Can Cover Data Be Used as a 

Surrogate for Seedling Counts in 

Regeneration Stocking Evaluations 

in Northern Hardwood Forests?

Todd E. Ristau

Susan L. Stout

United States Department of Agriculture

Forest 

Service

Research Note

NRS-198

Northern 

Research Station April 2014

The Authors

TODD E. RISTAU is a research ecologist and SUSAN L. STOUT is a project leader 

with the U.S. Department of Agriculture, Forest Service, Northern Research Station, 

335 National Forge Road, P.O. Box 267, Irvine, PA 16329. They can be reached at 

814-563-1040; fax 814-563-1048; email tristau@fs.fed.us or sstout@fs.fed.us.

Abstract

Assessment of regeneration can be time-consuming and costly. Often, foresters look 

for ways to minimize the cost of doing inventories. One potential method to reduce 

time required on a plot is use of percent cover data rather than seedling count data 

to determine stocking. Robust linear regression analysis was used in this report to 

predict seedling count data from percent cover data based on 3,800 plots on which 

both count and cover data were collected. Results showed very poor relationships of 

cover data to seedling counts overall. The weakest relationships were found in plots 

that had received a shelterwood seed cut without any other regeneration preparation 

in the past. The better relationship came from plots where competition was reduced 

through herbicide application and shelterwood seed cutting. Immediately following 

herbicide application, when total seedling numbers were lowest, the relationship of 

cover to counts was best, with r-squared values as high as 0.8 for black birch, and 

between 0.4 and 0.6 for the smallest black cherry and red maple. These numbers 

quickly declined as seedlings developed. Cover data cannot reliably serve as a 

surrogate for seedling counts.
2

INTRODUCTION

Accurate assessment of seedling stocking on sample plots is essential to prescribing 

treatments to meet landowner regeneration objectives for a stand (Marquis et al. 1992). 

Sampling requires substantial time to complete, especially in large stand areas. Stocking 

criteria for regeneration often are based on species identity, size, and stem counts and 

when numbers of desired species are present above a certain threshold size and count, a 

plot is considered stocked (Grisez and Peace 1973, Leak 1969, Marquis et al. 1992, Sander 

1971). Some foresters looking for ways to minimize the time required for regeneration 

assessment have considered the potential of simply quantifying cover by species and height 

class on sample plots. When stocking criteria based directly on percent cover are not 

available, this approach requires conversion equations that can accurately predict seedling 

counts from percent cover data.

The SILVAH stand inventory, analysis, and prescription decision support system requires 

stem counts by species and height class from either 6-foot-radius or milacre regeneration 

sample plots. The stocking standards for these plots were developed over time for 

Allegheny and northern hardwoods (Grisez and Peace 1973, Marquis 1974, Marquis et 

al. 1992) and through a collaborative expert synthesis of research conducted elsewhere 

for mixed oak forests (Brose et al. 2008, Stout et al. 2007). McWilliams et al. (1995) 

extended the SILVAH approach for use with intensive regeneration data collected on U.S. 

Department of Agriculture, Forest Service Forest Inventory and Analysis (FIA) plots across 

Pennsylvania. Later the Pennsylvania Game Commission began to use these FIA data as a 

key measure related to its third deer management objective of managing deer “for healthy 

and sustainable forest habitat” (Rosenberry et al. 2009: 65).

Recently, some users of the SILVAH stand inventory, analysis, and prescription decision 

support system (Brose et al. 2008, Marquis et al. 1992) and its extensions in the policy 

arena have asked for equations to convert percent cover data to estimates of stocking. In 

other words, they ask if we can translate the required stem count thresholds into percent 

cover thresholds, or provide equations that reliably predict stem counts from percent cover. 

To answer these questions, we used study data collected over 12 years on the Allegheny 

National Forest in northwestern Pennsylvania that included both percent cover and 

seedling count data in broad size classes on the same plots. The purpose of this analysis was 

to determine whether seedling counts can be accurately predicted from percent cover data.

METHODS

Data from a long-term regeneration study were used to construct robust linear regression 

models in SAS (SAS Institute Inc. 2011). The study was conducted at 10 sites on the 

Allegheny National Forest to study nontarget effects of a one-time herbicide application 

using glyphosate and sulfometuron methyl (Ristau et al. 2011, Stoleson et al. 2011, Trager 

et al. 2013). In this study, development of regeneration after a shelterwood seed cut 

with no further preparation of regeneration was contrasted with development following 

a shelterwood seed cut and a one-time herbicide treatment to reduce competition from 

understory vegetation known to limit regeneration development, such as ferns, American 
3

beech (Fagus grandifolia Ehrh.), and striped maple (Acer pensylvanicum L.) (Horsley and 

Bjorkbom 1983, Horsley and Marquis 1983). Data from both the shelterwood only and 

the shelterwood and herbicide plots were used for this analysis, with each analysis run 

separately.

Thirty temporary circular milacre sample plots were established in each sample year (1992, 

1994, 1995, 1996, 1998, and 2000) on a systematic grid to adequately cover the area. 

In 2002 and 2004, 20 plots per site were sampled rather than 30 because within-stand 

variability decreased as stand development progressed. Plants ≤5 feet tall within the plot, 

or with parts leaning into the plot, were identified and the percentage of the plot covered 

by each species was recorded. Height classes were <1 foot, 1 - 3 feet, and >3 - 5 feet. 

Cover in each of the three height categories was estimated visually in 1-percent intervals 

up to 5 percent, then by 5-percent intervals up to 100 percent. Because plants occurred in 

overlapping layers, the total cover on a plot could exceed 100 percent. Species present on 

the plot, but covering <1 percent of plot area, were recorded as 1 percent cover to indicate 

their presence.

Using the same plot centers, we counted seedlings by species in the same three height 

classes used for percent cover. There were eight sample years: 1992 and 1994 pretreatment 

and 1995, 1996, 1998, 2000, 2002, and 2004 post-treatment. Herbicide was applied in 

mid-August 1994. A total of 3,800 (1,600 treated and 2,200 control) plots with both 

seedling counts and percent cover data served as the basis for regression analyses. Sample 

plots from different years were considered independent because temporary plot locations 

were used rather than permanently marked plot centers. Regression was run with the 

PROC ROBUSTREG procedure in SAS (SAS Institute Inc. 2011).

The robust regression technique removed outliers and down-weighted high leverage 

points by using the mm estimation option, which uses high breakdown value estimation 

and efficient estimation techniques. Percent cover data were transformed with the arcsine 

(square root) transformation typically used with proportion data ranging from 0 to 1, and 

count data were transformed with a square root transformation as is typical with count 

data to ensure normality and homogeneous variance. Data were tested for normality 

before and after transformation and found to have normally distributed residuals after 

the transformation. Within a species and size class, any data points where both cover and 

count were equal to zero were eliminated from the regression because there were so many 

of these points in the data set. Regression lines were forced through the origin by using the 

NOINT option because when cover is zero, count is also zero for any species and size class. 

Equations were of the form: 

�ssssssssssssssss cccccc cc (ssssss ssssss xx) = β1 * ssssss−11 � pp cccccc (ssssss ssssss xx)

where β1 is the slope, and intercept was forced through zero. In addition to pooled plot 

regressions across years, data were separated by height classes and years to determine 

if regressions of a particular size class or time since disturbance produced stronger 

relationships than the pooled data.
4

RESULTS

Data from this study included 12 tree seedling species, of which 5 were consistently 

present and able to be used for regression analysis. Overall, the relationship between cover 

and counts was poor, especially in the shelterwood-only plots (Table 1). On these plots 

r-squared values ranged from 0.043 to 0.456 (Table 1). Black cherry (Prunus serotina) 

<1 foot tall had the best relationship (r2 = 0.456), followed by red maple (Acer rubrum) 

(r2 = 0.435) and black birch (Betula lenta) (r2 = 0.211). On shelterwood-herbicided plots 

r-squared values ranged from 0.006 to 0.554 following treatment (Table 2). The best 

relationship between cover of seedlings and counts of seedlings was that of <1 foot red 

maple (r2 = 0.554), followed by <1 foot black cherry (r2 = 0.510) (Table 2). A scatter plot 

and associated regression line (Fig. 1) show that the data had strongest representation 

from plots with low cover and low counts and data were highly variable.

If regression data were separated by year, seedling size class, and species, the proportion of 

variability accounted for by the regression varied with time (Figs. 2-3). Best regressions on 

shelterwood-only plots were for <1 foot black cherry (r2 ≈ 0.500) in all years and <1 foot 

and 1-3 foot red maple in 1995 and 1996 (r2 ≈ 0.600) (Fig. 2), both of which responded 

to additional light created by shelterwood seed cutting. On shelterwood-herbicide plots 

r-squared values were as high as 0.8 for black birch very shortly after the herbicide 

treatment (Fig. 3). All herbicide and shelterwood plot regressions were strongest for the 

five species in the first 2 years after treatment (1995 and 1996). However, red maple 

and black cherry <1 foot maintained similar relationships throughout the study (r2 ≈ 

0.600), and 1-3 foot red maple and black cherry increased their proportion of variability 

accounted for by the regressions through time (Figs. 2-3).

Table 1.—Results from regression analysisa of 2,200 sample plots following shelterwood 

seed cutting

Species Height (feet) N Slope r-squared

Acer pensylvanicum <1 524 2.764 0.126

1 – 3 416 2.022 0.143

3 – 5 347 0.600 0.045

Acer rubrum <1 2,145 18.140 0.435

1 – 3 332 5.109 0.142

Betula lenta <1 1,331 5.352 0.211

1 – 3 806 3.434 0.213

Fagus grandifolia <1 1,198 1.392 0.097

1 – 3 1,234 1.535 0.161

3 – 5 990 0.461 0.043

Prunus serotina <1 1,634 19.411 0.456

1 – 3 329 2.909 0.073

a The regression analysis compared percent cover by species and height class (x) and seedling counts (y) 

on the same plot through time. Only non-zero plots for a given species and size class are included, with 

number of plots shown as N. Equations were of the form:

�ssssssssssssssss cccccc cc(ssssss ssssss xx) = β1 * ssssss−11 � pp cccccc (ssssss ssssss xx) , where β1 is the slope, and intercept 

was forced through the origin.
5

Table 2.—Results from regression analysisa of 1,600 sample plots following shelterwood 

seed cutting and treatment with glyphosate and sulfometuron methyl herbicides

Species Height (feet) N Slope r-squared

Acer pensylvanicum < 1 424 3.307 0.112

1 – 3 259 1.418 0.058

3 – 5 105 0.306 0.010

Acer rubrum < 1 1576 18.210 0.554

1 – 3 479 6.850 0.296

Betula lenta < 1 999 3.165 0.146

1 – 3 476 2.920 0.205

Fagus grandifolia < 1 482 1.022 0.041

1 – 3 324 0.724 0.030

3 – 5 106 0.178 0.006

Prunus serotina < 1 1,584 19.738 0.510

1 – 3 484 7.076 0.212

a The regression analysis compared percent cover by species and height class (x) and seedling counts (y) 

on the same plot through time. Only non-zero plots for a given species and size class are included, with 

number of plots shown as N. Equations were of the form:

�ssssssssssssssss cccccc cc(ssssss ssssss xx) = β1 * ssssss−11 � pp cccccc (ssssss ssssss xx) , where β1 is the slope, and intercept 

was forced through the origin.

Figure 1.—Scatter plot of percent cover of <1 foot black cherry versus number of stems and 

associated simple linear regression line per milacre plot. Data are from 1,600 milacre plots in 

shelterwood seed cut and herbicided stands. 

0 20 40 60 80

Percent cover

0

500

1000

1500

N

umber of stems per milacre

1500

Number of stems per mil

acr

e
6

A. American beech 

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

B. Black birch

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

C. Black cherry

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

D. Red maple 

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

 elpam depirtS .E

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

Figure 2.—R-squared values by species and size class over time for the equation: 

�ssssssssssssssss cccccc cc(ssssss ssssss xx) = β1 * ssssss−11 � pp cccccc (ssssss ssssss xx) , where β1 is the slope, and intercept 

was forced through the origin. Data are from 2,200 milacre plots in shelterwood seed cut-only stands.
7

21 

A. American beech 

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

B. Black birch

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

C. Black cherry

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

D. Red maple 

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

E. Striped maple 

0.0

0.2

0.4

0.6

0.8

1.0

92 95 00 04

Year

r-squ

ared 

96 98 02

>3 - 5 ft

1 - 3 ft

<1 ft

Size class

Figure 3.—R-squared values by species and size class over time for the equation: 

�ssssssssssssssss cccccc cc(ssssss ssssss xx) = β1 * ssssss−11 � pp cccccc (ssssss ssssss xx) , where β1 is the slope, and intercept was 

forced through the origin. Data are from 1,600 milacre plots in shelterwood seed cut and herbicided stands. 
8

DISCUSSION

The conditions in the shelterwood-only plots are representative of much of Pennsylvania’s 

forest. McWilliams et al. (2007) report that grasses, forbs, and rhizomatous ferns 

dominate Pennsylvania forest understories. In these conditions, there is very little 

relationship between percent cover and stem counts of a species by height class. Where 

key sources of variation in this relationship—competing plants—are removed by herbicide 

treatment, a short window opens in which percent cover and stem counts are much more 

strongly related. This relationship is best for shade-intolerant or intermediate species 

like black cherry, red maple, and birch. But due to the other sources of variation in the 

relationship, the ability to predict counts from cover data does not persist for long.

One major reason for high variability is that seedling sizes within the broad size classes 

can vary greatly. A size class <1 foot may contain mostly seedlings nearly 1 foot in height 

and high cover, or perhaps the same number of very small seedlings and low cover. Time 

since establishment is often unknown when stocking is being assessed during prescription 

development, but can be a source of substantial variation in seedling size within a size 

class. Variability in size of individuals within a species can result from many other factors 

as well. Nutrient availability at a microscale, light availability, and water availability can 

all affect the size of individual seedlings (Beatty 1984, Grubb 1977, Watt 1947). Genetic 

variations and phenotypic plasticity differences among species and environment also play 

a substantial role in seedling size (Rice et al. 1993). High variability was likely a result of 

many factors combined.

Prediction of seedling counts from percent cover data by height classes is not reliable and 

cannot serve as a substitute for careful seedling count data collected on plots. Our data 

were collected on the Allegheny National Forest, where regeneration was dominated by 

red maple and black cherry with associated American beech, black birch, and striped 

maple. These species represent the range of shade tolerance classes found in any forest. 

Leaf morphology and variability in plant sizes seen in our study certainly exist elsewhere 

and we expect that our results apply broadly to any forested situation.

Assessments of advance regeneration stocking are implicitly predictions of stocking 

through stand development. The stem count methods used in SILVAH have been 

proven by adoption over a wide geographic area. Our results suggest that entirely new 

studies would be required in order for users to use percent cover data to predict future 

plot stocking. This approach may be possible, but the results from our work suggest 

it would not be as accurate as stocking standards and predictions based on seedling 

counts. Conversion of cover data to stem counts cannot be done accurately and reliably 

across species and size classes and through time. Despite the effort required to assess the 

adequacy of regeneration prior to silvicultural operations, stem counts remain critical to 

predicting and ensuring regeneration success.
9

ACKNOWLEDGMENTS

Databases were developed over many years with the technical assistance of Vonley Brown, 

John Crossley, Virgil Flick, David Saf, Julie Smithbauer, Harry Steele, Corinne Weldon, 

and Ernest Wiltsie.

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Ristau, Todd E.; Stout, Susan L. 2014. Can cover data be used as a surrogate 

for seedling counts in regeneration stocking evaluations in northern 

hardwood forests? Res. Note NRS-198. Newtown Square, PA: U.S. 

Department of Agriculture, Forest Service, Northern Research Station. 10 p.

KEY WORDS: cover data, SILVAH, Allegheny hardwood, regeneration stocking

Manuscript received for publication 26 March 2013.
Northern Research Station

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