#### Keywords

use, plant patches, change-point

#### Start Date

1-7-2008 12:00 AM

#### Abstract

The analysis of the consequences of land use (in particular forest use) may beconsidered as a partial step towards an integrated modelling of a land system. Let usconsider a forest territory, where a gap-cut is made, and after a given time period theeventual change in the spatial distribution of undergrowth plants and tree seedlings is to bedetected (see Mihók et al., 2005 and Gálhidy et al., 2006). If floristic data are collectedalong a line transect, we can try to detect the change in the plant distributions along thetransect, the so-called change-point, and see whether this occurs at the geometric frontierof the human intervention.The problem, on a theoretical level, can be addressed using the methodology of changepointanalysis which is a technically involved branch of mathematical statistics (see e.g.Brodsky and Darkhovsky, 1993; Csörgö and Horváth, 1997), widely used to explore thepossible temporal or spatial structure of local homogeneity from collected data. (The mainapplication fields of change-point analysis include meteorology, hydrology, orenvironmental studies, economy, quality control in industry, biology and medicine.) In thispaper we propose a practical, operative approach, using only technique of classicalstatistics.In our case, given a plant species, along a line transect quadrats have been located and ineach quadrat the individuals have been counted. We consider these data as samples of twodistributions of the same type but with different parameters, separated by a change-point K.Based on the maximum likelihood approach, an algorithm is given to estimate K.Since the distribution of the change-point estimate is not known, as a substitute of itsconfidence interval, the so-called change-interval will be calculated, using an adaptation ofthe bootstrap method. (For this widely applied simulation method see e.g. Efron andTibshirani, 1993, a justification of the use of bootstrap in this case can be found in Ferger,1993.) The implementation of the above algorithms was realized with the application ofthe statistical software “R”. As an illustration, for a concrete plant species, the maximumlikelihood estimation of the change-point and the calculation of the above mentionedchange-interval will be presented.

Statistical analysis of spatial plant patterns under the effect of forest use

The analysis of the consequences of land use (in particular forest use) may beconsidered as a partial step towards an integrated modelling of a land system. Let usconsider a forest territory, where a gap-cut is made, and after a given time period theeventual change in the spatial distribution of undergrowth plants and tree seedlings is to bedetected (see Mihók et al., 2005 and Gálhidy et al., 2006). If floristic data are collectedalong a line transect, we can try to detect the change in the plant distributions along thetransect, the so-called change-point, and see whether this occurs at the geometric frontierof the human intervention.The problem, on a theoretical level, can be addressed using the methodology of changepointanalysis which is a technically involved branch of mathematical statistics (see e.g.Brodsky and Darkhovsky, 1993; Csörgö and Horváth, 1997), widely used to explore thepossible temporal or spatial structure of local homogeneity from collected data. (The mainapplication fields of change-point analysis include meteorology, hydrology, orenvironmental studies, economy, quality control in industry, biology and medicine.) In thispaper we propose a practical, operative approach, using only technique of classicalstatistics.In our case, given a plant species, along a line transect quadrats have been located and ineach quadrat the individuals have been counted. We consider these data as samples of twodistributions of the same type but with different parameters, separated by a change-point K.Based on the maximum likelihood approach, an algorithm is given to estimate K.Since the distribution of the change-point estimate is not known, as a substitute of itsconfidence interval, the so-called change-interval will be calculated, using an adaptation ofthe bootstrap method. (For this widely applied simulation method see e.g. Efron andTibshirani, 1993, a justification of the use of bootstrap in this case can be found in Ferger,1993.) The implementation of the above algorithms was realized with the application ofthe statistical software “R”. As an illustration, for a concrete plant species, the maximumlikelihood estimation of the change-point and the calculation of the above mentionedchange-interval will be presented.