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)

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”

Study Area

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)

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)

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

Sampling Design

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)

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

Methods

• Ripley’s K(t) calculated for distance 0.5m to 11m by 0.5m intervals

n

i

n

j ij

ijt

w

uI

nn

AtK

1 1

)()(

~

tuif

tuifuI

ij

ijijt 0

1)(

rauif

ur

ura

rauif

wij

ij

ij

ij

ij /2

arccos1

1

222

• Edge correction applied to account for unsampled trees outside boundary

Methods• Edge effect means that therefore

ttK

tL

)(ˆ)(

nn

tKntKntK

)(~

)(~

)(ˆ

)(~

)(~

tKtK

• 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

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)

Plot 1

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

Plot 2

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

Plots 1 and 2

PLOT 1

PLOT 2

Plots 1 and 2

PLOT 1

PLOT 2

Plot 7

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

Plot 7

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

Sources of Error

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

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

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.

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.