Looking ahead: Will Free-growing stands produce the volumes we expect? Wendy Bergerud Research Branch Ministry of Forests and Range December, 2009 1 Planning for the future What do we want our forests to look like? After harvesting a stand or group of stands, we usually reforest them so that we can get . . . ?? What is our target/goal? We must make decisions now hoping that they will have the right long-term effect. 2 From here to there? How do we assess how recently reforested areas are doing? Whether we are likely to get the desired volume from that stand(s)? This means that we want a way to measure how a stand is doing NOW in order to predict whether we are likely to get the desired outcome at rotation. I am going to talk about which measure of density sampled NOW will do the trick. This is more of a methods talk. 3 Key Messages TASS and TIPSY now have well-spaced

density, free-growing density, and mean stocked quadrants as output variables. Can use to project volume at rotation Modeling young stands still hampered by lack of information on: Ingress Forest Health Vegetation Competition Mixed species and uneven aged stands 4 Key Messages Spatial distribution is very important when projecting volumes at rotation for current densities. So is Site Index. Under optimum conditions, well-spaced density 10 to 20 years after FG declaration should be about the same. The free-growing density might actually increase. Modeling stand dynamics with TASS and TIPSY require a good understanding of the assumptions that must be made. 5 Density & Volume with Stand Age Projected Volume Density 0

20 40 60 Stand Age 80 100 120 Us i ng TASS ver si on v20524 6 Factors affecting the prediction of projected merchantable volume as a function of density include: Species Site Index Spatial Distribution Growth Model used Health Effects Competition Unexpected events (e.g. MPB) Other factors? 7 Discussion Assumptions Spatially homogeneous, even-aged stands. No brush or competition issues No forest health issues or unexpected events

No OAFs Minimum inter-tree distance (MITD) is 2.0 m Minimum height to be free-growing is 2.0 m Well-spaced and free-growing density are all uncapped estimates. 8 Discussion Assumptions Preliminary results I reserve the right to correct, if necessary Look at the TRENDS, not the specific numbers The TRENDS are more likely to remain the same under a different set of assumptions than would the specific numbers presented. 9 10 Different Types of Density Nominal - TASS input (often called Initial density) Total - All trees (regardless of spacing) Well-spaced - depends on choice of MITD FG - Well-spaced with height restriction MSQ Mean stocked quadrant (All count only acceptable trees) 11 Total Density All trees or all healthy trees Total:

19 trees 3800 sph 50 m2 plot 2m 12 Well-spaced Density All trees a Minimum Inter-tree Distance (MITD) apart WSP: 9 trees 1800 wsph 50 m2 plot 2m 13 Free-growing Density Well-spaced trees taller than a minimum height Remove Short Trees First 50 m2 plot 2m 14 Free-growing Density Well-spaced trees taller than a minimum height Now look at the wellspaced trees remaini

ng FG: 6 trees 1200 fgsph 50 m2 plot 2m 15 Mean Stocked Quadrant (MSQ) Count of acceptable tree in each quadrant ? MSQ: 3 filled quadrant s or, is it 4? 50 m2 plot 2m 16 Example Density Map showing spatial distributions 900 sph (nominal density) 17 Which type of Density to use?

(assuming even-aged stands) Total - All trees (regardless of spacing) Easy to measure Projected Merchantable Volume (PMV) is sensitive to site index misspecification PMV very sensitive to spatial distribution misspecification 18 PMV (80 yrs) vs Total at 15 years (SI = 20) Projected Volume at 80 yrs Lodgepole Pine at Site Index of 20 0 500 1000 Total Density at 15 years 1500 2000 Us i ng TASS ver si on v20524 19 PMV (80 yrs) vs Total at 15 years (SI = 23) Projected Volume at 80 yrs

Lodgepole Pine at Site Index of 23 0 500 1000 Total Density at 15 years 1500 2000 Us i ng TASS ver si on v20524 20 PMV vs Total: Bigger SI > Waiting 20 yrs Projected Projected Volume Volumeatat100 80 yrsyrs Lodgepole Pine at Site Index of 2320 0 500 1000 Total Density at 15 years 1500 2000 Us i ng TASS ver si on v20524

21 Which type of Density to use? (assuming even-aged stands) Well-spaced - depends on choice of MITD. Not so easy to measure but PMV less sensitive to spatial distribution misspecification FG - Well-spaced with height restriction More sensitive to site index and to Stand age for ages less than 30 years or so (and in the field, more sensitive to brush and competition) 22 PMV vs WS at 15 years Projected Volume at 80 yrs Lodgepole Pine at Site Index of 23 0 500 1000 Well-Spaced Density at 15 years 1500 2000 Us i ng TASS ver si on v20524 23

PMV vs FG at 15 years Projected Volume at 80 yrs Lodgepole Pine at Site Index of 23 0 500 1000 Free-growing Density at 15 years 1500 2000 Us i ng TASS ver si on v20524 24 Which type of Density to use? (assuming even-aged stands) MSQ Mean stocked quadrant Easier to measure PMV less sensitive to spatial distribution misspecification Not as familiar to foresters Capped at 4 which occurs at all higher densities even extremely high densities 25 PMV vs MSQ at 15 years Projected Volume at 80 yrs

Lodgepole Pine at Site Index of 23 0.0 0.5 1.0 1.5 2.0 MSQ at 15 years 2.5 3.0 3.5 4.0 Us i ng TASS ver si on v20524 26 Relationships between Density Measures 27 WS and FG vs Total Density at 15 years Lodgepole Pine at Site Index of 23 2000 1500

1500 Free-growing Density at 15 years Well-spaced Density at 15 years Lodgepole Pine at Site Index of 23 2000 1000 500 0 1000 500 0 500 1000 1500 Total Density at 15 years 2000 2500 3000 UsingTASS version v20524

0 0 500 1000 1500 Total Density at 15 years 2000 2500 3000 UsingTASS version v20524 28 WS and FG vs Total Density effect of Site Index Lodgepole Pine at Site Index of 2023 2000 1500 1500 Free-growing Density at 15 years Well-spaced Density at 15 years Lodgepole Pine at SitSite Index of 2023 2000

1000 500 0 1000 500 0 500 1000 1500 Total Density at 15 years 2000 2500 3000 UsingTASS version v20524 0 0 500 1000 1500

Total Density at 15 years 2000 2500 3000 UsingTASS version v20524 29 WS and FG vs Total Density effect of Species (SI = 20) Lodgepole White SpruPine ce atatSitSiteeInIndexdexofof2023 2000 1500 1500 Free-growing Density at 15 years Well-spaced Density at 15 years Lodgepole White SpruPine ce atatSiSitteeIndex Indexofof2020 2000 1000 500

500 0 1000 0 500 1000 1500 Total Density at 15 years 2000 2500 3000 UsingTASS version v20524 0 0 500 1000 1500 Total Density at 15 years 2000 2500

3000 UsingTASS versi on v20524 30 MSQ vs Total and WS Density at 15 years Lodgepole Pine at Site Index of 23 4.0 3.5 3.5 3.0 3.0 2.5 2.5 MSQ at 15 years MSQ at 15 years Lodgepole Pine at Site Index of 23 4.0 2.0 2.0 1.5 1.5

1.0 1.0 0.5 0.5 0.0 0 500 1000 1500 Total Density at 15 years 2000 2500 3000 UsingTASS version v20524 0.0 0 500 1000 WS Density at 15 years

1500 2000 UsingTASS versi on v20524 31 But, what about all those trees? 32 Stands with the same WS density produce about the same Volume Curves for PL at Site Index 20 Well-spaced of 1200 at 15 years 1600 Total Spatial Trees at Volum Distributio 15 e at 80 n years yrs 1400 1200 Well- spaced or Free-Growin g Density 1000 Regular

1202 393 Natural 2336 385 600 Clump (3) 3199 378 400 Clump (2) 3669 378 200 Clump (1) 6224 380 800 0

Nomin al Density 5 10 15 20 Stand Age 1276 3906 25 30 2500 6944 35 3460 UsingTASS version v20524 33 Density values at 15 years (about 1200 wsph) Spatial Distribution Nominal Total Wellspaced Freegrowing

Total at 80 yrs Volume at 80 yrs Regular 1276 1202 1181 928 1087 393 Natural 2500 2336 1196 840 1114 385 Clump (3) 3460

3199 1217 958 1123 378 Clump (2) 3906 3669 1203 978 1092 378 Clump (1) 6944 6224 1151 1014 1070 380

34 But, what about all those trees? Curves for PL at Site Index 20 Well- spaced of 1200 at 15 years Curves for PL at Site Index 20 Well-s paced of 1200 at 15 years 1600 7000 1400 6000 500 400 1200 5000 300 4000 Total Density Merchantable Volume Well- spaced or Free-Growin g Density 1000 800 3000

200 600 2000 400 100 1000 200 0 5 10 15 20 Stand Age 25 30 35 UsingTASS version v20524 0 0 10 20

30 40 50 Stand Age 60 70 80 90 0 100 UsingTASS version v20524 Green: Regular at 1276 Red: Natural at 2500 Blue: Clumpy(3) at 3460 Black: Clumpy(2) at 3906 Purple: Clumpy(1) at 6944 35 Density values at 15 years (about 700 wsph) Spatial Distribution Nominal Total Wellspaced

Freegrowing Total at 80 yrs Volume at 80 yrs Regular 816 775 775 608 733 352 Natural 1111 1049 736 473 786 332 Clump (3)

1372 1276 696 469 695 295 Clump (2) 1736 1627 715 517 702 283 Clump (1) 3086 2860 706 595 757

305 Projected volumes not as close for lower wellspaced densities 36 But, what about all those trees? Curves for PL at Site Index 20 Well-spaced of 700 at 15 years Curves for PL at Site Index 20 Well-s paced of 700 at 15 years 1600 3000 500 1400 400 1200 2000 300 Total Density Merchantable Volume Well-spaced or Free-Growing Density 1000 800 200 600 1000

400 100 200 0 5 10 15 20 Stand Age 25 30 35 UsingTASS version v20524 0 0 10 20 30 40 50 Stand Age

60 70 80 90 0 100 Usi ngTASS versi on v20524 Green: Regular at 816 Red: Natural at 1111 Blue: Clumpy(3) at 1372 Black: Clumpy(2) at 1736 Purple: Clumpy(1) at 3086 37 What spatial distribution to use? How can we tell from field data which spatial distribution best matches the stand? There are several indices in the literature, e.g. Pielous index of dispersion or Morisitas index. We could also consider the ratio of the total trees to the well-spaced trees, both readily available from survey data. Preliminary work shows that this ratio is a simple function of the total trees. Ive been thinking about this for years, but havent been able to pull anything together yet. 38 Fort St John District Data District collected 895 standard silviculture

survey plots in many but not all of the Multiblock strata of the Fort St John Pilot Project (15 year old cutblocks) Also collected MSQ data plots divided into quadrants and presence of an acceptable tree determined for each quadrant values 0 to 4. Plots placed into 18 strata, regardless of cutblocks Three species groups: Pl, Pl/Sx, Sx Wide range of site index observed 39 WS and FG vs Total Density Fort St John District Data Curves for PL at Site Index 20 2000 1500 1500 Free-growing Density at 15 years Well-spaced Density at 15 years Curves for PL at Site Index 20 2000 1000 500 0 Species Group

1000 500 0 1000 2000 3000 Pl 4000 5000 Total Density at 15 years PlSx 6000 Sx 7000 0 8000 pl Species Group 0 1000 2000

3000 Pl 4000 5000 Total Density at 15 years UsingTASS version v20524 Data plotted without regard to estimated site index of the data PlSx 6000 Sx 7000 8000 pl UsingTASS version v20524 40 MSQ vs Total & WS Density Fort St John District Data 3.5 3.5 3.0 3.0 2.5

2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 Species Group Curves for PL at Site Index 20 4.0 MSQ at 15 years MSQ at 15 years Curves for PL at Site Index 20 4.0 0 1000

2000 3000 Pl 4000 5000 Total Density at 15 years PlSx 6000 Sx 7000 0.0 8000 pl Species Group 0 500 1000 Pl WS Density at 15 years UsingTASS version v20524 Data plotted without regard to estimated site index of

the data PlSx 1500 Sx 2000 pl UsingTASS version v20524 41 Post-free growing Survey Study FREP project with Alex Woods in Smithers Sixty stands in two areas declared free- growing between 1987 and 2001 were randomly selected using RESULTS Stands re-surveyed in 2005 (Lakes) and 2006 (Okanagan) using standard silviculture survey methodology and current forest health standards. FREP is now piloting a Stand Development Monitoring (SDM) program based on this work. 42 Purpose of Free-Growing Policy: free-growing requirements ensure that reforested stands remain successfully reforested. Forest Practices Board Special Report No. 16 (2003), The licensee obligation to create freegrowing stands is one of the few measurable results under the Forest

43 Features of the Silviculture Survey Uses 50 m2 plots (3.99 m radius -- 1/200th ha) Usually 1 plot per hectare placed in survey area Count number of acceptable, well-spaced trees Trees must be a minimum tree height to be counted in Free-growing surveys Well-spaced is defined by the Minimum Inter- tree Distance (MITD) Count is capped by the M-value (this is the equivalent plot count for the Target Stocking Standard, TSS, i.e., 44 Post-FG Surveys Stand Ages Declaration Post Free-Growing Age Range Lakes Okanagan Lakes Okanagan < 12 years 19

13 -- -- 12 - 18 years 35 26 9 8 19 - 21 years 4 11 9 2 22 - 28 years 2 10 34 23 29 - 33 years

-- -- 6 22 > 33 years -- -- 2 5 Average Age: 14 yrs 16 yrs 24 yrs 27 yrs 45 WS Density vs Total Density Lakes & Okanagan Data At Curves for PL at Site Index 20 Declaration 2000

At Post FG Survey Curves for PL at Site Index 20 2000 1500 Well-s paced Density at 25 years Well-spaced Density at 15 years 1500 1000 500 0 Age at Declaration 1000 500 0 1000 2000 3000 4000 5000 Total Density at 15 years

. 19-21 6000 7000 < 12 22-28 8000 12-18 UsingTASS version v20524 0 0 Age at PostFG Survey 1000 2000 3000 4000 5000 Total Density at 25 years 6000 . 19-21 29-33 7000

8000 12-18 22-28 >33 Dot colours show different age range of the cutblocks Curves use stand age of 15 or 25 years UsingTASS version v20524 46 WS Density vs Total Density Lakes & Okanagan Data At Curves for PL at Site Index 20 Declaration 2000 At Post FG Survey Curves for PL at Site Index 20 2000 1500 Well-s paced Density at 25 years Well-spaced Density at 15 years 1500 1000 1000

500 0 Study 500 0 1000 2000 3000 4000 5000 Total Density at 15 years Lakes 6000 7000 0 8000 Okanagan Study UsingTASS version v20524 0

1000 2000 3000 4000 5000 Total Density at 25 years Lakes 6000 7000 8000 Okanagan UsingTASS version v20524 Dot colours show cutblocks from different areas Curves use stand age of 15 or 25 years 47 Percent of stands falling below minimum stocking thresholds based on mean and LCL decision rules 70 57 60 Percent 50 40

60 48 % NFG (mean) % NFG (LCL) 37 33 30 18 20 10 18 7 0 Lakes Okanagan Strathcona Headwaters 48 Post FG Question: Should stands at 25 years of age (or older) have about the same well-spaced and freegrowing densities as at declaration? Or should these values have decreased, and if so, by how much?

Used TASS and TIPSY with the new output density variables to assess this. 49 Post FG Question: Curves for PL at Site Index 20 Using the Natural Dis tribution ' Total density at age 15 are shown above each curve 1600 3629 1400 1200 1000 Well-spaced or Free-Growing Density Nominal Densities were 3906, 2500, 1600, and 1111 2322 1502 800 1049 Solid lines show Well-spaced

Densities 600 400 200 0 5 10 15 20 Stand Age 25 30 35 40 Dashed lines are Free-growing Densities UsingTASS version v20524 50 Post FG Question: Curves for PL at Site Index 20 Using the Moderate Clumpy (1) Dis tribution '

Total density at age 15 are shown above each curve 1600 1400 1200 Nominal Densities were 3906, 2500, 1600, and 1111 Well-spaced or Free-Growing Density 1000 3634 800 600 2331 400 1473 1048 Solid lines show Well-spaced Densities 200 0 5

10 15 20 Stand Age 25 30 35 40 Dashed lines are Free-growing Densities UsingTASS version v20524 51 Answer to Post FG Question: Well-spaced Densities should decline a little from declaration to 25 or 30 years Free-growing Densities should either increase or hardly change depending upon the site index and tree age at declaration. That is, the MSS at 25 or 30 years should probably not be different from that at declaration. Under optimum conditions, stands at 25 or 30 years should still pass the same numerical FG tests as at declaration.

52 Percent of stands falling below minimum stocking thresholds based on mean and LCL decision rules 70 57 60 Percent 50 40 60 48 % NFG (mean) % NFG (LCL) 37 33 30 18 20 10 18 7 0 Lakes Okanagan

Strathcona Headwaters 53 Conclusions Spatial distribution and site index have a significant impact on PMV it is important to have good estimates for effective modeling. Well-spaced density minimizes these impacts, especially near target densities. Under optimum conditions, stands passing the FG tests at declaration should still pass them 10 to 20 years later. 54 The MITD reduces the effect of gaps in the spatial distribution It defines WS and FG density AND it helps maintain the Ministrys risk at a reasonable level 55 MITD and Projected Volume Losses Remember that there are many assumptions in all of the graphs in this presentation. Remember to look more at the TRENDS or patterns than the specific values these are more likely to remain the same under a different set of assumptions than would the specific values presented.

56 MITD and Projected Volume Losses Lodgepole Pine at Site Index of 23 Using the Natural Spatial Distribution 2.5 At MITD Minimum Inter-tree Distance 2.0 1.0 of 2 .0 m we see ~ 3% volume loss at 1200 fpgh 0.5 But at 700 1.5 0 0.0 400 600 800

1000 Free-growing Density 1200 1400 we have >7% volume loss 57 MITD and Projected Volume Losses Lodgepole Pine at Site Index of 23 Using the Clumped (3) Spatial Distribution 2.5 At MITD of Minimum Inter-tree Distance 2.0 2 .0 m we see 3 - 4% volume loss at 1200 fpgh 1.5

1.0 0.5 0.0 But at 700 400 600 800 1000 Free-growing Density 1200 1400 we have 1516 % 58 volume loss At TSS and MITD = 2 m, volume losses similar regardless of spatial distribution Lodgepole Pine atSite Index of 23 Using the Natural Spatial Distrib ution Lodgepole Pine at Site Index of 23 Using the Clumped (3) Spatial Distribution 2.5 2.0 2.0

1.5 1.5 Minimum Inter-tree Dis tance Minimum Inter-tree Distance 2.5 1.0 1.0 0 0.5 0.0 0.5 400 600 800 1000 Free-growing Density 1200 1400 0.0

400 600 800 1000 1200 1400 Free-growing Density 59 MITD and Projected Volume Losses At the target stocking of 1200 fgph with an MITD of 2.0 m, we see a similar volume loss regardless of spatial distribution. BUT at the minimum stocking of 700 fgph, the volume loss increases from ~7% for the natural distribution to ~15% for the standard clumped distribution in TIPSY. For the more clumpy distributions, the volume loss at 1200 remains about the same, but at the minimum the losses rise to about 20%. 60 What Lodgepol if ePiwe reduce the MITD? ne at Site Index of 23 Using the Natural Spatial Distribution 2.5

Reducing the MITD increases the volume loss. Increasing the MSS from 700 to 800 compensat es for this. Minimum Inter-tree Distance 2.0 1.5 1.0 0 0.5 0.0 400 600 800 1000 Free-growing Density 1200

1400 61 What Lodgepol if ePiwe reduce the MITD? ne at Site Index of 23 Using the Clumped (3) Spatial Distribution 2.5 Reducing the MITD increases the volume loss. Increasing the MSS from 700 to 830 compensat es for this. Minimum Inter-tree Distance 2.0 1.5 1.0 0.5 0.0

400 600 800 1000 Free-growing Density 1200 1400 62 At TSS and MITD = 1.5 m, volume losses differ more wrt spatial distribution Lodgepole Pine atSite Index of 23 Using the Natural Spatial Distrib ution Lodgepole Pine at Site Index of 23 Using the Clumped (3) Spatial Distribution 2.5 2.0 2.0 1.5 1.5 Minimum Inter-tree Dis tance Minimum Inter-tree Distance 2.5

1.0 1.0 0 0.5 0.0 0.5 400 600 800 1000 Free-growing Density 1200 1400 0.0 400 600 800 1000 1200

1400 Free-growing Density 63 Changing the MITD Changing the MITD from 2.0 m to 1.5 m without any other compensating changes can substantially increase the projected volume losses and the Ministrys risk. Projected volume losses at the TSS of 1200 fgsph are less sensitive to spatial distribution misspecification than at the MSS of 700 fgsph when an MITD of 2.0 m is used. 64 The M-value keeps poor stratification and/or heterogeneous strata from increasing the Ministrys risk too greatly 65 What if we dont stratify? (And average density is at MSS=700) 200 fgph 2000 fgph What proportion of area can be understocked? 66

What if we dont stratify? (And average density is at MSS=700) 200 fgph 2000 fgph The proportion of area that can be understocked 72% !! 67 What if we use the M-value? (And average density is at MSS=700) 200 fgph 2000 fgph The proportion of area that can be understocked only 50% 68 What if we dont use the M-value? (And average density is at MSS=700) 200 fgph 2000 fgph The proportion of area that can be understocked 72% !! 69 Percent Understocked Area

(with an overall average of 700 fpgh) Understocke d Density (fgph) 0 200 400 600 650 Density (fgph) in Stocked Areas 800 1000 1200 1600 2000 12.5 % 17 % 25 % 50 % 67 % 30 % 42 % 56 % 65 % 38 50 75 86 % % % % 50 62 83 91

% % % % 64 75 90 95 % % % % 72 81 93 96 % % % % 70 How does this effect the Projected Volumes? All the points on the following graphs represent cutblocks with an average density at the MSS value of 700 fgph. The projected volume loss increases the greater the disparity between the understocked and stocked densities. The M-value limits the possible extreme projected volume loss.

71 Average density of 700 fgph 280 100 260 90 240 600 800 220 1100 160 300 1200 60 200 1400 1600 120 1800

100 100 2000 50 Understocked Density (fgph) 40 0 80 30 60 20 Natural Distribution 40 20 0 0 10 20 30 40

50 Percent of cutblock understocked 60 70 80 Percent Stocked Density (fgph) 140 70 400 1000 180 Volume (m3/ha) 500 900 200 80 90 100

10 0 72 Average density of 700 fgph (Stocked density of 800 fgph) 280 100 260 90 240 600 800 220 1100 160 300 1200 60 200 1400 1600

120 1800 100 100 2000 50 Understocked Density (fgph) 40 0 80 30 60 20 Natural Distribution 40 20 0 0 10 20

30 40 50 Percent of cutblock understocked 60 70 80 Percent Stocked Density (fgph) 140 70 400 1000 180 Volume (m3/ha) 500 900 200

80 90 100 10 0 73 Average density of 700 fgph (Stocked density of 2000 fgph) 280 100 260 90 240 600 800 220 1100 160 300 1200 60

200 1400 1600 120 1800 100 100 2000 50 Understocked Density (fgph) 40 0 80 30 60 20 Natural Distribution 40 20 0

0 10 20 30 40 50 Percent of cutblock understocked 60 70 80 Percent Stocked Density (fgph) 140 70 400 1000 180 Volume (m3/ha) 500

900 200 80 90 100 10 0 74 Average density of 700 fgph (Stocked density of 1200 fgph) 280 100 260 90 240 600 800 220 1100 160

300 1200 60 200 1400 1600 120 1800 100 100 2000 50 Understocked Density (fgph) Percent Stocked Density (fgph) 140 70 400 1000

180 Volume (m3/ha) 500 900 200 80 40 0 80 30 60 20 40 0 10 Natural Distribution 20 0 10 20

30 40 50 Percent of cutblock understocked 60 70 80 90 100 0 75 Decision Rules LCL Decision Rule - NFG decisions MSS (Ministrys risk) Incorrect NFG 100 decisions occur here. 90

80 Ideal Decision Curve LCL Decision Rule % NFG Decis ions 70 NFG is correct decision in this area. 60 50 40 30 20 10 0 0 200 400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200

1400 1600 77 Clumped distribution LCL Decision Rule - NFG decisions MSS (Ministrys risk) 95 % Ministrys risk LCL Decision Rule 78 Clumped distribution LCL Decision Rule - NFG decisions (Ministrys risk) This decision rule sets 5% as the maximum risk for accepting as stocked an understocked stand. That is, no more than 5 out of 100 truly understocked stands would be accepted as free-growing. Or, we would correctly identify at least 95 out of 100 understocked stands as not freegrowing. 79 LCL Decision Rule - NFG

decisions MSS (Ministrys risk) 100 Incorrect NFG decisions occur here. 90 80 Mean Decision Rule % NFG Decis ions 70 LCL Decision Rule NFG is correct decision in this area. 60 50 40 30 20 10 0 0 200

400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200 1400 1600 80 Clumped distribution Mean Decision Rule - NFG decisions MSS (Ministrys risk) 95 % Mean Decision Rule Ministrys risk with LGL rule LCL Decision Rule Ministrys risk with Mean rule 50 %

81 Clumped distribution Mean Decision Rule - NFG decisions (Ministrys risk) This decision rule sets 50% as the maximum risk for accepting as stocked an understocked stand. That is, no more than 50 out of 100 truly understocked stands would be accepted as free-growing. Or, we would correctly identify at least 50 out of 100 understocked stands as not freegrowing. 82 Comparing Decision Rules (Ministrys risk) Which is better: LCL: At least 95 out of 100 understocked stands correctly identified as such, or Mean: At least 50 out of 100 understocked stands correctly identified as such? 83 Mean & LCL Decision MSS Rules 100

90 80 Mean Decision Rule % NFG Decis ions 70 LCL Decision Rule NFG is correct decision in this area. 60 50 40 30 20 10 0 0 200 400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000

1200 1400 1600 84 Clumped distribution Decision Rules Effect of Variability (Ministrys risk) LCL: Ministrys risk of 5% is always at the MSS. Mean: Ministrys risk of 5% changes depending upon variability but is always at a true free-growing density less than the MSS. 85 LCL Decision Rule Variability (Ministrys risk at the MSS) 100 90 80 % Reject Decis ions 70 60 Rejected 50

Accepted 40 30 20 10 0 0 200 400 600 700 800 Free-growing Density (fgph) 1000 1200 1400 1600 86 Mean Decision Rule Variability (Ministrys risk at some density < MSS) 100 90 80 % Reject Decis ions

70 60 Rejected 50 Accepted 40 30 20 10 0 0 200 400 600 700 800 Free-growing Density (fgph) 1000 1200 1400 1600 87 Decision Rules Effect of Variability

(Ministrys risk) LCL: Ministrys risk of 5% is always at the MSS = 700 fgph. Mean: Ministrys risk of 5% in graph ranges from 420 to 570 -- > but is always less than 700 fgph. This is an example only and other ranges are possible. 88 Projected Volume: FG Density (MITD = 2.0 m) 280 260 240 220 LCL Decision Rule 200 Projected Volume (m3/ha) 180 160 140 Regular 120 100

Natural 80 Clumped 60 Mean Decision Rule 40 20 0 0 200 400 600 1000 700 800 Free-Growing Density (fgph) at MITD of 2.0 m 1200 1400 1600 89 Projected Volume (MITD = 1.6 m)

280 260 240 220 200 LCL Decision Rule Projected Volume (m3/ha) 180 160 140 Regular 120 100 Natural 80 Clumped 60 Mean Decision Rule 40 20 0 0

200 400 600 1000 700 800 Free-Growing Density (fgph) at MITD of 1.6 m 1200 1400 1600 90 Projected Volume: Total Density (MITD = 0.0 m) 280 260 240 220 200 Projected Volume (m3/ha) 180 160 140 Regular 120 100

Natural 80 Clumped 60 40 Mean Decision Rule LCL Decision Rule 20 0 0 200 400 600 1000 700 800 Free-Growing Density (fgph) at MITD of 0.0 m 1200 1400 1600

91 Mean Decision Rule (Ministrys risk is high and unknown) Can easily lose a lot of projected volume if used carelessly. Could still control risk if require variability (measured by SE, LCL or CV) to be within a narrow limit. This might require larger sample sizes. Easier to simply use LCL rule at a lower MSS. 92 Licensees Risk LCL Decision Rule - FG decisions MSS (Licensees risk) 100 90 80 Ideal Decision Curve LCL Decision Rule % NFG Decis ions 70

FG is correct decision in this area. 60 50 40 Incorrect FG decisions occur here. 30 20 But where do we measure the risk? 10 0 0 200 400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200 1400

1600 94 Clumped distribution LCL Decision Rule - FG decisions MSS (Licensees risk) 100 90 80 Ideal Decision Curve LCL Decision Rule % NFG Decis ions 70 60 At TSS? 50 40 30 20 10 0 0 200

400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200 1400 1600 95 Clumped distribution LCL Decision Rule - FG decisions MSS (Licensees risk) 100 90 80 Ideal Decision Curve LCL Decision Rule % NFG Decis ions 70

60 50 40 30 20 10 5% 0 At fixed error rate? 0 200 400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200 1400 1600 96 Clumped distribution LCL & Mean Decision Rules

MSS 100 Ideal Decision Curve 90 80 Mean Decision Rule LCL Decision Rule % NFG Decis ions 70 FG is correct decision in this area. NFG is correct decision in this area. 60 50 40 30 20 10 0 0 200

400 600 800 Free-Growing Density (fgph) at MITD of 2.0 m 1000 1200 1400 1600 97 Clumped distribution Conclusions Stocking standards are currently measured in free-growing density NOT total density. The purpose of the Silviculture Survey is to make a decision. The LCL decision rule controls the Ministrys risk of incorrectly accepting understocked strata. 98 Conclusions The MITD is an essential part of the definition of free-growing. The M-value is important for

heterogeneous or clumpy areas, BUT Stratification can do a better job of ensuring that understocked areas are properly identified. 99 Conclusions Considerable preparation work is required to demonstrate that we will get the same results as before if: We change the method of determining if free-growing has been achieved. We change current standards from density measures to projected volume measures. 100