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Estimating Variation in Landscape Analysis
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Introduction General Approach –Create spatial database (GIS) –Populate polygons with sample data –Simulate change for variable of interest –Generate maps Common Uses –Managerial –Scientific –Public policy Spatial Landscape Analyses: how & why?
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Introduction Hessburg, P.F., Smith, B.G., and R.B. Salter. 1999. Detecting Change in Forest Spatial Patterns from Reference Conditions. Ecological Applications, 9 (4) 1232- 1252. Wales, B.C. and L.H. Suring. 2004. Assessment Techniques for Terrestrial Vertebrates of Conservation Concern. In: Hayes, J.L., Ager, A.A., and R.J. Barbour (Tech. Eds. Methods for Integrated Modeling of Landscape Change. USDA Forest Service GTR-610. pp 64-72. Spatial Landscape Analysis: what?
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Problem The results of landscape simulation are often reported without an estimate of uncertainty 2045 2095 1995 http://www.fsl.orst.edu/clams/prj_lamps_simulation.html
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Research Goals To examine the potential effects of variation in sample data on the results of landscape simulation To begin to develop ways to communicate these effects
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Study Objectives 1.Estimate the area of late seral forest (LSF) structure in a 6070 ha reserve over 30 years (FVS) Hummel) 2.Calculate the effect of sampling uncertainty on the estimates in each decade (Monte Carlo/SAS) (Cunningham)
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Methods: 1. LSF Area
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1:12,000
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Ø Ø 1 polygon 1=ABGR/ABCO 7ac (0.05%) Ø Ø Ø 1 polygon 1= PSME 10 ac (0.07%) 1 polygon 1=ABLA2/PIEN 3 49 ac (2.3%) 5 polygons 1=ABLA2/PIEN 2 7 ac (1.83%) 18 polygons 2= ABGR/ABCO 11=ABGR/PIEN 5=PSME 3139 ac (21%) 3 polygons 1=ABGR/ABCO 1=ABLA2/PIEN 1=PSME 38 ac (0.25%) Ø ØØ 1 polygon 1=PSME 49 ac (2.3%) 6 polygons 1=PICO 5=PSME 652 ac (4.3%) 2 polygons 2=PSME 41 ac (0.3%) Ø 44 polygons 6=PICO 22=PIPO 17=PSME 1115 ac (7.4%) 7 polygons 5=PIPO 2=PSME 343 ac (2.3%) 10 polygons 3=PICO 7=PSME 694 ac (4.6 %) 36 polygons 3=PICO 8=PIPO 25=PSME 7582 ac (50%) 15 polygons 2=PICO 6=PIPO 7=PSME 354 ac (2.3%) 4 polygons 4=PIPO 515 ac (3.4%) SISEOCSECCURYFMSOFMS 10 11 13 18 Landscape Summary Matrix
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Area of LSF Structure Basal area (BA) at least 55.2 m2/ha BA of trees greater than 61.0 cm dbh ≥ 8.3 m2/ha BA of trees greater than 35.6 cm dbh ≥ 33.1 m2/ha BA of trees less than 35.6 cm dbh ≥ 8.3 m2/ha If LSF=1 If not LSF=0
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Results 1: LSF area estimate
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Methods: 2. Sampling Error
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Bootstrap Re-sampling Developed in the 1980s (Efron), based on classical statistical theory from the 1930s. Computer-intensive method that creates an empirical distribution function of a statistic to estimate its true distribution function. The SD of a sample of bootstrap means is the bootstrap estimate of the true SD of the mean.
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X i=5 x* 1 x* 2 …… x* B 1 (15) 5 (12) 3 ( 7 ) …… 2 ( 4 ) 2 ( 4 ) 4 ( 9 ) 1 (15) …… 1 (15) 3 ( 7 ) 5 (12) 2 ( 4) …… 4 ( 9 ) 4 ( 9 ) 3 ( 7 ) 2 ( 4 ) …… 5 (12) 5 (12) 1 (15) 3 ( 7 ) …… 2 ( 4 ) = 9.4 = 11.0 = 7.4 …… = 8.8 What is a Bootstrap Sample?
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Bootstrapped Samples (200)
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SC 0 (4.8) PVT LSF Probabilities each Decade
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Results 2 : LSF mean & SE Decade 1 Decade 2 Decade 3 1690 ha (se 233 ha) 2060 ha (se 251 ha) 3674 ha (se 109 ha)
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Comparison of Results 1 & 2
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Acknowledgements Pat Cunningham Tom Gregg Tim Max Further information Gregg, T.F.; Hummel, S. 2002. Assessing sampling uncertainty in FVS projections using a bootstrap resampling method. In: Crookston, N.L.; Havis, R.N., comps. Second Forest Vegetation Simulator Conference; 2002 February 12-14; Fort Collins, CO. Proc. RMRS-P-25. Ogden, UT: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station: 164-167. shummel@fs.fed.us
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“…The oldest and simplest device for misleading folks is the barefaced lie. A method that is nearly as effective and far more subtle is to report a sample estimate without any indication of its reliability…” (Freese 1967)
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Overview Introduction Issue Objectives –1 & 2 Methods –1 & 2 Results –1 & 2 Implications
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