canadian Journal of Forest Research, 36(6), 1407–1414. Kleinn, C., & Vilc̆ko, F. (2006b). Design-unbiased estimation for point-to-tree distance sampling. Canadian Journal of Forest Research, 36(6), 1407–1414.
go back to reference Lessard, V., Reed, D. D., & Monkevich, N. (1994). Comparing n-tree distance sampling with point and plot sampling in northern Michigan forest types. Northern Journal of Applied Forestry, 11(1), 12–16.CrossRef Lessard, V., Reed, D. D., & Monkevich, N. (1994). Comparing n-tree distance sampling with point and plot sampling in northern Michigan forest types. Northern Journal of Applied Forestry, 11(1), 12–16.CrossRef
go back to reference Lessard, V. C., Drummer, T. D., & Reed, D. D. (2002). Precision of density estimates from fixed-radius plots compared to n-tree distance sampling. Forest Science, 48(1), 1–6. Lessard, V. C., Drummer, T. D., & Reed, D. D. (2002). Precision of density estimates from fixed-radius plots compared to n-tree distance sampling. Forest Science, 48(1), 1–6.
go back to reference Lurdes, B. S., Alves, M., Rui, B. E., & Silva, L. (2017). Comparison of T -square, point centered quarter, and N -tree sampling methods in pittosporum undulatum invaded woodlands. International Journal of Forestry Research, 2017. Article ID2818132, 13pp. Lurdes, B. S., Alves, M., Rui, B. E., & Silva, L. (2017). Comparison of T -square, point centered quarter, and N -tree sampling methods in pittosporum undulatum invaded woodlands. International Journal of Forestry Research, 2017. Article ID2818132, 13pp.
go back to reference Lynch, T. B. (2012). A mirage boundary correction method for distance sampling. Canadian Journal of Forest Research, 42(2), 272–278.CrossRef Lynch, T. B. (2012). A mirage boundary correction method for distance sampling. Canadian Journal of Forest Research, 42(2), 272–278.CrossRef
go back to reference Lynch, T. B., & Gove, J. H. (2014). The unbiasedness of a generalized mirage boundary correction method for Monte Carlo integration estimators of volume. Canadian Journal of Forest Research, 44(7), 810–819.CrossRef Lynch, T. B., & Gove, J. H. (2014). The unbiasedness of a generalized mirage boundary correction method for Monte Carlo integration estimators of volume. Canadian Journal of Forest Research, 44(7), 810–819.CrossRef
go back to reference Lynch, T. B., & Rusydi, R. (1999). Distance sampling for forest inventory in Indonesian teak plantations. Forest Ecology and Management, 113(2), 215–221.CrossRef Lynch, T. B., & Rusydi, R. (1999). Distance sampling for forest inventory in Indonesian teak plantations. Forest Ecology and Management, 113(2), 215–221.CrossRef
go back to reference Magnussen, S. (2014). Robust fixed-count density estimation with virtual plots. Canadian Journal of Forest Research, 44(4), 377–382CrossRef Magnussen, S. (2014). Robust fixed-count density estimation with virtual plots. Canadian Journal of Forest Research, 44(4), 377–382CrossRef
go back to reference Magnussen, S., Fehrman, L., & Platt, W. J. (2012). An adaptive composite density estimator for k-tree sampling. European Journal of Forest Research, 131(2), 307–320.CrossRef Magnussen, S., Fehrman, L., & Platt, W. J. (2012). An adaptive composite density estimator for k-tree sampling. European Journal of Forest Research, 131(2), 307–320.CrossRef
go back to reference Magnussen, S., Kleinn, C., & Picard, N. (2008). Two new density estimators for distance sampling. European Journal of Forest Research, 127(3), 213–224.CrossRef Magnussen, S., Kleinn, C., & Picard, N. (2008). Two new density estimators for distance sampling. European Journal of Forest Research, 127(3), 213–224.CrossRef
go back to reference Marquardt, T., Temesgen, H., & Anderson, P. D. (2010). Accuracy and suitability of selected sampling methods within conifer dominated riparian zones. Forest Ecology and Management, 260(3), 313–320.CrossRef Marquardt, T., Temesgen, H., & Anderson, P. D. (2010). Accuracy and suitability of selected sampling methods within conifer dominated riparian zones. Forest Ecology and Management, 260(3), 313–320.CrossRef
go back to reference McGarvey, R., Byth, K., Dixon, C. D. Day, R. W., & Feenstra J. E. (2005). Field trials and simulations of point-nearest-neighbor distance methods for estimating abalone density. Journal of Shellfish Research, 24(2), 393–399.CrossRef McGarvey, R., Byth, K., Dixon, C. D. Day, R. W., & Feenstra J. E. (2005). Field trials and simulations of point-nearest-neighbor distance methods for estimating abalone density. Journal of Shellfish Research, 24(2), 393–399.CrossRef
go back to reference Melville, G., & Stone, C. (2016). Optimising nearest neighbour information–a simple, efficient sampling strategy for forestry plot imputation using remotely sensed data. Australian Forestry, 79(3), 217–228.CrossRef Melville, G., & Stone, C. (2016). Optimising nearest neighbour information–a simple, efficient sampling strategy for forestry plot imputation using remotely sensed data. Australian Forestry, 79(3), 217–228.CrossRef
go back to reference Melville, G. J., Welsh, A. H., & Stone, C. (2015). Improving the efficiency and precision of tree counts in pine plantations using airborne LiDAR Data and flexible-radius plots: Model-based and design-based approaches. Journal of Agricultural, Biological, and Environmental Statistics, 20(2), 229–257.CrossRef Melville, G. J., Welsh, A. H., & Stone, C. (2015). Improving the efficiency and precision of tree counts in pine plantations using airborne LiDAR Data and flexible-radius plots: Model-based and design-based approaches. Journal of Agricultural, Biological, and Environmental Statistics, 20(2), 229–257.CrossRef
go back to reference Moore, P. G. (1954). Spacing in plant populations. Ecology, 35(2), 222–227.CrossRef Moore, P. G. (1954). Spacing in plant populations. Ecology, 35(2), 222–227.CrossRef
go back to reference Morisita, M. (1954). Estimation of population density by spacing method. Memoirs of Faculty of Science, Kyushu University, E1, 187–197. Morisita, M. (1954). Estimation of population density by spacing method. Memoirs of Faculty of Science, Kyushu University, E1, 187–197.
go back to reference Morisita, M. (1957). A new method for the estimation of density by the spacing method applicable to non-randomly distributed populations. Physiology and Ecology, 7, 134–144. In Japanese, but translated into English by the United States Department of Agriculture, Division of Range Management in 1960. Morisita, M. (1957). A new method for the estimation of density by the spacing method applicable to non-randomly distributed populations. Physiology and Ecology, 7, 134–144. In Japanese, but translated into English by the United States Department of Agriculture, Division of Range Management in 1960.
go back to reference Northrup, A., Saborowski, J., Nuske, R. S., & Stoyan, D. (2010). Density estimation based on k-tree sampling and point pattern reconstruction. Canadian Journal of Forest Research, 40(5), 953–967.CrossRef Northrup, A., Saborowski, J., Nuske, R. S., & Stoyan, D. (2010). Density estimation based on k-tree sampling and point pattern reconstruction. Canadian Journal of Forest Research, 40(5), 953–967.CrossRef
go back to reference Packard, K. C., & Radtke, P. J. (2007). Forest sampling combining fixed- and variable-radius sample plots. Canadian Journal of Forest Research, 37(8), 1460–1471.CrossRef Packard, K. C., & Radtke, P. J. (2007). Forest sampling combining fixed- and variable-radius sample plots. Canadian Journal of Forest Research, 37(8), 1460–1471.CrossRef
go back to reference Patil, S. A., Burnham, K. P., & Kovner, J. L. (1979). Nonparametric estimation of plant density by the distance method. Biometrics, 35(3), 597–604.CrossRef Patil, S. A., Burnham, K. P., & Kovner, J. L. (1979). Nonparametric estimation of plant density by the distance method. Biometrics, 35(3), 597–604.CrossRef
go back to reference Pollard, J. H. (1971). On distance estimators of density in randomly distributed forests. Biometrics, 27(4), 991–1002.CrossRef Pollard, J. H. (1971). On distance estimators of density in randomly distributed forests. Biometrics, 27(4), 991–1002.CrossRef
go back to reference Prodan, M. (1968). Punkstichprobe für die forsteinrichtung (A point sample for forest management planning). Forst und Holzwirt, 23(11), 225–226. Prodan, M. (1968). Punkstichprobe für die forsteinrichtung (A point sample for forest management planning). Forst und Holzwirt, 23(11), 225–226.
go back to reference Ramezani, H., Grafström, A., Naghavi, H., Fallah, A., Shataee, S. H., & Soosani, J. (2016). Evaluation of K-tree distance and fixed-sized plot sampling in zagros forests of western Iran. Journal of Agricultural Science and Technology, 18(1), 155–170. Ramezani, H., Grafström, A., Naghavi, H., Fallah, A., Shataee, S. H., & Soosani, J. (2016). Evaluation of K-tree distance and fixed-sized plot sampling in zagros forests of western Iran. Journal of Agricultural Science and Technology, 18(1), 155–170.
go back to reference Seber, G. A. F. (1982). The estimation of animal abundance (2nd ed.). London: Griffin. Reprinted in paperback by the Blackburn press, Caldwell, N. J. (2002). Seber, G. A. F. (1982). The estimation of animal abundance (2nd ed.). London: Griffin. Reprinted in paperback by the Blackburn press, Caldwell, N. J. (2002).
go back to reference Shen, G., Wang, X., & He, F. (2020). Distance-based methods for estimating density of nonrandomly distributed populations. Ecology, 101(10), e03143.PubMedCrossRef Shen, G., Wang, X., & He, F. (2020). Distance-based methods for estimating density of nonrandomly distributed populations. Ecology, 101(10), e03143.PubMedCrossRef
go back to reference Thomas, L., Buckland, S. T., & et al. (2010). Distance software: Design and analysis of distance sampling surveys for estimating population size. Journal of Applied Ecology, 47(1), 5–14. Thomas, L., Buckland, S. T., & et al. (2010). Distance software: Design and analysis of distance sampling surveys for estimating population size. Journal of Applied Ecology, 47(1), 5–14.
go back to reference Thompson, H. R. (1956). Distribution of distance to the nth neighbor in a population of randomly distributed individuals. Ecology, 37(2), 391–394.CrossRef Thompson, H. R. (1956). Distribution of distance to the nth neighbor in a population of randomly distributed individuals. Ecology, 37(2), 391–394.CrossRef
go back to reference Thompson, I. D., Ortiz, D. A, Jastrebski, C., & Corbett, D. (2006). A comparison of prism plots and modified point-distance sampling to calculate tree stem density and basal area. Northern Journal of Applied Forestry, 23(3), 218–222.CrossRef Thompson, I. D., Ortiz, D. A, Jastrebski, C., & Corbett, D. (2006). A comparison of prism plots and modified point-distance sampling to calculate tree stem density and basal area. Northern Journal of Applied Forestry, 23(3), 218–222.CrossRef
go back to reference White, J. C., Coops, N. C., Wulder, M. A., Vastaranta, M., Hilker, T., & Tompalski, P. (2016). Remote sensing technologies for enhancing forest inventories: A review. Canadian Journal of Remote Sensing, 42(5), 619–641.CrossRef White, J. C., Coops, N. C., Wulder, M. A., Vastaranta, M., Hilker, T., & Tompalski, P. (2016). Remote sensing technologies for enhancing forest inventories: A review. Canadian Journal of Remote Sensing, 42(5), 619–641.CrossRef
go back to reference Yang, H., Magnussen, S., Fehrmann, L., Mundhenk, P., & Kleinn, C. (2016). Two neighborhood-free plot designs for adaptive sampling of forests. Environmental and Ecological Statistics, 23(2), 279–299.CrossRef Yang, H., Magnussen, S., Fehrmann, L., Mundhenk, P., & Kleinn, C. (2016). Two neighborhood-free plot designs for adaptive sampling of forests. Environmental and Ecological Statistics, 23(2), 279–299.CrossRef
go back to reference Zhu, X. Z., Gao, T., & Zhang, J. T. (2014). Point-centred quadrangle method: A novel distance method for density estimation. Advanced Materials Research, 1073–1076, 479–483.CrossRef Zhu, X. Z., Gao, T., & Zhang, J. T. (2014). Point-centred quadrangle method: A novel distance method for density estimation. Advanced Materials Research, 1073–1076, 479–483.CrossRef
Metadata
Title
Closest Distance and Nearest Neighbor Methods
Authors
George A. F. Seber
Matthew R. Schofield
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-39834-6_6

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