Optimization of Sampling Methods for Within-Tree Populations of Red ...

SAMPLING

Optimization of Sampling Methods for Within-Tree Populations of Red Oak Borer, Enaphalodes rufulus (Haldeman) (Coleoptera: Cerambycidae) D. J. CROOK,1 M. K. FIERKE,1 A. MAUROMOUSTAKOS,2 D. L. KINNEY,1

AND

F. M. STEPHEN1,3

Environ. Entomol. 36(3): 589Ð594 (2007)

ABSTRACT In the Ozark Mountains of northern Arkansas and southern Missouri, an oak decline event, coupled with epidemic populations of red oak borer (Enaphalodes rufulus Haldeman), has resulted in extensive red oak (Quercus spp., section Lobatae) mortality. Twenty-four northern red oak trees, Quercus rubra L., infested with red oak borer, were felled in the Ozark National Forest between March 2002 and June 2003. Infested tree boles were cut into 0.5-m sample bolts, and the following red oak borer population variables were measured: current generation galleries, live red oak borer, emergence holes, and previous generation galleries. Population density estimates from sampling plans using varying numbers of samples taken randomly and systematically were compared with total census measurements for the entire infested tree bole. Systematic sampling consistently yielded lower percent root mean square error (%RMSE) than random sampling. Systematic sampling of one half of the tree (every other 0.5-m sample along the tree bole) yielded the lowest values. Estimates from plans systematically sampling one half the tree and systematic proportional sampling using seven or nine samples did not differ signiÞcantly from each other and were within 25% RMSE of the “true” mean. Thus, we recommend systematically removing and dissecting seven 0.5-m samples from infested trees as an optimal sampling plan for monitoring red oak borer within-tree population densities. This optimal sampling plan should allow for collection of acceptably accurate within-tree population density data for this native wood-boring insect and reducing labor and costs of dissecting whole trees. KEY WORDS Enaphalodes rufulus, native pest, Cerambycidae, insect sampling, Quercus

Red oak borer, Enaphalodes rufulus (Haldeman) (Coleoptera: Cerambycidae), was recently indicated as an important contributing agent to oak mortality (Quercus spp.) in Arkansas forests (Stephen et al. 2001, Fierke et al. 2005a, b). Heavily attacked trees in the recent outbreak exhibited as many as 58 red oak borer emergence holes per square meter (Fierke et al. 2005a). Those infestation densities were dramatically higher than other published Þndings and may call for a redeÞnition of terms with regard to red oak borer population outbreak densities because Hay (1974) deÞned a “severe infestation” as one beetle emerging per tree. Hay (1974) reported an average of 2.9 active attacks on the bottom 1.8 m of 480 examined trees, and Donley and Rast (1984) examined the entire bole of 144 oaks in Pennsylvania and 277 oaks in Indiana and found the average number of attacks per tree was 2.0 and 3.6, respectively. These numbers are in stark contrast to recent Þndings of Fierke et al. (2005a), who found an average of 30.1 active attacks (current generation galleries) on the basal 1.5 m of 24 trees and 1 Department of Entomology, University of Arkansas, AGRI 319, Fayetteville, AR 72701. 2 Department of Agricultural Statistics, University of Arkansas, AGRI 319, Fayetteville, AR 72701. 3 Corresponding author, e-mail: [email protected].

noted average successful current generation galleries of ⬇600 per tree on 38 northern red oaks. The red oak borerÕs basic biology and 2-yr synchronous life cycle is becoming well known (Hay 1969, 1972a, b, 1974, Donley 1978, Donley and Acciavatti 1980, Solomon 1995, Stephen et al. 2001, Crook et al. 2004, Fierke et al. 2005a). Previous methods for assessing red oak borer densities were based on counting adults caught in emergence traps placed on tree boles (Hay 1972a), by counting “active larval attack sites” near the tree base (Hay 1974) or on whole trees (Donley and Rast 1984). Active attack sites with evidence of frass extrusion are comparable with counts of phloem-feeding galleries initiated by the current generation. Current generation galleries are a preferred variable to measure compared with attack sites on the bark surface, which are distinctive and easily counted but do not heal over and so are cumulative over several red oak borer cohorts (Fierke et al. 2005a). Research is ongoing to understand causes for recent changes in population levels, to evaluate mortality factors acting on within-tree red oak borer populations, and to predict population trends (Stephen et al. 2001, Crook et al. 2004, Fierke et al. 2005a, b). Five red oak borer population variables, attack sites, emer-

0046-225X/07/0589Ð0594$04.00/0 䉷 2007 Entomological Society of America

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gence holes, current generation galleries, live larvae, and previous generation heartwood galleries were measured using intensive whole tree sampling (Fierke et al. 2005a). An acceptably accurate extensive sampling method using subsamples of nine 0.5-m sample bolts taken proportionally from infested tree boles was developed based on intensive data and a rapid estimation procedure that allows grouping of trees into red oak borer infestation history classes (Fierke et al. 2005a, b). Although the nine-sample proportional plan has proven acceptably accurate at high population densities, ⬎25 current attacks/m2 (Fierke et al. 2005a), there may be a more optimal sampling plan for estimating within-tree red oak borer population densities. We use the term “optimum” as did Stephen and Taha (1976), to imply the minimum number of samples needed to yield statistically reliable estimates. The speciÞc objective of this research was to determine an optimal sampling plan for estimating within-tree red oak borer population densities based on average performance considering both precision and accuracy. Density estimates for sampling plans were calculated using variable numbers of 0.5-m sample bolts, taken both randomly and systematically (based on a proportional sampling scheme). We anticipate that the optimum sampling method reported here will help guide future researchers developing sampling plans to obtain accurate within-tree population density data, with minimal dissection of whole trees.

A rapid estimation procedure (REP) (Fierke et al. 2005b), based on crown condition and emergence hole density from 0 to 2 m on the tree bole, enabled separation of trees into three red oak borer infestation history classes. Class I trees had relatively low, class II had moderate, and class III had high red oak borer infestation histories. Using these REP classes, data were combined across more homogeneous groups for comparison of sampling plans to true means and to compare sampling plans to each other. Trees chosen for initial sampling were selected before development of the REP yielding unequal numbers of trees in the different classes. Phloem and xylem tissues for some class III trees had deteriorated to the extent that not all population variables could be measured. Data Analysis. Density estimates based on various extensive sampling plans, using varying numbers of sample units taken both randomly and systematically, were compared with measurements of the entire tree using SAS 9.1 (SAS Institute 2004). An estimator T ⫽ t(X1, . . . , Xn) is deÞned to be an unbiased estimator of an unknown Þxed parameter ␶(␪) if and only if its mean equals the unknown Þxed parameter. All simple random sampling plans of various size will lead to unbiased estimators with variable precision [Var(T)] depending on the sample size. Mean square error (MSE) is composed of two components, variance (precision) and bias of the estimator T (accuracy), and is deÞned as:

Materials and Methods

MSEt共 ␪ 兲 ⫽ Var共T兲 ⫹ 兵Bias其 2

Study Area. Study trees were collected from oakhickory dominated stands in the Ozark National Forest of northern Arkansas. Northern red oaks, Quercus rubra L., infested with red oak borer were selected from three areas: Fly Gap (UTM Zone 15ÐS NAD83 0431660, 3954978), White Rock (UTM Zone 15-S NAD83 412668, 3949429), and Oark (UTM Zone 15-S NAD83 0450792, 3952369). Field Methods. Field research was initiated in March 2002 and concluded in June 2003. Trees were selected based on evidence of red oak borer infestation, accessibility, and varying amounts of crown dieback. Twenty-four trees were felled and intensively dissected following methods previously developed (Fierke et al. 2005a). After tree felling, presence of attack and emergence holes was visually assessed to determine height of infestation up the tree bole. The infested bole was cut into 0.5-m sample bolts, with the initial bolt taken from 0.5 to 1 m. Samples were labeled and transported to the University of Arkansas Forest Entomology Laboratory for intensive dissection. Samples were kept refrigerated at 2⬚C to inhibit red oak borer development until dissection. Red oak borer population parameters measured were phloem-feeding galleries initiated by the current generation or cohort of red oak borer (current generation galleries), live red oak borer, emergence holes on the bark surface, and heartwood galleries formed by previous generations of red oak borer (previous generation galleries).

Systematic plans are inherently biased, resulting in over- or underestimates. We chose, among all sampling plans, random and systematic, the ones with the smallest root mean square error (RMSE). RMSE was calculated by taking square root of MSE, and it accounts for both variance and bias of the estimate compared with a true mean (Mood et al. 1974). Although SE of the estimator T, which equals SD of the estimator T, provides a measure of random sampling error, it fails to account for a systematic bias. For systematic sampling plans, there is no sampling error; therefore, we present data as RMSE values rather than SE (note that for an unbiased sampling method, RMSE would be equal to SE of T). Actual or “true” means and all estimates are given as densities (number/m2) based on bark surface area. Sampling plans using Þve, seven, and nine samples were selected for comparison. All sampling plans included the sample located at 1.5Ð2.0 m because previous red oak borer sampling tended to concentrate observations/efforts on the basal portion of trees (Hay 1972a, 1974, Fierke et al. 2005b). Remaining samples were selected randomly or systematically along the rest of the infested tree bole. For systematic plans using Þve, seven, and nine samples, these were chosen at 30, 50, 70, and 90%, 20, 40, 50, 60, 80, and 90%, and 20, 30, 40, 50, 60, 70, 80, and 90%, respectively, up the infested tree bole. Estimates were also calculated for plans using one half the samples from trees. Odd- and even-numbered samples were both analyzed; how-

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CROOK ET AL.: RED OAK BORER SAMPLING

591

Table 1. Tree and red oak borer pop density (per m2) means (ⴞSE) for 24 trees sampled from the Ozark National Forest in northwestern Arkansas Infestation class

Age

DBH (cm)

Infested height (m)

Current gen. gall.

Live red oak borer

Emergence holes

Previous gen. gall.

I (n ⫽ 12) II (n ⫽ 7) III (n ⫽ 5)

74.8 (2.8) 82.0 (2.5) 83.0 (5.2)

27.6 (1.1) 27.6 (0.9) 31.8 (1.8)

13.6 (0.4) 14.1 (0.7) 14.5 (0.5)

46.4 (11.1) 70.4 (6.2) Ñ

6.0 (2.2) 18.7 (8.3) 6.9 (1.9)

2.9 (0.8) 13.6 (4.0) 29.9 (7.0)

2.2 (0.5) 24.4 (8.4) 66.3 (Ñ)

Class I trees had relatively healthy crowns and a low infestation history, class II trees had declining crowns and a moderate infestation history, and class III trees had poor crowns and a high red oak borer infestation history. Current generation galleries are phloem-feeding galleries initiated by the current generation or cohort of red oak borer. Previous generation galleries are formed by larvae from previous generations of red oak borer. Red oak borer population variables were not measured on all trees. DBH, diameter at breast height.

ever, data are presented only for odd plans because estimates were nearly identical for both. Because random sampling plans can potentially use any set of subsamples from trees, 1,000 separate simulations were run for each tree in an effort to stabilize the mean estimate for each random plan. Before analysis for signiÞcant differences among plans, RMSE values for estimates from each sampling plan (n ⫽ 503) were converted to %RMSE as a function of the true mean. This was done to standardize RMSE values between measured red oak borer variables. Variability in %RMSE values among sampling plans (as the subunit treatments) and REP classes (as the main unit treatments) were evaluated using PROC MIXED (SAS 9.1; SAS Institute 2004) and Tukey honestly signiÞcant difference (HSD) test at ␣ ⫽ 0.05. Results Mean tree and red oak borer population data are summarized by red oak borer infestation history class in Table 1. Tree age for 24 intensively sampled whole trees ranged from 50 to 100 yr, with a mean of 79 yr. Diameter at breast height (dbh) ranged from 22.5 to 36 cm, and mean dbh was 28.5 cm. Infested tree height averaged 13.9 m and ranged from 11 to 17 m. Number of sample bolts per tree ranged from 23 to 35, depending on infested bole height. Counts per tree ranged from 200 to 915 for current generation galleries (n ⫽ 8 trees: 5 class I and 3 class II), 0 to 577 for live red oak borer (n ⫽ 23 trees: 12 class I, 7 class II, and 4 class III),

0 to 671 for emergence holes (n ⫽ 24 trees: 12 class I, 7 class II, and 5 class III), and 7 to 790 for previous generation galleries (n ⫽ 9 trees: 5 class I, 3 class II, and 1 class III). Densities derived from individual whole tree census data (true means) and density estimates derived from the eight sampling plans are listed separately in Tables 2Ð5, for the four red oak borer population variables evaluated. A review of tables indicated that systematic sampling seven or nine samples or one half the tree yielded the smallest RMSE values for the four population variables measured. Percent RMSE values for random plans were signiÞcantly larger than for systematic plans for all population variables (F7,42 ⬎ 3.2, P ⬍ 0.007). Systematic sampling of one half the tree yielded signiÞcantly smaller %RMSEs than either the random plans or the Þve sample systematic plan for current generation galleries, live red oak borer, and emergence holes (F7,191 ⬎ 3.2, P ⬍ 0.0078). Percent RMSE values from systematic sampling one half of the tree were not signiÞcantly different than those from systematic proportional sampling seven or nine samples for any population variables. Percent RMSE values were not signiÞcantly different among REP classes for any population variables (F2,191 ⬍ 3.7, P ⬎ 0.041). Discussion Collection of data for study of red oak borer population dynamics requires sampling techniques based on the red oak borerÕs cryptic and synchronous 2-yr

Table 2. “True” current generation gallery densities for trees in two infestation history classes and density estimates (RMSE) using eight sampling plans

MEAN

MEAN

Class

True

Rnd5

Rnd7

Rnd9

Rnd…

Sys5

Sys7

Sys9

Sys…

I I I I I I II II II II

31.8 51.8 86.0 25.1 30.9 45.1 64.3 79.1 57.0 66.8

28.6 (8.7) 62.0 (16.7) 84.4 (14.3) 22.9 (7.0) 30.9 (5.9) 45.8 (10.5)a 73.0 (16.7) 86.9 (14.2) 69.9 (17.0) 76.6 (16.0)a

30.0 (6.9) 58.5 (12.7) 84.6 (11.8) 23.8 (5.4) 30.6 (5.0) 45.5 (8.3)a 69.8 (13.5) 84.3 (11.3) 65.5 (12.4) 73.2 (12.4)a

30.1 (5.9) 56.0 (9.9) 85.2 (9.5) 24.2 (4.5) 30.6 (4.3) 45.2 (6.8)b 68.2 (10.6) 82.8 (9.4) 62.9 (10.2) 71.3 (10.1)b

30.8 (4.3) 54.9 (7.7) 85.2 (8.2) 24.5 (3.8) 30.7 (3.1) 45.2 (5.4)b 66.5 (7.6) 79.1 (6.4) 59.6 (5.3) 69.0 (6.4)b

33.2 (1.4) 49.4 (2.5) 84.1 (1.9) 25.6 (0.5) 32.9 (2.0) 45.0 (1.6)c 46.3 (18.0) 96.9 (17.8) 77.8 (20.9) 73.7 (18.9)

28.0 (3.8) 57.0 (5.2) 79.7 (6.3) 31.3 (6.2) 35.9 (5.0) 46.4 (5.3)b 62.0 (2.3) 82.1 (3.0) 61.9 (4.9) 68.6 (3.4)c

35.8 (4.0) 53.6 (1.7) 86.2 (0.2) 29.0 (3.8) 36.2 (5.4) 48.1 (3.0)b 54.7 (9.6) 85.7 (6.6) 63.9 (7.0) 68.1 (7.7)b

33.1 (1.2) 52.8 (0.9) 90.1 (4.2) 23.7 (1.5) 27.3 (3.6) 45.4 (2.3)c 62.6 (1.7) 71.5 (7.6) 67.4 (10.5) 67.2 (6.6)b

Root mean square error (RMSE) is given in parentheses beside sampling plan estimates. RMSE is within a16 Ð25, b6 Ð15, or cⱕ5% of the true mean. Rnd, random; Sys, systematic.

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Table 3. “True” live red oak borer densities for trees in three infestation history classes and density estimates (RMSE) using eight sampling plans

MEAN

MEAN

MEAN

Class

True

Rnd5

Rnd7

Rnd9

Rnd…

Sys5

Sys7

Sys9

Sys…

I I I I I I I I I I I I II II II II II II II II III III III III III

12.0 22.2 10.0 8.8 5.5 1.3 0.2 0.7 3.1 1.7 3.9 5.8 45.5 46.7 4.2 10.4 1.9 5.2 5.9 17.1 11.5 1.5 7.8 8.0 7.2

10.1 (4.1) 27.3 (9.5) 8.6 (3.8) 7.3 (4.0) 4.6 (3.2) 1.1 (0.7) 0.1 (0.2) 0.6 (0.7) 2.7 (2.6) 1.4 (1.0) 3.2 (1.3) 5.6 (2.8) 52.1 (15.2) 56.7 (14.8) 5.6 (2.5) 9.5 (4.1) 1.9 (1.0) 4.7 (2.0) 5.6 (1.6) 19.4 (5.9) 10.4 (3.2) 1.3 (0.7) 11.9 (5.3) 6.7 (2.5) 7.6 (2.9)

10.9 (3.1) 25.5 (7.2) 9.0 (2.9) 7.8 (3.2) 4.9 (2.5) 1.1 (0.6) 0.1 (0.2) 0.6 (0.6) 2.7 (2.0) 1.5 (0.8) 3.5 (1.0) 5.6 (2.2) 49.4 (12.6) 53.1 (11.0) 5.0 (2.0) 10.0 (3.4) 2.0 (0.8) 4.9 (1.6) 5.7 (1.4) 18.6 (4.7) 10.7 (2.6) 1.4 (0.6) 10.5 (3.7) 7.1 (1.9) 7.4 (2.2)

11.0 (2.6) 24.3 (5.8) 9.4 (2.5) 8.1 (2.7) 5.0 (2.1) 1.2 (0.5) 0.1 (0.2) 0.7 (0.5) 2.8 (1.7) 1.6 (0.7) 3.6 (0.8) 5.6 (1.8) 48.6 (9.8) 51.1 (9.1) 4.9 (1.7) 9.9 (2.9) 1.9 (0.7) 5.0 (1.3) 5.8 (1.1) 18.2 (3.8)a 11.0 (2.2) 1.4 (0.5) 9.6 (2.9) 7.4 (1.6) 7.3 (1.8)a

11.65 (1.9) 23.9 (4.5) 9.4 (2.0) 8.5 (2.0) 5.2 (1.8) 1.2 (0.4) 0.1 (0.1) 0.7 (0.3) 2.8 (1.5) 1.7 (0.5) 3.8 (0.5) 5.7 (1.4)a 47.2 (7.1) 49.0 (5.6) 4.5 (1.0) 10.2 (2.3) 1.9 (0.5) 5.1 (1.2) 5.9 (0.8) 17.7 (2.6)b 11.3 (1.5) 1.4 (0.3) 9.0 (2.2) 7.6 (1.2) 7.4 (1.3)a

11.1 (1.0) 22.3 (0.0) 8.9 (1.2) 10.6 (1.8) 8.1 (2.7) 0.5 (0.8) 0.5 (0.3) 1.9 (1.2) 4.1 (1.0) 3.3 (1.6) 4.9 (1.0) 6.3 (1.1)a 29.5 (16.0) 65.6 (18.9) 4.5 (0.3) 11.0 (0.6) 1.4 (0.6) 3.5 (1.7) 5.5 (0.5) 17.3 (5.5) 15.3 (3.8) 1.3 (0.2) 10.6 (2.8) 7.8 (0.2) 8.8 (1.7)a

10.7 (1.4) 28.2 (5.9) 8.9 (1.1) 10.0 (1.2) 9.1 (3.6) 1.3 (0.1) 0.3 (0.2) 0.9 (0.1) 2.9 (0.2) 1.0 (0.7) 4.3 (0.4) 6.5 (1.3)a 45.5 (0.1) 49.1 (2.3) 4.9 (0.7) 8.4 (2.0) 1.6 (0.4) 5.8 (0.6) 6.7 (0.8) 17.4 (1.0)b 13.6 (2.1) 1.5 (0.0) 10.9 (3.1) 7.2 (0.8) 8.3 (1.5)a

13.6 (1.5) 24.4 (2.1) 9.7 (0.3) 11.3 (2.5) 7.7 (2.2) 1.3 (0.0) 0.3 (0.1) 1.1 (0.3) 2.3 (0.8) 2.1 (0.4) 4.1 (0.3) 6.5 (1.0)a 38.1 (7.4) 54.0 (7.2) 5.0 (0.8) 11.3 (1.0) 1.7 (0.2) 5.1 (0.1) 6.2 (0.3) 17.3 (2.4)b 13.4 (1.9) 1.2 (0.4) 9.4 (1.6) 6.8 (1.2) 7.7 (1.3)a

11.8 (0.3) 23.8 (1.6) 9.7 (0.3) 8.5 (0.3) 6.1 (0.7) 1.4 (0.1) 0.3 (0.2) 0.6 (0.1) 2.3 (0.8) 1.0 (0.7) 4.1 (0.2) 5.8 (0.5)b 42.4 (3.1) 38.4 (8.4) 5.0 (0.8) 7.9 (2.5) 2.0 (0.0) 4.3 (0.9) 5.7 (0.3) 15.1 (2.3)b 11.5 (0.0) 1.8 (0.3) 5.7 (2.2) 7.5 (0.5) 6.6 (0.8)b

Root mean square error (RMSE) is given in parentheses beside sampling plan estimates. RMSE is within a16 Ð25 or b6 Ð15% of the true mean. Rnd, random; Sys, systematic.

life cycle that provide statistically reliable information coupled with reasonable costs considering labor and time. It is therefore advantageous to determine the minimum or optimum number of samples needed to accurately estimate densities of desired population

variables. This is important because the time needed to sample an entire infested red oak tree can exceed 100 h (Fierke et al. 2005a). Estimates with small %RMSEs relative to a true mean imply they are more acceptable with small bias

Table 4. “True” emergence hole densities for trees in three infestation history classes and density estimates (RMSE) using eight sampling plans

MEAN

MEAN

MEAN

Class

True

Rnd5

Rnd7

Rnd9

Rnd…

Sys5

Sys7

Sys9

Sys…

I I I I I I I I I I I I II II II II II II II II III III III III III III

0.2 2.2 0.9 6.6 0.4 3.3 2.2 3.7 3.3 6.0 8.4 3.1 19.3 30.5 5.5 4.0 1.1 17.6 14.3 13.2 56.0 30.0 19.8 18.2 22.1 29.2

0.2 (0.3) 2.3 (1.2) 0.8 (0.6) 5.5 (2.8) 0.4 (0.5) 2.7 (1.8) 1.8 (1.2) 4.0 (1.5) 2.8 (2.9) 5.8 (2.0) 7.6 (2.6) 2.8 (1.6) 16.7 (8.2) 25.1 (9.4) 4.6 (2.5) 3.8 (1.7) 1.3 (0.7) 15.8 (4.3) 15.2 (3.3) 11.8 (4.3) 50.4 (11.2) 30.2 (6.6) 22.8 (6.3) 22.2 (6.0) 21.2 (4.4) 29.4 (6.9)a

0.2 (0.2) 20.3 (0.9) 0.8 (0.5) 5.8 (2.2) 0.4 (0.4) 2.9 (1.5) 1.9 (1.0) 3.9 (1.3) 2.9 (2.3) 5.9 (1.7) 7.9 (2.2) 2.9 (1.3) 17.4 (6.7) 27.2 (7.2) 4.9 (2.1) 3.8 (1.4) 1.2 (0.6) 16.6 (3.4) 14.7 (2.7) 12.3 (3.4) 51.8 (8.6) 30.2 (5.5) 21.5 (5.0) 20.8 (4.4) 21.7 (3.6) 29.2 (5.4)a

0.2 (0.2) 2.2 (0.8) 0.8 (0.4) 6.2 (1.8) 0.4 (0.3) 3.1 (1.3) 2.0 (0.8) 3.8 (1.1) 3.0 (1.9) 5.9 (1.4) 8.0 (1.9) 3.0 (1.1) 17.8 (5.6) 28.3 (6.1) 5.0 (1.8) 3.9 (1.2) 1.2 (0.5) 17.0 (2.8) 14.7 (2.2) 12.6 (2.9)a 53.3 (7.5) 30.1 (4.8) 21.1 (4.5) 19.8 (3.6) 21.6 (3.0) 29.2 (4.6)a

0.2 (0.2) 2.2 (0.6) 0.9 (0.4) 6.4 (1.4) 0.4(0.3) 3.2 (0.9) 2.1 (0.6) 3.8 (0.9) 3.1 (1.7) 6.0 (1.0) 8.2 (1.2) 3.0 (0.8) 18.7 (4.0) 29.3 (4.0) 5.3 (1.1) 4.0 (1.0) 1.2 (0.4) 17.0 (2.5) 14.5 (1.6) 12.9 (2.1)a 54.6 (4.9) 29.9 (3.3) 20.4 (3.0) 19.4 (2.7) 21.8 (2.5) 29.2 (3.3)b

0.0 (0.2) 2.4 (0.2) 2.3 (1.4) 9.5 (2.9) 0.0 (0.4) 2.6 (0.7) 2.2 (0.0) 4.8 (1.1) 6.9 (3.6) 10.3 (4.3) 8.8 (0.4) 4.1 (1.4) 22.8 (3.4) 22.4 (8.1) 6.9 (1.4) 3.4 (0.7) 0.4 (0.7) 16.3 (1.3) 19.2 (5.0) 13.1 (2.9)a 50.0 (6.1) 37.1 (7.1) 20.0 (0.2) 23.8 (5.6) 22.2 (0.1) 30.6 (3.8)b

0.0 (0.2) 0.9 (1.3) 0.6 (0.3) 6.3 (0.3) 1.1 (0.7) 3.9 (0.6) 1.1 (1.1) 6.3 (2.7) 5.5 (2.2) 5.8 (0.2) 9.2 (0.8) 3.4 (0.9) 15.7 (3.6) 32.0 (1.5) 7.7 (2.2) 3.7 (0.3) 0.6 (0.5) 17.1 (0.5) 14.6 (0.3) 13.1 (1.3)b 58.4 (2.4) 31.9 (1.9) 21.7 (1.9) 21.4 (3.2) 25.8 (3.7) 31.8 (2.6)b

0.0 (0.2) 1.7 (0.5) 1.3 (0.4) 7.9 (1.3) 0.9 (0.4) 3.0 (0.3) 1.2 (1.0) 5.2 (1.6) 4.5 (1.2) 7.5 (1.5) 9.3 (1.0) 3.5 (0.8) 17.8 (1.5) 32.9 (2.4) 6.7 (1.2) 4.1 (0.0) 0.5 (0.6) 19.3 (1.7) 16.2 (1.9) 13.9 (1.3)b 58.1 (2.1) 35.8 (5.8) 20.7 (0.9) 20.4 (2.2) 23.7 (1.6) 31.7 (2.5)b

0.0 (0.2) 3.1 (0.9) 0.8 (0.1) 5.8 (0.8) 0.7 (0.2) 2.6 (0.7) 2.0 (0.2) 4.0 (0.3) 3.5 (0.2) 5.3 (0.7) 8.3 (0.1) 3.0 (0.4)b 20.3 (1.0) 30.1 (0.4) 5.4 (0.1) 3.1 (0.9) 1.1 (0.0) 19.2 (1.7) 13.2 (1.1) 13.2 (0.7)b 51.9 32.1 (2.1) 21.1 (1.3) 14.0 (4.2) 23.9 (1.8) 28.6 (2.7)b

Root mean square error (RMSE) is given in parentheses beside sampling plan estimates. RMSE is within a16 Ð25 or b6 Ð15% of the true mean. Rnd, random; Sys, systematic.

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CROOK ET AL.: RED OAK BORER SAMPLING

593

Table 5. “True” previous generation gallery densities for trees in three infestation history classes and density estimates (RMSE) using eight sampling plans

MEAN

MEAN

Class

True

Rnd5

Rnd7

Rnd9

Rnd…

Sys5

Sys7

Sys9

Sys…

I I I I I I II II II II III

0.7 2.8 4.2 1.0 3.7 2.5 26.5 35.6 7.8 23.3 65.81

0.6 (0.6) 2.8 (1.4) 4.1 (2.8) 0.8 (0.8) 3.0 (1.5) 2.3 (1.4) 22.8 (11.2) 29.4 (10.8) 6.4 (3.3) 19.5 (8.4) 58.17 (13.5)

0.6 (0.5) 2.8 (1.1) 3.9 (2.2) 0.9 (0.6) 3.2 (1.2) 2.3 (1.1) 23.7 (9.3) 31.7 (8.2) 6.9 (2.7) 20.8 (6.7) 60.39 (10.2)

0.7 (0.4) 2.8 (1.0) 4.1 (1.9) 0.9 (0.5) 3.4 (1.0) 2.4 (1.0) 24.4 (7.6) 32.9 (6.9) 7.1 (2.5) 21.5 (5.7)a 62.05 (8.9)

0.7 (0.3) 2.8 (0.8) 4.1 (1.6) 0.9 (0.5) 3.6 (0.7) 2.4 (0.8) 25.7 (5.4) 34.2 (4.6) 7.5 (1.4) 22.5 (3.8)a 64.06 (5.7)

1.1 (0.3) 3.9 (1.2) 6.5 (2.2) 0.5 (0.4) 3.4 (0.3) 3.1 (0.9) 29.7 (3.1) 30.1 (5.5) 8.4 (0.6) 22.7 (3.1)b 58.01 (7.8)

0.8 (0.0) 1.4 (1.4) 3.3 (0.9) 1.8 (0.9) 2.9 (0.7) 2.0 (0.8) 22.3 (4.3) 38.9 (3.3) 9.2 (1.4) 23.4 (3.0)b 67.45 (1.6)

0.6 (0.2) 2.5 (0.2) 3.6 (0.6) 1.7 (0.8) 2.9 (0.8) 2.3 (0.5)a 24.7 (1.9) 39.7 (4.1) 8.3 (0.5) 24.2 (2.2)b 67.28 (1.5)

0.5 (0.3) 4.0 (1.3) 4.8 (0.5) 1.5 (0.5) 3.2 (0.5) 2.8 (0.6)a 26.9 (0.4) 36.4 (0.8) 7.7 (0.1) 23.7 (0.4)c 61.49 (4.3)

Root mean square error (RMSE) is given in parentheses beside sampling plan estimates. RMSE is within a16 Ð25, b6 Ð15, or cⱕ5% of the true mean. Rnd, random; Sys, systematic.

and variance. Estimating population densities with an SE of ⬇25% of the true mean for insect pests that exhibit 10- or 100-fold population changes in a single season is considered sufÞcient for damage assessments and control studies (Church and Strickland 1954). This level of accuracy allows for doubling or halving of the population to be detected and can be used when red oak borer populations undergo dramatic changes. For life table studies involving natural populations, a higher level of precision between 10 and 15% SE is deemed necessary based on the majority of studies done thus far on Þeld, forest, and orchard insects (Lyons 1964, Southwood and Henderson 2000). Data analysis revealed that random plans did not yield acceptable %RMSE values and that systematic sampling plans overall had lower values (Tables 2Ð5). This leads us to recommend a systematic sampling plan as an optimal sampling plan to obtain statistically reliable estimates for red oak borer population variables using a minimum number of samples. Systematic sampling of one half of the tree had the lowest %RMSE, followed by systematic proportional sampling of nine and seven samples, none of which were signiÞcantly different from each other. Greater accuracy of systematic proportional sampling compared with random sampling has been previously documented for within-tree populations of other steminfesting beetles (DeMars 1970, Coulson et al. 1975, Pulley et al. 1977, Nebeker et al. 1978). With respect to studying forest insect outbreaks at an area-wide level, a compromise between accuracy and number of samples taken must be met. Current generation galleries and live red oak borer are important variables for monitoring population densities. Systematic sampling incorporating seven subsamples had %RMSEs below the 25% threshold for these variables (Tables 2 and 3). This was true even in healthy trees with the lowest densities. Based on these results, use of this plan should allow monitoring of population changes both at outbreak densities and at lower historic densities, e.g., less than Þve attacks per tree (Hay 1974, Donley and Rast 1984). This leads us to recommend the seven-sample systematic proportional plan as the optimal sampling plan for monitoring red oak

borer population densities because it would allow an appreciable reduction in the amount of time necessary for sampling. Systematic sampling of one half of the tree yielded %RMSEs close to 15% for population variables evaluated and for trees of varying red oak borer infestation levels. For studies needing a higher level of precision or when monitoring other density parameters, such as previous generation galleries, we recommend that researchers review data tables and individual parameter summaries before deciding on which sampling plan to use. Acknowledgments This research was funded in part by the University of Arkansas Agricultural Experiment Station; the Arkansas Forest Resources Center; and grants from the USDA Forest Service, Special Technology and Development Program, and Forest Health Monitoring programs, Pineville, LA, and Atlanta, GA, and grants from the USDA Forest Service, Southern Research Station, Asheville, NC. We thank K. Thompson for statistical assistance; V. Salisbury, L. Chapman, B. Kelley, S. Wingard, and M. Hardy for help with data collection and processing; and A. Sawyer (APHIS USDA, MA) for reviewing an earlier draft of the manuscript.

References Cited Church, B. M., and A. H. Strickland. 1954. Sampling cabbage aphid populations on brussel sprouts. Plant Pathol. 3: 76 Ð 80. Coulson, R. N., F. P. Hain, J. L. Foltz, and A. M. Mayyasi. 1975. Techniques for sampling the dynamics of southern pine beetle populations. Texas Agricultural Experiment Station, College Station, TX. Crook, D. J., F. M. Stephen, M. K. Fierke, D. L. Kinney, and V. B. Salisbury. 2004. Biology and sampling of red oak borer populations in the Ozark Mountains of Arkansas, pp. 223Ð228. In M. A. Spetich (ed.), Proceedings, symposium: upland oak ecology symposium: history, current conditions, and sustainability. USDA Forest Service, Southern Research Station, Asheville, NC. DeMars, C. J. 1970. Frequency distributions data transformations and analysis of variations issued in determination of optimum sample size and effort for broods of the western pine beetle, pp. 42Ð 65. In R. W. Stark and D. L.

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Dahlsten (eds.), Studies on the population dynamics of the Western Pine Beetle Dendroctonus brevicomis LeConte (Coleoptera: Scolylidae). University of California, Division of Agricultural Sciences, Berkley, CA. Donley, D. E. 1978. Oviposition by the red oak borer, Enaphalodes rufulus Coleoptera: Cerambycidae. Ann. Entomol. Soc. Am. 71: 496 Ð 498. Donley, D. E., and R. E. Acciavatti. 1980. Red oak borer. Donley, D. E., and E. Rast. 1984. Vertical distribution of the red oak borer, Enaphalodes rufulus (Coleoptera: Cerambycidae), in red oak. Environ. Entomol. 13: 41Ð 44. Fierke, M. K., D. L. Kinney, V. B. Salisbury, D. J. Crook, and F. M. Stephen. 2005a. Development and comparison of intensive and extensive sampling methods and preliminary within-tree population estimates of red oak borer (Coleoptera: Cerambycidae) in the Ozark Mountains of Arkansas. Environ. Entomol. 34: 184 Ð192. Fierke, M. K., D. L. Kinney, V. B. Salisbury, D. J. Crook, and F. M. Stephen. 2005b. Development of a rapid estimation procedure for red oak borer (Coleoptera: Cerambycidae) in the Ozark Mountains of Arkansas. Forest Ecol. Manage. 215: 163Ð168. Hay, C. J. 1969. The life history of a red oak borer and its behavior in red, black and scarlet oak. Proc. North Central Branch Entomol. Soc. Am. 24: 125Ð128. Hay, C. J. 1972a. Red oak borer (Coleoptera: Cerambycidae) emergence from oak in Ohio. Ann. Entomol. Soc. Am. 65: 1243Ð1244. Hay, C. J. 1972b. Woodpecker predation on red oak borer in black, scarlet and northern red oak. Ann. Entomol. Soc. Am. 65: 1421Ð1423. Hay, C. J. 1974. Survival and mortality of red oak borer larvae on black, scarlet and northern red oak in eastern Kentucky. Ann. Entomol. Soc. Am. 67: 981Ð986.

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