USDA Forest Service Res. Note RMRS-RN-8. 2000 1

Abstract—We estimate number of tree species in National

Forest populations, using the nonparametric estimator,

CM f c fc c s 2 2 1

2 = + ( ) 2 / , where cs is the number of species

observed, c1 and c2 are the numbers of species occurring once

and twice, respectively, in the sample plots, and f is the finite

population correction for sampling. Data from the Current

Vegetation Survey (CVS) of Region 6 of the USDA Forest

Service were used to estimate the number of tree species with

a plot close in size to the Forest Inventory and Analysis (FIA)

plot and the actual CVS plot for the 5.5 km FIA grid and the

2.7 km CVS grid.

Ignoring seedlings, FIA missed seven out of 55 species

estimated by the CVS plot on the 2.7 km grid, five with the 5.5

km grid. For observed tree species, FIA missed three species

observed on the CVS plot. For the 2.7 km grid including

seedlings, FIA missed six out of 53 species, four tallied on the

CVS plot were not tallied on the FIA plot. For the 5.5 km grid,

FIA missed six estimated to be there with CVS, CVS observed

five species not observed by FIA. Ignoring seedlings, the

estimate indicates that five species were not observed on the

CVS plots, with seedlings two species were not observed, but

number of species estimated was less than if seedlings were

not considered in estimation. Similar results were obtained by

zones and forests except that the results were sometimes

erratic because of the small sample sizes involved. Even for the

large sample of over 10,000 plots over the whole region, the

number of species estimated if seedlings were included was

two less (53 versus 55) than if they were ignored in estimation.

One more species was actually observed when seedlings were

included than when they were ignored (51 versus 50).

There is a definite dilemma. Clearly a first step in protecting rare and endangered species is to determine if they are

there. For this purpose the CVS plot and grid intensity are a

must at a minimum but still not adequate. To ensure all

species are observed requires an even more intensive grid.

The problem may be more acute though in Oregon and

Washington with the large number of tree species occurring

there than in other areas that are more homogeneous in tree

species such as the Intermountain West.

Keywords: number of tree species, plot design, plot intensity,

nonparametric estimation

Introduction ____________________

The USDA Forest Service is charged with inventorying all forest lands in the United States through its

Forest Inventory and Analysis (FIA) units. Traditionally interest has been primarily in timber-oriented

variables and the focus has been on timberland. However, the information collected can also be used for

other ecological variables of interest. One parameter

that has been ignored is estimating the number of tree

species in a population. The objective of this paper is to

apply the estimator CM2f recommended by Schreuder

and others (1999) to all National Forests in Region 6 of

the Forest Service combined, in zones, and by National

Forest using the Current Vegetation Survey (CVS) plot

used by Region 6 and a plot more or less equivalent to

the current FIA plot used for both the 2.7 km (1.7 mile)

grid of the Region and the 5.5 km (3.4 mile) national

grid used by FIA to determine what is gained by an

increase in plot sample size and grid intensity.

Review of Literature _____________

Considerable literature is available on estimating

the number of species in a population. It is usually a

difficult prediction problem1 but may be less so for FIA

United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

Research Note

RMRS-RN-8

October 2000

Estimating the Number of Tree Species

in Forest Populations Using Current

Vegetation Survey and Forest Inventory

and Analysis Approximation Plots and

Grid Intensities

Hans T. Schreuder

Jin-Mann S. Lin

John Teply

Hans T. Schreuder is Mathematical Statistician, Rocky Mountain

Research Station, Fort Collins, CO. Jin-Mann S. Lin is a Graduate

Research Assistant, Department of Statistics, Colorado State

University, Fort Collins, CO. John Teply is a former Forester (retired)

Region 6, Portland, OR.

1

Bunge and Fitzpatrick (1993) note that I. J. Good told them in

1991 that it is usually not possible to estimate the number of unseen

species but only a lower bound to that number because there are often

many extremely rare species.
2 USDA Forest Service Res. Note RMRS-RN-8. 2000

and similar surveys because with FIA a probabilistic

sample is used to estimate the number of species in a

finite rather than a hypothetical population (or situation). Other data sources may be available to support or

contradict the findings obtained and lead to improved

estimation techniques. In some other disciplines this

is not possible, for example, how many words did

Shakespeare know or how many different coins by year

of issue are still in existence (Efron and Thisted 1976).

Bunge and Fitzpatrick (1993) note that if n sample

units are drawn from a population consisting of C

classes (species), where C is unknown, then the outcome can be represented by N* = (n1, ..., nC), where ni is

the number of sample units in class i. The observed

sample is c = (c1, ..., cn) where cj is the number of classes

represented j times in the sample {ni: ni = j}, j = 1, ..., n;

and c c s j

j

n

=

=

Â1

is the number of classes in the sample. C

is to be estimated based on the sample c.

Bunge and Fitzpatrick (1993) summarized the methods available for estimating C. They are not optimistic

about using data-analytic methods. They argue that

deriving a relationship between an expected number of

observed classes and a function of the size of the sample

from a sampling model is likely to be less efficient than

direct estimation of C by survey sampling methods.

Based on a simulation study, Bunge and others (1995)

recommend a nonparametric estimator CM3, discussed

later, for estimating number of species in a population.

We believe that nonparametric estimators will have

to be used to estimate number of tree species because

forest populations are frequently disturbed.

For situations where no assumptions are made about

the probabilities, pi, of selecting species, no unbiased

estimators exist. And the bias of any estimator of C

based on the sample c has no bound over all possible

populations because there is no way to disprove the

existence of an arbitrarily large number of classes with

very small probabilities. A nonparametric lower bound

estimator (CM2) of C is

CM c c c 2 2 s 1

2 = + ( ) 2 / (1)

Another nonparametric estimator (CM3) based on

the idea of sample coverage is (Chao and Lee 1992):

CM c

c n

c

c n

s 3

1 1 1

1

1

2 = - +

/ / ( ) - gˆ

= - [ ] + n

n c

c c s 1

1

2 gˆ (2)

where 

)

g is an estimator of g, the coefficient of variation

of the pi’s. Chao and Lee propose CM3 because the

coverage of a sample is m p = ( ) >

=

Â i x

i

c

I i 0

1

where m = the

sum of the probabilities pi for the c observed classes in

the sample and I = 1 if class i is in the sample and = 0

otherwise. Sample coverage (CCOV) can be estimated

by mˆ = 1 – c1/n under the hypothesis m = cs/C. Thus:

CCOV = cs/(1 – c1/n) (3)

and CM3 = CCOV 

+

c1 2

mˆ g

) .

Bunge and Fitzpatrick (1993) note that there is some

empirical and theoretical evidence that CM3 is preferable to CM2 when used in actual applications.

Schreuder and others (1999) recommend the

use of CM2f for use with FIA data where

CM f f CM f c 2 21 = +- s * * ( ) . If c2 = 0, CM2f is undefined. In this case, we set it equal to cs.

They note that a large sample is necessary for reliable estimation, something on the order of at least 500

to 700 sample units.

Criteria for Selecting a Preferred

Estimator ______________________

Given the heavy emphasis on protecting rare species,

it is desirable to not overestimate the number of tree

species in a National Forest. In this way we have some

assurance that if our estimate is larger than the observed number of species, cs, that at least some species

were missed in our sample. In addition, although CVS

has a large sample of ground plots in each forest, the

sample sizes are still small for several forests. Hence,

good performance with a (relatively) small sample size

is desirable as is consistency over populations. Convergence of estimation to C as nÆN is guaranteed by

adding the finite population correction f N n

N = ( ) - to

each estimator in an appropriate manner. Hence, the

criteria recommended for selecting an estimator are:

1. It should not overestimate C.

2. Given several estimators, select the one consistently closest to C for small sample sizes over a

wide range of populations.

Given the criteria used and this caveat, Schreuder

and others (1999) recommended CM2f in estimating C

for a given population, and it was used here. They also

note that large sample sizes of the order of 500 to 700

units are desirable and probably essential for reliable

estimation of number of species. This is to a considerable degree due to the fact that the nonparametric

estimators such as CM2f rely on the number of times a

given species occurs only once or twice in the sample to

improve the estimation beyond the actual number of

species, cs, observed. For small sample sizes anomalous

results can be expected because of that, and when this

appears to be the case we will compare the actual

number of species observed instead.
USDA Forest Service Res. Note RMRS-RN-8. 2000 3

FIA and CVS Methods for

Estimating C ___________________

In FIA we select a cluster of four circular 0.017 ha (1⁄24

acre) subplots on a 5.5 km (3.4 mile) grid for forest

surveys (Birdsey and Schreuder 1992). The four subplots can be considered a sample of a 1 ha primary

sample unit. The CVS plot design used by Region 6 of

the Forest Service uses a 1 ha primary sample unit

subsampled by five locations. At each of the latter,

three subplots are located and trees are measured on

0.017 ha (1⁄24 acre) subplots for 7.6 to 32.8 cm (3.0 to 12.9

inch) trees, 1⁄5.3 acre (0.076 ha) for trees 32.9 to 81.0 cm

(13.0 to 31.9 inch) trees on the east side and 32.9 to

121.9 cm (13.0 to 47.9 inches) on the west side, and

trees larger than 81.0 cm (32.0 inches) on the east side

or larger than 121.9 cm (48.0 inches) on the west side

(Max and others 1996). Seedlings—trees less than 7.4

cm (3.0 inches)—are tallied on 0.004 ha (1⁄100 acre)

subplots. Every tree selected is identified by species,

and n plots are selected with each plot (cluster) of trees

containing various tree species.

The FIA plot was not implemented on the 1 ha CVS

plots, but we approximated it by considering it

equivalent to sampling a 1⁄5 ha subplot of the CVS

plot, representing roughly 1⁄5 of the CVS plot.

All CVS plots available, 10,567 plots, were used. In

addition this was broken down by individual National

Forests, which in turn were combined into six ecological zones recognized as such by the Region.

Results ________________________

Assuming the subsampled 1⁄5 ha plot selected at

random from the five 1⁄5 ha subplots in the CVS plot to

be equivalent to an FIA plot and the subsampled 1 ha

plot as the CVS plot, we conclude the following using

the 2.7 km grid ignoring seedlings (table 1). Clearly we

will have more confidence in the results for the larger

sample sizes and we start with those:

1. All forests combined for a sample size of 10,567

plots.

- Missed 7 out of 55 species using FIA plot

relative to the CVS plot using CM2f.

- 5 of the species were missed with the CVS plot

at this intensity of sampling.

- Three of the species tallied on the CVS plot

were not tallied on the FIA plot.

Table 1—Estimating number of species with various subplot sizes (with observed number in parentheses) using CM2f on a 2.7 km

grid intensity.

Forest 1⁄5 ha 2⁄5 ha 3⁄5 ha 4⁄5 ha 1 ha Missed Sample

Deschutes 24(19) 19(19) 20(20) 23(21) 31(23) 7(4) 717

Fremont 13(12) 13(13) 13(13) 13(13) 14(13) 1(1) 570

Gifford Pinchot 23(23) 24(24) 25(24) 25(24) 27(25) 4(2) 602

Malheur 11(11) 11(11) 12(12) 12(12) 12(12) 1(1) 720

Mt. Baker-Snoqualmie 17(17) 17(17) 21(20) 21(21) 22(21) 5(4) 580

Mt. Hood 22(22) 24(23) 23(23) 26(25) 25(25) 3(3) 477

Ochoco 9(9) 9(9) 9(9) 9(9) 9(9) 0(0) 443

Okanogan 19(19) 19(19) 19(19) 19(19) 21(20) 2(1) 581

Olympic 18(18) 20(19) 20(20) 20(20) 23(21) 5(3) 287

Rogue River 25(25) 32(27) 29(27) 28(28) 30(30) 5(5) 299

Siskiyou 35(31) 32(31) 32(31) 34(32) 32(32) –3(1) 482

Siuslaw 13(13) 28(15) 15(15) 20(16) 21(17) 8(4) 315

Umatilla 11(11) 12(11) 11(11) 11(11) 11(11) 0(0) 609

Umpqua 33(29) 31(30) 36(31) 35(33) 34(33) 1(4) 481

Wallowa-Whitman 13(12) 12(12) 14(13) 13(13) 13(13) 0(1) 887

Wenatchee 28(24) 25(24) 26(25) 28(26) 36(30) 8(6) 707

Willamette 28(27) 27(27) 29(28) 28(28) 28(28) 0(1) 734

Winema 16(14) 14(14) 14(14) 15(15) 15(15) –1(1) 510

Colville 14(14) 14(14) 16(15) 15(15) 15(15) 1(1) 566

Ecological Zone 1 25(25) 26(26) 26(26) 26(26) 28(28) 3(3) 1,469

Ecological Zone 2 32(30) 31(31) 32(32) 38(33) 35(33) 3(3) 1,526

Ecological Zone 3 36(36) 36(36) 37(37) 38(38) 41(39) 5(3) 1,262

Ecological Zone 4 21(21) 22(21) 22(22) 32(24) 38(25) 17(4) 2,240

Ecological Zone 5 14(14) 14(14) 14(14) 14(14) 14(14) 0(0) 2,216

Ecological Zone 6 27(25) 25(25) 27(26) 29(27) 37(31) 10(6) 1,854

All forests 48(47) 49(49) 49(49) 50(50) 55(50) 7(3) 10,567

Note: The cs values are listed in the parentheses. FIA samples at about 1⁄5 the rate of R6 CVS, about 1⁄5 ha versus 1 ha.
4 USDA Forest Service Res. Note RMRS-RN-8. 2000

Table 2—Estimating number of species with various subplot sizes using CM2f (with observed number in parentheses) on a 5.5 km

grid intensity.

Forest 1⁄5 ha 2⁄5 ha 3⁄5 ha 4⁄5 ha 1 ha Missed Sample

Deschutes 19(17) 17(17) 17(17) 17(17) 17(17) –2(0) 187

Fremont 11(11) 11(11) 11(11) 11(11) 11(11) 0(0) 143

Gifford Pinchot 21(21) 22(23) 22(24) 22(22) 22(22) 1(1) 168

Malheur 9(9) 9(9) 10(10) 10(10) 12(11) 3(2) 188

Mt. Baker-Snoqualmie 17(15) 18(16) 21(19) 19(19) 20(19) 3(4) 197

Mt. Hood 19(18) 20(20) 21(21) 22(22) 22(22) 3(4) 140

Ochoco 7(7) 7(7) 7(7) 7(7) 7(7) 0(0) 114

Okanogan 18(18) 19(19) 20(19) 19(19) 19(19) 1(1) 207

Olympic 19(16) 16(16) 18(17) 17(17) 17(17) –2(1) 80

Rogue River 33(25) 30(27) 35(27) 32(27) 33(28) 0(3) 87

Siskiyou 28(26) 27(26) 27(26) 26(26) 26(26) –2(0) 143

Siuslaw 9(9) 10(10) 10(10) 12(12) 12(12) 3(3) 79

Umatilla 9(9) 9(9) 9(9) 9(9) 10(10) 1(1) 183

Umpqua 21(21) 24(24) 33(25) 33(27) 28(28) 7(7) 131

Wallowa-Whitman 10(10) 10(10) 11(11) 11(11) 11(11) 1(1) 266

Wenatchee 21(21) 22(21) 27(22) 27(22) 43(25) 22(4) 236

Willamette 25(23) 26(25) 27(25) 25(25) 25(25) 0(2) 213

Winema 14(13) 14(14) 14(14) 14(14) 14(14) 0(1) 137

Colville 13(13) 13(13) 13(13) 13(13) 13(13) 0(0) 146

Ecological Zone 1 42(24) 24(24) 26(25) 25(25) 25(25) –17(1) 445

Ecological Zone 2 26(26) 28(28) 29(29) 32(30) 31(30) 5(4) 432

Ecological Zone 3 33(32) 36(34) 34(34) 35(35) 35(35) 2(3) 361

Ecological Zone 4 18(18) 18(18) 18(18) 18(18) 18(18) 0(0) 581

Ecological Zone 5 11(11) 11(11) 12(12) 12(12) 13(13) 2(2) 637

Ecological Zone 6 23(23) 24(23) 26(24) 26(24) 39(26) 16(3) 589

All forests 44(43) 54(46) 46(46) 47(47) 47(47) 5(4) 3,045

Note: The cs values are listed in the parentheses. FIA samples at about 1⁄5 the rate of R6 CVS, about 1⁄5 ha versus 1 ha.

2. For zones 1 through 6, with sample sizes ranging

from 1,262 to 2,240:

- 0-17 species were missed with FIA plot relative to the CVS plot using CM2f.

- 0-6 were missed in actual observations.

- CVS missed from 0-6 species estimated to be

there with CM2f.

3. For individual forests with sample sizes ranging

from 287 to 887:

- The FIA plot missed from 0-8 species relative to

CVS with CM2f with the exception of the Siskiyou

and Winema forests, where the FIA plot estimates,

respectively, 3 and 1 more species than CVS. This

is likely due to the small sample size yielding odd

results at times, depending on the number of times

1 species is observed only once or twice.

- When looking at the actual observed number

of species, certainly a safer statistic in this

case of smaller sample sizes, 0-6 species are

missed, 1 for the Siskiyou and 1 for the Winema

with the FIA plot relative to the CVS plot.

- Estimation with the CVS plot using CM2f

indicates that up to 8 species were not observed in the field.

When we use the 5.5 km FIA grid, we get the following

equivalent results to the above (table 2):

1. For all forests, with a sample size of 3,045 plots:

- FIA missed 5 species using both CM2f and the

actual number of species observed relative to

the CVS plot at this grid intensity.

- CVS observes all 47 species estimated to be

there with CM2f.

2. For ecological zones 1 through 6, with sample sizes

of 361 to 637:

- From 0 to 16 species were missed with FIA

relative to CVS with CM2f estimation except

that 17 extra species were estimated with FIA

for zone 1.

- With actual number of observed species, FIA

missed 0 to 4 species observed by the CVS plot.

3. For individual forests, with sample sizes of

79-266:

- From 0 to 22 species were missed by FIA CM2f

estimation relative to CVS CM2f estimation

except for -2 for the Deschutes, Olympic, and

Siskiyou.

- With these small sample sizes it is clearly

better to rely on only the observed species,
USDA Forest Service Res. Note RMRS-RN-8. 2000 5

and there the FIA plot misses from 0 to 7

species.

When we also include seedlings, we obtain the following results for the 2.7 km grid (table 3).

1. All forests combined. For this sample of size 10,720

plots:

- We miss 6 out of 53 species using the FIA plot

relative to the CVS plot using CM2f.

- 2 of the species were missed with the CVS plot

at this intensity of sampling.

- 4 of the species tallied on the CVS plot were

not tallied on the FIA plot.

2. For zones 1 through 6, with sample sizes ranging

from 1,275 to 2,277:

- 1 to 5 species were missed with FIA plot

relative to the CVS plot using CM2f; 1 to 5

were missed in actual observations.

- CVS missed from 0 to 2 species estimated to

be there with CM2f.

3. For individual forests with sample sizes ranging

from 289 to 910:

- The FIA plot misses from 0 to 21 species

relative to CVS with CM2f with the exception

of the Deschutes, Siskiyou, and Umpqua

Forests, where the FIA plot estimates, respectively 10, 1, and 17 more species than

CVS. This is likely due to the small sample

size as indicated earlier.

- When looking at the actual observed number

of species 0-6 species are missed, 3 for the

Deschutes, 1 for the Siskiyou, and 5 for the

Umpqua.

- Estimation with the CVS plot using CM2f

indicates that up to 18 species may not have

been observed in the field.

When we use the 5.5 km FIA grid, we get the following

equivalent results to the above (Table 4):

1. For all forests, with a sample size of 3083 plots:

- FIA respectively misses 6 and 5 species using

CM2f by the actual number of species observed relative to the CVS plot at this grid

intensity.

- CVS observes 49 out of 53 species estimated

to be there with CM2f.

2. For ecological zones 1 through 6, with sample sizes

of 365 to 649:

- From 0 to 7 species were missed with FIA

relative to CVS with CM2f estimation except

Table 3—Estimating number of species with various subplot sizes using CM2f (with observed number in parentheses) on a 2.7 km

grid intensity—includes seedlings.

Forest 1⁄5 ha 2⁄5 ha 3⁄5 ha 4⁄5 ha 1 ha Missed Sample

Deschutes 34(21) 24(22) 32(24) 29(24) 24(24) –10(3) 724

Fremont 13(12) 13(13) 13(13) 13(13) 14(13) 1(1) 578

Gifford Pinchot 24(24) 27(26) 27(27) 27(27) 27(27) 3(3) 616

Malheur 12(12) 12(12) 12(12) 12(12) 12(12) 0(0) 738

Mt. Baker-Snoqualmie 25(20) 22(20) 24(22) 25(23) 25(23) 0(3) 587

Mt. Hood 27(27) 32(28) 35(30) 32(30) 34(30) 7(3) 483

Ochoco 9(9) 9(9) 9(9) 9(9) 9(9) 0(0) 459

Okanogan 22(22) 24(22) 22(22) 22(22) 23(23) 1(1) 583

Olympic 18(18) 22(20) 20(20) 20(20) 22(21) 4(3) 289

Rogue River 29(27) 29(29) 29(29) 30(30) 50(32) 21(5) 303

Siskiyou 34(32) 32(32) 32(32) 33(33) 33(33) –1(1) 486

Siuslaw 13(13) 23(15) 15(15) 16(16) 25(17) 12(4) 320

Umatilla 11(11) 12(12) 12(12) 12(12) 12(12) 1(1) 613

Umpqua 57(31) 34(32) 41(33) 33(33) 40(36) –17(5) 486

Wallowa-Whitman 12(12) 14(13) 15(14) 14(14) 16(15) 4(3) 910

Wenatchee 29(25) 25(25) 27(26) 30(28) 35(31) 6(6) 715

Willamette 27(27) 27(27) 28(28) 29(29) 30(30) 3(3) 742

Winema 14(14) 14(14) 14(14) 15(15) 15(15) 1(1) 516

Colville 16(15) 15(15) 16(16) 16(16) 17(17) 1(2) 572

Ecological Zone 1 27(27) 30(29) 31(29) 29(29) 30(30) 3(3) 1,492

Ecological Zone 2 33(33) 42(34) 42(36) 43(37) 38(37) 5(4) 1,545

Ecological Zone 3 40(38) 38(38) 39(39) 40(39) 42(42) 2(4) 1,275

Ecological Zone 4 23(23) 27(24) 33(25) 34(26) 27(26) 4(3) 2,277

Ecological Zone 5 14(14) 14(14) 14(14) 14(14) 15(15) 1(1) 2,261

Ecological Zone 6 31(28) 29(28) 31(29) 35(31) 35(33) 4(5) 1,870

All forests 47(47) 49(49) 51(49) 56(51) 53(51) 6(4) 10,720

Note: The cs values are listed in the parentheses. FIA samples at about 1⁄5 the rate of R6 CVS, about 1⁄5 ha versus 1 ha.
6 USDA Forest Service Res. Note RMRS-RN-8. 2000

that 10 extra species were estimated with FIA

for zone 6.

- With actual number of observed species, FIA

missed 0-4 species observed by the CVS plot.

3. For individual forests, with sample sizes of 80

to 273:

- From 0 to 8 species were missed by FIA CM2f

estimation relative to CVS CM2f estimation

except for -1 for the Deschutes, Fremont, and

Malheur forests, 5 for the Gifford-Pinchot, 3

for the Umpqua, and 13 for the Wenatchee.

- Considering only observed species, the FIA

plot missed from 0 to 5 species.

- Note that the number of species estimated by

CM2f including seedlings is smaller than ignoring seedlings even though 1 more species

is actually observed when seedlings are included. This too illustrates the problem of

small sample sizes. Even though a sample of

over 10,000 plots is usually considered very

large, it can still cause problems for rare

events such as estimating the presence of a

rare tree species.

Discussion _____________________

The FIA plot size and grid intensity is clearly not as

good in Region 6, Oregon and Washington, to estimate

the number of tree species relative to the CVS plot and

grid intensity. Three species tallied on the CVS plot

were not observed on the FIA plot sampling both on the

2.7 km grid. FIA misses seven out of 55 species estimated to be there with the CVS CM2f estimator but the

CVS plot only observed 50 of those species. With the 5.5

km grid, FIA missed five of the species observed on the

CVS plot whereas at this intensity the CVS plots

observe all 47 species estimated to be there with the

CM2f estimator. Region 6 is rich in tree species, so the

problem may not be as acute in several other regions

such as the Intermountain West, but a similar problem

with missed species may well occur in the South.

Clearly there is a dilemma from an ecological point of

view in several parts of the country. A first step in

protecting rare and endangered species is to determine

if they are there, and even the CVS plot with its 2.7 km

intensity grid does not accomplish that. To ensure that

all species are observed requires an even more intensive grid or perhaps a complete 1 ha tally on the CVS

Table 4—Estimating number of species with various subplot sizes using CM2f (with observed number in parentheses) on a 5.5 km

grid intensity—includes seedlings.

Forest 1⁄5 ha 2⁄5 ha 3⁄5 ha 4⁄5 ha 1 ha Missed Sample

Deschutes 20(18) 20(19) 19(19) 19(19) 19(19) –1(1) 189

Fremont 12(11) 11(11) 11(11) 11(11) 11(11) –1(0) 146

Gifford Pinchot 28(22) 22(22) 23(23) 24(23) 23(23) –5(1) 171

Malheur 12(11) 11(11) 11(11) 11(11) 11(11) –1(0) 193

Mt. Baker-Snoqualmie 16(16) 17(17) 20(19) 19(19) 19(19) 3(3) 198

Mt. Hood 22(22) 28(24) 38(25) 25(25) 30(25) 8(3) 142

Ochoco 7(7) 7(7) 7(7) 7(7) 7(7) 0(0) 117

Okanogan 23(21) 22(22) 22(22) 24(22) 24(22) 1(1) 207

Olympic 16(16) 16(16) 18(17) 18(18) 19(18) 3(2) 80

Rogue River 28(25) 29(27) 27(27) 29(27) 28(28) 0(3) 88

Siskiyou 28(26) 28(26) 29(27) 28(27) 28(28) 0(2) 145

Siuslaw 10(10) 11(11) 11(11) 12(12) 12(12) 2(2) 81

Umatilla 9(9) 11(11) 11(11) 12(11) 11(11) 2(2) 183

Umpqua 31(23) 30(25) 27(25) 28(28) 28(28) –3(5) 132

Wallowa-Whitman 11(11) 11(11) 12(12) 12(12) 12(12) 1(1) 273

Wenatchee 41(23) 23(23) 25(24) 26(25) 28(26) –13(3) 239

Willamette 24(23) 25(25) 25(25) 26(26) 26(26) 2(3) 215

Winema 13(13) 14(14) 14(14) 14(14) 14(14) 1(1) 137

Colville 13(13) 14(14) 14(14) 16(15) 18(16) 5(3) 147

Ecological Zone 1 24(24) 24(24) 26(26) 26(26) 26(26) 2(2) 449

Ecological Zone 2 30(28) 30(30) 31(31) 32(32) 37(32) 7(4) 438

Ecological Zone 3 34(32) 36(34) 35(35) 37(35) 35(35) 1(3) 365

Ecological Zone 4 19(19) 22(20) 20(20) 20(20) 20(20) 1(1) 589

Ecological Zone 5 13(13) 13(13) 13(13) 13(13) 13(13) 0(0) 649

Ecological Zone 6 39(26) 27(26) 29(27) 30(28) 29(28) –10(2) 593

All forests 46(44) 60(47) 55(47) 62(49) 53(49) 6(5) 3,083

Note: The cs values are listed in the parentheses. FIA samples at about 1⁄5 the rate of R6 CVS, about 1⁄5 ha versus 1 ha.
USDA Forest Service Res. Note RMRS-RN-8. 2000 7

plots, neither one of which appears practical with

current funding.

The results show that a large sample size is critical.

With both plots and grids, the CM2f estimator in

several cases estimated a substantial number of species more than observed for small sample sizes. Ideally

one would not estimate number of tree species for small

sample sizes such as for the individual Forests even

with the CVS plot and grid. But if that is not possible,

it is clearly preferred to use the observed number of

species over CM2f because the latter can be quite

misleading for such sample sizes.

References _____________________

Birdsey, R. A.; Schreuder, H. T. 1992. An overview of forest inventory

and analysis estimation procedures in the eastern U.S.—with an

emphasis on components of change. USDA Forest Service, Rocky

Mountain Research Station. Gen. Tech. Rep. RM-214. 11 p.

Bunge, J.; Fitzpatrick, M. 1993. Estimating the number of species: a

review. J. Amer. Stat. Assoc. 88: 364-373.

Bunge, J.; Fitzpatrick, M.; Handley, J. 1995. Comparison of three

estimators of the number of

 species. J. Appl Stat. 22:45-59.

Chao, A.; Lee, S-M. 1992. Estimating the number of classes via

sample coverage. J. Amer. Stat. Assoc. 87: 210-217.

Efron, B.; Thisted, R. 1976. Estimating the number of unseen

species: how many words did Shakespeare know? Biometrika 63:

435-447.

Max. T.A.; Schreuder, H.T.; Hazard, J.W.; Teply, J.; Alegria, J. 1996.

The Region 6 Vegetation Inventory and Monitoring System. USDA

Forest Service, Pacific Northwest Station. Res. Pap. PNW-RP493. 22 p.

Schreuder, H.T.; Williams, M.S.; Reich, R. 1999. Estimating the

number of tree species in a forest population using survey data.

Env. Mon. and Asst. 56:293-303.

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