Examining Variation in Stand Structure and Spatial Arrangements Over Time Valerie LeMay1, Arne Pommerening2, and Peter Marshall3 1
Department of Forest Resources Management, University of British Columbia, 20452424 Main Mall, Vancouver, BC V6T 1Z4, Canada,
[email protected] 2 Bangor University, College of Natural Sciences, School of the Environment and Natural Resources, Bangor, Gwynedd, LL57 2UW, Wales, UK.
[email protected] 3 Department of Forest Resources Management, University of British Columbia, 20452424 Main Mall, Vancouver, BC V6T 1Z4, Canada,
[email protected]
Introduction Variations in stand structure and in spatial patterns of trees in forests impact growth, regeneration, and mortality, and impact on habitat suitability for wildlife species. High biodiversity is associated with stands where there are multiple tree species and sizes (Buongiorno et al., 1994), and structural diversity can indicate overall species diversity (Kimmins, 1997). As a result, managing forests for biodiversity may be accomplished by managing for structural diversity (Önal, 1997). As measures of horizontal complexity, spatial indices can be useful for comparing point patterns (Goreaud & Pélissier, 1999) and for interpreting the ecology of species (Goreaud & Pélissier, 1999; Davis et al., 2000). This diversity in stand structure and spatial patterns impacts reflectances and therefore, remotely sensed imagery data. A number of measures of stand structural variability have been suggested that use forest inventory variables measured at one point in time, including indices by Staudhammer & LeMay (2001) based on variances in diameter at breast height (dbh; 1.3 m above ground), total tree height, and species. Using remotely sensed data and imputation of ground data to each pixel or group of pixels, variation of stand structure within stands can be estimated (LeMay et al. 2008). Stand structure changes over time can be examined by calculating structural indices on plots that are repeatedly measured. Alternatively, changes in stand structure over time can be estimated by using a stand dynamics model that grows individual trees and by calculating stand structure metrics for each forecast. For forest inventories, the challenge then becomes connecting the stand dynamics model to the forest inventory data (e.g., Temesgen et al., 2003). Point process analyses are commonly used to examine spatial patterns. Greater variation in spatial patterns is often coupled with greater stand structure complexity, including greater diversity in species and sizes. Commonly, univariate and bivariate Ripley’s K functions and derivatives of these functions (i.e., L(r) and pair correlation, g(r), where r distance between events; Ripley 1981; Illian et al. 2008) are used to examine point patterns at a location and time. However, very few methods are available for comparing spatial patterns where repeated measures in time and space are available. In our recent paper (LeMay et al. In Press), we suggested that the use of random coefficients mixed
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models may aid in examining variation in spatial point patterns over monitoring locations and over time. In that paper, the approach was demonstrated by examining the spatiotemporal patterns of pure interior Douglas-fir (Pseudotsuga menziesii var glauca (Mirb.) Franco) stands growing on dry sites under fire protection for more than 50 years, using replicated, repeated measures data. As with stand structure changes, changes in spatial patterns over time can be estimated by using a stand dynamics model that grows individual trees along with retaining a spatial map of trees. The approach used for repeated measures data could then be used with the forecasted trees. As with stand structure, the challenge is connecting the spatially explicit, stand dynamics model to the forest inventory data. In this paper, we briefly discuss the use of chronosequences rather than true repeated measures for examining stand structures and spatial patterns over time. We also briefly discuss a process for spatial processes over time, since full details are provided in LeMay et al. (In Press). Repeated Measures Versus Chronsequence Data In repeated measures forestry data, the same plot is repeatedly measured over time (i.e., permanent sample plots or continuous forest inventory plots). Using repeated measured data, the “dots can be connected” in time, since the same plot is remeasured. As a result, any changes in stand structure, spatial arrangements, and other measures are true changes in time. The use of repeated measures data requires continued investments of funds over time. A greater number of repeated measurements in time over a longer time period provide better quality data than only a few measurements and/or a short period of time. An alternative approach that is often used involves selecting a number of plots to measure at one time that appear to represent the development sequence of one type of stand. This is often termed a chronosequence, where a set of plots in space is used as a proxy for repeated measures in time. Most researchers take great care in locating these plots. However, the “the dots cannot be connected in time” in that changes over the chronosequence may be due to actual changes in time, may be due to changes over space, or they may be due to a mixture of the two. A chronosequence may not, in fact, represent a development sequence. As a result, conclusions regarding changes over time using this type of chronosequence data may be suspect. Conclusions concerning changes over time using repeated measures data are not suspect as these represent true change. Changes in Spatial Patterns Over Time As mentioned, changes in stand structure can be examined by interpreting changes in stand structure indices or measures over time. Commonly spatial patterns are represented as functions of distance between trees. Therefore, changes in the spatial pattern functions over time are used to examine changes in the spatial patterns. For a few plots measured only a few times, graphical approaches can be used (e.g. Biondi et al. 1994). Where there are many plots measured for a larger number of times, the graphical approaches become cumbersome. In LeMay et al. (In Press), we suggested the use of a random coefficients
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modelling approach instead. The approach involves obtaining the spatial pattern function for each plot and time. Variation over space and time are then included as random effects through random coefficients modelling. As a result, the relative contributions of changes in space and time can be assessed.
Conclusions Changes in stand structure and spatial patterns over time can be used for a large number of forest inventory uses. Where ground data are available, the use of repeated measures gives true changes over time, whereas chronsequence data using space as a proxy for time may not. The use of random coefficients mixed models has been shown to be a tool for examining changes in spatial pattern functions over time. For forest inventory, connections to stand dynamics models that forecast tree growth, mortality, regeneration, and spatial positions over time would be needed, since ground data are not available for each stand. Therefore, the challenge is to connect a spatially explicit, stand dynamics model to forest inventory data as a means of examing changes in stand structure and spatial patterns over time.
References Cited Biondi, F., Myers, D.E., & Avery, C.C. 1994. Geostatically modelling stem size and increments in an old-growth forest. Canadian Journal of Forest Research, 24:1354-1368. Buongiorno, J., Dahir, S., Lu, H.C., & Lin, C.R. 1994. Tree size diversity and economic returns in uneven-aged forest stands. Forest Science, 40(1):83-103. Davis, J.H., Howe, R.W., & Davis, G.J. 2000. A multi-scale spatial analysis method for point data. Landscape Ecology, 15:99-114. Goreaud, F. & Pélissier, R. 1999. On explicit formulas for edge effect correction for Ripley’s K-function. Journal of Vegetation Science, 10:433-432. Kimmins, J.P. 1997. Biodiversity and its relationship to ecosystem health and integrity. The Forestry Chronicle, 73:229-232. Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. 2008. Statistical analysis and modelling of spatial point patterns. John Wiley & Sons, Ltd., Mississauga, Ontario. LeMay, V., Maedel, J., & Coops, N. 2008. Estimating stand structural details using variable-space nearest neighbour analyses to link ground data, forest cover maps, and landsat imagery. Remote Sensing of Environment, 112:2578–2591.
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LeMay, V.M., Pommerening, A. & Marshall, P.L. In Press. Spatial-temporal structure of multi-storied, uneven-aged interior Douglas fir (Pseudotsuga menziesii var glauca (Mirb.) Franco) Stands. Journal of Ecology. Önal, H. 1997. Trade-off between structural diversity and economic objectives in forest management. American Journal of Agricultural Economics, 79:1001-1012. Ripley, B.D. 1981. Spatial Statistics. John Wiley & Sons, New York. Staudhammer, C.L. & LeMay, V.M. 2001. Introduction and evaluation of possible indices of stand structural diversity. Canadian Journal of Forest Research, 31:1105-1115. Temesgen, H., LeMay, V.M., Froese, K.L., & Marshall, P.L. 2003. Imputing tree-lists from aerial attributes for complex stands of south-eastern British Columbia. Forest EcolOgy and Management, 177:277-285.
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