landscape ecology and nature reserve design in the … · 2017. 9. 27. · ecology, 70( 1 ), 1989,...

Ecology, 70( 1 ), 1989, pp. 23-350 1989 by the E c o l o g i c a l Society A m e r i c a

LANDSCAPE ECOLOGY AND NATURE RESERVE DESIGNIN THE BOUNDARY WATERS CANOE AREA, MINNESOTA’

W ILLIAM L. BAKERYDepartment of Geography, University of Wisconsin, Madison, Wisconsin 53706 USA

Abstract. Temporal change in the biosphere occurs at different rates and in differentways, depending on spatial scale. One hypothesis is that in environments where disturbancesproduce patches and temporal instability in small areas, the aggregate mosaic of thesepatches on larger areas may be constant, so that a “shifting-mosaic steady state” occurs.If so, then the appropriate minimum size for a nature reserve might be the minimum landarea on which the patch-mosaic is stable.

To test for a stable patch-mosaic I subdivided the Boundary Waters Canoe Area (BWCA)into smaller units at five spatial scales and used the fire history data published by Hein-selman to reconstruct temporal changes in the patch-mosaic on each unit.

A temporally stable patch-mosaic was not evident at any scale, largely due to (1) spatialheterogeneity in the fire-regime and/or environment, and (2) a mismatch between the grainof fire-patches and the grain of the environment. The pattern of temporal instability presenton the BWCA as a whole was not replicated on smaller areas.

Nature reserve design and management practices that focus on the landscape level,community level, or species level may conflict. If the management goal is to perpetuatenatural fluctuations in landscape structure, then certain species dependent on landscapestructure may fluctuate as well. Maintaining stable populations of these species may entaillandscape manipulations that lower the value of the reserve for perpetuating landscapeprocesses and structures.

Key words: fire; landscape ecology; Minnesota; nature reserves; patch-dynamics; stability; steadystate.

Ecological processes may operate on a variety oftemporal and spatial scales. A systematic perspectiveon scale effects (e.g., Delcourt et al. 1983) is importantas researchers direct more attention toward under-standing the effect of human-induced fragmentation ofthe biosphere (Burgess and Sharpe 198 1, Harris 1984).Scale is also important in the study of the dynamics ofdisturbance patches (Pickett and White 1985a). Smallpatches are common in many kinds of communities,such as in forests (Runkle 198 l), intertidal commu-nities (Paine and Levin 198 l), and grasslands (Mc-Naughton 1983). But patches also occur on the land-scape scale, due to large fires (Heinselman 1973), massmovements (Veblen et al. 198 l), and other large dis-turbances.

A premise of landscape ecology is that integrationof human use with natural landscape-level processeswill increase the sustainability of human use (Gulinck1986) and the viability of biosphere fragments, suchas nature reserves (Harris 1984, Noss and Harris 1986).But relatively little is known about the dynamics oflandscape patches, although landscape dynamics havebeen modelled (Weinstein and Shugart 1983, Hall et

’ Manuscript received 2 November 1987; revised 13 May1988; accepted 16 May 1988.

’ Present address: Department of Geography, University ofKansas, Lawrence, Kansas 66045 USA.

al. 1987) and studied historically (Sharpe et al. 198 1,Romme and Knight 1982, Hall et al. 1987). Moreover,it remains unclear how human use of the biospherecan be integrated with landscape dynamics.

Human-induced fragmentation of the biosphere mayaffect species, communities, and ecosystems. Naturereserves are often small fragments of an originally larg-er or more continuous ecosystem. The effect of frag-mentation on the species inside fragments is being ex-plored experimentally (Lovejoy et al. 1984), as well asthrough modelling (Wright and Hubbell 1983), andempirical research (e.g., Levenson 198 1). One goal ofsuch studies is to determine “minimum viable popu-lations” (Shaffer 198 l), and thus needed reserve area,for the target species in a reserve. Comparable researchon ecosystems and landscapes has lagged these speciesefforts (Noss 1983, Noss and Harris 1986). In distur-bance-mediated landscapes, an analogous question ishow much land area would be needed to perpetuatethe essential structural and functional attributes of alandscape? Is there, in other words, an analogous “min-imum viable patch population” that can be used todetermine needed reserve area?

The existence of such a minimum viable patch pop-ulation has not been explored directly, but has beensuggested repeatedly. Cooper ( 19 13), for example, rec-ognized the patchy “mosaic” structure of temperateforests, and suggested that while the state of a smallpart of a forest may fluctuate widely with time, due to

24 WILLIAM L. BAKER Ecology, Vol. 70, No. 1

disturbances, on some larger area the proportion of aforest in a particular state will remain constant. Thisconcept has been called the “shifting-mosaic steadystate” (Bormann and Likens 1979).

The shifting-mosaic steady state may not occur inall landscapes. Pickett and White (1985b) theorizedthat steady-state patch-mosaics are most likely wheredisturbances are small and frequent in a large area ofhomogenous habitat. Other authors (Zedler and Goff1973, Connell and Sousa 1983, DeAngelis and Water-house 1987) have suggested that large areas are morelikely than small areas to have stable mosaics. A mod-elling experiment (Shugart and West 198 1) suggestedthat a stable mosaic is more likely on areas ~50 ormore times the patch size. There is empirical evidencefor a stable mosaic in some temperate forests disturbedby wind (Sprugel 1976) and in flood-disturbed riparianwoodlands (Everitt 1968) but not in a 73-km2 forestedwatershed subject to recurring fires (Romme 1982).

There are a variety of patch-mosaic attributes, whosetemporal stability might be analyzed. But in temperateforests subject to large disturbances, an important at-tribute is the distribution of patch ages. The “landscapeage class structure,” as it might be called to distinguishit from age class structures inside forest patches, is theattribute implied by the shifting-mosaic steady-statehypothesis (Bormann and Likens 1979).

If a stable mosaic occurs on some landscape scale,then the size of the “minimum viable patch popula-tion” might be operationally defined as the number ofpatches included within the smallest land area thatcontains the stable mosaic. The reserve design prob-lem, then, is to determine this minimum land area.

In this paper I attempt to determine empirically theminimum area for perpetuating the landscape age classstructure in a case study of the fire-prone forests of theBoundary Waters Canoe Area (BWCA), Minnesota. Iuse the fire-year maps published by Heinselman (1973)to reconstruct the history of changes in landscape ageclass structure. I test the hypothesis that a stable mosaicoccurs at a particular spatial scale. I then discuss theimplications of the stable mosaic, or lack of it, andlandscape dynamics in general in designing and man-aging nature reserves.

STUDY AREAForests in the Boundary Waters Canoe Area and

vicinity mapped by Heinselman (1973) are transitionalbetween the Great Lakes-St. Lawrence and boreal for-est regions, and are dominated by pines (Pintrs banks-iana, P. strobus, and P. resinosa), spruces (Picea mari-ana and P. glauca), balsam fir (Abies balsamea),tamarack (Lark laricina), white cedar (Thuja occiden-talis), quaking aspen (Populus tremuloides), and paperbirch (Betula papvrifhra). The landscape is one of slighte .relief, with numerous lakes and rocky islands, shallowsoils, and glacial landforms superimposed over Pre-cambrian rocks. The climate is continental, with long

TABLE 1. Spatial scales, equivalent unit areas, and numberof units at each scale.

Scale Area (ha) Number of units

1 404 858 12 202 429 24 101215 48 50 607 8

1 6 25 304 1 6

cold winters and short warm summers (Heinselman1973). Prior to settlement, fires burned the equivalentof the entire area about every 100 yr (Heinselman 1973).

M ETHODS

Units and scales

I divided Heinselman’s 404 OOO-ha study area into16 equal-area (lakes excluded) rectangular “subunits”(Fig. 1). The 16 subunits were aggregated to produce“units” of five sizes (Table 1). Throughout the paperI will identify each unit by referring to its scale (Table1) and which of the 16 subunits it contains. For ex-ample, “scale 4, subunits 5-8” is a 10 1 2 15ha unitcomposed of subunits 5-8. The scales were chosen tospan the range of scales within which the stable mosaicand the minimum area might be found. Shugart andWest (198 1) suggested that a land area = 50 times thepatch size would be needed in order to have a stablemosaic. I calculated the mean fire-generated patch sizefor the 14 1 -yr study period as 4650 ha. An area 50times this size (232 500 ha) is a little more than halfof the study area. The number of scales that could beconsidered was limited by a substantial computationalburden, which is minimized by using a geometric se-quence of scales.

The configuration of subunits is not unique at anyscale. The computational burden precluded replicatedtrials with different configurations. I suspect that a dif-ferent configuration would change the actual patternon a unit, but would not significantly change the overallinterunit and interscale comparisons. Unit shape couldalso have an effect, but could not be investigated here.

I transferred the fire-year maps and my subunitboundary map (Fig. 1) to mylar sheets, at a uniformscale so they could be exactly aligned with one another.By overlaying these I could determine the age of theforests in each unit at the time of a particular fire byreferring to the time of the last fire. I determined thearea of forest of a particular age by counting a dot grid.Preliminary tests on the same subunit resulted in ~2%variation in the counts.

Fire history data

I focused on the 1727-l 868 period (141 yr), whichis the period of good fire record prior to Europeansettlement. Because it pre-dates the time when Euro-pean peoples significantly affected these forests, it is

February 1989 LANDSCAPE ECOLOGY AND NATURE RESERVE DESIGN 25

OC M”es0 5 1 0 2 0 30 Kilometres

- Study Area Boundary

- Subunit Boundary. . ‘ . y*.

“‘:j$$ig 1796 F i re Area- . ,

- U . S . A . - C a n a d a B o r d e r

FIG. 1. Study area, boundaries of subunit areas (numbered), and example fire-year (1796) map.

the period most useful for understanding the “natural”dynamics of the patch-mosaic. Heinselman (1973: Fig.3) published fire-year maps for the 15 major fire yearsbetween 1727 and 1868. As an example, the 1796 fireyear is illustrated (Fig. 1).

In interpreting any fire history reconstruction it isimportant to be aware of the limits of the data. In thiscase, Heinselman ( 197 3) first prepared “stand-originmaps” by using aerial photographs, 1948 United StatesForest Service Cover-Type Maps, and 823 plots with2-5 aged trees on each plot, supplemented by another100 data sets with tree ages (collected by Ohmann andReam), as well as analysis of wedges or cores from 295fire-scarred trees. The “fire-year maps” I use were thenconstructed for the 404 OOO-ha area by “intercon-necting the mapped limits of all stands that seem tohave resulted from coalescent bums of the same year”(Heinselman 1973: 337). Heinselman suggests that thefire-year maps are conservative estimates of the actualfire history, because the frequency of surface fires isprobably under-estimated (Heinselman 197 3). But thisis of little importance for my purposes, because land-scape structure is primarily affected by large stand-destructive fires, not such surface fires.

Burned areas in the BWCA may be fully restockedwith trees within 5 yr after a stand-destructive fire(Ohmann and Grigal 1979). It is thus likely that post-fire forests are relatively even aged.

Matrix notation and transition matrices

Quantitative details of how the disturbance regimechanges the landscape structure can be summarized inmatrix notation. The matrices are used, at this point,only as convenient notation, not as models; thus noassumptions about the matrices or their elements arerequired. These assumptions will be discussed later,when projections are made.

To set up the matrices, the number of age classesand the age class limits must first be chosen. Age classlimits are a trade-off between class width and classnumber, constrained by a substantial computationalburden. Given the 16 10 age class distribution, the old-est possible forest in 1868 is 4 16 yr. I chose to dividethis age span into seven 60-yr age classes, extendingfrom O-4 19 yr.

Consider a row vector, it 1 , whose elements are thefraction of land area in each of the seven age classesat time 1, just after the first fire. Then, the age classdistribution after the next fire, at time 2, can be foundfrom:

n2 = M12, (1)

where P,, is a “fire-year” matrix, whose elements arep,,, the fraction of age class i that changes to age classj during the interval from time 1 to time 2. Land areaburned enters the first age class, while unburned land

26 WILLIAM L. BAKER

area grows (ages) into older age classes, or remains inan age class. Note that fires, and thus time steps, arenot equally spaced. Nonetheless, matrix multiplicationrules mean that:

n3 = n 1pnp237

or more generally:

n, = nlp,zp23 * * * q-l)(r).

Moreover:pi, = PEP,, * * * P(,--I,(,, 7

so that:

n, = nlP1,.

In this study, the fire history is known, but the initialage class distri bution, n 1, is not known and must beestimated. The fire history da ta indicate only what landarea burned, not how old the forest was that burned.This means that the elements, pu, of P,, are dependenton the initial distribution. A map of the initial age classstructure would uniquely determine ntl, PIZ, and allsubsequent It,., but such a map is not available.

Nevertheless, if the patch-mosaic were stable, thenthe age class structure would be the same, by definition,regardless of the time of observation. From a theoret-ical standpoint, landscape age class structures in fire-prone forest ecosystems may have a negative expo-nential or a Weibull distribution (Johnson and VanWagner 1985) but there are an infinite number of suchdistributions that would be stable (Stephenson 1987).However, if there is a stable mosaic in the study area,then the form of the age class distribution at the endof the study period, in 1868, ought to be the same asin 1727. The 1868 distribution is also unknown, butas the best approximation to it, I used the 19 10 dis-tribution. To estimate the 19 10 distribution I excludedthe 3% of the study area burned since 19 10 (Heinsel-man 1973: Table 4) and calculated the age class dis-tribution of the remaining forests. Because there is somefire record extending back to 16 10, I assigned this ini-tial distribution to the time just before the 16 10 fire.The 1727 “initial distributions” thus vary somewhatfrom unit to unit.

The general procedure, then, was to set up a “straw-man” stable mosaic scenario with the initial age classstructure as close as possible to what it might havebeen at the end of the 1727-1868 period. The degreeof stability of the age class structure could then beevaluated by considering how closely the actual fireregime maintained this initial age class structure duringthe course of the 1727-l 868 period. Note that on theBWCA as a whole this procedure fixes and equalizesthe 16 10 and 1868 distributions, forcing the age classstructure to start with and return to the same distri-bution, but this does not force the distribution to re-main constant (stable) during the period. On smallerunits the 1868 distribution may or may not have di-

Ecology, Vol. 70, No. 1

verged substantially from the initial distribution, de-pending on the actual pattern of fires on the unit.

Although there are limits to this method, it is animprovement over earlier methods (e.g., Romme 1982)of reconstructing past landscape age class structure, asit incorporates the mapped fire record. Moreover, aftera mapped fire, the age of the forest can be preciselydetermined. Thus the errors introduced by this esti-mation procedure only persist through a few fires. Iwill later consider the extent of errors that may havebeen introduced by this estimation procedure.

Projected distributions

It is also useful to assess the potential long-termtrends to be expected on a unit under the assumptionthat the fire regime during the 14 1 -yr study periodremain s constant indefinite1Y. This longer term eval-uation is important because (1 ) short-term sligh t dis-similarity may be amplified over the long term, and(2) short-term temporal instability may be equal inmagnitude but different in timing on two units, so thatlong-term trends differ.

Once the %27-1868 matrix is known, from Eqs. 4 and5, and n 1 has been estimated, then n, can be calculatedat 14 1 -yr intervals, under the assumption that the 1727-1868 fire regime remains constant, by:

n, = n,Pm7-1868 (6)where nl is n in 1727. This multiplication procedurecan be used to project each unit’s age class distributionforward to a common longer term end point.

The matrix P1727-1868 is a transition matrix, and ifcertain conditions are met, then there are matrix prop-erties that can be used to determine an end point usefulfor comparisons. Elements in the matrix are maximumlikelihood estimates of transition probabilities (Ke-meny and Snell 1960). The matrix can thus be used todevelop a Markov chain model (Kemeny and Snell1960, van Hulst 1979) under certain assumptions. First,I assume the underlying process is a first-order Markovprocess, because I do not have the data required to testfor higher order processes. But the projection is forheuristic purposes only, to provide a common frame-work for comparing longer term trends in a relativesense, not to test how well short-term transitions ac-tually predict longer term outcomes. Second, I assume,for the same reasons, that the transitions are constant.As each age class in the model can ultimately be reachedfrom every other age class, the Markov chain is ergodic.All matrices, when powered (P”), converged to a lim-iting distribution, which means that the Markov chainsare all regular, rather than cyclic (Kemeny and Snell1960). The limiting distribution in a population con-text has been called a “stable age distribution” (e.g.,Krebs 1978), but I will refer to it as a “final distribu-tion,” to avoid confusion, because the existence of a“stable age distribution ” has no bearing on whether astable patch-mosaic exi sts.


FIG. 2. Patch age class distribution during the 1727-l 868period, scales l-4. (Scales are given in Table 1.) Vertical axisis the fraction of the unit area in a particular age class. Thereare seven 60-yr age classes along the “AGE CLASS” axis (O-59 yr, . . . , 360-4 19 yr), with the fraction of unit area in eachage class plotted at the lower boundary of that age class. The25 x 25 grid of lines is for display purposes only. Subunitsare those areas numbered in Fig. 1. (a) hypothetical steadystate, (b) scale 1, subunits 1-16, (c) scale 2, subunits 1-8, (d)scale 2, subunits 9-16, (e) scale 4, subunits 1-4, (f) scale 4,subunits 5-8, (g) scale 4, subunits 9-12, (h) scale 4, subunits13-16.

Matrix projections such as these have been criticizedas inaccurate models of succession (e.g., McIntosh 1980,Usher 198 l), largely because transitions may not beconstant in nature, or because transitions are calculatedbased on invalid assumptions about “plant-to-plant”replacement. These criticisms are not relevant here, asI assume constant transitions and a first-order Markovprocess for a heuristic purpose only, and transitionsare between age classes, not species. No assumptionsabout plant-to-plant replacement are required.

Cri ter ia for determining minimum area

When enough land area has been included in a naturereserve so that it includes the minimum area for patch-mosaic stability, a number of testable conditions, whichcan be represented as graphic models, should occur.

These can be formalized as three criteria, which canbe used to evaluate the presence of a stable mosaic anda minimum area:

Criterion 1: On areas larger than the minimum area,as area increases the patch-mosaic age class structureshould remain temporally constant (Fig. 2a).

Criterion 2: On areas larger than the minimum area,as area increases there should be no further increasein the mean similarity with the unit at the largest scale(see Fig. 6a).

Criterion 3: On areas larger than the minimum area,as area increases there should be no further increasein mean among-unit similarity (see Fig. 6b).

Criterion 1 is a restatement of earlier comments onpatch-mosaic stability. Note that “constancy” is onlyone concept of stability (Orians 1975) but I believe itis the one implied by the “shifting-mosaic steady state”hypothesis. Criteria 2 and 3 follow from the assump-tion that the BWCA is spatially homogeneous, so thatonce the minimum area has been found, then all units

FIG. 3. See legend for Fig. 2. (a) scale 8, subunits 1-2, (b)scale 8, subunits 5-6, (c) scale 8, subunits 9-10, (d) scale 8,subunits 15-16, (e) scale 16, subunit 2, (f) scale 16, subunit5, (g) scale 16, subunit 7, (h) scale 16, subunit 8.


S C A L E4

S C A L E

1

1 A/’A---/ ’A’ A----S C A L E A----

SUBUNIT - I 2 3 4

S T E A D YSTATE

AGECLASS

5 6 7 8 9 IO II I2

\ \ \ \

LLlL.JlLLLlI4 I5 I6

FIG. 4. Final patch age class distributions on all units at five spatial scales. The scales are given in Table 1. Dotted linesshow how the subunits were aggregated at the different scales. Subunits, listed along the bottom of the figure, are shown inFig. 1. The hypothetical steady-state distribution is in the upper right of the figure. Vertical and horizontal axes on all graphsare identical to those in this steady-state graph. Age classes are: 1 = O-59 yr, 2 = 60-l 19 yr, 3 = 120-l 79 yr, 4 = 180-239yr, 5 = 240-299 yr, 6 = 300-359 yr, 7 = 360-4 19 yr. The vertical axis scale has been omitted from all but the left-mostgraph at each scale.

at or larger than that area will have the same patchdynamics as occur on the whole BWCA. Criteria 2 and3 are likely to identify the same minimum area. Cri-terion 1 alone is not sufficient to identify the minimumarea, because on areas less than the minimum area,among-unit variation may be large enough so that someone unit will exhibit short-term temporal stability, whilean adjoining unit may be temporally unstable.

These three criteria may be applied to both the tem-poral pattern during the 1727-I 868 period (Figs. 2 and3) and to the final distributions projected from the1727-I 868 transition matrices (Fig. 4).

If patch-mosaic stability (Criterion 1) is not found,Criteria 2 and 3 can still be used to determine if thereis some minimum area that will contain essentially thesame pattern of temporal instability as occurs on thewhole BWCA.

Similarity indices

To compare short-term (14 1 -yr) temporal patterns(Figs. 2 and 3) I used a two-dimensional (surface) sim-ilarity index:

SIM(x, y ) = 100 - c 1 x,, - y , 1 ,

where x,, is the fraction of land area in age class i for

fire-year j for the first temporal pattern, and y,, is thefraction of land area in age class i for fire-year j for thesecond temporal pattern. This index is the Manhattannon-Euclidean analog of the matrix correlation coef-ficient (Lelkovitch 1984).

To evaluate to what extent the short-term temporalpatterns were stable, I used index (7) to compare thetemporal pattern on each unit at a particular scale tothat of the hypothetical steady-state temporal pattern(Fig. 2a). To see if Criterion 1 was met, I then graphedthese index values and the mean of these index valuesvs. scale. To see if Criterion 2 was met, I first calculated,using index (7) the similarity of each unit’s temporalpattern with the temporal pattern on the largest area(Fig. 2b). I then calculated the mean of these similarityvalues, for each scale, and graphed the means vs. scale.To see if Criterion 3 was met, I first calculated, usingindex (7) the similarity of each unit’s temporal patternwith the temporal pattern on all other units at the samescale. I then calculated the mean of these similarityvalues, for each scale, and graphed the means vs. scale.

To compare final distributions I calculated a “Man-hattan” similarity index:

SIM(x, y) = IO0 l c 1 X, - y, 1 , (8)

February 1989 LANDSCAPE ECOLOGY AND NAT1 RE RESERVE DESIGN 29

where X, is the fraction of land area in age class i forthe first distribution, and V, is the fraction of land areain the same age class i for the second distribution. Thisindex is preferable to Euclidean measures (e.g., Pearsoncorrelation) that overemphasize the most abundant ageclass (Noy-Meir and Whittaker 1977).

To evaluate to what extent the patch-mosaic wouldhave been stable on the long term, I used index (8) tocompare the final distribution on each unit at a par-ticular scale to that of the hypothetical steady-state finaldistribution (Fig. 4). To see if Criterion 1 was met, Ithen graphed these index values and the mean of theseindex values vs. scale. To see if Criterion 2 was met,I first calculated, using index (8) the similarity of eachunit’s final distribution with the final distribution onthe largest area (Fig. 4). I then calculated the mean ofthese similarity values, for each scale, and graphed themeans vs. scale. To see if Criterion 3 was met, I firstcalculated, using index (8) the similarity of each unit’sfinal distribution with the final distribution on all otherunits at the same scale. I then calculated the mean ofthese similarity values, for each scale, and graphed themeans vs. scale.

RESULTS AND D I S C U S S I O N

Patch- mosaic stability

The patch age class structure on the whole study areavaried dramatically over the 1727-1868 period (Fig.2b). Aging of the unburned part of the 1727 “cohort”dominated the temporal pattern. Fires during the 1727-1868 period, while extensive, were not sufficient tomaintain a stable patch-mosaic.

Similarity of temporal patterns with the hypotheticalstable pattern is generally low (Table 2, Figs. 2, 3, and5a) on all spatial scales, averaging between 30 and 40%,with the mean similarity little affected by scale (Fig.5a). There is much more variation, in similarity withthe stable pattern, among units of small area than amongunits of large area. Similarity of the final distributionswith the steady-state final distribution is also generallylow (Table 2) again with mean similarity only slightlyless on units of smaller area (Fig. 5b), and with morevariation apparent among smaller units (Fig. 5b).

How closely do long-term (final distribution) resultsrellect short-term temporal patterns? Unit temporalpattern similarities with the steady state (Table 2) arenot highly correlated with corresponding unit final dis-tribution similarities with the steady state (Table 2) onsmall areas (r = 0.099 for scale 8, r = 0.432 for scale16). This suggests that short-term, somewhat stabletemporal patterns may lead to either relatively stableor relatively unstable longer term outcomes, probablybecause slight short-term differences can be amplifiedin the long term.

What effect does the form of the steady-state distri-bution (Fig. 2a) have on the results? During the 47 yrfrom 1863 to 19 10, three of the four largest fires in the

0 0 = 1 unit

0 =2 or more units

0 = mean for unit area

00

0

000

0(a)

0 25 50 101 202 404

UNIT AREA (1000 ha)

00 = 1 unit

0 =2 or more units

00 D=mean for unit area

80

8

0 0

w;5 ;o 161 262

UNIT AREA \lOOO ha)

464

FIG. 5. Effects of unit area on mean similarity of the patch-mosaic age class structure with that of the hypothetical steadystate. Percent similarities, which range from 0 to loo%, arediscussed in Methods: Similarity Indices. (a) temporal pat-terns during the 1727-1868 period, (b) final distributions.

368 yr since 1542 occurred (Heinselman 1973). Thus,the unknown 1868 distribution (and 1727 distribution)probably included more old forest than occurred in19 10, and the steady-state distribution in Fig. 2a mayhave too little older forest. The general effect of thiswould be that the actual similarity values (with thesteady state) would all be raised somewhat, but theirrelative relationships would probably not change.

What effect does the form of the assigned initial dis-


TABLE 2.distribuunit.

Percetions*

,ntWl

similarity of temporal pat terns and finalth the hypothetical steady state, for each

Temporal FinalScale Subunit(s) patterns distributions

2 l-8 38.6 48.32 9-16 40.0 58.6

4 l-4 40.6 48.54 5-8 33.9 47.54 9-12 32.0 43.74 13-16 44.7 56.6

8 l-2 40.5 42.18 3-4 37.5 58.38 5-6 22.6 50.38 7-8 41.7 28.78 9-10 43.2 44.48 11-12 15.4 24.38 13-14 37.3 58.78 15-16 47.2 29.5

1 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 6

89

1 0111 21 31 41 51 6

13.5 35.556.6 43.921.1 32.355.0 66.834.5 65.0

6 . 1 3.90.6 4.0

78.0 45.343.8 41.642.0 46.810.7 46.624.1 49.728.6 81.339.8 46.851.8 33.937.8 24.0

1-16 40.8 56.8

* Defined in Methods: Projected Distributions.

tribution have on the results? This can be estimatedby devising an initial distribution most favorable forthe steady state, and then calculating the actual simi-larity with the steady state that would result. By over-laying all the fire-year maps for the 1727-l 868 periodI found that 29.5% of the study area was not burnedby any fire during this period. This unburned area isscattered throughout the study area (Table 3) but aboutthree-quarters of it occurs on subunits 1-8 and mostof that is in subunits 1, 3, 6, and 7. Regardless of theinitial distribution, the 29.5% of the study area thatdid not burn would be at least 14 1 yr old (1868 - 1727= 14 1) in 1868. If it is assumed that the remainder ofthe study area that did bum (70.5%) has a temporalpattern exactly like that in Fig. 2a, then the similarityof the temporal pattern with the steady state would be~70%. But the actual fire regime on the 70.5% thatdid burn was not, in fact, sufficient to keep all theforests young, as in Fig. 2a. The fire regime would comeclosest to doing this if the 70.5% of the study area thatdid burn were all aged 0 in 1727. Using this initialdistribution, most favorable to finding a steady state,I recalculated the sequence of age class distributions

for the whole study area, and then calculated the per-cent similarity of the resulting temporal pattern withthe steady-state pattern. With this 1727 distribution,the percent similarity with the steady-state pattern isstill only 54.8%. This sets an upper limit on the effectof errors in estimating the initial distribution.

Minimum areaGiven that the patch-mosaic was temporally unsta-

ble over the 1727-1868 period at all scales, Criterion1 was not met and a minimum area does not exist.But, in such non-steady-state environments, a less re-strictive concept of the minimum area might be useful.If only Criteria 2 and 3 had to be met, the minimumarea would be the area having the same essential pat-tern of instability as occurred on the whole study area.Smaller areas (25 000 and 50 000 ha) have temporalpatterns and final distributions on the average only~50-80% similar to that on the whole study area (Fig.6c and e). Mean similarity among final distributions(Fig. 6f) suggests that over the long term, individualsmaller units may diverge greatly from each other. Onlarger areas (10 1 000 and 202 000 ha) over the shortterm (Fig. 6c, and Fig. 2c and d vs. 2b) nearly the sametemporal pattern occurs on either half of the study area

TABLE 3. Distribution of unburned area among units.

2 l -8 21.91 43.822 9-16 7.59 15.18

4 l-4 8.31 33.244 5-8 13.60 54.404 9-12 3.18 12.724 13-16 4.4 1 17.64

8 l-28 3-48 5-68 7-88 9-108 11-128 13-148 15-16

3.774.547.546.062.001.181.293.12

30.1636.3260.3248.4816.009.44

10.3224.96

1 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 6

89

1 0111 21 31 41 51 6

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UNIT AREA (IO00 ha) UNIT AREA (IO00 ha) UNIT AREA (IO00 ha)

FIG. 6. Effects of unit area on mean similarity of the patch-mosaic age class structure with that of the largest area, andamong units. Percent similarities, which range from 0 to loo%, are discussed in Methods: Similarity Indices. (a) hypotheticalmodel illustrating the minimum area using Criterion 2, (b) hypothetical model illustrating the minimum area using Criterion3, (c) mean similarity of temporal patterns during the 1727-1868 period with the temporal pattern on scale 1 (the wholeBWCA), illustrating Criterion 2, (d) mean similarity, among units at a given scale, in temporal patterns during the 1727-1868 period, illustrating Criterion 3, (e) mean similarity of final distributions with the final distribution on scale 1 (the wholeBWCA), illustrating Criterion 2, (f) mean similarity, among units at a scale, in final distributions, illustrating Criterion 3.

(scale 2) as occurs on the whole study area, but finaldistributions on the two halves are only W30% similarto that on the whole study area (Fig. 6e). This is partlydue to the greater amount of unburned forest on sub-units 1-8 (Table 3). Thus, even on areas as large ashalf the BWCA it is not clear that a minimum area

may be in some age class that is critical for a particularspecies’ survival. Finally, spatial heterogeneity canconfound the determination and interpretation of theminimum area.

occurs.

Spatial heterogeneity , the nonshlfting mosaic,and mosaics qf mosaics

Moreover, other considerations suggest there is no There is clearly significant spatial variation in thesimple, objective minimum area. Researchers exam- fire-patch regime and/or environment. The spatialining the species-area relationship have argued that variation in unburned area, one manifestation of thethere is no objective way to determine minimum area, fire regime, is substantial at all scales, even on scale 2because the shape of curves, such as those in Fig. 6, (Table 3). That the short-term temporal pattern on theand consequently the unit area where a plateau be- two halves of the study area is ~90% similar (Fig. 6d)comes apparent, are determined by the ratio of the axis suggests that a greater rate of burning must have oc-scales (Kershaw 1973). In addition, the similarity val- curred on the burned parts of subunits l-8 (which wereues might be used to make an informed judgment, but 44% unburned) than on the burned parts of subunitsit is not clear what level of similarity is significant. For 9-l 6 (which were 15% unburned) to balance the muchexample, if two alternative reserves have 80% similar greater unburned area on subunits 1-8. In the long termtemporal patterns, the source of the 20% dissimilarity the two halves have divergent distributions (Fig. 4)

TABLE 4. Relationship between patch size characteristics and unit areas. Entries are the unit area divided by the mean orlargest patch area.

Unit area (1000 ha)

25 50 1 0 1 202 404

Mean patch size (4650 ha) 5.44 10.88 21.77 43.53 87.07Largest patch size (73 606 ha) 0.34 0.69 1.38 2.75 5.50


8 16 24 32 40 48 56 64 72 80

SIZE OF F IRE PATCH (1000 ha )

ha area is only 5.5 times the largest burn patch, butthe steady state on this large area is missing not becausefires burn too much of the study area, but because theyburn too little and are spatially heterogeneous. Theresult is that the 1727 “cohort” is able to survive onthe unburned part of the study area and to influencesignificantly the age class structure throughout the 14 1yr period. The “shifting-mosaic” simply did not shiftinto 29.5% of the study area, in spite of substantialarea burned.

If the landscape does not contain a single steady-state mosaic, could it consist of a “mosaic of differentsteady-state mosaics ?” If I had divided the study areainto a mosaic of environmentally homogeneous sub-units prior to the analysis, would different steady stateshave been found in these different environments? Themean similarity with the steady state was about thesame on all scales (Fig. 5a and b), not greater on smallscales as would be expected if the mosaic of differentsteady-state mosaics occurred. Moreover, every unitat all scales failed to maintain a steady state due toinsufficient burning. Thus, the landscape cannot be amosaic of different steady-state mosaics.

Perhaps the landscape, then, consists of a “mosaicof steady-state and non-steady-state mosaics.” Thispattern is suggested, because a high similarity with thesteady-state pattern is more common on small than onlarge areas (Fig. 5) suggesting that the fire regime mightbe more concentrated in these areas, allowing a steadystate to occur. But this high similarity occurs not be-cause the fire-patch regime is more concentrated inthese areas, but because of a chance alignment, or tim-ing, of fires. Such a chance timing of fires is well illus-trated on subunit 8. In 1692,75% of the subunit burned,and in 1727, 28% of it burned, so that the forests were

FIG. 7. Distribution of fire patch sizes for all fire patchesvery young at the beginning of the 1727-l 868 period.

during the 1727-l 868 period in the BWCA study area. Yet these were the only two fires in the 19 1 -yr periodfrom 16 10 to 180 1. If they had occurred earlier, theshort-term similarity with the steady state would have

only ~70% similar (Fig. 6f). because of these differ- been much lower. A similar chance timing of fires oc-ences in the environment and in the fire-patch regime. curred on subunit 4. Moreover, the number of fires perPossible sources of this spatial variation in the fire- unit area decreases with unit area (Fig. 8) with littlepatch regime include spatial variation in ignition change in variance, suggesting again that it is not asources, drought severity, fuel load, and fire-spread more concentrated fire regime on some small areas thatprobability. results in a closer similarity with the steady state, but

How do my results fit Pickett and White’s (1985h) a chance alignment of a few fires.suggestion that steady-state patch-mosaics are most The landscape in the study area must, then, consistlikely where disturbances are small and frequent in alarge area of homogenous habitat? In this study area

of a “ mosaic 0 f different non -steady-state mosaics.”There is clear1Y grain in ei ther the environment or the

there is a negative exponential relationship between fire ignition pattern that creates spatial heterogeneity,the number of fire-patches and their size (Fig. 7) as so that some areas do not burn. There is another grainhas been reported elsewhere (Minnich 1983, van Wag- in the fire-patch regime, so that there is a limited tem-tendonk 1986). The log-transformed curve is approx- poral and spatial spectrum of patches. The two areimately normal, with a mean of 4650 ha. The largest interdependent, but the steady state is precluded herefire patch was 73 606 ha. It seems surprising that a on large areas because the location of fire-patches issteady state does not occur on the 404 858-ha study limited by spatial variation in environment, so thatarea, which is 87 times the mean patch size (Table 4). some areas do not burn or burn only very infrequently.The steady state may be prevented because the 404 858- The steady state is precluded on smaller areas that do


burn because fire-patches are too large in relation tothe size of homogenous individual environmentalgrains. And finally, the steady-state mosaic is not rel-evant, because of the absence of patch-producing dis-turbances, on the smaller areas that do not burn.

Non-steady-state mosaics such as this one may becommon in temperate zone forests. My analysis sug-gests that the steady state requires a different relation-ship between environmental grain size and disturbancegrain size, and less environmental heterogeneity, thanoccurs in the study area. But the study area is a rela-tively homogenous environment in comparison withregions of greater topographic relief, such as are com-mon in much of North America. Moreover, large areasof homogenous, low-topography forests in continentalclimates are prone to potentially very large fires (e.g.,Seitz 1986) so that there is a feedback relationship thatmaintains a perpetual mismatch between disturbancegrain and environmental grain. Because both environ-mental heterogeneity and environmental homogeneitydiscourage a steady state, the possibility of a steady-state patch-mosaic in fire-prone temperate regions maybe low.

NATURE RESERVE DESIGN AND MANAGEMENT

Designing nature reserves in non-steady-state envi-ronments is difficult because of spatial heterogeneity,but also because reserves often must be small fragmentsof originally more continuous ecosystems, and frag-mentation may itself alter the patch regime. Considerthe sources of disturbance in a continuous forest (Fig.9). Each unit of such a forest has a different trajectory

INTERNALREGIME

FIRE-PATCH

CHANGES IN

AGE-CLASSSTRUCTURE

F I G. 9. sources of change in thestant-i n-time, on a unit.

patch-mosaic at an in-

the external fire-patch regime (fires originating in ad-joining areas), which also varies among units and scales.One effect of fragmentation is that the ratio of distur-bance size to forest size increases with fragmentation,which is a source of the variation among scales (Figs.2 and 3). The internal fire-patch regime may also bechanged. In the BWCA, for example, the probabilityof within-fragment lightning ignition is undoubtedlylower in smaller fragments. Finally, the external fire-patch regime may also be changed by fragmentation(Grimm 1984).

If, after reserve creation, fires no longer originateoutside the reserve and burn into the reserve, the re-serve may be “supersaturated” with patches and mayundergo a subsequent “patch-relaxation” process. Su-persaturation and the relaxation process followingreserve isolation were first described for species(Diamond 1972). The extent of patch-relaxation andspecies-relaxation processes depends partly on the re-servediffer

context, butfrom those

contexts favorablefor landscapes. For

for species mayexample, crop-

land, in contrast to secondary forest, would be a bettercontext for species in a tropical forest reserve, as fewerspecies would invade from cropland (Janzen 1983) butin landscapes like that of the BWCA, the fire-patchregime in secondary forests, in contrast with the patchregime in cropland, may better mimic the patch regimein the unfragmented ecosystem, so that secondary for-est might be a better context.

Given some limited total area available for reserves,a classic reserve design question is whether there shouldbe a single large reserve or several small reserves (the“SLOSS” question; e.g., Simberloff and Abele 1982,Soule and Simberloff 1986)? A single large reserve has


several advantages in perpetuating the patch-mosaic ACKNOWLEDGMENTS

in a setting like that of the BWCA. First, a large reserve Comments of T. R. Vale, T. T. Veblen, D. Paulson, andwould have less total edge, and thus would be less two anonymous reviewers improved the manuscript. Figuresinfluenced by changes in the external fire regime. A were prepared by the University of Wisconsin Cartographic

corollary is that the internal fire regime would also be Laboratory. The author was supported by a University of

less altered, because such fires would less often reach Wisconsin Graduate Fellowship.

the reserve edge. Second, choosing a single large reservemaximizes the chance that temporal change in the re- LITERATURE CITED

serve matches as closely as possible the change that Bonnicksen, T. M., and E. C. Stone. 1985. Restoring nat-

would have occurred in the unfragmented BWCA eco- uralness to national parks. Environmental Management 9:

system (Fig. 6f). Finally, several small reserves, each479-486.

smaller than the maximum patch size, of 70-80 000Bormann, F. H., and G. E. Likens. 1979. Catastrophic dis-

turbance and the steady state in northern hardwood forests.ha (Fig. 7) may each have truncated patch-regimes. I American Scientist 67:660-669.

have shown that these very large patches have had Burgess, R. L., and D. M. Sharpe. 198 1. Forest island dy-

important effects on landscape structure on the BWCA namics in man-dominated landscapes. Springer-Verlag, New

as a whole.York, New York, USA.

Canham, C. D., and 0. L. Loucks. 1984. Catastrophic wind-Nonetheless, several reserves could be a better choice throw in the presettlement forests of Wisconsin. Ecology

in some instances. If the reserves were each large rel- 65803-809.

ative to the grain of the fire regime, then the overall Connell, J. H., and W. P. Sousa. 1983. On the evidence

landscape heterogeneity might be better represented inneeded to judge ecological stability or persistence. Ameri-can Naturalist 1211789~824.

a system of several reserves. For example, in the BWCA, Cooper, W. S. 19 13. The climax forest of Isle Royale, LakeSuperior, and its development. I. Botanical Gazette 55: l-a reserve with many lakes and a reserve with few lakes

might be chosen, if each reserve could be made largerelative to the grain of the fire regime (Fig. 7). But thisapproach requires historical data on spatial variationin the fire regime and on maximum fire sizes, and thesedata are not often available.

If there is no temporally stable patch-mosaic at anyspatial scale, then fluctuation and change may predom-inate within reserves of any size, even without signif-icant change in external environment, simply becausedisturbances vary in size and timing, and the grain ofthe disturbance regime may not match the grain of theenvironment. This has two important implications.

44.DeAngelis, D. L., and J. C. Waterhouse. 1987. Equilibrium

and nonequilibrium concepts in ecological models. Eco-logical Monographs 57: l-2 1.

Delcourt, H. R., P. A. Delcourt, and T. Webb III. 1983.Dynamic plant ecology: the spectrum of vegetational changein space and time. Quaternary Science Reviews 1: 153-l 75.

Diamond, J. M. 1972. Biogeographic kinetics: estimationof relaxation times for avifaunas of southwest Pacific is-lands. Proceedings of the National Academy of Sciences(USA) 69:3 199-3203.

Everitt, B. L. 1968. Use of the cottonwood in an investi-gation of the recent history of a flood plain. American Jour-nal of Science 266:4 17-439.

Grimm, E. C. 1984. Fire and other factors controlling theFirst, habitat for certain species, such as moose, that Big Woods vegetation of Minnesota in the mid-nineteenthdepend upon particular landscape structures (Heinsel- century. Ecological Monographs 54:29 l-3 11.

man 1973) has fluctuated significantly (Fig. 2b). To Gulinck, H. 1986. Landscape ecological aspects of agro-

preserve populations of such species, manipulations ofecosystems. Agriculture, Ecosystems and Environment 16:79-86.

landscape structure might be considered, but if land- Hall, F. G., D. E. Strebel, S. J. Goetz, K. D. Woods, and D.scape processes are to be perpetuated, it is essential B. Botkin. 1987. Landscape pattern and successional dy-

that patch-mosaics be allowed to fluctuate without in- namics in the boreal forest. Pages 473-482 in Proceedings

tervention. Second, if the patch regime has been altered of IGARSS 1987 Symposium, Ann Arbor, Michigan, 18-

by human action, then restoration of presettlement21 May 1987. University of Michigan, Ann Arbor, Mich-igan, USA.

landscape structure might be considered (Bonnicksen- Harris, L. D. 1984. The fragmented forest. University of

and Stone 1985) but extensive presettlement fluctua- Chicago Press, Chicago, Illinois, USA.

tion in the BWCA landscape means that there is no Heinselman, M. L. 1973. Fire in the virgin forests of the

single unique presettlement structure to restore.Boundary Waters Canoe Area, Minnesota. Quaternary Re-search 3:329-382.

A new emphasis on managing forest structure on alandscape scale (Harris 1984) is important, but should

Janzen, D. H. 1983. No park is an island: increase in in-terference from outside as park size decreases. Oikos 41:

include consideration of temporal fluctuation in land- 402-410.

scape structure and landscape processes themselves, Johnson, E. A., and C. E. Van Wagner. 1985. The theory

not just how these processes affect species. The poten-and use of two fire history models. Canadian Journal ofForest Research 15:2 14-220.

tial significance of such fluctuation for communities Kemeny, J. G., and L. R. Snell. 1960. Finite Markov chains.and species must be more fully clarified, as well as how D. van Nostrand, Princeton, New Jersey, USA.

much this fluctuation is controlled by climate, envi- Kershaw, K. A. 1973. Quantitative and dynamic plant ecol-

ronmental heterogeneity, and the biota, and at whatogy. Second edition. American Elsevier, New York, NewYork, USA.

spatial scale these influences are important. Krebs, C. J. 1978. Ecology, the experimental analysis of


distribution and abundance. Second edition. Harper andRow, New York, New York, USA.

Lefkovitch, L. P. 1984. A nonparametric method for com-paring dissimilarity matrices, a general measure of biogeo-graphical distance, and their application. American Natu-ralist 123:484-499.

Levenson, J. B. 198 1. Woodlots as biogeographic islands insoutheastern Wisconsin. Pages 13-39 in R. L. Burgess andD. M. Sharpe, editors. Forest island dynamics in man-dominated landscapes. Springer-Verlag, New York, NewYork, USA.

Lovejoy, T. E., J. M. Rankin, R. 0. Bierregaard, Jr., K. S.Brown, Jr., L. H. Emmons, and M. E. Van der Voort. 1984.Ecosystem decay of Amazon forest remnants. Pages 29%325 in M. H. Nitecki, editor. Extinctions. University ofChicago Press, Chicago, Illinois, USA.

McIntosh, R. P. 1980. The relationship between successionand the recovery process in ecosystems. Pages 1 l-62 in J.Cairns, editor. The recovery process in damaged ecosys-tems. Ann Arbor Science, Ann Arbor, Michigan, USA.

McNaughton, S. J. 1983. Serengeti grassland ecology: therole of composite environmental factors and contingencyin community organization. Ecological Monographs 53: 29 l-320.

Minnich, R. A. 1983. Fire mosaics in southern Californiaand northern Baja California. Science 219: 1287-l 294.

Ness, R. F. 1983. A regional landscape approach to main-tain diversity. Bioscience 33:700-706.

Ness, R. F., and L. D. Harris. 1986. Nodes, networks, andMUMS: preserving diversity at all scales. EnvironmentalManagement 10:299-309.

Noy-Meir, I., and R. H. Whittaker. 1977. Continuous multi-variate methods in community analysis: some problemsand developments. Vegetatio 33179-98.

Ohmann, L. F., and D. F. Grigal. 1979. Early revegetationand nutrient dynamics following the 197 1 Little Sioux for-est fire in northeastern Minnesota. Forest Science Mono-graph 21.

Orians, G. H. 1975. Diversity, stability and maturity innatural ecosystems. Pages 139-150 in W. H. van Dobbenand R. H. Lowe-McConnell, editors. Unifying concepts inecology. Dr. W. Junk, The Hague, The Netherlands.

Paine, R. T., and S. A. Levin. 198 1. Intertidal landscapes:disturbance and the dynamics of pattern. Ecological Mono-graphs 51: 145-178.

Pickett, S. T. A., and P. S. White, editors. 1985~. The ecol-ogy of natural disturbance and patch dynamics. AcademicPress, New York, New York, USA.

Pickett, S. T. A., and P. S. White. 1985b. Patch dynamics:a synthesis. Pages 371-384 in S. T. A. Pickett and P. S.White, editors. The ecology of natural disturbance and patchdynamics. Academic Press, New York, New York, USA.

Romme, W. H. 1982. Fire and landscape diversity in sub-alpine forests of Yellowstone National Park. EcologicalMonographs 52: 199-22 1.

Romme, W. H., and D. H. Knight. 1982. Landscape di-versity: the concept applied to Yellowstone Park. Bio-Science 32:664-670.

Runkle, J. R. 198 1. Gap regeneration in some old-growthforests of the eastern United States. Ecology 62: 104 l-l 05 1.

Seitz, R. 1986. Siberian fire as “nuclear winter” guide. Na-ture 323: 116-l 17.

Shaffer, M. L. 198 1. Minimum population sizes for speciesconservation. Bioscience 31: 13 l-l 34.

Sharpe, D. M., F. W. Steams, R. L. Burgess, and W. C. John-son. 198 1. Spatio-temporal patterns of forest ecosystemsin man-dominated landscapes of the eastern United States.Pages 109-l 16 in S. P. Tjallingii and A. A. de Veer, editors.Perspectives in landscape ecology: contributions to re-search, planning and management ofour environment. Pro-ceedings of the International Congress organized by theNetherlands Society for Landscape Ecology, Veldhoven,The Netherlands, 6-l 1 April 198 1. Centre for AgriculturalPublishing and Documentation, Wageningen, The Neth-erlands.

Shugart, H. H., Jr., and D. C. West. 198 1. Long-term dy-namics of forest ecosystems. American Scientist 69:647-

Usher, M. B. 1981. Modelling ecological succession, withparticular reference to Markovian models. Vegetatio 46:11-18.

van Hulst, R. 1979. On the dynamics of vegetation: Markovchains as models of succession. Vegetatio 40:3-14.

van Wagtendonk, J. W. 1986. The role of fire in the Yo-semite wilderness. Pages 2-9 in R. C. Lucas, compiler.Proceedings of the National Wilderness Research Confer-ence: Current Research. United States Forest Service Gen-eral Technical Report INT-212.

Veblen, T. T., C. Donoso Z., F. M. Schlegel, and B. EscobarR. 1981. Forest dynamics in south-central Chile. Journalof Biogeography 8:2 1 l-247.

Weinstein, D. A., and H. H. Shugart. 1983. Ecological mod-eling of landscape dynamics. Pages 29-45 in H. A. Mooneyand M. Godron, editors. Disturbance and ecosystems: com-ponents of response. Springer-Verlag, New York, New York,USA.

Wright, S. J., and S. P. Hubbell. 1983. Stochastic extinctionand reserve size: a focal species approach. Oikos 41:466-476.

Zedler, P. H., and F. G. Goff. 1973. Size-association analysisof forest successional trends in Wisconsin. EcologicalMonographs 43:79-94.

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