1

A Method For Determining Stand Relative Density

And Using The Information to Prescribe a Thinning

For Even-aged Northern Hardwoods In New York State

Ralph D. Nyland

Distinguished Service Professor Emeritus – Silviculture

Department of Forest and Natural Resources Management

Based On A Methodology Described in:

Marquis, D.A., R.L. Ernst, and S.L. Stout. 1984. Prescribing silvicultural

treatments in hardwood stands of the Alleghenies. US For. Serv. Gen. Tech.

Rpt. NE-96.

Nyland 2017

Roach and Gingrich 1968

Roach and Gingrich developed the first stocking guide

as an aid in planning thinning ...

FOR OAK STANDS

… for oak community types

in the central states

2

But Roach later tried it with Allegheny hardwoods ...

... with poor results

After Roach 1977

Until he accounted for species composition ...

... separating

CAPS (bc, wa, and tulip-poplar)

OTHERS (all other species)

… demonstrating that species composition made a difference

3

With a separate line for each species group ...

... each A line to represent

a different proportion

of basal area in CAPs

Roach 1977

And then adding a family of B lines ...

... one for each species group

(set at 60% of each A line)

B

... and this worked well

in most cases

4

So Stout asked ...

WHAT IF I add additional species groups?

But experience suggested that this guide needed

enhancement ...

... particularly to account for stands with

lots of red maple

TREE-AREA RATIO (TAR)

- a mathematical device for apportioning

ground area by size of stem diameter

- where the area of the a stand is expressed

as a function of D & D2

- (TAR) of all trees present = 1.00

She approached it using the Tree-Area Ratio (TAR) …

5

RELATIVE DENSITY = (TAR)

- expressed in CENTACRES

- the TAR’S for different species can be compared

to determine how to best account for species

composition when assessing competition in and

and among forest stands

-TAR values differ between CAPS and two other

species groups

Stand relative density = (Tree relative density)

Tree relative density = ƒ (Tree diameter and species)

Stout and Nyland 1986

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So three groups ...

CAPS – bc, wa, & tulip

HM-BE – hm, be, stm, oaks except ro

OTHER – all other species

This defines the contribution of individual trees to stand relative density …

... by species

... e.g., for 16-inch tree

Stout and Nyland 1986

... the CAPS

... the red maple group

... the hm-be group

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Stout 1990

Stout later showed that

the number, shape, and position of the lines

depends upon the species mix and regional conditions ...

Generally, the NY relative density factors …

… work best for stands with ≤ 40% – 50%

of basal area in black cherry and white ash

… use WKSHTNY

… for stands with more BC & WA, use the

PA relative density factors

… use WKSHTPA

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Stout 1990

… only two species groups works better

for even-aged northern hardwoods in New York

But …

… and with simple tests showing the difference in

calculated relative density using PA and NY factors

Using NY stand data

9

So how to use it ...

... in practical application

Tim Davis 2001

So complicated … ...

Marquis et al. 1984

Try this field sheet ...

RD factors

included

(Pennsylvania)

10

Acceptable

Growing

Stock

Quality considered ...

Unacceptable

Growing

Stock

Poor trees, too ...

Marquis 1984

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Unacceptable Growing Stock (UGS)

(… what Nyland uses)

-- a fruiting body on the main stem*

-- holes in the main stem

-- ≥25% of major branches dead or dying

in the upper crown

*Also signs of beech bark disease

This example defines UGS as follows …

These criteria identify high risk trees that likely

will die or deteriorate within a 15-20 year period …

… making them candidates for salvage

UGS …

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And species group …

Marquis et al. 1984

Three groups for northern hardwoods ...

CAPS – BC, WA, Tulip

HM-BE – HM, BE, STM, oaks except RO

OTHER – all other species

BC – black cherry BE – American beech

WA – white ash STM – striped maple

Tulip – tulip-poplar RO – red oak

HM – sugar maple

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Also by diameter class

within each grouping …

Marquis et al. 1984

Commonly used diameter classes …

SAP – 1.0-5.5 inches dbh

POLE -- 5.6-11.5 inches dbh

SST -- 11.6-17.5 inches dbh

LST -- ≥17.6 inches dbh*

* Some people separate MST and LST.

We will not.

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Commonly used diameter classes …

SAP – 1.0-5.5 inches dbh

POLE -- 5.6-11.5 inches dbh

SST -- 11.6-17.5 inches dbh

LST -- ≥17.6 inches dbh*

* Some people separate MST and LST.

We will not.

This approach includes all trees

1.0 inches and larger …

… that makes the assessment more objective

… that shows us the entire stand structure

… that better depicts species stratification

in a stand

… 1.0 inches and larger

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As an example:

Develop thinning prescriptions for Cuyler C-7

using relative density measures to control the

intensity of a crown thinning …

Stand __________

1.20

0.77

0.67

0.64

0.64

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

1.20

0.77

0.67

0.64

0.64

USING THIS WORK SHEET …

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1.20

0.77

0.67

0.64

0.64

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

0.63

1.70

0.44

0.76

0.76

1.20

0.77

0.67

0.64

0.64

But note that it uses the NY RD factors …

… with NO difference between CAPS and RM group

You need point sample information

about a stand to determine stand

relative density …

… by convention we install at least 15 point samples in an even-aged

stand

… using a BAF-10 prism

… and laid out at random

or along a randomly

placed grid of points

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Heiberg Forest

Stand 97

Grid points at 2- x 2-chain intervals

Dashed lines show boundaries of

study plots to receive specified

treatments.

So let’s use this stand

to illustrate the process …

North

… providing a data set that looks like this

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For clarity presented here in a printed format …

So lets figure out how to do the calculations

and develop a prescription for crown thinning …

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… this instruction sheet

shows how to do

the calculations using

a pocket calculator

FIRST determine the BA conversion factor …

[Carry this to 3 places]

BA Convert = (BAF factor / # point samples)

= 10 / 18 = 0.556

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Now the BA per diameter class …

BA/ac = (Trees sampled * BA Conversion factor)

So for the Small Sawtimber (SST) in CAPs …

14 trees * 0.556 = 7.78

[Carry this and subsequent

calculations to 2 places]

… and done for all cells on the sheet … done for all cells by row and column

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… then sum the totals from each segment

to determine overall stand conditions

Next determine the average diameters …

D = average for all size classes

DM = average for trees ≥ 6 inches dbh

… using the separate diameter calculation worksheet

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… using this worksheet

… first writing in the

basal area by size class

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… then making these calculations for D

DIA BA

FOR FOR

CLASS CLASS = Di * BAi

3 1.67 = 5.01

8 45.57 = 364.56

14 68.35 = 956.90

20 9.45 = 189.00

26 4.45 = 115.70

TOTAL 129.49 1631.17 / 129.49 12.6 D

>=6" 127.82 1626.16 / 127.82 12.7 DM

… a weighted average

across all diameter

classes

… using BA/size class

as the weighting factor

DIA BA

FOR FOR

CLASS CLASS = Di * BAi

3 1.67 = 5.01

8 45.57 = 364.56

14 68.35 = 956.90

20 9.45 = 189.00

26 4.45 = 115.70

TOTAL 129.49 1631.17 / 129.49 12.6 D

>=6" 127.82 1626.16 / 127.82 12.7 DM

… done using only

poles and larger

… and those for DM

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… use WKSHTNY to get an answer

quickly and accurately from BAF-10

prism point data

… as follows

But once you understand the process …

HBG 97

Heiberg Forest

4 Nov 09

2009

Class

After studying the instructions pages, open the FIELD DATA page…

… and enter stand

identification information

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… also the

number of

point samples

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HBG 97

Heiberg Forest

4 Nov 09

2009

Class

Then enter the prism BASAL AREA FACTOR …

Class

18

Don’t forget to enter this 10

HBG 97

Heiberg Forest

4 Nov 09

2009

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NEW YORK VERSION

FIELD TALLY FORM AND MANUAL

SUMMARY WORKSHEET

Cherry Group Red Maple Group

AGS Dot tally BA/a RDf RD/a

SAP 1-5 0 0.00 1.70 0.00

POLE 6-11 1 0.56 0.44 0.25

SST 12-17 14 7.78 0.63 4.90

MST 18-22 9 5.00 0.76 3.80

LST 23+ 6 3.33 0.76 2.53

AGS Total 30 16.67 11.48

HBG 97 (18 sample points)

Then go to the

SUM page …

… entering the field

tally data in the

yellow columns

Automatically giving you a summary output … Class

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DIA BA

FOR FOR

CLASS CLASS = Di * BAi

3 1.67 = 5.01

8 45.57 = 364.56

14 68.35 = 956.90

20 9.45 = 189.00

26 4.45 = 115.70

TOTAL 129.49 1631.17 / 129.49 12.6 D

>=6" 127.82 1626.16 / 127.82 12.7 DM

To calculate D and DM …

… PUSH buttons on

the D / DM page

HBG 97 18 pt samples … the results

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This stand has …

129 ft2/ac of basal area

a DM of 12.7 inches

a relative density of 92%

71% relative density of AGS

… shown in the box at the bottom of the SUM page

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Now lst’s use these findings to prescribe a thinning …

… taking out 35% of the relative density

… but not reducing the stand below 60%

Note: if taking 35% reduces RD below 60%,

adjust the intensity to leave 60%

You should find these values on the MARKING page …

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As a next step, determine what to cut from trees of

different sizes to do a crown thinning …

… that generally means taking 1/3 of the cut

from trees > D or DM

… and 2/3 of the cut from trees < D or DM

… representing a crown thinning

Luckily, Marquis et al. (1984) used research

data and experience to translate that into a

DISTRIBUTION OF CUT chart …

It presents a suggestion for what they call a

COMMERCIAL and a COMBINED thinning …

… the former does thinning

only among trees ≥ 6 inches dbh

… both versions of

Crown thinning

… numbers indicate the % of

cut RD to take out of each

size class

… based on the stand DM or D

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… so WKSHTNY enters a trial distribution of cut

from that table

… for DM 12.72

… rounding

dbh to the

nearest

inch

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… so WKSHTNY enters a trial distribution of cut

from that table

… with this result

Then as a trial run …

… it calculates the amount to

remove from each diameter class

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Cut / dia class = RD in class * % to remove

= 34.18 * 0.68 = 21.61

Col 2 = the proportion of total cut to take from

each diameter class …

… so the SUM of Col 2 = 100%

BUT …

… does that approach make sense for this stand

… will it satisfy the objectives

Given an objective that thinning should reduce UGS

of sawtimber size to salvage the volume …

… at least to the degree feasible …

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Note that unthinned stands at high latitude

often have appreciable numbers of trees

affected by ice, snow, and wind …

… with some trees of all size classes

having past injuries and other

defects that make them UGS

Unacceptable Growing Stock (UGS)

(… what Nyland uses)

-- a fruiting body on the main stem*

-- holes in the main stem

-- ≥25% of major branches dead or dying

in the upper crown

*Also signs of beech bark disease

So try this …

… copy the original UGS

to this column

Given that objective …

… the trial prescription would not work

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… and subtract the

original UGS from

the trial cut

… Col 3 – Col 6

… a NEGATIVE result

means some UGS

will still remain

So …

… adjust the cut to remove UGS of ST sizes

Indicating that you

must make a change

to satisfy the assigned

objectives …

Remember the objective …

… reduce UGS in sawtimber classes to the degree possible

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… the first trial cut

would leave some UGS

of SST

… so adjust the cut to

remove all the UGS of SST

… the first trial cut

would leave some UGS

of SST

… so adjust the cut to

remove all the UGS of SST

… try starting this process by removing UGS from LST,

then go to MST, and then to SST

… that seems to work best

As a \practical matter …

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… but DO NOT drop

RD below the target

level

… here 60%

… WKSHTNY determines the proportion to cut

from each diameter class

Finally …

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% to cut = 9.96 45.23 = 0.22 or 22% :

… translated into 1/5 for practical application

1/5

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The end point of the analysis …

MARK

NONE

3/5

1/5

1/4

1/4

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AGS

&

UGS

TOTAL STAND

SAPS

POLES

SSAW

MSAW

LSAW

COL

NONE

3/5

1/5

1/4

1/4

… look at the original basal area

To get a picture of the effect in more tangible terms …

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… and see what proportion of basal area to cut

Cut BA = Original BA * % RD to cut

= 68.35 * 0.22 = 15.05 ft2/ac

… and check the expected residual basal area

Residual BA = Original BA - Cut BA

= 68.35 - 15.05 = 53.3 ~ 53 ft2/ac ~

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… and what we LEAVE

THE RESIDUAL STAND

(Ft2/ac)

SAPS 2

POLES 20

SST 53

MST 7

LST 3

TOTAL 85

And what would we cut …

DIA CUT

CLASS BA/AC

SAP --

POLE 26

SST 15

MST 2

LST 1

ALL 44

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… when all else fails, read the instructions again

As my mother-in-law’s friend commonly said …

So what to do now?

And she said …

Background reading:

Chapter 17, in Nyland, R.D. 2002. Silviculture: Concepts and Applications. Waveland Press. Long Grove, IL.

Sources cited:

Marquis, D.A., R.L. Ernst, and S.L. Stout. 1984. Prescribing silvicultural treatments in hardwood stands

of the Alleghenies. US For. Serv. Gen. Tech. Rpt. NE-96.

Roach, B.A. 1977. A stocking guide for Allegheny hardwoods and its use in controlling intermediate cuttings.

US For. Serv. Res. Pap. NE-373.

Roach, B.A., and S.F. Gingrich. 1968. Even-aged silvicutlure for upland central hardwoods. US Dept. Agric.,

Agric Handbk. No. 355.

Stout, S.L., and R.D. Nyland. 1968. Role of species composition in relative density measurement in

Allegheny hardwoods. Can. J. For. Res. 16:574-579.

Stout, S.L. 1990. Progress Report For Relative Density In Northern Hardwoods Throughout The Northeast.

US For. Serv. For. Sci. Lab, Warren, PA.