Estimating Variation in Landscape Analysis

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?

Introduction Hessburg, P.F., Smith, B.G., and R.B. Salter Detecting Change in Forest Spatial Patterns from Reference Conditions. Ecological Applications, 9 (4) Wales, B.C. and L.H. Suring 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 Spatial Landscape Analysis: what?

Problem The results of landscape simulation are often reported without an estimate of uncertainty

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

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)

Methods: 1. LSF Area

1:12,000

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 Landscape Summary Matrix

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

Results 1: LSF area estimate

Methods: 2. Sampling Error

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.

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?

Bootstrapped Samples (200)

SC 0 (4.8) PVT LSF Probabilities each Decade

Results 2 : LSF mean & SE Decade 1 Decade 2 Decade ha (se 233 ha) 2060 ha (se 251 ha) 3674 ha (se 109 ha)

Comparison of Results 1 & 2

Acknowledgements Pat Cunningham Tom Gregg Tim Max Further information Gregg, T.F.; Hummel, S 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:

“…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)

Overview Introduction Issue Objectives –1 & 2 Methods –1 & 2 Results –1 & 2 Implications