regeneration surveys and evaluation

Regeneration Surveys andEvaluation

William I. Stein

IntroductIon 347Survey objectives 348Factors affecting survey design 350

Silvicultural standards 350Regeneration goal 350Acceptable tree 351Nonstocked area 352

Administrative considerations 353Principles of sampling 354

Field sampling 354Statistics applicable to survey data 356

Calculations involving normaldistrIbutions 356

Calculations involving binomialdistributions 357

Sampling methods 358Fixed-area plots 359

Stocked-quadrat 359Plot-count 362Staked-point 365

Variable-area plots 367Distance 367Vertical-line and vertical-point 370

Aerial methods 371Comparisons of survey methods 374

Field procedures 374Statistical comparisons 376

Summary 376InformatIon needed 376Field methods 377Interpreting data 378Conclusion 378

Literature cited 378

346

INTRODUCTION

Knowing the status of regeneration is indis-pensable for wisely managing timber productionareas. The presence or absence of regenerationaffects the choice of harvest method and the sub-sequent steps taken to preserve regenerationor establish It. Reforestation efforts are usuallynot concluded on an area until a survey demon-strates that Its regeneration meets prescribedgoals or standards.

Usually, the status of regeneration must bedetermined by field sampling. No single sur-vey method or sampling intensity can provideanswers to all the questions that ailse concerningregen-eration. On the other hand, common sam-pI-ing principles are applicable in most surveysand reforestation situations. Over the past 60years, much insight has accumulated on sam-pling methodology and on the key factors thatgovern the choice of survey system. The informa-tion needed, the silvicultural standards, thesampling concepts and principles, and the admin-istrative and financial constraints must be iden-tified and clearly understood so that the mostsuitable system may be devised. This chapter pro-vides a brief historical overview, a discussion offactors Influencing every survey, and the con-cepts, strengths, and limitations of availablesampling methods. The information provided isintended to help everyone evaluate regenerationmore precisely and efficientiy.

The art and science of surveying regenerationdeveloped sporadically in the western UnitedStates and Canada. Concern about survey meth-ods originated with the need to evaluate natural

Regeneration Surveys and Evaluation 347

regeneration of conifers on large acreages follow-ing wildfire or harvest cutting (Lowdermilk 1921and 1927, Haig 1929 and 1931, Cowlin 1931 and1932). There was no central direction in the devel-opment of regeneration survey methods: newtechniques and information were reported piece-meal by individuals studying different aspects ofthe subject. By mid-century, cooperative effortsproduced suggested stocking standards but onlybrief descriptions of survey methodology (Munger1945, West Coast Forestry Procedures Committee1946, Reynolds et al. 1953).

From the 1940s onward, state and provincialforest conservation laws have been implementedby issuance of prescribed methods for determin-ing whether minimum regeneration requirementshave been met. Designated standards variedamong states and changed over time, as didthe methods prescribed for evaluating regenera-tion (Bever 1949 and 1961, State of California1975 and 1984, State of Oregon 1975, State ofWashington 1975, Washington State ForestPractices Board 1982, Stein 1983, Wyeth 1984).Meanwhile, public agencies and private compa-nies set regeneration standards consistentwith management objectives on their landsand prescribed their own methods for determin-ing regeneration status. Not all evaluation meth-ods used are conceptually sound, nor do theyproduce comparable data, particularly in termsof stocking.

As forest management intensified and conser-vation laws became more stringent, concernincreased about the adequacy of methodsused to evaluate regeneration. In technical pro-grams sponsored by the Western Forestry andConservation Association, existing methods were

348 Regeneration Surveys and Evaluation

reviewed and debated (Stein 1974, WesternReforestation Coordinating Committee 1974 and1975); a subsequently appointed task force stud-ied regeneration survey methods in substantialdetail. These efforts led, directly or indirectly, toadditional discussion of regeneration evaluation(Stein 1978 and 1985), a systematic comparisonof methods (Kaltenberg 1978), and comprehensivecoverage of the subject at the National Conventionof the Society of American Foresters in Portland,Oregon (Society of American Foresters 1984). Keyinformation developed by those activities is includ-ed in this chapter.

SURVEY OBJECTIVESRegeneration surveys are made to fulfill two dis-

tinctly different purposes. Broad-scale surveysdetermine the status of regeneration over large

areas or in a variety of conditions. Informationobtained from such surveys provides the basis forregional estimates of reforestation conditions,trends or needs, workloads, and recommended pro-grams. Site-specific surveys determine the status ofregeneration on a specified area. Their primary pur-pose is to obtain Information needed to prescriberegeneration and management efforts for that area.If the same procedures are used, data from site-specific surveys may be additive and can contributeto broad-scale surveys, but that is not their prima-ry purpose. Only site-specific surveys are discussedin this chapter, but many of the considerations andprinciples also apply to broad-scale surveys.

During the regeneration period, which extendsfrom pre-harvest planning to establishment of thenew stand, several kinds of regeneration informa-tion are needed for individual areas (Table 15-1).Because the information cannot all be obtained atone time, nor need all of it be equally precise, there

Figure 15-1. Reconnaissance surveys or walk-throughs are commonly made to observe development andneeds of young plantations.


Table 15-1. Site-specific reforestation information usually obtained by survey during the regenerationperiod.

When In formation needed Type of survey

Pre-harvest Amount, quality, and compositionof advanced regeneration; sameinformation for seed sources.

Key site factorssoil, aspect,slope, animals present, prospec-tive vegetative competition, etc.

Post-harvest Base map for confirming acreageand showing site featuresrockyareas, slash accumulations, residualvegetation, etc.; and for plottingtreatments on overlays.

Post-treatment survey of problemareaswere contract specificationsand site treatment objectivesachieved?

Does the planting meet contractspecifications?

First-year plantation developmentand evidence of problemsone ormore exams.

Second-year plantation developmentand evidence of problems.

Third-year plantation developmentand evidence of problems. Haveforest practice and silviculturalrequirements been met or willthey be met?

Fifth-year plantation developmentand evidence of problems. Isregeneration adequate in number oftrees and growth rate for yieldprojections?

is good reason to use both extensive and intensivesurvey methods. Intensive surveys involve gather-ing speciflc data on a designated series of plots;extensive, or reconnaissance, surveys primarilyinvolve observationand perhaps verilring impres-sions by sampling a few random plots along ameandering route of travel (Figure 15-1). A pre-

Reconnaissance

Reconnaissance

Photo orreconnaissance

Reconnaissanceor intensive

Intensive

Reconnaissance

Reconnaissanceor intensive

Intensive

Intensive

harvest reconnaissance might be made to deter-mine whether regeneration is already present orwhat environmental conditions exist that mighthinder seedling establishment. Post-harvestreconnaissances are often used to determine theplantability of an area, the condition of new plant-ings, and the need for protection from animals or


reduction of competing vegetation; and to deter-mine if an intensive survey is needed. Intensivesurveys may be made to check on planting con-tract performance, compliance with conservationlaws, and effectiveness of the regeneration method;andmost importantlyto determine whetherregeneration objectives prescribed for the areahave been or will be attained. In a concludingintensive survey, stocking and growth data mightbe obtained concurrently so that future yields canbe projectedan increasingly common practice(Stage and Ferguson 1984).

The first step In planning a regeneration surveyis to identii' the survey objectivesthe questionsto be answered, the new data needed, and theaccuracy required. Information obtained by recon-naissance may be fully adequate either whenregeneration establishment appears to be pro-gressing satisfactorily or when it Is obviouslysparse or abundant. An intensive survey is need-ed when an area's regeneration status is not obvi-ous or when management decisions hinge onnumerical data.

FACTORS AFFECTINGSURVEY DESIGN

All regeneration surveys, even reconnaissances,are shaped by the same considerationsthe infor-mation to be obtained, the silvicultural standardsthat apply, and the constraints of time, money,facilities, and personnel. Facets of these topics thatneed to be considered in designing and selectingthe survey method are discussed in this section.

Silvicultural Standards

Regeneration goal

The usual reason for surveying regeneration isto determine whether a prescribed goal has been oris likely to be met. The regeneration goal Is set bymanagement and prescribes the stocking, density,and composition of the desired present or futurestand for an area. The goal Is often defined rela-tive to the theoretical full stand of trees desired ata given stage of stand development (for example,the end of the regeneration period, the time of

crown closure, or just before the first commercialthinning), and may or may not allow for anticipat-ed mortality. Failure to achieve the regenerationgoal would probably trigger prescribed follow-upaction. For example, if 70-percent stocking withreasonable distribution were deemed sufficient,then 30- to 70-percent stocking might call for fill-inplanting, and less than 30-percent stocking mightrequire full replanting. The regeneration goal mustbe explicitly stated in a silvicultural prescription orelsewhere so that survey results can be measuredagainst It.

In defining the regeneration goal, there is a com-mon tendency to increase initial seedling densityto compensate for anticipated mortality. Thisapproach might work if mortality always oc-curred randomly, but often it is concentrated inlimited areas. Thus, increasing seedling density tocompensate for anticipated mortality may oftenprove counterproductive, resulting in a few non-stocked openings plus overcrowding in the rest ofthe stand.

Stocking, density, and spatial arrangement aremeasurable attributes of plant communities,including young and mature tree stands. Stockingis a measure of the proportion of an area actuallyoccupied by trees (Ford-Robertson 1971), usuallyexpressed as a decimal or percentage. Density is ameasure of tree occupancy per unit area, precise-ly expressed as trees per acre within the stockedpart of an area, or more loosely as the number peracre for the entire area. Spatial arrangement refersto the placement pattern of trees on an area, e.g.,uniform, random, or clumped (Figure 15-2).

Although stocking and density have distinctmeanings, their interrelatedness must also be rec-ognized. To be stocked, a plot or an area must havetrees at a specified minimum density or greater.Nonstocked areas may have some trees, but notenough for the specified density per unit area. Thedistinction between stocking and density is veryimportant in stands of regeneration where manytrees may be present per unit area. The distinc-tion becomes blurred in older stands as crownsclose and excess stems are crowded out. Bothstocking and density must be included in a well-defined regeneration goal.

Determining stocking is the primary concern ofall regeneration surveys. Some surveys may alsomeasure stand density. The identification and

riLI

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S S S S SSS

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S..1.... ;r.,. S % S S,,,,,t5, .'%'q

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c4 .s.r'

sjr4,

SS S

: ,i %. ..l1S

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Figure 15=2. Spatial arrangement, the distributionpattern of regeneration on an area, may be relativelyuniform (A), random (B), or clumped (C).


interpretation of spatial arrangement are general-ly not attempted because the required Informationis laborious to collect, difficult to Interpret, and notneeded for correct application of the most com-monly used survey methods.

Acceptable tree

Not all trees present on an area or plot areequally suitable as components of the developingstand. Some are the wrong species; others are tooyoung, small, unhealthy, damaged, old, crowded,or overtopped. What species, size, quality, com-petitive position, and distribution requirementmust a tree meet to be considered acceptable(Figure 15-3)? What level of damage or unhealthi-ness makes a tree unsuitable? Should overtoppedtrees or those showing little growth be counted aspart of stocking? These questions need to beanswered to define, in a statistical sense, the pop-ulation to be sampled. If only regeneration is to besampled, older and larger trees should be exclud-ed. If the population Is the whole stand, then treesof all ages and sizes should be included. Every cri-terion chosen to define an acceptable tree affectsfield procedures and the interpretation of result-ing data.

Regeneration survey methodology in the Westhas largely centered on the conceptcentral to thediscussion in this chapterthat a single accept-able tree is sufficient to stock a plot, a specifiedunit area. This concept works particularly wellwith conifers provided any of several species maybe suitable and the chances are high that, if anacceptable tree is present, it will become the croptree. If some species are more suitable than others,however, or if It is unlikely that any of the treespresent will become the crop tree, some combina-tion of trees may be defined as necessary to con-sider a plot stocked. Such a definition might beapplied in areas where the site or competition issevere, in mixed stands of conifers and hardwoods,and particularly in hardwood stands where regen-eration is abundant and composed of many specieswith markedly different potential for survival andgrowth. Various combinations of species, quanti-ty, and size of trees, for example, provide accept-able stocking on plots of a 6-ft radius in hardwoodforests of the Allegheny region (Marquis 1987,Marquis et al. 1990).


Figure 15-3. What species, size, quality, and compet-itive position criteria must a tree meet to stock aplot? Which of the trees pictured should be countedas a meaningful regeneration component (A) in acrowded multitude? (B) Among those damaged bybrowsing? (C) Of those overtopped by vegetativecompetition?

Nonstocked area

When trees are abundant in parts of an area andsparse or absent elsewhere, it Is easy to Identifywhich parts are stocked and which are not (Figure15-4). Often, however, trees are present on mostof an area but their density varies, and inter-spersed among them are variously sized openingsdevoid of trees. When does an opening in a standconstitute a nonstocked area (a void") rather thansimply a less dense area of the stand? This ques-tion should be dealt with when setting the regener-ation goal by specifying the smallest opening thatconstitutes a void. In addition, the allowable num-ber of such voids should be specified by definingwhat constitutes minimum acceptable stocking.

In defining minimum acceptable stocking, thequestion of how to deal with voids is very chal-lenging. Small, scattered voids may be relativelynumerous yet not affect stand development Inany significant way (Staebler 1948 and 1949).Furthermore, because few stands will be perfectlydistributed, an expectation of 100 percent stock-ing, without any voids at all, is unrealistic unlessexcessively dense stands are being surveyed. Largevoids (openings), on the other hand, represent lostproductivity and thus must often be locatedfor retreatment.

If survey objectives Include the locating of oper-able-sized openings, their minimum size must bespecified. The sampling intensity chosen must pro-vide a reasonable probability that all openings willactually be discovered. Questions such as howmany consecutive small voids (nonstocked plots)define an operable opening, and what other obser-vations are needed to delineate openings, must beanswered. In general, discovery of all nonstockedopenings requires more closely spaced samplelines than have been used in most regenera-tion surveys.

Sampling techniques are commonly based onthe premise that trees can grow In all parts of theregeneration area. But some microsites within astand are not stockable because of rock outcrops,swampy ground, streambeds, very shallow soil,and so forth; and others may be temporarilyunavailable for seedlingsfor example, compact-ed skid roads, slash piles, and landings. Definingwhat constitutes a nonstockable plot (void) andhow such plots are to be tallied and dealt with in

S0

SS

ss Jo

S S (ô 0 0° oo S 0 0

S

sS

s 10 0 0S 1 Nonstocked area

SS

0 0 0

SS

S s \o 0

Stoked S S Ss areas__

7 s = stockedo = nonstocked

Figure 15-4. Stocking found on 4-milacre sampleplots systematically spaced in a hypothetical regen-eration area. Stocking on the entire area: 280150plots = 56 percent, or at least 140 well-spaced treesper acre, but unevenly distributed. Area clearly non-stocked: 15 of 50 plots =30 percent. Stocking inarea satisfactorily stocked: 28 of 35 plots = 80 per-cent, or at least 200 well-spaced trees per acre, rea-sonably well distributed.

stocking calculations Is an Important considera-tion In planning a regeneration survey and in real-istically predicting potential yields per acre. Inareas with significant numbers of nonstock-able plots, stocking should be calculated on thebasis of total stockable plots sampled rather thanon total plots sampled, to avoid underestimatingthe stocking.

Sites that can support only low numbers ofmedium-sized to large trees per acre present spe-cial regeneration-evaluation problems. If the distil-butlon of sparse crop trees could be reasonablyuniform, large sample plots may suffice. If the dis-tribution of crop trees cannot be uniform, meansmust be devised for recognizing stockable areasand the density of regeneration that should be pre-sent in those areas.

Administrative ConsiderationsNo matter how worthy or critically needed, every

survey is limited by time, cost, and other adminis-trative considerations. Scope and methods must betailored to match the money and time available.


The number of plots that can be completedper day must be estimated realistically, given thefield conditions and the Information to be obtained.Shortfalls can sometimes be overcome by ex-panding the scope of the survey so that infor-mation for more than one purpose may begathered simultaneously.

Choosing the information to be collected In aregeneration survey should be given substantialthought and attention. Although stocking and den-sity are most Important, additional pertinent infor-mation Is usually obtained, e.g., the total height,diameter, or growth rate of crop trees; the species,relative size, or density of competing vegetation;descriptors of the site; animal damage, etc. Whatinformation is vital and what is subsidiary? Whatsupplemental information would be highly usefuland could be obtained readily with minimumadded effort? Is there a definite use for every cate-gory of observation planned? Even before the avail-ability of computers, there has been a commontendency to collect a variety of subsidiary infor-mation premised on the hope or belief that It wouldprove useful. All too often, much of that data didnot get summarized, much less adequately inter-preted. Before field work starts, the summary stepsrequired, and the answers to be obtained fromevery type of observation, should be carefullythought out and documented.

The talents and skills needed to conduct thesurvey must also be considered. How muchrecruitment and training will be needed? Howmuch followup checking should be done to ensurethat data are collected consistently by dif-ferent field crews? Consistent and accurate meth-ods are always critically important and must bemaintained to obtain comparable data as the sur-vey system Is used by different crews over a peri-od of years.

Before field work starts, an efficient systemshould be worked out for Integrated data collec-tion, storage, retrieval, and analysis. The format forwritten or electronic recording of data should havean easy-to-follow arrangement for entering fieldobservations and transferring them to computer.The system should include a ready means of mak-ing a preliminary summary of survey results whilestill in the field. Field observations are meaninglesswithout adequate documentationthe formats andheadings, data codes, definitions, class intervals,

354 Regeneration Surieys and Evaluation

sampling method, and other explanatory Informa-tion must be worked out and written down.Preferably, summary table formats and analysisprocedures should also be developed before fieldwork starts. The computational steps can be iden-tified and tested on some preliminary field data.Although these preparatory steps may delay thestart of full-scale field work, solving problems atthis stage could avoid major grief later on.

Adequate map records are also essential.Locating survey lines and sample plots on a map ofthe area is a key step in interpreting survey data. Ifplots are shown as stocked or nonstocked, ormarked by the number of trees found, the stock-ing or density pattern and its association withgeography will become evident (Figure 15-4).Information from plots plus Incidental observa-tions can be used to delineate the actual locationsand sizes of nonstocked openings. Plotting surveylines also records how the area was sampled andpermits reasonably close resurveys without use ofstaked plots.

PRINCIPLES OF SAMPLINGGenerally recognized principles of sampling are

broadly applicable in surveying regeneration.These principles must be followed in designing aformal, quantitative survey, but they should alsobe heeded when making a reconnaissance or rel-atively subjective observations of regenerationconditions. A brief review of these principlesshould provide a better understanding of the sur-vey techniques described in the next section.Many publications on statistical methods discussthe principles of sampling: see Freese (1962and 1967) for concise and specific coverage of for-est sampling.

Field Sampling

Surveying regeneration usually entails makingobservations on a sample of trees and related con-ditions that are representative of a larger group orpopulation. The population to be sampled isIdentified In the planning stages, when surveyobjectives, data needs, and acceptable trees aredefined. The population may be either extensiveand diverse, or narrow in extent and variation.

Whatever limits are used to define the populationalso carry through to the breadth of Inference thatcan be made about that population. For example, Ifthe population is defined as the regeneration on awhole clearcut, results from a representative sam-ple indicate the average situation for the entireclearcut: whereas If the population is defined asthat located only on the north slope of the clearcut,the results of sampling reflect regeneration condi-tions only on the north slope.

Clearly, It is critical that the sample be repre-sentative of the population. Obtaining a represen-tative or accurate sample, one whose attributesare similar to those for the population, Involveschoices on the number of observations to make orplots to survey, the spatial distribution of thoseobservations or plots, and means of avoiding built-in error and unknown bias. Statistical theory isbroadly based on random sampling, but locatingmany individual plots at random is so cumbersomethat most regeneration surveys involve systematicsamplingtaking plots at stated intervals alongsystematically located traverse lines (Figure 15-4).An element of randomness can be maintained byplacing the first plot at random on the first tra-verse line sampled, or by designating a randomstart on each of the systematically spaced tra-verse lines. Estimates obtained through system-atic sampling are usually as precise as (or evenmore precise than) those obtained from randomsampling, but the logical basis for calculatingstandard error of the sample mean is less certain(Freese 1962, Snedecor and Cochran 1980).

Obviously, the size of the sample is criticallyimportant. If too many observations or plots aretaken, time, money, and talent are wasted: if toofew are taken, the resulting information may beInadequate or misleading. Critical silviculturaland economic decisions are then likely to bemade on faulty information.

The number of observations or plots requiredto obtain an adequate sample varies with thediversity of the population and the level of accu-racy required. To achieve a given level of accura-cy, more observations or plots are required tocharacterize a diverse population than a uniformpopulation (Figure 15-5). Thus, it is wise to strat-i1r and sample separately, if possible, parts of aregeneration area known or suspected to be sub-stantially different in stocking or site conditions.

Diversity of the regeneration population Is oftenunknown, however; measuring its variation mightbe one of the survey objectives.

The level of accuracy needed is an impor-tant factor in determining the number of plotsrequired. A higher level of certainty (confidencelevel) is required for some Information than forother Information. Thus, a 95-percent confidencelevel might be required for Information about den-sity, for example, whereas a 67- or 80-percentconfidence level may be entirely adequate to indi-cate broad trends for such variables as animaldamage or competition. The number of plots sam-pled for stocking is often based on achieving aconfidence level of 90 percent.

Distribution pattern for plots In an area isachieved by varying the number of traverse lines


and the spacing of plots along them. In tests onsimulated, clustered populations, MacLeod (1977)determined that estimates of the mean had lessvariation when plots were evenly distributed overan area than when they were concentrated on justa few lines. A single plot taken at each samplingpoint also produced a mean with less variationthan the mean produced by surveying an equalnumber of plots clustered at fewer samplingpoints. Traverse lines should be oriented on a unitto cross rather than parallel the main topograph-ic features. When plantations are spaced on a veryprecise grid, traverse lines must be located toavoid congruence with the planting pattern.

The size of plot to sample Is a key decision forboth conceptual and practical reasons. In general,the precision of an estimate for stocking or trees

Figure 15-5. The more variable the regeneration, the more plots are needed to obtain a good estimate of stock-ing or total trees per acre.


per acre tends to Increase with plot sizethat Is,

variability among plots becomes less (Ghent 1963,Kaltenberg 1978). Consequently, fewer plots areneeded to achieve the same level of accuracy. Ifthe plots sampled are too large, however, valuesfrom each one may be more in the nature of amean that masks the true variability on the area.Effectiveness of sampling may also be ImpairedIf only a few plots are taken, the actual diversityon an area may not be discovered. The choice ofplot size should generally be based on one or twoof the key variables to be observed on the plot.For example, If stocking is of primary Interest, theplot size might be based on the area a single treeis expected to occupy when crowns close. If num-ber of trees is of primary interest, plot size shouldbe large enough that at least one tree is likely tobe found on most plots.

Physical conditions in the field must alsobe consideredsome plot sizes may be far morepractical than others. For example, if seedlingsare abundant, a full count on large plots mayprove too time-consuming. Large plots are alsomore difficult to search completely, especially onsteep or brushy terrain. In general, the timerequired to completely search a plot increas-es with the size of the plot, the smallness of theseedlings sought, and the density of the vegeta-tion present.

In considering plot size and number of samples,these points should be kept in mind:

More than a few plots are generally required toachieve a good estimate of stocking or density(Baten and Arend 1954).Precision of an estimate decreases as distribu-tion of the seedling population varies from uni-form to random to clumped (Kaltenberg 1978).There is no substitute for good coverage tolearn whether an area is adequately regenerat-ed.

Statistics Applicable to Survey DataIn sampling, variables of interest such as stock-

ing, number of trees, tree height, and stem diam-eter will differ from plot to plot. This variation (orlack of it) is of key interest. For example, large dif-ferences In tree height or density may indicatethat part of the stand is developing differentlyfrom the rest. Statistical procedures are available

for characterizing or measuring the extent of suchnatural variation.

As variables differ one from the other in theirintrinsic nature, so do the statistical proceduresthat apply. Tree height and stem diameter areconsidered continuous variables because they canbe measured on a numerical scale having anynumber of subdivisions. Variation in other vari-ables is discontinuousit occurs in discrete unitssuch as a "yes" or "no" for the presence of regen-eration, or a count of the number of trees present.Discrete variables are further classed into thosethat can be expressed as a proportion (e.g., "yes"and "no" answers summed as percent stocking),and those of a count nature that cannot beexpressed as a proportion (e.g., number of treesper plot).

The appropriate statistical treatment for a vari-able also depends on the relative frequency withwhich different values of the variable occur. Ingeneral, the bell-shaped curve of a normal distil-bution usually applies in dealing with continuousvariables, the binomial distribution in proportionvariables, and the Poisson distribution In counts,particularly very low counts. When samples arelarge, the distribution of their means approachesnormal, so even data for discrete variables canoften be handled by statistics for normal distri-butions. Formulas for calculating the most com-mon statistics applicable to survey data are brieflypresented below; consult standard statistical texts(e.g., Freese 1962 and 1967, Cochran 1977,Snedecor and Cochran 1980) for variations thatapply in particular circumstances.

Calculations involving normal distributions

The general formula for calculating the num-ber of samples needed from a large population fora normally distributed variable is:

t2s2n=E2

where n = the required number of observationsor plots,

t = the value listed in a two-tailed t-dis-tribution table for a chosen level ofprobabilityassuming the number

of samples Is 30 or more, t is about1.7, 2.0, and 2.7 for 90-, 95-, and99-percent probability, respectively,

s2 = an advance estimate or preliminarycalculation of the population vari-ance, and

E = the margin of error that will be toler-ated in the estimate of the mean.

The estimated variance (s2) and E value must be onthe same scale of measurement.

The mean or average of the observations com-prising a sample, which is an estimate of the meanof the population sampled, and the statistics thatcharacterize it are calculated as follows:

1.

MeanSum () of the Individual observations (y1,y2,y3...,y,j

Number of observations (n)

or

2. The estimated variance (2), which character-izes the variance of individual values in a popu-lation, Is the standard deviation squared,calculated as:

s2= n-i

3. The standard deviation (s), which characterizesthe dispersion of individuals about the mean, iscalculated as:

I

(Y)2

s=1 n-ior

s=

4. The standard error of the mean (s). a measureof the variation among possible sample means,is calculated as:

s- =y


if the sample is a small fraction (5 percent orless) of the population, or

f2( ns-= iil--Y N

if the sample is a relatively large fraction of thepopulation (N): e.g., the total number ofseedlings, or total number of possible samples inthe population.

5. Confidence limits, or an estimate of the reliabil-ity of the mean, can be calculated as:

where the value of t is based on the probabilitylevel desired and the number of observationsrepresented by the mean minus 1.

See Table 15-2 for a worked-out example of theabove statistics based on hypothetical data from acount of seedlings on a limited number of 4-milacre plots.

Calculations involving binomialdistributionsThe general formula for calculating the number

of samples needed when a variable involves eitherproportion or the presence and absence of anattribute is:

n=pE2

where n = the required number of observationsor plots,

t = the value listed in a two-tailed t-dis-tribution table for a chosen level ofprobabilityassuming the numberof samples is 30 or more, t is about1.7, 2.0, and 2.7 for 90-, 95-, and99-percent probability, respectively,

p = an advanced estimate of the propor-tion found (expressed as a decimalor percent),

q = 1 p. andE = the margin of error that will be tol-

erated in the final estimate of p(expressed in the same unit as p).


Table 15-2. Statistics calculated using hypothetical treecount data obtained on a preliminary sample of 4-milacreplots.

Basic data

Plot No. of trees(y)2

y y

1 2 42 3 93 0 04 8 645 4 166 2 47 1 1

8 1 1

9 2 410 5 2511 3 912 6 36

Total 12 37 173

Mean: = = 3.08 trees per plot

Trees/acre: 3.08 x 250 = 770Stocking: 11 of 12 plots = 92%

2

(Y)2Population variance: $ ni n

173 (1369)2 12 =5.36

Standard deviation: s =6= 2.32

536Standard error: s= =/''' = 0.67

Mean with standard error: 3.08 ± 0.67

Confidence limits (at .05) for mean: ± t(s7)

or3.08± 2.2 (0.67)

3.08± 1.47

Size of sample for 90% probability level:

t2s2 (1.7)2(5.36)n= = =62E2 (5)2

Sample size for commonly expected values of pcan also be read from tables listing confidenceintervals for binomial distributions (Freese 1962and 1967). The highest number of samples Isrequired when p is about 0.5.

The proportion (p) developed from a set of bino-mial observations and the statistics that charac-terize it are determined as follows:

1.

Proportion (p)Number of observations with the specified attribute

Total number of observations (n)

2. The standard error (se) of a proportion is:

s=i' Yn-1

If the sample Is a small fraction of the total pop-ulation (N), or

=' In-1 N

if the sample is a relatively large fraction of thetotal population (N).

3. Confidence limits, or an estimate of the reliabil-ity of the estimated proportion, can be calculat-ed for large samples (n>250) as:

P±(t(s)+_)

where t = the value listed in a two-tailed t-dis-tribution table for a chosen levelof probability.

Confidence limits for small samples can readilybe looked up in tables that cover a wide rangeof possible proportions (Mainland et al. 1956,Freese 1962 and 1967).

SAMPLING METHODSThe methods used to sample regeneration fall

into three general categories: those based on fixed-area plots, those based on variable-area plots, andthose based on aerial photography. The methodsdiffer in concept, approach, and the kind of data

produced. Each permits sampling at differentintensities and can be modified to satisfy morethan one objective. In concept and application,methods based on fixed-area plots are betterdeveloped and far more frequently used thanthe others.

Fixed-area Plots

Three different survey methods involve the useof fixed-area plots: the stocked-quadrat, the plot-count, and the staked-point. Each method hasits strengths and weaknesses. Using them incombination is often the best way to get the vail-ety of regeneration answers needed.

Several sizes and shapes of fixed-area plotshave been used in a variety of random and sys-tematic sampling designs. The same sizes,shapes, and distribution of such plots can servethree distinct evaluation objectives: (1) determin-ing the presence or absence of trees, species, orother objects of interest, (2) obtaining a quantita-tive estimate of trees, vegetation, or other objectsper unit area, and (3) measuring changes in num-ber, size, or composition of trees, vegetation, orother objects over time.

Stocked-quadratThe stocked-quadrat method primarily eval-

uates tree distribution. The presence or absenceof trees (stocking) on a given size of plot is deter-mined, not the total number of trees (density).The method Is fast and reliable, but it hassometimes been misapplied or its results mis-interpreted.

The stocked-quadrat method has been usedfor many years. W. C. Lowdermilk (1921) firstadvanced the concept of basing regeneration eval-uation on a unit of area rather than on the indi-vidual seedling. A decade later, I.T. Haig (1931)used the term "stocked-quadrat method" and suc-cinctly defined its basic concept:

the stocked-quadrat method, isbased on the assumption that if a givenarea is divided into squares of such a sizethat one established seedling or tree persquare will fully stock the square at matu-rity, then the percentage of units so

Regeneration Suiveys and Evaluation 359

stocked, regardless of total number ofseedlings per acre, indicates the proportionof land being utilized by tree growth.

The developers of the stocked-quadrat methodclearly identified its two key design features:

Actual stocking Is automatically comparedagainst full stocking, defined as a uniform dis-tribution of trees representing a specified den-sity per acre, andthe size of the sample plot used must have adirect and logical relationship to full stocking.

These two features are easily overlooked, andthrough the years they have been overlooked alltoo often.

When the stocked-quadrat method was firstdeveloped, square 1-milacre plots (Yi000-acrequadrats) were sampled, but for several reasonsthe use of square 4-milacre plots (V250 acre) wassoon recommended (Cowlin 1931 and 1932, HaIg1931). The larger plot size approximated the aver-age space per stem found in rotation-age whitepine or pole-size Douglas-fir stands. Full stock-ing in such natural stands averaged about 250reasonably well-distributed stems per acre.Modern-day full stocking goals can easily be seton a different basisthe number of well-dis-tributed trees per acre desired prior to the firstcommercial thinning, for example, or the numberof well-distributed trees required at the end of thereforestation period. Whatever the basis, fullstocking must be clearly defined in order to imple-ment use of the stocked- quadrat system.

To correctly apply the stocked-quadrat method,the size of the plot used must be the reciprocal ofthe number of stems per acre that constitute fullstocking (Table 15-3). For example, if full stockingis defined as 250 well-distributed trees per acre,presence of trees should be checked on plots /25o

acre (4 milacres) in size; if full stocking is 150 or500 trees per acre, plot size should be, respec-tively, '/50 or '/ acre.

If the plot-size requirement is not met, stockingwillbe overestimated or underestimated relativeto the goal specified. If too large a plot is used, theestimate is likely to be high because the largerthe plot, the greater the chance that it will beoccupied by a tree, yet the estimated number ofwell-spaced trees per acre is lower. For example,50-percent stocking (half the area occupied) as


Table 15-3. Dimension of stocked plot representing agiven number of uniformly distributed trees per acre.

Number of Plot dimension

uniformly distributed Area per Radius Side oftrees per acre plot of circle square

Milacres Ft Ft100 10 11.78 20.87125 8 10.53 18.67200 5 8.33 14.76250 4 7.45 13.20300 3.33 6.80 12.05400 2.50 5.89 10.44500 2 5.27 9.33600 1.67 4.81 8.52700 1.43 4.45 7.89800 1.25 4.16 7.38900 1.11 3.93 6.96

1,000 1 3.72 6.60

determined by 4-milacre ('/o-acre) plots indicatesthat 125 well-spaced trees per acre are presentin the entire area (at a minimum density level of250 per acre in the stocked portion), whereas 80-percent stocking by 8-milacre ('/,s-acre) plots Indi-cates that only 100 well-spaced trees per acre are

present. If too small a plot is used, the estimateof stocking is likely to be low because the smallerthe plot, the less the chance that it will be occu-pied by a tree, yet the estimated number of well-spaced trees per acre is greater. For example,40-percent stocking as determined by 2-milacre('/500-acre) plots indicates that only 40 percent ofthe area is occupied, but if the estimate wereexpressed in terms of the entire area, 200 well-spaced trees per acre are present. Density in thestocked area (40 percent of the total) is assured tobe at least 500 trees per acre.

Surveying regeneration by the stocked-quadratmethod Is fast and simple (Figure 15-6). Sampleplots are usually located at designated intervalsalong traverse lines evenly spaced across the areato be evaluated. Use of a single plot at each sam-pling point is recommended. Sampling a cluster ofplots at each point does not provide truly inde-pendent data for each quadrat in the cluster, nordoes it foster good distribution of plots over thearea. Chain-length (66-ft) intervals between plotsand close spacing of lines produced the mostaccurate estimates in an Idaho study (Haig 1929).

Figure 15-6. In the stocked-quadrat method, searching of a plot ceases as soon as the first acceptabletree is found.

In a comparison of four methods in BritishColumbia. sampling a single 4-milacre quadrat ateach point was cheapest, and results comparedfavorably with those produced by four quadrats persampling point (Allen et al. 1951). CIrcular plots areusually used now instead of square plots becausethey are easier to delineate and search from a sin-gle center point. The sampling intensity is general-ly low; the area sampled usually totals less than 1percent of the tract.

A sample plot Is considered stocked if at leastone acceptable tree is found and nonstocked if noacceptable tree is found. Stocking status of a plotcan be determined seconds after its center point islocated if trees are abundant, good-sized, or unob-scured by competing vegetation. If no acceptabletree Is spotted at first glance, the plot area is sys-tematically searched. Searching ceases as soonas the first acceptable tree is found. Searchingthe plot for individual species or making supple-mental observations or growth measurements canalso be done, but such additional tasks severelyreduce the speed and simplicity of the stocked-quadrat method.

A single stocking percentage is calculated for thearea surveyed by dividing the number of stockedplots by the total number sampled or by the num-ber considered stockable (Figure 15-4). The stock-ing percentage thus calculated is a compositevaluean estimate of the proportion of the totalarea that is occupied by well-distributed trees. ifthe stocking percentage Is high, good distribution oftrees over most of the area is certain. If it is mediumor low, the indicated number of trees per acre mayor may not be well distributed. For example, 50percent stocking could indicate either that everyother plot was stocked throughout the total area (auniform distribution at low density) or that all plotswere stocked in half the area and none werestocked in the other half (a poor distribution rela-tive to the total area). Stocking results must beplotted to determine how uniform or nonuniformstocking Is over the area being evaluated.

Stocking pattern can readily be determined byplotting stocked and nonstocked plots on a map ofthe area. Voids may then be identified by inspectionor defined by the number and arrangement of non-stocked plots that constitute an undesirable gap.Observations recorded by field examiners abouttree occurrence or distribution along and adjacent


to traverse lines can be very helpful for interpret-ing the plotted stocking pattern.

From the stocking percentage, one can logicallyInfer the minimum density of suitably spaced treespresent per acre (stocking percent times numberof trees required per acre for full stocking equalsminimum density). Actual density is frequentlymuch greater. For example, a conversion curve pre-pared by Bever and Lavender (1955) for naturallyestablished conifers on clearcuts in western Oregonindicates that, on the average, 50-percent stockingby 4-milacre plots represented an actual density ofnearly 400 trees per acre, and 75-percent stockingrepresented 900 or more trees per acre. Theassured minimum density indicated by these stock-ing percentages is only 125 and 188 trees per acre,respectively. The minimum density deduced fromthe stocking percentage is most useful for judgingwhether an area meets a prescribed standard forminimum number of well-distributed trees peracre. In many plantations, the minimum densitymay be only slightly less than the actual density.

Over the years, various stocking classes andstocking standards have been used. Stocking class-es recommended by the Pacific Northwest Seedingand Planting Committee (Reynolds et al. 1953), andthe range in likely number of naturally establishedtrees per class, are shown in Table 15-4. In plant-ed stands, good stocking usually comprises sub-stantially fewer trees than in natural regeneration.unless substantial natural nil-in has occurred. inthe past, 65- to 70-percent stocking of 4-milacreplots or 30- to 40-percent stocking of 1-milacreplots has been considered satisfactory. Currentlythere is no consensus on what level is satisfactory;as already emphasized, management objectivesdictate the stocking goal.

Table 15-4. Stocking classes adopted by the PacificNorthwest Seeding and Planting Committee (Reynoldsetal. 1953).

Stocking class Stocking level (%) Likely tree density4 milacres 1 milacre (no. per acre)

Nonstocked 0-9 0-4 0-35Poor stocking 10-39 5-19 36-319Medium stocking 40-69 20-49 320-1,459Good stocking 70-100 50-1 00 1,460+


Stocking data are appropriately analyzed bystatistical procedures for binomial distribu-tions (see Principles of Sampling, this chapter).Relationships between stocking and variables of abinomial nature can be tested by contingency-table methods. The procedures and interpretivelimits for such methods are found in statisticaltextsfor example, Freese (1967) or Snedecorand Cochran (1980).

The stocked-quadrat method is flexible as wellas simple because one size of plot will accommo-date all sizes of trees, from the smallest accept-able seedling to the largest size encompassedby the definition of full stocking. Trees withcrowns larger than those included in the full-stocking definition cause minor complications,for they may dominate plots not occupied by theirstems. Such plots might be classed as condi-tionally stocked, as Dick (1963) suggested, orthey might be classed as nonstockable in termsof regeneration.

If the presence of a second or third tree isrecorded for stocked plots, particular care isneeded in data summation not to negate the dis-tribution concept of the stocked-quadrat system.For example, weighting plots by the number oftrees found will raise the stocking percentage, butthe resulting value no longer represents the areaoccupied by well-distributed trees.

Stocking percentages derived from sets of plotsof different sizes are not comparable values andthus may not be added or averaged together. Eachsize of plot represents a different standard forevaluating regeneration, and each resultingstocking percentage reflects what proportion ofthe plots examined met that standard. If averagestocking is to be calculated for a group of regen-eration areas, the plot size used on all areas mustbe the same. Some empirical calculations havebeen made relating stocking on one size of plotto that on another size (Weliner 1940, Allen et al.1951, Grant 1951, Ghent 1969), but there is nostraightforward conversion among stocking per-centages based on different-sized plots.

Plot-count

The plot-count method primarily evaluatesdensitythe average number of trees per acre. Itis a well-known method used both to evaluate

regeneration and to inventory older stands. Use ofthe plot-count method is simple and straightfor-ward. Generally, plots of uniform size and shapeare systematically located along equally spacedtraverse lines. Each plot is searched entirely todiscover and count all acceptable trees (Figure15-7). Neither a specified stocking goal nor a cer-tain size or shape of plot are required for correctapplication of the method unless percent stockingis also to be determined.

It is often desirable and efficient to determinestocking, density, and growth of regenerationfrom observations made on the same set of plots.This can be done by the plot-count method if theplot size reflects the stocking goal, as emphasizedfor the stocked-quadrat method. Stocking, treeheight or growth rate, and tree-count data fromthe same plots can be summed, analyzed, andinterpreted separately, each kind according to thestatistical procedures that apply.

In the plot-count method, several other consid-erations also affect choice of plot size. The entireplot area must be searched for trees, so searchtime Is directly proportional to size of the plot.Large plots are more difficult than small plots tosearch thoroughly without resorting to partition-ing. The shape of the plot influences how readilyit can be laid out and searched; round plots aregenerally used. Many small trees may be foundon some plots; counting them all can provetedious, and many trees on Just a few plots maysharply increase the estimate of the average num-ber per acre. Such an average does not reflect thenumber of trees per acre common on most of thearea, or the number likely to become crop trees.The stocked-quadrat concept was develop-ed to overcome precisely this problem (Lowder-milk 1927).

When trees are likely to be numerous In aregeneration area, the size of plot may be reducedto facilitate plot counts. If plot size must be keptlarge to yield a valid stocking estimate, treesmight be counted only on a specified fraction ofeach plot, or an upper limit (perhaps 10) might beset on the number of trees counted per plot. Ifsuch a restriction is placed on the tree count, a trueaverage for trees per acre cannot be determined.

Although it is easy to include trees of all sizesin plot counts, a broad mix of sizes and ages caus-es some problems. A pooled count of large and


Figure 15-7. In the plot-count method, each plot is searched completely to obtain a total count of acceptabletrees.

small trees yields an average that is intrinsicallydifferent from one based on trees of similar sizebecause fewer large trees than small trees canoccupy any given area. For such mixed stands,counting and interpretation methods might bemodified. Seedlings and saplings could be count-ed on relatively small plots and larger trees count-ed or measured for diameter or basal area on largerplots, or the regeneration inventory might simplybe restricted to a count of seedlings and saplings.If large and small trees are counted separately,some means of combining the results is necessary,both to provide a logical basis for comparing actu-al trees present to the number desired and to iden-tify the portion of the area unavailable forregeneration because It is occupied by larger trees.

Supplemental information on site conditionscan be obtained just as readily on plots where treesare counted as on those where only the presence orabsence of trees is noted. Numerical values for thetrees present and for site conditions permits cor-relation or regression comparisons that are notpossible when only the presence or absence oftrees is recorded.

Tree-count data can be summed and averagedeasily (Table 15-2). Statistical procedures for nor-mal populations are most often applicable to tree-count averages (see Principles of Sampling, thischapter) unless the occurrence of seedlings is soinfrequent that statistics for the Poisson distribu-tion are more appropriate. The average for treesper acre is calculated by multiplying the average


Figure 15-8. Only acceptable trees spaced a designated distance apart are tallied in one modification of theplot-count method. Ribbons mark four acceptable trees spaced 8 ft apart on this plot.

number per plot by the reciprocal of the plot size.This average is a composite value that provides lit-tle or no Information about tree distribution.Plotting tree counts on a map is necessary to learnwhere trees are abundant, sparse, and absent.

In recent years, the plot-count method hassometimes been modified to include a tree-spac-ing requirement. Relatively large plots ('Iwo acre orlarger) may be searched, and only acceptable treesthat are spaced a prescribed minimum distanceapart are tallied (Figure 15-8). Tree counts fromsuch plots can readily be summed and reportedas the number of well-spaced trees per acre.Variability can also be determined, but calculationof confidence limits is hampered to the extent thatthe Inherent frequency distribution of spaced tree

counts is unknown. Stocking estimates may alsodiffer in meaning because spaced tree counts areusually made on plots whose size does not direct-ly reflect the stocking goal. Plotting the number ofspaced trees per plot on a map is probably lessinformative than plotting the full count of treesper plot.

Knowing the average number of trees per acreis more informative for an older stand than for astand of young regeneration. When trees reachsapling size or larger, natural competition hasalready produced some uniformity of distribution;whereas in very young stands, few seedlings havebeen suppressed and large numbers of seedlingsmay be found on very small areas. An average fortotal number of young seedlings per acre may look

impressive but be quite deceiving, for ittells little about the actual area occupied,the stand density common to most of thearea, the spatial distribution, or the num-ber of trees likely to become crop trees. Ahigh average per acre could represent aneven distribution of trees over the area, orit could mean that half or less of the areais crowded and the rest sparsely stockedor nonstocked. Thus, the unmodified plot-count method of sampling regeneration isgenerally less useful than the stocked-quadrat method.

The nature of the tree distribution (spa-tial arrangement) on an area can be deter-mined from the tree count data obtainedon fixed-area plots. A nonrandomnessindex is calculated by the formula(Payandeh 1970):

NI =

where NI = nonrandomness index bythe fixed-plot (quadrat)method,

V = the variance of the numberof trees per plot,

y

nM

(E)2


Figure 15-9. Repeated examinations at staked points or plots pro-= number of trees on a given vide the best insights on regeneration dynamics.

plot,= number of plots, and= the mean number of trees per plot.

The expected outcome from this calculation is 1 forrandom populations, less than 1 for uniform pop-ulations, and greater than 1 for clustered or aggre-gated populations. The size of plot used affects theestimate produced by this formula (Greig-Smith1952, Payandeh 1970).

Staked-pointThe staked-point method is primarily used to

ascertain changes in the same trees or plots overtime and only secondarily, If at all, to determinethe stocking or number of trees per acre. It is

commonly used in research and operational stud-ies, and under certain conditions it is used toevaluate results of routine reforestation efforts.

Repeated examination of the same trees orplots provides insights on regeneration and vege-tation dynamics (Figure 15-9). It is the most directmethod of evaluating results of a new refores-tation practice or comparing results of differentpractices in small-plot, pilot-scale, or large fieldtrials. From a statistical standpoint, samplingvariation is reduced by repeated measurement ofthe same trees or plots, and covariance analysistechniques can be used.

In the staked-point method, either individualtrees are tagged or plots of various sizes andshapes are established and marked. The data


obtained through repeated observations may be"yes" or "no" responses, numerical counts, ormeasurements; the appropriate summation andanalysis techniques will vary accordingly.Depending on study design and objectives, It maybe appropriate to plot results on a planimetricmap to discover the influence of field location onsurvival or growth.

The staked-point method is flexible in scope,design, layout, and choice of permanent pointsor plots. Such flexibility also has drawbacks. Eacheffort tends to become an unreplicated case study,thus Impairing opportunities for combining re-sults and strengthening inferences from similarefforts. Moreover, permanent study plots are morecostly in labor and materials than the temp-orary plots used In the stocked-quadrat or plot-count methods.

The most useful operational application of thestaked-point method is to monitor the outcomeof planting or spot-seeding efforts. If sample trees

or spots are marked during planting or seeding,the marked locations can be reexamined with thecertain knowledge that regeneration or seed wasoriginally there. The choice of sample to markvaries slightly depending on the objective. If theobjective is to evaluate a reforestation method, auniformly high quality of planting or seedingshould be achieved to fairly test the method. Ifthe objective Is to determine the average resultsfor an area or crew, the sample should representa cross section of crew work, with efforts of allcrew members about equally represented. Foreither objective, enough samples must beobtained to determine consistency of response ondifferent days, aspects, slopes, and other envi-ronmental strata.

If planting or seeding is done at precise spac-ing and with very few skips, as In a Christmas-treeor progeny-test plantation, It is possible to evalu-ate survival using the staked-point approach with-out actually staking trees or spots (Figure 15-10).

Figure 15-10. Accurate survival estimates can be made witho Ut prior staking of trees if they have been plantedat a known, precise spacing.

A simple way is to count the points where treesare present and absent in specified rows or areas.Reforestation success can be expressed as percentof the total number of points in the sample that areoccupied by acceptable trees. Successful use ofthis technique hinges on knowing for certain thattrees (or seeds) actually had been placed wherethey are now absent.

Evaluations based on precision spacing arecommonly used in New Zealand (M.I. Menzies,Survival assessment in young stands; Forestestablishment report 23, New Zealand ForestResearch Institute, Rotorua, New Zealand, 1971).A plot size one planting row wide and 10 or moreplanting spaces long is used to assess survival.Several schemes for offsetting successive plots areemployed to avoid sampling the same rows acrossthe tract. Up to 10 percent of the area may be partof the sample. In one variation of the method, threeor more trees missing consecutively constitute anundesirable gap. One-hundred-percent effectivestocking equals the number of trees original-ly planted.

The staked-point method requires costly andsustained effort in laying out plots, staking andtagging trees, renewing markings, and makingrepeated examinations, but it is the best way tolearn how regeneration develops and how it isinfluenced by competition and other environmentalfactors. Because it focuses only on marked trees orspots, it may not adequately measure stocking ortrees per acre, particularly when natural regener-ation supplements the initial planting. A stocked-quadrat or plot-count regeneration survey mayoften be needed at the end of the reforestation peri-od to provide a comprehensive evaluation of allregeneration present.

Variable-area Plots

Some attributes of regeneration stands can beevaluated best by variable-area plot methods.Although opposites in sampling concept, variable-plot and fixed-plot methods share common evalu-ation objectivesdetermining stocking, density,and spatial arrangement of regeneration. In vail-able-plot methods, plot size is not fixed; it isdefined plot by plot by the density or height of theregeneration being sampled. An informativediscussion of the relationship between fixed- and


variable-plot evaluation methods can be foundin MacLeod and Chaudhry (1979). Two generalforms of variable-plot methods that pertainto regeneration evaluation are described inthis section.

DistanceThe term "distance method" encompasses a

variety of techniques in which primary emphasisis placed on determining spatial arrangement,stocking, or stand density by measuring the spac-ing between plants instead of estimating theseattributes from the number of plants found onplots of known area. Distance measurements fortrees or other plants have been expressed in fourgeneral forms:(1) as the distance from a randomly located point

to the nearest tree,(2) as the distance from a randomly selected tree

to its nearest neighbor,(3) as the point-to-tree distance as defined in (1),

then as the distance to the tree's nearestneighbor located beyond a line drawn throughthe tree at a right angle to the original point-to-tree line (T-square sampling), and

(4) as the distances from a randomly located pointto the first, second, third,.. .and nth nearesttrees (Dennis 1984).

Distance methods were developed to meet theneed for speedily characterizing vegetation in eco-logical studies. When discrete plants can be iden-tified, it is faster to measure the distance betweena point and a plant or between two plants than tomake a total count of plants on fixed plots ingrass, forb, or shrub communities. Alternates tofixed-plot methods were also sought because esti-mates of spatial arrangement are strongly influ-enced by plot size (Pielou 1977). The use ofdistance methods to evaluate forest stands, par-ticularly regeneration, has been quite limited, butusing them corredily may sometimes supply need-ed information most efficienUy (Daniels 1978).

Distance methods are generally preferred overfixed-plot methods for determining spatialarrangement, and they offer a flexible way to esti-mate stocking. They are less useful for determin-ing density because the nature of the populationsampledwhether it is uniform, random, or clus-teredinfluences results. Although much effort


has been expended to date, no single distancetechnique has proved suitable for estimating den-sity In all kinds of populations. Only the best devel-oped, most useful distance techniques will bedescribed here; consult ecological texts such asPielou (1977) and Vandermeer (1981) for theoreti-cal and empirical concepts and limitations of dis-tance methods.

To determine spatial arrangement, the distancefrom a randomly or systematically designated pointto the nearest tree is measured at enough points toprovide a representative sample of the populationbeing evaluated. A dispersion index can be calcu-lated from the point-to-tree measurements by theformula developed by Pielou (1959) and used byPayandeh and Ek (1986) in the form:

NI=7tDW(

where NI = Pielou's nonrandomness index,it; = 3.14159,D = an Independent estimate of density

from quadrat sampling,= the average squared distance from

W random points to the nearest tree ateach point, and

m = number of distances measured.

The expected value is 1 for a random population,less than 1 for a uniform population, and greaterthan 1 for a clustered or aggregated population.Departures from 1 can be judged by inspection ortested for significance by chi-square test (Pielou1959, Mountford 1961).

In ranking three satisfactory methods forassessing spatial distribution, Payandeh (1970)concluded that the quadrat method was most sen-sitive, but results may be greatly affected byquadrat size. The point-to-plant distance methodwas not affected by plot-size considerations andwas easier to use than the Hopkins pooled coeffi-cient of aggregation method. He concluded, there-fore, that the point-to-plant distance methodwas best.

Even though spatial arrangement is best identi-fied by distance measurements, the need for datafrom fixed-area plots is not completely eliminated.A valid estimate of density cannot be developedfrom the distance measurements themselves

unless it Is known beforehand that the populationbeing sampled is random (Pielou 1977). Thus,when testing for randomness of an unknown pop-ulation, an independent estimate of density has tobe made by use of fixed-area plots. Pielou (1977)also points out that a random sample of individu-als in a population is not obtainable by selectingthose that are nearest to random points becauserelatively Isolated individuals will be overrepre-sented in such a selection procedure.

Stocking can readily be determined from a setof distances obtained by measuring from randompoints to the nearest tree (Figure 15-11). In fact,such measurements provide a means of calculat-ing stocking for more than one size of fixed plotand concomitant stocking goal (MacLeod andChaudhry 1979). All distances from a point to atree that are shorter than the radius of a circularplot of a designated size represent stocked plots.Distances greater than the chosen radius repre-sent unstocked plots. Percent stocking equals thenumber of plots (distances) stocked divided by thetotal number examined.

A set of distance measurements also provides aready means for evaluating the sizes of unstockedopenings. In effect, each distance measured froma point to the nearest tree defines a circular,unstocked opening. The number of measurementsthat represent openings greater than a definedspacing can be counted. Minimum, maximum, andaverage size of opening can be determined also,provided some distance measurements have notbeen truncated by limiting them to an arbitrarymaximum distance, as is often done. Large sam-pies are needed to obtain dependable estimates ofthe frequency of open space (Persson 1964). Aswith fixed plots, the stocking or the size of open-ings can be plotted on a map to gain an under-standing of the occupancy pattern on the sam-pled area.

Several forms of the distance method providereliable estimates of stand density when the pop-ulation sampled is randomly distributed (Morisita1957, Batcheler 1971, Payandeh and Ek 1986).Estimates for populations whose distributions areuniform or clustered are often biased; i.e., the den-sity estimates are either high or low relative to theactual known population. Many adjustment fac-tors have been proposed and tested in the hope offinding one that would be universally applicable,


Figure 15-11. Data obtained by measuring the distance from sample points to the nearest tree permit estimatesof stocking relative to different density goals.

but so far all have proved unsatisfactory because ofestimate biases or impracticality (Lyon 1968,Mawson 1968, Batcheler 1971, Laycock andBatcheler 1975, Kaltenberg 1978, Dennis 1984,Delince 1986, Payandeh and Ek 1986). Given thisstate of knowledge, stand density should be esti-mated by distance methods only when populationsare known from experience to be randomly dis-tributed or to depart from random distribution Insuch a way that the extent and direction of biasesare known and can be dealt with.

In sampling regeneration that Is distributed ran-domly, distance is measured from a point to thenearest tree at enough randomly or systematicallylocated points to provide a representative sample.Density Is then calculated (Morisita 1957, Laycockand Batcheler 1975) as:

n-1LI

r2

where D = average number of plants per ft2,

n = total number of distances measured,it =3.14159, andr = distance in feet from sampling point

to nearest plant;and the variance of D as:

VananceD = n-2The average spacing is calculated as:

-frr=n

If density estimates are desired for individualspecies, a separate set of distance samples must betaken for each species. Treating all species as asingle population and determining compositionfrom the proportion of times each species occurs Inthe total measurements results in biased compo-sition estimates (Laycock and Batcheler 1975).


Vertical-line and vertical-point

Vertical-line and vertical-point methods of eval-uating regeneration are based on the concept ofsampling with probability proportional to treesize, the same concept widely used in samplingolder stands. In such stands, diameter is the mea-sure of size sampled from "horizontal" pointsor lines, whereas in regeneration stands, heightis the measure sampled from "vertical" pointsor lines (Bickerstaff 1961, Beers and Miller1976). Height is used for evaluating regenerationbecause it is a more meaningful and practical cr1-tenon than diameter, particularly for smallseedlings. The four applications of the variable-probability concepthorizontal-point, horizontal-line, vertical-point, arid vertical-lineare alsoreferred to as polyareal methods.

Techniques for use of vertical-line sampling arewell developed (Beers 1974, Beers and Miller1976, Eichenberger et al. 1982), whereas those forvertical-point sampling are not. The underlyingconcept is the same for both, but the line methodis preferable because sampling is proportional toseedling height rather than to the square of theheight (Bickerstaff 1961). When used for evaluat-ing regeneration, the vertical-line method canproduce unbiased estimates of frequency (interms of height), density, and linear feet of heightper acre.

Illustrated descriptions of the concept, fieldtechniques, and statistical calculations for verti-cal-line sampling are given by Bickerstalf (1961)and by Beers and Miller (1976), and use of themethod In an Integrated sampling system is dis-cussed by Eichenberger et al. (1982). BrIefly,short sample lines are systematically or random-ly located and regeneration is surveyed on oneside of each line, designated at random (Figure15-12). A line 43.56 ft long Is recommended whichwould contain 10 segments or quadrats each4.356 ft long. Other lengths of line can be used ifappropriate adjustments are made in the mathe-matics involving length of line. Likewise, a verticalangle of 45° Is recommended because of its sim-plicity for determining which trees are in andwhich are out. If 45° is used, trees can be judgedas "In" simply by determining whether they aretaller than the horizontal distance measured atright angles from the sample line to the base of

It

Sample line

Figure 15-12. In the vertical-line method, seedlingsand saplings are sampled proportional to their height(Beers and Miller 1976).

the tree. Thus, most of the regeneration count canbe based on visual height estimates, confirmedas necessary wIth a calibrated pole. A 45° anglegauge Is used to determine if taller and more dis-tant trees exceed the height subtended by thegauge. Procedures for correctly gauging the heightof trees on slopes and for judging the inclusion ofborderline or leaning trees are detailed by Beersand Miller (1976). The count of "in" trees can berecorded by species and height classes for theentire length of line or can be tallied for eachquadrat If confidence limits are to be calculated.

Beers and Miller (1976) report that the usualcalculation for number of samples required (seenormal distributions in Principles of Sampling,this chapter) results In unreasonably high num-bers of lines needed on areas less than 200 acresIn size. An appropriate formula based on variationin line data has not yet been developed. They sug-gest a rule of thumb of no fewer than 10 lines perarea under 10 acres, 1 per acre for areas 11-40acres, and 0.5 per acre for areas 4 1-80 acres.

Frequency or stocking on individual lines maybe calculated for a single species, for all species,or for any of a designated group, as:

Erequency (%)Number of quadrats in which the species occurred x 100

Number of quadrats sampled (usually 10)

An average frequency Is calculated by averagingthe frequencies from all lines sampled. Take notethat these frequency values are not the same asfrequency, occurrence, or stocking values obtainedfrom sampling fixed-area plots. Percent frequencyobtained by the vertical-line method denotes therelative number of quadrats that are stocked by agiven species or group to a height level equivalentto at least 10,000 lineal ft per acre. To obtain theusual kind of frequency or stocking estimate,observations must be taken on fixed-area quadratslocated along the sample lines.

The average number of trees per acre (density)for any height class Is calculated as:

1 10,000 ) Tree countDensit'I Fleight class midpoint Total quadrats sampled)

when the regeneration sample is based on a gaugeangle of 45°, a line length of 43.56 ft divided Intoten 4.356-ft segments, and a height factor (Z) of10,000 ft. If other parameters are used, a differentheight factor must be calculated (see Beers andMiller 1976). Total number of trees per acre isobtained by summing trees per acre for all speciesand height classes.

The lineal feet of height per acre for a species, aheight class, or for all classes, is calculated as:

Tree countHeht Z quadts sampled)

where Z = a height factor, usually 10,000.

If height or tree-count data are tallied by indi-vidual line segments or Individual lines, standardstatistical formulas can be used to calculate thepopulation variance, standard deviation, stan-dard error of the mean, and confidence limits (seenormal distributions In Principles of Sampling,this chapter).


Aerial Methods

Direct aerial observation and photogrammetricinterpretation of aerial photographs can yieldsubstantial Information about regeneration.Aerial methods currently complement groundsurvey methods in western forests, but in someregions they are becoming a primary means ofevaluating regeneration and site conditions(Nelson 1977, Goba et al. 1982, Kelder 1983,Goba 1984, Hall 1984, Hunter et al. 1985). Aerialmethods make it possible to cover many areasrapidly and economically, and they provide anoverview and pictorial record not obtainable byother means.

The use of aerial photographs is now a rou-tine part of some western preplanting efforts(Figure 15-13). After logging is completed, large-scale pictures are taken and photogrammetricmethods used to determine the exact acreageand to produce a base photo map of the area. Thephotos also provide Information about slash,residual vegetation, and surface conditions need-ed to complete site-preparation and reforesta-tion plans. Overlays can be produced thatdelineate acreage to receive site preparation, ani-mal protection, and different kinds of stock. Afterregeneration is established, aerial photos can beretaken for broad-scale monitoring of tree andvegetation development and to determine theextent of seedling damage from frost, root rots,and other highly visible damaging agents.

The evaluation of stocking and densityfrom aerial photos has been tried in the West,but results have been less specific than desired.Low-level photos of plantations in the TillamookBurn in northwestern Oregon were first stud-ied In 1955; a study in 1964 compared resultsfrom photos taken at several altitudes withresults of ground surveys in eight planta-tions (Smith 1964). These pioneering efforts indi-cated that:

Photographed from a 1,000-ft altitude, conifertrees with a crown diameter of 2.5 ft or largercould be recognized as trees 80-85 percent ofthe time.Where evergreen plants such as salal, swordfern, and Oregongrape were common, errors ofomission and commission ranged from 24 per-cent to over 50 percent.


Figure 15-13. Large-scale aerial photos with overlays facilitate evaluation of site conditions and delineation ofareas for site preparation, planting, and animal and vegetation control. From USDA Forest Seivice, WaldportRanger District, Siuslaw National Forest.

Mineral soil had distinctive coloration, allowingan accurate delineation of areas with receptiveseedbed.Conifers overtopped by leafless alders could beevaluated for density, size, and possible releasetreatment.In another study, ponderosa pine seedlings

4-10 Inches tall were readily Identified in rela-tively bare areas near Klamath Falls. Therewas enough spectral differentiation to make Itpossible to Identify the larger seedlings among aheavy cover of weeds and debris (Schaefer 1978).In the same study, over 90-percent accuracywas reported for Identification of 14- to 16-inch-tall Douglas-firs in weeds and brush nearSpringfield, Oregon, and for 1-year-old Douglas-firs interplanted among 2- to 8-year-old residualDouglas-firs and hemlocks near Twin Harbors,Washington. A trial survey of conifer stock-ing under leafless vine maple and cherry inwestern Washington indicated that trees lessthan 3-4 ft tall were too small or did not contrastsufficiently with background vegetation to be seenamong the hardwoods (Haapala and Neu-mann 1972).

Evergreen species such as chinkapin, Ore-gongrape, salal, and sword fern hindered seed-ling counts in these studies. Occurrence ofevergreen plants with conifers is commonthroughout the West. To distinguish them fromsmall conifers on aerial photographs remains avexing problem.

The development of aerial methods to evaluateconifer regeneration is most advanced in easternCanada, where the status of regeneration had tobe determined on large areas. Aerial surveys per-mitted the classification of areas as regenerated,not regenerated, or doubtful, and thus substan-tially reduced the amount of ground work need-ed (Goba et al. 1982, Hall 1984). Techniques foridentifying species and for estimating stockingand stand density on fixed-area photo plots havebeen worked out and tested, and limited compar-isons have been made between results of aerialand ground surveys (Ball and Kolabinski 1979,Goba et al. 1980 and 1982, Kirby 1980, Goba1984, Hall 1984, Ashley and Cohen 1985, Hunteret al. 1985). These conclusions were drawn,based primarily on efforts to assess stocking anddensity on 1- to 4-milacre plots:


By use of aerial methods, the forest managercan obtain a graphic understanding of regenera-tion conditions on the area.At scales of 1:600 and larger, photography canbe used to accurately assess regeneration 30cm In height and taller.Species Identification of trees 90 cm in heightand taller is possible with over 90-percent accu-racy.Stocking can be more readily assessed thanseedling density. Areas that appear well stockedon aerial photos require no ground checkingbecause actual density will be greater than theamount visible.Some ground surveying will always be neces-sary, if only to maintain accuracy of photo inter-pretation.

The usefulness of aerial methods for reconnais-sance and for quickly stratifying tall regenerationinto broad classes was clearly evident. For detect-ing the presence of small seedlings it was lessthan satisfactory.

Low-level infrared photography has been used toevaluate regeneration in some southern pine plan-tations since 1972 (Kelder 1983). The gains report-ed include better use of field crews, more accurateacreage figures, more reliable input data for yieldprojections, and timely replanting of regenera-tion failures.

More use of combined aerial and ground surveytechniques is likely in the West as the technologyimproves. There are several obstacles to overcome,however. The presence or absence of smallseedlings must be discovered early in the refor-estation process so that needed remedial actioncan be taken promptly: even in later surveys, thepresence of small seedlings often has important sil-vicultural implications. Ways must also be found todistinguish conifer seedlings from associated ever-green vegetation on photographs of many areas.The varied weather conditions in the West canmake it difficult to take photos exactly when need-ed. Conifer regeneration should be photographedfrom late fall through early spring when decidu-ous plants are leafless and dormant. Good flyingweather can be infrequent during the dormant sea-son, and many regeneration areas are covered withsnow until early spring. The short time availableto take photos may be offset, however, by the sub-sequent flexibility afforded by those photos in


evaluating regeneration. Finally, It is unlikely thataerial methods will be useful for evaluating re-generation under shelterwoods or semi-closedcanopies or in old-growth stands.

COMPARISONS OF SURVEYMETHODS

The preceding descriptions of ground surveymethods would not be complete without providinginformation about their relative usefulness, ease offield application, and reliability of data produced.Such comparisons are not straightforward or sim-ple because the survey methods are based ondifferent concepts and objectives and are notdesigned to gather identical information. In fact,the choice of survey method depends, inpart, on what kinds of data are to be obtained.Nevertheless, some experimental comparisonshave been attempted, and an objective look at theprocedures required also seems possible.

Field Procedures

Three distinct time components can be recog-nized in sampling regeneration on an area: (1)walking time between plots, (2) boundary delin-eation and search time at the point or plot, and(3) tIme required to tally Information. Of these,the plot delineation and search time is the compo-nent likely to vary most among the different sur-vey methods.

Walking between plots takes up a large portionof the total time required by every survey method.Walking time is likely to be similar for all surveymethods if equally good coverage of the area andequally precise estimates are to be obtained.Topography, vegetation, weather conditions, andother physical factors heavily influence the rate oftravel (Figure 15-14). Time studies conducted in20-year-old cutovers in coastal forests of BritishColumbia Indicated that about 3 hours wererequired per mile of travel between plots (Allen etal. 1951). The time required may be substantiallyless in recent cutovers where burning of slash andtemporary reduction of competing vegetationmakes travel easier. Careful planning of the sur-vey route to minimize lead-in and backtracking

distances can speed sampling on a set of trav-erse lines.

The time required for laying out and searchingplots Is strongly Influenced by their number,shape, and size. Since many observations areneeded to obtain good estimates of stocking andstand density, the number of sample plots requiredmay not differ greatly among survey methods.

Circular plots are generally used now in regen-eration surveys because they are usually easier todelineate and search than plots of other shapes.Circular plots /00 acre in size or smaller can readi-ly be located and searched by one person, where-as a two-person crew is desirable for rectangular orlinear plots when placement of a large frame orstretching of a measuring tape is required. Theshape of plot to use is largely a matter of conve-nience, whereas the size of plot affects both searchtime and data Interpretation.

The time required to search a plot for seedlingsis generally proportional to the size of the plot, butthere are exceptions, depending on which surveymethod is being used and whether a search of theentire plot is necessary. Clearly, methods thatrequire a complete search of every plot are moretime-consuming than those that do not. Thus,among fixed-area methods, the stocked-quadratmethod is the fastest and the plot-count methodthe slowest. In the comparison trials by Allen etal. (1951), search and tally time required for thestocked-quadrat method was about half as longas for the plot-count method. It appears thatsearch time in variable-area methods would gen-erally fall somewhere in between the time requiredfor the stocked-quadrat and plot-count methods.In trials by MacLeod and Chaudhry (1979), dIs-tance measurements required about 25 percentmore time than determining stocking on clustered,rectangular milacre plots.

The abundance of regeneration has a markedinfluence on the search time required per plot. Ifseedlings are sparse and not readily visible amongcompeting vegetation, search time willbe substan-tial and will not differ materially among methods.The stocked-quadrat method will still be fastest,however, for search on a plot can stop as soon asthe first acceptable seedling is found; whereas theplot-count method requires that every plot besearched entirely. The difference between the twomethods in search time widens as seedlings

')I

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p&

's4

-:a

- - k 2

I*_'f.*'*I f_


.,,.' ;_

-1w- -.

e. i' -. ... p

-c:'. - ..

:1-.,. -

- e'

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Figure 15-14. Walking time between plots, strongly dependent on topography, woody residues, vegetation, andweather conditions, comprises a large portion of total time in every survey method.

become more abundant, since the first qualifyingseedling will be found with little searching, where-as the entire plot must still be searched andnumerous seedlings counted In the plot-countmethod. Search time In the stocked-quadratmethod may actually be less for large plots than forsmall plots because it is more probable that a high-ly visible seedling will occur on a larger plot thanon a smaller plot. Time comparisons made InBritish Columbia (Allen et al. 1951) provIde somemeasured evidence of these logical relationships.

The claimed advantage that no plots have to belaid out in variable-area or "plot-less" methods Issomewhat misleading, particularly for distancemethods. Although the actual measurement Ismade from a point to the nearest tree, a plot of that

radius must be searched to ensure that the iden-tified tree is actually the nearest one. When treesare abundant, only a small area needs to besearched, and search time may hardly be greaterthan for the stocked-quadrat method. But If treesare sparse, more area may have to be searchedthan would be required by the plot-count method.Although it is not heavily emphasized in the liter-ature, distance from a point to the nearest tree (orbetween nearest neighbors) is central to correctapplication of the distance concept; accepting thenearest readily visible tree reduces search time butis a marked departure from the concept. The dis-tance to the nearest tree must also be measuredat each point, which may take more time thanmeasuring to occasional borderline trees on fixed-

376 Regeneration Surieys and Evaluation

area plots. Hence, distance methods may oftenrequire search of a substantial area and do notappear to offer appreciable savings in search time.

Stratified sampling and sequential sampling aresuggested techniques to improve accuracy andminimize the number of piots required to achievea given level of statistical reliability, but each tech-nique has limitations. It is sound procedure todivide (stratify) into more homogeneous groupsand sample separately regeneration populationsknown or suspected to be dissimilar. The surveyresults will then not reflect as much of an "apples-and-oranges" mix and are likely to be easier tointerpret. The number of plots required per stra-tum may be less than for the undivided area, butthe total number for two or more strata could begreater. It is often uncertain before a survey ismade whether stratification is desirable or not.Likewise, fewer samples are needed to reliablysample a homogeneous population, but the degreeof population homogeneity Is usually not knownuntil survey data demonstrate it.

Sequential sampling has been advocated asa statistically sound procedure for minimizingthe number of samples taken (Smith and Ker 1958,Dick 1963, Fairweather 1985), but it has draw-backs, too. In sequential sampling, the variabilityamong samples is calculated or tallied as samplingprogresses. Sampling ends when the calcula-tions show that the data in hand meet the desig-nated level of statistical reliability. In concept,sequential sampling is based on successive ran-dom samples; fewer might be required, but locatingsuccessive random samples may be quite time-consuming. If sequential sampling is used inconjunction with systematic plot placement,only part of the area may get sampled, and re-generation conditions on the rest of the area willremain unknown.

Statistical ComparisonsEstimates of stocking and stand density have

been made for known or simulated populations tocompare the accuracy, precision, and efficiency offixed-area and variable-area methods (Kaltenberg1978, MacLeod and Chaudhry 1979). Samplingmethods vary in accuracy and precision; somehave been proven to yield biased estimates. Allmethods described In this chapter can yield unbi-

ased estimates of stocking or stand density if theyare used for the intended purposes and within thelimits described.

Distance methods have the greatest potential forbias in the estimation of stand density because theestimates are influenced by the distribution of thepopulation sampled. The nature and extent of suchbias has already been discussed briefly in the sec-tion on distance methods.

In general, the mathematical concepts and com-putations applicable to variable-plot methods aremore involved and complex than those applicableto fixed-plot methods. They are also not as welldeveloped and tested. With the availability of elec-tronic calculators and computers, the computa-tional requirements certainly present no handicap,but the added training required to use these meth-ods could be a substantial constraint.

SUMMARYThe status of regeneration needs to be evaluated

periodically during reforestation phases of standmanagement for a variety of purposes and at dif-ferent levels of precision. Not every regenerationsurvey should be a full-scale effort; often a well-planned reconnaissance will provide enough infor-mation to decide what the next silvicultural stepshould be. Forest managers and reforestation spe-cialists must identify regeneration- evaluationneeds and choose the sequence of evaluations thatwill best supply the required information.

In formation NeededRegeneration is evaluated best by applying sci-

entifically sound methods with good judgment.Information can be obtained on many differentattributes of regeneration by means of an array ofsampling techniques. Even before the explosionin computer technology, more information wastypically collected than was ever summarized andinterpreted. With the electronic processing capa-bilities now available, it is tempting to collect largequantities of data, but the need remains to keepregeneration surveys reasonably simple, flexible,and manageable. An admonition often seen postedin dining halls can be appropriately paraphrasedand applied to the collection of information on

regenerationcollect what you need and use allyou collect.

Insight, critical judgment, and restraint mustbe exercised in deciding what the key informa-tion needs really are. Obviously, stocking infor-mation is vitalto determine whether enoughtrees are present that management objectivesspecified for the area can be attained. But whatadditional information is essential? Number peracre? Height or growth of crop trees? Presence ofimpeding factors such as competing vegetationor biotic damage? Spatial arrangement? Eachattribute to be observed adds cost and complex!-ty to the survey.

Managers should examine critically whetheran average for total trees per acre is really needed.There Is a common tendency in managementplans and forest practice statutes to loosely defineregeneration goals in terms of trees per acre. Butare such goals based on total number or dis-tributed number of trees per acre? An estimateof total number per acre should usually not beneeded; In fact, such estimates can often be moremisleading than useful. In older stands, an aver-age for total number per acre is Informativebecause it reflects a spacing component thatdeveloped as stands closed and competitorsdropped out. In young regeneration, however, thisspacing effect has not yet occurred, so literallyhundreds of trees may be found in a small area.High numbers of trees on just a few plots can pro-duce a misleading average for total trees per acre.If a total count of trees; i.e., a density estimate.is not needed, either stocked-quadrat or distancemethods, which are substantially faster than plotcounts, can be used to estimate distribution;I.e., stocking.

Stability and continuity are Important featuresof any survey system. Once a system has beencarefully planned, field tested, and adjusted asnecessary, It should be used without modificationfor lengthy periods. Two purposes are served:comparable data are produced for successive fieldunits so that common attributes and differencescan be detected, and a data base will accumulatethat can be summarized periodically to showaccomplishments and trends. Soundly conceivedregeneration surveys made consistently for anumber of years can produce much informationto help improve reforestation practices.


Field Methods

Field sampling needs to be done by experiencedand conscientious observers who keep askingwhether observations on plots seem consistentwith what they see between plots. Accurately col-lected numerical data need to be supplementedby notes and general observations. Such obser-vations are invaluable for mapping voids and forhelping interpret the summarized data. Fieldobservers should be encouraged to diagnose andinterpret what they see. They are on the groundand usually have better insight on what the nextstep in the reforestation effort should be thananyone reviewing the data later. In the improvedsurvey system used by the British ColumbiaMinistry of Forests, observers are required to sumup survey data in the field and make an on-siteevaluation of silvicultural alternatives (Wyeth1984).

The use of intensive survey methods should bereasonably flexible. Minimize time and effortwhere regeneration status is self-evident--eitheradequate or inadequate. Save resources for moreIntensive sampling where regeneration status Isreally in doubt. Many samples are generallyrequired to produce good estimates, especiallywhen stocking is moderate and tree distribu-tion variable.

In sampling an individual area, it is critical torecognize that obtaining regeneration statisticsat specified confidence levels, although impor-tant, is not the primary objective. The primaryobjective is to learn the status of regeneration onthe area. This means sampling and looking atthe whole areanot stopping as soon as datashow that the mean for stocking or for numberof trees Is within specified levels of accuracy.When the area has been surveyed, it Is nice If theresulting mean has a low standard error, for Itindicates that the regeneration present Is reason-ably uniform, but if the standard error Is notlow, Information about the status of regenera-tion is still valid. A high standard error simp-ly means regeneration Is quite variable on thearea, and a suitable silvicultural follow-up willbe Indicated.

Timeliness is crucial. If regeneration is doingpoorly for any number of reasons (competition,frost, or damage from animals, Insects, or disease)


and is likely to be Inadequate, that Informationmust be known early enough so that deadseedlings can be replaced or other correctiveaction taken. Well-timed, periodic regenerationsurveys should produce information to guidereforestation efforts as well as to inventory regen-eration status for posterity. Both objectives needto be served, but making sure regeneration is ade-quate comes first.

Tradeoffs are often necessary in the timing ofregeneration surveys. It is easier to spot conifersamong competing vegetation during the dormantseason, but the intensity of competition fromdeciduous vegetation is best observed in the grow-ing season. Ease of spotting seedlings in the dor-mant season may be offset by the more adverseworking conditions often associated with that sea-son. Surveys should be scheduled for the timeof year when the primary objectives can bestbe attained.

Interpreting DataIt is vital that data summaries and ensuing

interpretations be made within the conceptualframework of the sampling method used.Choosing analysis techniques appropriate for thepopulation distributions involvedgenerally nor-mal, binomial, or Poissonis the key first step.

Avoid confusion as well as misinterpretation ofdata by careful Identification and use of the terms,stocking and density. These terms are not synony-mous, though they are often loosely used inter-changeably in describing older stands. Thedifference in meaning as well as their relationshipto each other are critically important when char-acterizing regeneration.

Units of measure can be a source of gross error.Values entered In formulas must be in the correctunits. Likewise, weighting of values can cause dif-ficulty. Be particularly wary when the presenceof more than one tree per plot is noted in a sur-vey; stocking must be tallied as the presenceor absence of any tree on a plot. Weighting of plotsby the number of trees found negates the in-formation on tree distribution that stocking val-ues represent.

Anyone devising a complex field sampling andsummarization system should enlist the help of astatistician and a computer programmer. These

specialists can suggest efficient techniques forobtaining and processing the information required.

ConclusionFixed-area, variable-area, and aerial methods all

have strengths and shortcomings for evaluatingregeneration. More reliance on a combination ofmethods can be anticipated. Increased use of aeri-al photos to complement ground methods seemsdesirable in the rough and steep topography of theWest. Distance methods have useful features, butestimating stand density by these methods Is notlikely to become truly satisfactory. Linear feet ofseedling height per acre is an interesting regener-ation parameter produced by vertical-line sam-pling: perhaps it will get enough use to provide aworking perception of what it means silvlcultural-ly and ecologically.

-

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Inventory Working Group, Society of AmericanForesters. Colorado State University, Ft. Collins.

BEERS, T.W., and C.I. MILLER. 1976. LIne sam-pling for forest inventory. AgricultureExperiment Station, Purdue University, WestLafayette, Indiana. Research Bulletin 934. 34p.

BEVER, D.N. 1949. A study of a stocking surveysystem and the relationship of stocking percentas determined by this system to number of treesper acre. Oregon State Board of Forestry, Salem.Research Bulletin 1. 40 p.

BEVER, D.N. 1961. Surveying forest lands forstocking. Oregon Forest Research Center,Corvallis. Research Note 44. 8 p.

BEVER, D.N., and D.P. LAVENDER 1955. Revised"number of trees per acre" curves. Oregon StateBoard of Forestry, Salem. Research Note 25. 3-p.

BICKERSTAFF, A. 1961. A variable quadrat regen-eration survey method. Forestry Chronicle37:39-53.

COCHRAN, W.G. 1977. Sampling Techniques.Third edition. John Wiley and Sons, New York.428 p.

COWLIN, R.W. 1931. Classifying stocking inDouglas fir reproduction by the stocked quadratmethod. USDA Forest Service, Pacific NorthwestForest and Range Experiment Station, Portland,Oregon. Forest Research Note 7:6-7.

COWLIN, R.W. 1932. Sampling Douglas fir repro-duction stands by the stocked-.quadrat method.Journal of Forestry 30:437-439.

DANIELS, R.F. 1978. Spatial patterns and distancedistributions in young seeded loblolly pinestands. Forest Science 24:260-266.

DELINCE, J. 1986. Robust density estimationthrough distance measurements. Ecology67:1576-1581.

DENNIS, B. 1984. Distance methods for evaluatingforest regeneration. P. 123-128 in New Forestsfor a Changing World, Proceedings, 1983 Societyof American Foresters National Convention.Society of American Foresters, Bethesda,Maryland.

DICK, J. 1963. Forest stocking determined bysequential stocked-quadrat tally. Journal ofForestry 6 1:290-294.

EICHENBERGER, J.K., G.R. PARKER, and T.W.BEERS. 1982. A method for ecological forest


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FREESE, F. 1962. Elementary forest sampling.USDA Forest Service, Washington, D.C.Agriculture Handbook 232. 91 p.

FREESE, F. 1967. Elementary statistical methodsfor foresters. USDA Forest Service, Washington,D.C. Agriculture Handbook 317. 87 p.

GHENT, A.W. 1963. Studies of regeneration In for-est stands devastated by the spruce budworm.Ill. Problems of sampling precision and seedlingdistribution. Forest Science 9:295-310.

GHENT, A.W. 1969. Studies of regeneration in for-est stands devastated by the spruce budworm.IV. Problems of stocked-quadrat sampling.Forest Science 15:417-429.

GOBA, N.L. 1984. Regeneration success surveyaided by aerial Infrared photography. P. 117-122 in New Forests for a Changing World,Proceedings, 1983 Society of American ForestersNational Convention. Society of AmericanForesters, Bethesda, Maryland.

GOBA, N.L., J.L.A. NARRAWAY, aM S. PALA.1980. Integration of remote sensing technologywith assessment of coniferous regeneration suc-cess. P.147-159 in Remote Sensing Symposium,Proceedings O-P-8, Canada-Ontario JointForestry Research Committee, 1979.Environment Canada, Ottawa.

GOBA, N., S. PALA, and J. NARRAWAY. 1982. Aninstruction manual on the assessment of regen-eration success by aerial survey. OntarioMinistry of Natural Resources, Ontario Centrefor Remote Sensing, Toronto, Ontario. 57 p.

GRANT, J.A.C. 1951. The relationship betweenstocking and size of quadrat. University ofToronto Press, Toronto, Ontario. University ofToronto Forestry Bulletin 465. 35p.

GREIG-SMITH, P. 1952. The use of random andcontiguous quadrats in the study of the struc-

380 Regeneration Surv'eys and Evaluation

ture of plant communities. Annals of Botany.N.S. 16(62):293-316.

HAAPALA, F.H., and P.O. NEUMANN. 1972.Determining stocking of conifer reproductionwith large scale color Infrared aerial photogra-phy. Washington State Department of NaturalResources, Olympia. DNR Report 28. 5p.

HAIG, I.T. 1929. Accuracy of quadrat sampling instudying forest reproduction on cut-over areas.Ecology 10:374-381.

HAIG, I.T. 1931. The stocked-quadrat method ofsampling reproduction stands. Journal ofForestry 29:747-749.

HALL, R.J. 1984. Use of large-scale aerial pho-tographs In regeneration assessments.Canadian Forestry Service, Northern ForestResearch Centre, Edmonton, Alberta.Information Report NOR-X-264. 31 p.

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LOWDERMILK, W.C. 1927. A method for rapid sur-veys of vegetation. Journal of Forestry 25:181-185.

LYON, J.L. 1968. An evaluation of density sam-pling methods In a shrub community. Journal ofRange Management 21:16-20.

MacLEOD, D. 1977. Accuracy of regenerationstocking estimates: tests with simulated data.Forestry Chronicle 53:77-81.

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