Examining Overstory-Regeneration Relationships in Interior Douglas-fir Stands Using Ripley’s K(t) Statistic

1. Examining Overstory-Regeneration Relationships in Interior Douglas-fir Stands Using Ripley’s K(t) Statistic Katrina Froese (M.Sc. Candidate), Valerie LeMay (PhD., RPF), Peter Marshall (PhD., RPF) and Abdel-Azim Zumrawi (PhD., RPF)

2. Background • Primary Objective: predict understory attributes (regeneration abundance, small tree height growth) based on stand level predictors and assess effectiveness • Secondary Objective: use spatial and substrate data to further examine understory dynamics • This Presentation: using point pattern analysis to examine relationship between overstory trees and loci of regeneration “clumps”

3. Study Area

4. Study Area • IDFdm2, Invermere Forest District, Nelson Forest Region, southeastern British Columbia • Valley bottoms and lower slopes, Rocky Mountain Trench, 900-1200m elevation • Soil moisture deficit and frost important • Generally uneven aged stands, managed with partial cutting (some clearcuts)

5. Study Area • Stands are Douglas-fir (Pseudotsuga menziesii var. glauca) or Douglas-fir with: • ponderosa pine (Pinus ponderosa) • lodgepole pine (Pinus contorta var. latifolia) • western larch (Larix occidentalis) • hybrid white spruce (Picea glauca x Engelmannii ) • trembling aspen (Populus tremuloides) • paper birch (Betula papyrifera) • History of partial cutting and fire suppression (last 50-100 years)

6. Sampling Frame • All areas within the IDFdm2 study area disturbed within the last 5-25 years • Candidate openings selected from sampling matrix based on: • Number of years since disturbance • Silvicultural system • BEC site series • Elevation • Good geographic range of sites was obtained • North to south along trench • East to west

7. Sampling Design

8. Sampling Design • One in four 11.28 m radius plots were spatially mapped (for a total of 25 plots) • Distance and bearing to: • Large trees (DBH, species) • Small trees (DBH, species) • Regeneration clumps (species, height class, length, width, axis) • Stumps (diameter at 0.15 m) • Windthrow (DBH, length, axis) • Large slash piles (as regen) • Large clumps of shrubs (as regen)

9. Point Pattern Analysis • Test observed spatial patterns vs. null hypothesis of underlying Poisson (random) process • Competition -> uniformity/regularity • Favourable sites -> clustering/aggregation • Spatial indices: single value for an area • Ripley’s K(t): relative randomness as a function of scale (distance) • Ripley’s K(t): uses all pairs of points, not just nearest neighbours

10. Methods • Ripley’s K(t) calculated for distance 0.5m to 11m by 0.5m intervals • Edge correction applied to account for unsampled trees outside boundary

11. Methods • Edge effect means that therefore • Result transformed to L(t), linearizing K(t) and providing expected value of zero under Poisson • L(t): difference between no. points found within point-pair radius and expected no. points

12. Methods • Univariate analyses: live+dead (initial overstory), live, and dead overstory trees (release) • Bivariate analyses: 3 types of overstories vs. advance+subsequent, advance, and subsequent regeneration clumps • Monte Carlo simulation of 90% confidence envelopes (univariate and bivariate analyses) • Assumptions (bivariate): • center of clump represents origin • overstory affects location of clumps (causal)

13. Plot 1 Initial BA: 40 m2/ha Current BA: 19 m2/ha BA Removal: 49 % Years Since Dist: 18 No. Clumps: 10 Avg. No. Stems: 39 Slope: 0 Aspect: 44 Moisture: 01/03 Elev: 903 m

14. Plot 2 Initial BA: 36 m2/ha Current BA: 10 m2/ha BA Removal: 70 % Years Since Dist: 11 No. Clumps: 18 Avg. No. Stems: 7 Slope: 28 Aspect: 248 Moisture: 03 Elev: 924 m

15. Plots 1 and 2

16. Plots 1 and 2

17. Plot 7 Initial BA: 38 m2/ha Current BA: 2 m2/ha BA Removal: 95 % Years Since Dist: 18 No. Clumps: 9 Avg. No. Stems: 5 Slope: 6 Aspect: 317 Moisture: 01 Elev: 1152 m

18. Plot 7

19. Results • Generally, overstory trees prior to harvesting and/or mortality exhibited significant clustering at short distances • Relationship between regeneration clumps and overstory (pre-mortality, live, and dead) was often significant but extremely variable • Variability in results was not easily explained by simple site level variables

20. Sources of Error • Mapping of stems at POG – lean, slope • Edge effect correction • Improper assumptions • Missing cause of variability • No error – testing wrong relationship

21. Conclusions • Replication essential - variability • Keep in mind what question you’re asking (e.g., causal factors) • Appropriate tool? • Clumps are not points • Need to be able to interpret results

22. Special Thanks to the world's best supervisor, Dr. Val LeMay Funding for this research provided by Forest Renewal BC and Forestry Innovation Investment.In-kind contributions were supplied by the BC Ministry of Forests, the University of BC Faculty of Forestry, Tembec Industries, Slocan Forest Products, and Riverside Forest Products.

23. References • Moeur, M. 1993. Characterizing spatial patterns of trees using stem-mapped data. For. Sci. 39(4): 756-775. • Moeur, M. 1991. Spatial Variation in Conifers Regenerating Beneath Old Growth Forest Canopies. Ph.D. Dissertation, University of Washington, College of For. Res., Seattle, WA. 301 p. • Nigh, G. 1996. Identification and simulation of the spatial pattern of juvenile lodgepole pine in the sub-boreal spruce biogeoclimatic zone, Stuart dry warm and Babine moist cold variants. BC Min. For. Res. Br., Victoria, BC. FRDA Rept. 244. 28 p. • Ripley, B.D. 1998. Statistical Inference for Spatial Processes. Cambridge Univ. Press, Cambridge. 148 p. • Ripley, B. D. 1977. Modelling spatial patterns. J. Royal Stat. Soc. B 39(2): 172-212. • Upton, G.J.G. and B. Fingleton. 1985. Spatial Data Analysis by Example, Vol. 1: Point Pattern and Quantitative Data. John Wiley & Sons, Chichester. 410 p.