Population Dynamics of the Spruce Budworm Choristoneura Fumiferana Author(S): T

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Population Dynamics of the Spruce Budworm Choristoneura Fumiferana Author(s): T. Royama Source: Ecological Monographs, Vol. 54, No. 4 (Dec., 1984), pp. 429-462 Published by: Ecological Society of America Stable URL: http://www.jstor.org/stable/1942595 . Accessed: 26/03/2011 12:59

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http://www.jstor.org Ecological Monographs,54(4), 1984, pp. 429-462 ? 1984 by the Ecological Society of America

POPULATION DYNAMICS OF THE SPRUCE BUDWORM CHORISTONEURA FUMIFERANA'

T. ROYAMA MaritimesForest Research Centre,Canadian ForestryService, Departmentof the Environment,P.O. Box 4000, Fredericton, New BrunswickE3B 5P7, Canada

Abstract.Using the latest observations, experiments, and theoreticalstudies, I have reanalyzed sprucebudworm data fromthe Green River Project, and now proposea newinterpretation of the populationdynamics of the species. Sprucebudworm populations in theProvince of New Brunswickhave been oscillatingmore or less periodicallyfor the last two centuries, the average period being z35 yr.Local populationsover theprovince tend to oscillatein unison,though their amplitudes and meanlevels are notalways the same. The local populationprocess in the sprucebudworm is composedof two majorparts, a basic oscillation,and secondaryfluctuations about this basic oscillation.The basic oscillationis largely determinedby the combined action of severalintrinsic (density-dependent) mortality factors during thethird to sixthlarval instars. These factorsinclude parasitoids and, probably, diseases (e.g., mi- crosporidianinfection), and, most important, an intriguingcomplex of unknown causes, which I term "thefifth agent" (a largenumber of larvae with no clearsymptoms died during the population decline in thelate 1950s). Othermortality factors, including predation, food shortage, weather, and lossesduring the spring and falldispersal of young larvae, are notcauses of the basic, universally occurring oscillation. Becauseof immigrationand emigrationof egg-carryingmoths, the ratio of all eggslaid to the numberof locally emerged moths (the E/M ratio, or theapparent oviposition rate) fluctuates widely fromyear to yearbut independently of thebasic oscillationof densityin thelocal populationsthat werestudied. The fluctuationin thisratio is themain source of the secondary fluctuation in density aboutthe basic oscillation,and is highlycorrelated with the meteorological conditions that govern theimmigration and emigration of moths. The E/Mratio is themajor density-independent component ofbudworm population dynamics. Contraryto commonbelief, there is no evidenceto indicatethat invasions of egg-carrying moths fromother areas upsetthe assumedendemic equilibrium state of a local populationand trigger outbreaks.Moth invasions can onlyaccelerate an increasein a localpopulation to an outbreaklevel, butthis happens only when the population is alreadyin an upswingphase of an oscillationcaused by highsurvival of thefeeding larvae. In otherwords, the "seed" ofan outbreaklies in thesurvival of feedinglarvae in thelocality, and mothinvasions can act onlyas "fertilizers." The weightof evidence is againstthe idea thatan outbreakoccurs in an "epicenter"and spreads to thesurrounding areas through moth dispersal. Rather, the egg-mass survey data in NewBrunswick since1952 favor an alternativeexplanation. If the trough of a populationoscillation in a certainarea stayscomparatively high, as in centralNew Brunswickin the 1960s, or ifthe area is moreheavily invadedby egg-carryingmoths when the populationsin thatarea are in an upswingphase, these populationsmight reach an outbreaklevel slightly ahead of the surrounding populations, all ofwhich are oscillatingin unison. If a local populationoscillates because of theaction of density-dependent factors intrinsic to the local budwormsystem, it mayappear to be difficultto explainwhy many local populationsover a widearea oscillate in unison.However, Moran's (1953) theory shows that density-independent factors (suchas weather)that are correlatedamong localities will bring independently oscillating local pop- ulationsinto synchrony, even if weather itself has no oscillatorytrend. I illustratethis with a simple time-seriesmodel. The samemodel also illustratesa principle behind the fact that outbreaks occurred fairlyregularly in New Brunswickand Quebecduring the past two centuries but rather sporadically in otherregions of eastern Canada. Finally,I reviewthe commonly accepted theory of outbreaks based on thedichotomy of endemic and epidemicequilibrium states and arguethat the theory does not applyto thespruce budworm system. Keywords: Choristoneurafumiferana (Clem.); Green River Project; insect life-table analysis; in- sectoutbreaks; moth dispersal; population dynamics; spruce budworm.

INTRODUCTION Almost 20 yr have passed since publication of the budwormpopulation study of the Green River Project. monograph(Morris 1963a) based on the classic spruce During those 20 yr, spruce budworm populations in I Manuscriptreceived 23 December1982; revised and ac- theProvince of New Brunswickdeclined once and sub- cepted15 August1983; final version received 28 November sequentlyhave risento thecurrent outbreak level. Now, 1983. again,we are in themidst of controversy about whether 430 T. ROYAMA Ecological Monographs Vol. 54, No. 4 "to spray or not to spray" insecticidesto protectthe the Baskerville(1976) task-forcereport. In particular, forests.A few years ago, a task forcewas formedto I criticallyexamine the notion of a dichotomyof en- evaluate budwormcontrol alternatives for better forest demic and epidemic states and the alleged role of cli- resource management of the province (Baskerville mate and moth dispersal in the initiationand spread 1976). This task forcerelied heavily on a foresteco- of outbreaks. systemmodel thatwas based primarilyon the Morris (1 963a) monograph.However, thispioneering work is Life cycle 20 yr old and, in many respects,inadequate from a The spruce budworm (Choristoneurafumiferana currentpoint of view. Besides thelack ofadequate data, [Clem.],Lepidoptera: Tortricidae) is univoltinein east- the major problems of the early work were its inap- ern Canada. Moths emergefrom mid-July to earlyAu- propriatetreatment of time-seriesdata and its inade- gust in the Green River area of northwesternNew quate understandingof the concept of densitydepen- Brunswick.Females lay eggs over several days. Egg dence (Royama 1977, 198 la, b). Unfortunately,certain masses are laid on the foliageof conifers,mainly bal- of its interpretationshave continued to be accepted sam fir,Abies balsamea (L.), and severalspruce (Picea) virtuallyunchanged even in the most recent Royal species. Each egg mass contains an average of about Commission reporton the spruce budworm outbreak 20 eggs. Females raised in normal feedingconditions in Newfoundland(Hudak and Raske 1981). lay from 100 to 300 eggs, with an average of :200, The presentpaper reinterpretsthe originallife tables but heavydefoliation caused by a highdensity of larvae fromthe Green River Project,incorporating recent in- can reduce fecundityto one-half. The eggs hatch in formationfrom field observations, laboratory experi- 10 d. Soon afterhatching, the first-instarlarvae dis- ments,and theoreticalstudies. The task is somewhat perse withintree or stand, or even beyond by wind. like restoringa prehistoricanimal fromfragments of Survivinglarvae spin hibernacula withinwhich they fossilized bones. Morris's life tables provide a basic moltto thesecond instar. No feedingoccurs until spring. skeletal structurebut are insufficientfor full restora- Second-instarlarvae overwinterin hibernaculauntil tion; missingpieces have had to come frominference early May. Soon afteremergence, they disperse again or supposition.Whenever I need to deduce indirectly, and settleat feedingsites on host trees.They mine in I argue only qualitatively,steering between the riskof 1-2 yr old needles, or in seed and pollen cones when makinga falseinference and thatof hesitatingto adopt available. Duringthe thirdto sixthinstars, from about a potentiallycorrect hypothesis. earlyJune to earlyJuly, larvae feedon thecurrent-year This paper consists of four major sections. First, I shoots.If current-yearshoots become depleted,the lar- brieflydescribe the life cycle of the spruce budworm vae will feed on older foliage,but this oftenresults in and the cyclic patternof its population fluctuation, reduced size and fecundityof adults. Pupation nor- restoredfrom recent quantitative information and sup- mally takes place on the foliage in early July.Moths plementedby more qualitative records of outbreaks. eclose in :8-12 d, completingthe cycle. These records include the results of the analysis of Recent radar studies of moth dispersal (Greenbank radial growthrings of some host trees that survived et al. 1980) have revealed that both female and male budwormattacks in the past two centuries.': sprucebudworm moths are strongfliers. Dispersal takes In the second section, the analysis of the life-table place in the evening. Female moths usually emigrate data, I identifytwo major components that govern afterlaying part of theiregg complementat the place yearlychanges in sprucebudworm populations, name- of emergence.Moths in exodus flightclimb decisively ly, survival of larvae during their feedingstage and to > 100 m in altitudeand thenfly to new sites,which apparentoviposition rate (i.e., the ratio of all eggslaid are normally50-100 km downwind,but whichcan be to the numberof locallyemerged moths; E/M ratio for as faras 450 km (the distance between the east coast short). The larval survival rate determinesthe basic of New Brunswickand the west coast of Newfound- oscillatorypattern in population fluctuations,a trend land). Female moths usually deposit at least some of that is subject to perturbationby the E/M ratio. Im- their eggs where they firstland, but they may leave migrationand emigrationof egg-carryingmoths cause thereand deposit eggs at othersites over several eve- the E/M ratio to fluctuatewidely fromyear to year, nings. but withoutany noticeabletrend. I raiseall conceivable Dispersal flightis governedby meteorologicalcon- factorsthat could influencethe two componentsand, ditions,particularly temperature; no exodus occurs at by elimination,I narrow the possibilities to the few < 14'C, and if the moths encountersuch a low tem- most plausible ones. peraturein flight,they descend withwings folded. No In the thirdsection, I attemptto synthesizespruce flightwas observed at temperatures> 300. budwormpopulation dynamics by simulationsthat use a simple time-seriesmodel. In the last section,I show Patternof population fluctuation how my view of the populationdynamics of the spruce Local budworm populations fluctuatebetween ex- budwormdiffers from other theories, which have been tremelevels. At highdensities, budworm larvae cause elaborated in models such as the one incorporatedin extensive damage to firand spruce stands, and even December 1984 SPRUCE BUDWORM 431

150 _-s

0.05

I S4 E - . 04 0.14- 16195194 195 195 17 95 18 0.05- ForesResarch ent4).- 1945 1950 1955 1960 1965 1970 1975 1980 Generationyear FIG. 1. Yearlychanges in sprucebudworm. density (number/rn2 offoliage, logarithmic scale) in northwesternNew Bruns- wickbetween 1945 and 1980. 0 third-to fourth-instarlarvae in plotG4 nearthe GreenRiver field station; 0 egg-mass densitiessampled in wider,unsprayed areas, including the Green River area (data providedby E. G. Kettela,Maritimes ForestResearch Centre). kill trees. In contrast,when larvae are scarce, even Brunswickhave been changingin unison for at least intensivesampling over a wide area may findonly a the past 30 yr. fewlarvae (Greenbank 1963a). An earlier widespread budworm outbreak in New Commencingin 1945, densitiesof third-to fourth- Brunswickbegan about 1912 and subsided about 1920 instar larvae in a few selected study plots in north- (Tothill 1922, Swain and Craighead 1924). From then westernNew Brunswickwere determinedannually by untilthe mid- 1940s, budwormpopulations throughout intensive sampling (Fig. 1, 0), as part of the Green the province remained extremelylow (Greenbank River Project (see Introduction:Source of Data). Al- 1963a). One otheroutbreak that occurred around 1878 thoughthe Green River Project was terminatedin 1972, is well documented in the local literature(Swain and a less intensive egg-mass sampling in many sample Craighead 1924), which noted that the budworm be- plots over all of New Brunswickhas been carriedout came scarce afterseveral yearsof extremelyhigh den- to date formonitoring budworm density in relationto sity.We have now begun to see a patternof oscillation theprovince's program of aerial sprayingof insecticide. in budwormpopulation change,which has completed The graphwith solid circlesin Fig. 1 shows the annual threefull cycles in the past 100 yr. changes in the average densityof egg masses in some Even older outbreaksof the budwormcan be traced ofthosesample plotsthat were free from aerial spraying by examiningradial growthpatterns of some food trees in the northwesterncorner of the province,including that survived severe defoliation caused by the bud- the Green River area. An egg mass contains, on av- worm (Swain and Craighead 1924, Blais 1962). These erage, :20 eggs,and : 15% of the eggswill surviveto outbreaks,marked by the firstsign of growth-ringre- third-to fourth-instarlarvae. Therefore,the egg-mass tardation,began about 1770, 1806, 1878, 1912, and graphin Fig. 1, if shiftedupward by about one step on- 1949 (Blais 1958, 1968, Greenbank 1963a); the last the vertical(logarithmic) scale, can be used to approx- threecoincide withthe directexperience already men- imate annual changes in larval densityfrom 1968 on. tioned. The presentoutbreak is probablyat its peak. It looks as thoughbudworm populations oscillate. Similarly,Blais (1965) foundevidence of outbreaksin This patternof population change is not an isolated theLaurentide Park regionof Quebec, northof Quebec local case, but occurs widely over New Brunswick,as City,beginning about 1710, 1755, 1812, 1838, 1914, revealed in egg-masssurveys since 1952. I divided the 1953, and the currentoutbreak concurrentwith the provinceinto 30 blocks and, in each block, calculated one in New Brunswick. the average egg-mass density (Fig. 2). We see some Synthesizingthe above facts,I restoredthe pattern regionaldifferences in thepattern of populationchange. of budwormpopulation dynamics in Fig. 3. The graph In particular,the troughtends to be much shallower priorto 1945 is a schematicrepresentation of the his- in centralregions than in both northernand southern torical documents and the tree-ringanalyses already parts of the province. Also, the populations in the quoted; after1945, the graph is based on actual sam- southeasterncorner appear to have startedincreasing pling, as in Fig. 1. The intervalsbetween periods of slightlyahead of therest of the province.Nevertheless, heavy defoliationregistered in the tree rings are re- despite fuzzyyear-to-year fluctuations, the troughin markablyregular, particularly in New Brunswick(solid each graphis clearlyconcurrent among all populations. arrows),with the exception of a wide gap between 1806 In other words, the budworm populations in New and 1878; thisgap is about twiceas long as the average 432 T. ROYAMA Ecological Monographs Vol. 54, No. 4

F Quebec A Year 0) 0) 0) 0)

400 U 0 M0 E 50 VI

MaineIl A -~~~~~- 41J~~~~~~Nova Scotia

1 2 3 4 5 6 7 FIG. 2. Yearly variations in average egg-massdensity (number/M2 of foliage,logarithmic scale) across New Brunswick (outlinedby brokenlines) since 1952, calculated fromthe Aerial Spray Programdata provided by E. G. Kettela (Maritimes Forest Research Centre).In each block, egg-massdensity is plottedon the verticalaxis (logarithmicscale) and calendar years on the horizontalaxis as shown in block E6. intervalbetween other successive outbreaks. A similar fromplot G4 in Green River ( Fig. 1) is one such low- gap occurredin Quebec between the 1838 and 1914 densitycase. Thus, placinga small peak at about 1840 outbreaks(dotted arrows). This led Blais (1968) to re- in Fig. 2 restoresthe regularityof oscillations.I know mark that "data on past outbreaksindicate that epi- ofno tree-ringdata fromNew Brunswickfor the period demics of thisinsect do not recurat regularintervals." around 1710, when the Quebec specimensshowed de- However,there were comparatively light defoliation foliationmarks. marksin treesfrom Quebec around 1838, when there Includingthe possible hidden peaks, the average cycle was littlesign in the specimens fromNew Brunswick; lengthwas 35 yrin New Brunswick(7 peaks over 210 conversely,there were clear marks in treesfrom New yr),and 38.5 yr in Quebec (8 peaks over 270 yr). The Brunswickaround 1878, when therewere few in the longeraverage forQuebec is due to two long intervals Quebec specimens. Is it not likelythen that the pop- between17 10 and 18 12. This degreeof difference would ulations in both provincespeaked more or less at the not be unusual between two series of stochasticpop- same time, as in other outbreaks,but that the popu- ulation processes that share a common endogenous lationsin one provincedid notreach a level highenough density-dependentstructure and, hence, the same ex- to affectthe tree rings?The supportingfacts for such pected (mean) periodicity. a hidden peak are that (1) otheroutbreaks in the two Even duringthe low-densityperiods betweenmajor provincestended to occurfairly closely together in time, outbreaksin this century,a few scatteredpatches of (2) the populations in New Brunswickin recentyears comparativelyhigh density always remained on the have oscillatedin unison (Fig. 2), and (3) peak densities budworminfestation maps of easternCanada (Brown of some local populationsin the Green River area dur- 1970, Kettela 1983). These are probablythe areas where ingthe 1949 outbreakdid not reacha level highenough the troughsof population oscillations stayedcompar- to cause heavy defoliation.Nevertheless, these popu- atively high, as in central regions of New Brunswick lations did oscillate in parallel with otherpopulations in the 1960s (Fig. 2). I discuss the stochasticnature of thatreached an extremelyhigh density. The population these population oscillations in Synthesis. December 1984 SPRUCE BUDWORM 433

0 I 75 CL

CL 0

1700 1750 1800 1850 1900 1950 Year FIG. 3. Sprucebudworm population cycles (logarithmic scale) in thepast two centuries, restored from sampling data since 1945(- **; afterFig. 1),from historical records since 1878 ( ), and fromradial growth-ring analysis of some surviving trees(-- -). Arrowsindicate the years of firstsign of ring retardation. Solid and dottedarrows are forNew Brunswickand Quebec,respectively. For a smallpeak around 1840, see text.

Source of data The second longest set of life-tabledata, the 9 yr Life-tablestudies of the Green River Project were between 1949 and 1957, comes fromplot G5, 5 km carried out in locations free from aerial sprayingof northof plot G4. This was an "immature" firstand DDT and werebased mainlyon samplingfir and spruce (<40 yrold in 1945). Again, it was an isolated, "atyp- foliage at three phases in the life cycle of the spruce ical" stand,where budworm density stayed even lower budworm;namely, (1) soon afterall eggshad hatched, than thatin plot G4. Nevertheless,the patternof pop- (2) when the majorityof larvae were in the thirdand ulationchange during the studyperiod was again much fourthinstars, and (3) at the time of 60-80% moth the same as in otherareas. eclosion. The lengthof a foliatedsample branch was Additionallife-table data used in thepresent analysis multiplied by its midpoint width to calculate the are fromplots K1 (maturein 1945, as in G4) and K2 "branch (or foliage) surfacearea." Budworm density (immature,as in G5), both 15 km northeastof G4. was thenexpressed as numberper square metre(orig- These two plots are part of an extensivefir forest, typ- inally numberper 10 ft2)of the foliagesurface. ical ofnorthwestern New Brunswick,where a highden- The above sampling schedule determined(1) egg sity of budworms caused successive years of heavy density,(2) initial density of first-instarlarvae (i.e., defoliationand much tree mortality.Unfortunately, thoseeggs successfully hatched), (3) densityof "feeding the data fromthese plots covered no more than 7 yr larvae," the majoritybeing in thirdto fourthinstars, (1952-1958) of the decliningphase of the outbreak. (4) densityof pupae, includingempty pupal cases still Plot G2, 5 km south of G4 and with similar stand remainingattached to the sample foliage,and (5) total characteristics,yielded an even shorterset of life-table numberof moths thatemerged. data, whichwill be used in the presentanalysis as sup- Althoughsampling was carriedout at some 20 scat- plementaryinformation only. tered plots, the period duringwhich most plots were After 1959, budworm densityin the Green River sampled extendedover onlya fewyears and is not long area fell so low that it became extremelydifficult to enough foranalysis of temporalchanges in budworm findlarvae late in the season. Consequently,it became density.Only one plot, G4, a maturefir stand thatwas technicallyimpossible to carryon a fulllife-table study. >50 yr old in 1945, yielded 12 yr of uninterrupted Onlythird- to fourth-instarlarvae continuedto be sam- samplingdata between 1947 and 1958, a period cov- pled at plots G4 and K1. Unfortunately,egg sampling eringa major part of the outbreakin the province in was also discontinuedafter 1959. Althoughthe pop- the early 1950s. Since it covered the longest period, ulation began to increase after 1968, leading to the the set of data fromthis plot is the main source of currentoutbreak, the project,regrettably, was termi- informationused in the presentanalysis. nated afterthe 1972 season. However, in plot G4 the budworm densitynever Long-rangemoth dispersal has been studied by air- reacheda level highenough to cause heavy defoliation craftand radarin recentyears (Greenbank et al. 1980). and tree mortality.The investigatorsconsidered the Some resultsfrom this study will be used in thepresent plot to be atypicalsince it was isolated fromother parts analysis. of the forestby earlierclear-cutting operations. None- theless,the rise and fall of population densityin this Notation and terminology plot followed much the same patternas in the other In this paper, densityof the insectis denoted by the areas where densityclimbed to extremelevels. Thus, lowercaseletter n, and the rate of change in n between from the point of view of budworm population dy- two points in the life cycle by h; this is the survival namics, I do not see thatthe population in plot G4 is rate in the intervaldefined, with the exception of the atypical. adult-to-eggrate of change. The naturallogarithms of 434 T. ROYAMA Ecological Monographs Vol. 54, No. 4 TABLE1. Life-tablenotation and life-historystages.

a. Summaryof life-tablenotation. n, = Density at the beginningof stage s in generationt (s = 1 to 5) N, = log n,, hi! = ns+I /nst (s = 1 to 4): survival rate in stages h5t = n,,t+/n5t: apparent oviposition rate (or E/M ratio) H3t = log h3t hg, = intragenerationsurvival rate H,, = HI + H2 + H3 + H4: log (intra)generationsurvival rate Rst = N3t+1- Nt: log rate of change in densityfrom stage s in generationt to the same stage in generationt + 1 R.! = H4v+ H5t:log rate of change in egg density R3t = H3t + H4t + H5t + HI I,' + H2t+3,:log rate of change in third-to fourth-instar(L3) density b. Parameternotation and stage designationsin life-tabledata. Stage Gen- Initial sur- Stage era- den- vival Stage Code (s)t Period tion sity Remark rate Remark Eggs E 1 Late summer t n, All eggs laid of year t - 1 he Egg(E) survival Young LI 2 Fall ofyear t n2t All eggs hatched* larvae t - 1 h2, Survivalof young (L1)larvaet Old lar- L3 3 Earlysummer t n3t Majorityin 3rdand 4thinstars* vae of year t h3t Survivalof old (L3)larvae? Pupae P 4 Mid-summer t n4t All pupaeand pupalcases at time ofyear t of 60-80% mothemergence h4, Pupal (P) survivall Moths M 5 Late summer t n5t All pupalcases at timeof ofyear t 60-80% mothemergence, and moths reared fromremaining pupae* h5t E/Mratio (apparent ovipositionrate)JI Eggs E 1 Late summer t + 1 nl,+ ofyear t t s numbersas in Table 1a. * Time sampled;see Introduction:Source of Data. t Referredto as "smalllarvae" in Morris(1963a). ? Referredto as "largelarvae" in Morris(1963a). 11Mainly later part of pupal stage; see Introduction:Source of Data. ? Eggsper moth on foliage.

n and h are denoted by the correspondinguppercase in the calendar year t - 1 belong to generationyear t, lettersN and H (the same notationswere used in Roy- and the subscriptt in Nt, Ht, etc. indicates the gener- ama 198 la, b). Throughoutthis paper, natural loga- ation year. In graphs,these parametersare normally rithmsare identifiedwith the abbreviation"log." plottedagainst generation year t; only in a fewgraphs Life-cyclestages and generationsare indicated by are theyplotted against calendar years. two subscripts.For example, n,, and NS, are density The parameterand stage symbols used throughout and log densityat thebeginning of stages ofgeneration this paper are summarized in Table 1; details of the t. The survival rate fromthe beginningof stage s to timingof the five stages listed in the table have been that of stage s + 1 withingeneration t is then: givenin Introduction:Source of Data. As alreadynoted, hs fors = 1 to 4 is a stage survivalrate. In many pub- hat= ns+llnst (la) lished works, the survival rates h3 and h4 are often or, takingthe logarithms, referredto as "large larval survival" and "pupal survival" after the Green River H=Ns -N (l b) Project terminology. However, h3includes the effectof mortalityin part of As mentionedin Introduction:Life Cycle, one gen- the pupal stage,and, conversely,h4 excludes the early erationin the budwormlife cycle spans fromthe late part of pupal mortality.Unlike other h's, h5tdefined summerof one yearto thatof thefollowing year. Thus, as n 1t+l/n5tis not a survival rate, but is an apparent the eggs,the firstinstar, and part of the second instar oviposition rate per moth (male and female moths December 1984 SPRUCE BUDWORM 435 combined),as it includes the effectsof gain and loss of To imply thatthis "trend" is a section of a trendin a eggs throughmoth migration.I shall call this rate the longerseries requiresadditional knowledge. "E/M ratio." Reliabilityof data In the presentdata, H5 is always positive (or h5 > 1) despite the physical possibilityof a negativevalue Spruce budwormsampling in the Green River Proj- resultingfrom an extremelyhigh rate of emigration. ect was very intensiveto ensure a high level of reli- As opposed to this,the H's in all otherstages are neg- ability(Morris 1954, 1955). Nonetheless,the data suf- ative; i.e., a net loss, though net gain of larvae has fervarious types of errorsor loss of information.In actually been observed in a few plots at the time of thefirst few years of the project, egg and pupal densities second-instardispersal (Miller 1958). were not adequately determined,and the correspond- Some successive H values may be lumped. For in- ing survival rates were indirectlyestimated. Although stance, lumpingthe firsttwo stages, Hit + H2,, gives a large sample was taken each time to ensure an ac- the log survival rate fromegg to thirdto fourthinstar curateestimate of density,no sample was taken in the in generationt. Lumping fromHit to H4,, and desig- intervalbetween third- to fourth-instar(L3) and pupal nating the sum as H,,, gives the log intrageneration (P) stages (Table lb), so that littlewas known about survivalrate, though this term assumes zero mortality changes in densityduring that importantinterval. in egg-layingmoths; the effectof the moth mortality The pupal density(n4) tends to underestimatethe is in factincluded in H5t,the log E/M ratio. We may actual numberof larvae that pupated, because preda- lump all log stage survival rates to H5t,giving the log tors, for example, could have removed some pupae intergenerationrate of changein eggdensity from gen- withouttrace before the scheduledsampling. Also, the erationst to t + 1. This will be denoted by RI,; i.e., value n5 in Table lb tends to overestimatethe total number of moths that actually emerged in the field, Rlt= -NNt+-Nit and this, in turn,underestimates the E/M ratio (h5). = + + ..*+ Hit H2t Hot This is because n5 is the sum of all pupal exuviae on = Hg1+ (2) H5t. the sample foliageplus thenumber of remaining pupae In general,we may defineR1t (s = 1, 2, . . .) such that rearedto adults in the laboratory,the latterbeing protected frompredation or loss in the field. These are = Rst Nst+ -Nst probablyminor errors, however. The variation in the + + = Hst + Hs+1 t Hs- It+l- (3) timingof L3 samplingfrom year to year influencedthe For example, R3t is the t to t + 1 intergeneration(log) estimationsof h2and h3,the survivalof youngand old rateof changein the third-to fourth-instardensity and larvae. I discuss this in detail in Analysis:Analysis by is the sum H3t + H4t + . . . + H2,t + 1 Stage Survival Rates. The log intergenerationrate of change in densityof Graphedlife tables a given stage (R in Eq. 3) has oftenbeen referredto in the literatureas the "index of population trend,"since Graphs oflife-table data fromplots G4, G5, K1, and Balch and Bird (1944) coined the term(Morris 1957). K2 are shown in Figs. 4 to 7. As mentionedin Intro- This is an unfortunateterminology, because the year- duction: reliabilityof data, densitiesat some stagesin to-yearrate of change cannot indicate population trend the firstfew years are indirectestimates, as are the in the usual statisticalsense; i.e., a fairlyconsistent subsequentlycalculated survival rates. These indirect tendencyover a comparativelylong period of time. To estimatesare indicated by open circlesin the figures. reveal a trend,observations must extend many more than 2 yr. ANALYSIS OF LIFE-TABLE DATA A tendencyfor a population to increase or decrease over a comparativelyshort period of time (for example, Two major componentsof population not much more than 10 yr)may be called a short-term fluctuations trend,though it could have been merelyan increasing Fig. 8 is equivalent to Fig. 1, but plots log year-to- or decreasing phase of an oscillation of many more year rate of change in density (i.e., Rt = N,,, - Nt, yearsin length.Further observations might reveal that ratherthan Nt in Fig. 1) againstgeneration year t. The thesystem is merelyoscillating about a horizontallevel, log rateR exhibitsfrequent secondary fluctuations about in which case the systemwould be said to have no its principal oscillation. (Note that the oscillation in long-termtrend or, alternatively,to exhibit a short- log density[Fig. 1] and the oscillation in the log rate termtrend that changes its directionperiodically, de- of change in density[Fig. 8] lag in phase; a peak or a pendingon which aspect is emphasized. In this paper, troughin Fig. 1 correspondsto a zero in Fig. 8.] I shall I use the term"trend" in the above sense ratherthan now showthat the log generation survival rate Hg mainly in the Balch-Birdsense. determinesthe basic oscillation(smooth curve in Fig. Note also thata "trend" in a seriesof no more than 8), and the log E/M ratio H5 is largelyresponsible for five or six points can occur by chance, as would be the secondaryfluctuations. observed not infrequentlyin a purelyrandom series. Recall thatthe log rateof changein eggdensity (R1t) 436 T. ROYAMA Ecological Monographs Vol. 54, No. 4 lation, and that the log E/M ratio (H5) is largelyre- H2-21 b y+@ -2 sponsible forsecondary fluctuation about the trend. I -6 The log generationsurvival rate Hg, however,does -1 b -3 not always show a smoothoscillation, but shows some H2 -2 -4 h sporadic dips, as in the 1953 generationin plot G4 -3 + -5- (Fig. 9b) and in 1947 and 1951 in plot G5 (Fig. Si); a ' -6 V very low Hg in 1952 in plot K1 (Fig. 6i) is probably CI one such dip, thoughthe data series is too short.In- H3-2 4 - terestingly,all thesedips in thegeneration survival rate are caused by dips in survival rates among feeding H -472 Ra3-4 larvae (H3); compare graph c with graph i in Figs. 4, 7-e 5, and 6. These dips in Hg thatare caused by H3 may H 195 50 60 2 in turncause dips in thelog rateof change in eggdensity (R1); for example, the one in the 1951 generationin 3 -0 I plot G5 (Fig. Si and j). Therefore,Hg, like H5, can be -2 a cause of secondary fluctuationsin the log rate of 6 -f 2 k change in density(Fig. 8). However, a dip in H3 may be counteredby a high log E/M ratio (H5), as in the 4 -N3 R3 0 1953 generationin plot G4; consequently,the dip in 3 -1 H3 would not show in the log rate of change (Fig. N 2 -2 R, I L2? se 4e, i, and j). On thewhole, the variation in thelog E/M ratioH5 is a farmore importantcause of the secondary rto 0 o R4d fluctuationin the log rate of population change than -2 - FIG-34. /-Grpe lif tale inpltG erth re ie are sporadic dips in the log generationsurvival rate -42 -3 Hg, thoughthe latteris an importantsubject fromthe 1945 50 55 60 1945 50 55 60

Generation year H1 0a0 Ia HI ~J +_ -2a g FIG. 4. Graphedlife tables in plot G4 nearthe Green River -I -3 - fieldstation. Log survivalrates in (a) eggs(H,), (b) young larvae(H2), (c) old larvae(H3), (d) pupae(H4); (e) logE/M ratio(H.); (f) log densitiesof eggs(N,), old larvae(N3), and -2 - Hg -4 - pupae (N4); (g) log survival rate frombeginning of egg stage -3 z -5 0 to end of younglarval stage (H, + H2); (h) log survival rate to end of old larval stage (H, + H2 + H3); (i) log intrageneration survivalrate (Hg = + H2 + H3 + H4); () log inter- H3~ f -6 0 H, - -3 generationrate of change in egg density(R. = Hg + H.); log -6 -41 Hg -5 0 rates of change in densities of (k) old larvae and (1) pupae - (R3 and R4, respectively).o- -o indirectestimates. H4 5 d -6 7- fromgeneration t to t + 1 is partitionedinto the log H5 6 - 2 j 1 and the E/M ratio 4 - 1 generationsurvival (H.1) log (H,,); 0-01R1RI c i.e., R1, = Hgt+ H., (Table la). In Fig. 9, I duplicate 3 - - the relevantgraphs fromFig. 4 (life-tabledata from 6 - -2 plot G4) for ease of comparison. It is obvious that a 5 --3 decliningtrend and a secondaryfluctuation about the 4-f N 2- k trendin R1 (Fig. 9a) are determined,respectively, by 2 - ~~R3 0 Hg (Fig. 9b) and H. (Fig. 9c). 2~~~~~~~~ We do not have data on the rate of change in egg 62 3 --R density(R1) after1959. However, R1 is highlycorre- N N -2 lated withR3 (log rate of change in L3 density,Fig. 9a, 0). No doubt, the correlationmust have held after -4 ~ ~ 4 -2- 1959; as I show later, survival fromeggs to third-or -5 -6 O'-36 fourth-instarlarvae is largelydensity independent, so 1945 50 55 60 1945 50 55 60 the above correlationis unlikelyto be affected.There- fore,we can substituteR3 in Fig. 8 for R1 and can conclude,by extrapolation,that the log generationsur- Generationyear vival rate Hg determinesthe basic population oscil- FIG. 5. Same as Fig.4 butin plotG5. December 1984 SPRUCE BUDWORM 437

W biological controlpoint of view. What causes the dips . a X I is currentlyunknown. HI 0L a + 92-2 g9 \~ IE -3 E/M ratio I? b '-3 Fig. 10 compares the graphs of H5 (log E/M ratio) 12 2- t -4 h taken fromFigs. 4-7. The dashed line in each graph -3 I -5 - indicatesone-half of the mean potentialfecundity (full -I6 eggcomplement) of a local femalemoth; I call thisthe -2-3- C-3 - mean fecundityper moth (includingmales) and refer to it by the symbolfi. I use this measure to compare Hg5- with the E/M ratio because the denominator of the H dd., .-6 ratio includes all locally emerged moths, whose sex 7- ratio is usually 1:1 (McKnight 1968, T. Royama, per- H 6 e 2i j sonal observation).If neithermoth dispersalnor mor- a- | l talityhas occurredin the locality the E/M 5 l lRl l l concerned, 3 ratio should coincide with the dashed line. -gj - Note threefeatures in the graphsof Fig. 10: (1) the 7 N-2 6 fN log E/M ratios(H5) oftendeviate widelyfrom the mean 5 - 0N3 2 k 5 potentialfecundity per moth ---); (2) the (logsf, H5's 0 oftenfluctuate in unisonbetween plots, but at distinctly FIGN4 R3S lower levels (as compared with---) in the K than in 2 -2- the G plots; (3) no trendis apparentin the H5's in the N i--2 -I G plots (the series in the K plots are too short). To aid in explainingthese features,I use a model -4~~~~~~~~~~ n 0: number2ofmoths that emerge-2 composed of the followingsix parameters. -5 -31 1945 50 55 60 1945 50 55 60

0- a I ~ -209- HI _ X Ha-2 it+ -2 - Generation year IF -3 FIG. 7. Same as Fig.4 but in plot K2. 0 b h H2-2 - +-4 -3 -56 n,: numberof moths that emergedlocally - H2 i -3 | H -61: A: mean potentialfecundity of a local moth,including males H3 -2 C -3 p1: proportionof f laid locally beforeemigration 55 m: numberof immigrants H4 5 d 55 -6 f2: mean number of eggs carried per immigrant,in- 7- cludingmales 6 - P2: proportionof laid at the site before - e 2- f2 landing re- H 5 I emigration

3- Note thatPi takes into account the effectsof the rate 7-4 N1 ~~~~~~~~4-2 of emigration,the preemigrationrate of oviposition, 6 f 23 and the preemigrationmortality among the emigrants; 5 -32 k P2 takes into account the same effectsapplied to the 3 ~~~~R3_I immigrantsthat reemigrate. 2 N- -2 The total number of eggs laid locally is the sum N I 2 ftpln5 + f2p2m, and dividing the sum by n, gives the 0 FIG 6. Sam Fi.4btinpo -1 RI E/M ratio h5; i.e., -2 - R4 0I /% h5 =f1p1 +f2p2m/n5. (4) -3 -- -4 -2- This equation applies, withoutnotational change, to a -5b- 1945 50 55 60 1945 50 55 60 more generalsituation, as in Appendix 1. Deviation ofE/M ratiofromfecundity.-The potential fecundityof a femalemoth (2f1)is linearlyrelated Generation year to its pupal size, is usually <250 eggs, and is rarely FIG. 6. Same as Fig.4 butin plotKi. >300 eggs(Miller 1963a: Fig. 13.3). The dashed lines 438 T. ROYAMA Ecological Monographs Vol. 54, No. 4

3 C e02

0 .s

0 -

*~-3

0 1945 1950 1955 1960 1965 1970 1975 1980 Generation year, t

FIG. 8. Equivalent to Fig. 1, but shows yearlyfluctuation in log rate of change in L3 density(R31, 0) fromgeneration t to t + 1, plotted against t, and the log rate of change in egg-massdensity (Rlt, 0). The smooth trendcurve is drawn by eye. Arrowsindicate years of moth invasions fromoutside; see Analysis: Frequencyof Moth Invasions.

in Fig. 10 are theaverage f's estimatedfrom the pupal size sampled in each plot (Miller 1957, 1963a). Low fecundityin the K plots is associated with heavy de- o foliationof the current-yearshoots (Table 2). An E/M ratio well above the dashed line indicates I I immigrationof egg-carryingmoths. Because of mor- Qo I talityamong laying moths, only 60-80% of the full R d It complementof eggsmay be laid locally (Thomas et al. 1980, and Appendix 2), even if local femalemoths do 0 -2 a '1,0 not emigrate.Therefore, an E/M ratio fallingbetween -3 the potentialfecundity f and 0.6f1does not necessarily in -3_ indicate emigration.However, many points Fig. 10 are well below log 0.6f1,indicating net emigration. -4 _-H Note that althoughthe lowest average fecundityin Hg -5 b the heavily defoliatedK plots was as low as one-half -6 b ae of thatin the G plots,such a differencehad littleeffect -7 - on variation in the E/M ratio. Thus, variation in fe- cundityis a trivialfactor in budwormpopulation dynamics relativeto moth dispersal. Climaticinfluence on E/M ratio.-Fig. 11 compares H55F______7 the average net moth dispersal over the Green River area withthree meteorological factors during the adult period forthe years 1950-1958. The threefactors are (1) number of cold frontspassing over the area, (2) number of thunderstorms,and (3) mean daily mini- 6 3 mum relativehumidity (data taken fromthe firstnine rows in Greenbank's [1963b] Table 14.3). Note that N14 Greenbank's net moth dispersal (fifthcolumn in his 3i4 table) is proportionalto my E/M ratio. The inverted mean dailyminimum relative humidity (graph c) seems 2 to be the best predictorof the log E/M ratio H5. A good correlationbetween inverted mean daily minimum relative humidityand E/M ratio seems to 1945 1950 1955 1960 hold over a much longerperiod. As shown in Fig. 9, Generation year we have a directmeasurement of the E/M ratio in a few plots, but only between 1946 and 1958. During FIG. 9. The log rateof changein eggdensity in plotG4 this period, the fluctuationin the log E/M ratio H5 in (R., 0, grapha) is partitionedinto survival log generation plot G4 was nearlyidentical with that in the log rate (Hg,graph b) and logE/M ratio (H5, graph c). The lograte of changein L3density (R3, grapha, 0) is highlycorrelated with ofchange in L3 density(R3), exceptfor a decliningtrend R1.All graphshere are takenfrom Fig. 4. in R3 and a lack of it in H5. Thus, allowing for this December 1984 SPRUCE BUDWORM

TABLE 2. Averagepotential fecundity* oflocal female moths in relationto defoliationof current-year shoots on balsam r fir,Abies balsamea, in GreenRiver area. G4 G plotst K plotst Defolia- Defolia- tion Fecundity tion Fecundity Year (%) (eggs/9) (%) (eggs/9) 1947 5 normal? _ 1 1948 17 normal 1949 7 normal 3 i ~~~~~~~I ~~ I I 1950 24 186 - -

I2 4 - 1951 11 178 73 159 1952 9 178 96 139 1953 11 176 99 93 2 1954 26 normal 99 121 1955 10 normal 58 136 1956 13 normal 68 150 6 _ ,, 1957 17 normal 51 170 5 _ K * Estimatedfrom pupal size; see text. t Averageof G2, G4, and G5. t Averageof KI and K2. ? Normal(unstarved) pupal size, indicating the average fe- cunditywas ;200 eggs. 2 _A IIDash indicatesno data.

fromthe meteorologicalrecord in each year (Fig. 13, 0). The series of these estimated degree-daysis well correlatedwith the series of log E/M ratios (H5; Fig. 13, 0) from 1946 to 1958 and is still quite well correlatedwith the series of R3 (log rate of change in L3

1945 1950 1955 1960 8 - 0 FW - a Generation year C 6k- FIG. 10. Patternsof fluctuations inthe log eggs/moth (E/M) ratio (H5) in plots G4, G5, K1, and K2. Dashed line in each .0 2 - graphis thelog mean potential fecundity per locally emerged 7o moth(logs,); details are in thepresent section.

0 e , difference,we could use R3 in Fig. 8 (plot G4) as an 0 0 indicatorof fluctuationin H5 after1959. We also have daily readings of minimum relative humidityat the Green River fieldstation, 2.5 km south of G4, from Z~~ :~ I I I I I IX 1946 to 1972. However, I have to estimatethe dates I 1 of the adult period in each year indirectlyin the fol- 0- lowingway. -351905 52 65 75 First,accumulated heat units(in degree-days)above .04) 3--]0 0c -a &_. I a thresholdtemperature of 5.60C can adequately pre- ) 0 I E dict the developmentof the spruce budworm (Miller et al. 1971). We have thedates on whichmoth eclosion -2 I ~~~~~~E peaked each year at the Green River stationbetween 195051 52 53 54 555657 58 1949 and 1957 (Fig. 12, 0), fromwhich I calculated theaverage accumulatedheat unitsto be 607.2 degree- Year days. The date on which this number of degree-days FIG. 11. Effectof climateon theeggs/moth (E/M) ratio, was accumulated in each year was in turnread from afterGreenbank (1 963b: Table 14.3).a. Numberof cold fronts the meteorologicalrecord at the station;I take this as passingover the GreenRiver area duringthe mothflight the day of peak moth eclosion foreach year (Fig. 12, period.b. Numberof thunderstorms. c. Mean daily minimum 0). Over an intervalof 20 d, withthe estimatedpeak- relativehumidity (%, *, invertedscale on theright), and the logarithmsof Greenbank's index of net moth dispersal (pro- day in the middle, as an effectiveadult period, I cal- portionalto myE/M ratio)averaged over the GreenRiver culated the mean daily minimum relative humidity area (0, scaledon theleft). 440 T. ROYAMA Ecological Monographs Vol. 54, No. 4

o 10

0 > 5

a 20 e=Lo <>20ttO~~~~~~~~l ; 0

0 10 _

a 1946 48 50 52 54 56 58 60 62 64 66 68 70 72 Year FIG. 12. Estimationof dates of peak moth eclosion in theGreen River area from 1946 to 1972.0 recordedpeak eclosion dateson whichheat units had accumulatedto, on average,607.2 degree-daysabove 5.60C. 0 dateson whichheat units had just accumulatedto 607.2 degree-days. density,x ), a substitutefor the H. seriesbetween 1959 sity is another controllingfactor. Moths do not take and 1971. Note thatboth R3 and invertedmean daily offmuch before 1900 regardlessof temperature(an minimumrelative humidity exhibited an upwardtrend exception was the unusually earlier flightsduring a after1963, whichwas probablycoincidental (see Anal- 95% sun eclipse in New Brunswickat 1735 on 10 July ysis: influenceof weather). 1972). The minimumrelative humidity of a day normally Greenbanket al. (1980) have shownthat peak hours occursin theearly afternoon, and mothdispersal takes of exodus tend to be earlier on cold nightsthan on place in the evening. Then, why is there an inverse warm nights.However, a cold nightis likelyto reduce correlationbetween E/M ratio and mean daily mini- the overall chance forexodus. A cold nightmay also mum relativehumidity? Probably, meterological con- forceimmigrants to land if they happen to be flying ditionsthat affect moth dispersal activity in theevening over the area. Therefore,in a year when cold nights are correlatedwith the minimum relative humidity. prevail,more eggstend to be depositedlocally, result- Greenbanket al. (1980) observed thatthe eveningex- ing in a high E/M ratio in the area, and vice versa. odus flightof a moth usually occurredbetween 1930 Since a low minimum relativehumidity tends to in- (AtlanticDaylight Saving Time) and midnight(the peak dicate a cool night(and vice versa),we getthe observed was at about 2130), and mostly at temperaturesat inverserelation between E/M ratioand the mean daily canopy level of between 180 and 230C; no exodus was minimumrelative humidity. observed below 14.5?, above 29.50, in heavy rain, or The warmthof a nightmay be indicated by average in still air. Their observations by radar and aircraft temperaturesbetween 1930 and midnight.However, revealed that moths on the wing, immigratingfrom as shown in Fig. 14, a nightwith a high initial tem- elsewhere,were forcedto land withtheir wings folded peratureand a steep decline (curve a) could be just as whenencountering a cold air mass (presumably< 140C); "warm" as one witha lower initial temperatureand a iftemperatures remain high enough, however, the moths less-steepdecline (curve b). Chances forexodus flight mightcontinue to flyeven aftermidnight. Light inten- probablyare less on a "cold" night,as in curved rather

. 3 8 _ _ 20

la 2 7 - . -30 V) 1~~~~~: I / - 0~~~~~~0 a, Lo0 3 I~~t15 , 96I 95 17 1950 195 196 4965 197

Year FIG. 13. Comparisonbetween fluctuations in meandaily minimum relative humidity (%, 0; invertedscale) during the estimatedeffective adult period, and thelog eggs/moth (E/M) ratio (He, 0), supplementedby log rate of change in L3 density (R3, x) after1959. Data fromplot G4. For theestimation of effective adult period, see Analysis:Climatic Influence on E/M Ratio. December1984 SPRUCE BUDWORM 441

25 occurredevenly over an area containingseveral plots, theE/M ratioshould be highin a plot wherethe density 0Q of local femalesis low, and vice versa. This idea, however, does not adequately explain the observed rela- b tionshipin Fig. 15, because net emigrationevidently occurred toward the higherend of the densityspec- 20 trum. E Immigrantsare probablyunable accuratelyto assess local population density(n5) beforethey land, so their 0) number,m in Eq. 4, would be essentiallyindependent of n5in each plot. However, as long as climatepermits, theimmigrants could reemigrateif the local population was highenough to have caused substantialdefoliation. 14 In otherwords, it must be emigration,reemigration, and preemigrationoviposition rates that become in- 2000 2100 2200 2300 0000 versely dependent on local density,at least above a Hour (A.D.T.) certaindensity level; thatis, a major partof the preemigrationoviposition rates P1 and P2 in Eq. 4 must be FIG. 14. A schematicrepresentation of"warm night" con- inverselydependent on n5 at higher values. (I shall ditions ( a and b) and "cold night" conditions ( --- c discuss a low-densitysituation shortly.) andd) inrelation to moth dispersal activities. Hour is Atlantic DaylightSaving Time. For details,see Analysis:Climatic In 1954, log E/M ratios (H5) in those plots in Fig. Influenceon E/MRatio. 15 whereN5 < 2 were much lower than those in 1955 and 1956 forthe same range of log moth densityN5, thoughdifferences were less toward the higherend of than curve c, even if the average temperatureis the the densityspectrum. This implies eitherthat no plots same. As far as I am aware, Greenbank et al. (1980) received immigrantsin 1954, or that, under the fa- did not discuss the effectof these differences. vorable weatherconditions indicated by thehigh mean Synchronousfluctuations between plots, and spatial daily minimum relative humidityin 1954 (Fig. 11), density-dependenceinE/M ratio.-Fig. 10 revealsthat emigrationand reemigrationoutweighed immigration thelog E/M ratioH5 oftenfluctuated in unison between by a substantiallygreater margin than in 1955 and plots. But H5 in the G plots varied about the log po- 1956. tential fecundity per moth (logf; - - -), whereas in the Thus, the proportionof eggs the immigrantslay at K plots, H5 was nearlyalways below log f1; compare, theplace theyland is dependenton thelevel of defolia- in particular,plots G5 and K1. These differencesmust tion and the duration of the immigrants'stay at that be related to differencesin local population density. place, which in turn depends on climatic conditions. To test this idea, I regressedthe log E/M ratio H5 Because theimmigrants stay at least untilthe following againstthe log densityof locally emergedmoths N5 for evening,some proportionof eggs would be deposited all plots where data were available in each of the cal- there,even if defoliationwas heavy; it is veryunlikely endar years 1954, 1955, and 1956 (Fig. 15). Since my presentinterest is the differencesbetween plots, data fromeach of the 3 yrare shown separately;there were insufficientplots in other years for such an analysis. "' 6 The 1955 and 1956 data show similar inverse rela- tionshipsbetween H5 and N5,whereas the relationship 6 5 - is somewhatdifferent in 1954. X Variationsin fecundityand mothmortality could be :E X- X0 'x densitydependent, but the effectsof these variations N 3 _ (O LU x \ are unlikelyto be a major cause of the inverse rela- a) 2 0 x tionship in Fig. 15. This is because the variation in X oviposition rate withoutdispersal would be confined mostlywithin narrow limits, with the upper one being the average potential fecundity(Jj in Eq. 4) and the -3 -2 -I 0 2 3 4 5 lowerone due to mothmortality (;0.6f, forthe reason log moth density, N5 given in Appendix 2). Many points in Fig. 15 are out- side theselimits, suggesting that the relationship in Fig. FIG. 15. The dependenceof the log eggs/moth (E/M) ratio (H5) on log mothdensity (N5) of thevarious plots in 15 must be due to in moth dis- years densitydependence 1954(x), 1955(0), and 1956(0). The curveis drawnbyL eye persal. throughthe 1955 and 1956 data. Upper- -- log potential Greenbank(1 963b) remarkedthat if moth invasion fecundity(log fl); lower --- log l.6fl 442 T. ROYAMA Ecological Monographs Vol. 54, No. 4 that the immigrantslay no eggs duringtheir stay. It the observed n, and h5 were on average 0.065 (N5 = makes sense,then, that the log E/M ratios should fluc- -2.8) and 700 (H5 = 6.55), respectively.The calcu- tuate in unison between the plots (Fig. 10), but at a latedf2p2m in thesetwo plotsis, by theabove equation, much lower level in the K than in the G plots. in the orderof 40 eggs/M2 of foliage.In the otherfour Data on mothdispersal and ovipositionrate relative plots, where the observed n5 and h5 were on average to local populationdensity that might support the above 0.75 (N5 = -0.29) and 415 (H5 = 6.0), the calculated deductionare mostlycircumstantial. Greenbank et al. f2p2mis in the order of 250 eggs,which is more than (1980: Table 8) summarizeda setof observations, made six times largerthan the calculated value for the two between 1971 and 1976, on the rate of emigration(di- lowest densityplots. Certainly,in the two lowest den- rectcount of mothstaking off) relative to pupal density sityplots, immigration could have been, by chance, as at fivelocalities scattered widely over New Brunswick, low as calculated. However, I thinkthat in these plots and anotherset made in 1976 at fourlocalities in On- the rateof emigrationor reemigrationwas high,rather tario.The data show thatthe rateof emigrationtended thanthat the rate of immigration was low. Presumably, to be much lower in low-densitythan in high-density at the heightof widespreadoutbreaks, a verylow den- localities. However, no clear relation was detected sity means a poor habitat for the budworm, which among the seven high-densitylocalities (10-50 moths/ mighthave provokedemigration and/or reemigration. m2 of foliage)in New Brunswick.Indeed, in two plots Finally,the spatial density-dependenceof the E/M the rate of emigrationwas negligibledespite moder- ratiohas an importantimplication in the synchronized ately high moth densities of 23 and 50 moths/M2 of population oscillation between plots. Notice in Figs. foliage.Differences in climate between years and be- 4-7 that the log generationsurvival rate (Hg, graphi) tweendistant localities probablymasked the relation- over the same generationswas on averagemuch higher ship. in the K than in the G plots. This tendencywas as- Blais (1953) observedthat female moths in a severely sociated withlower log E/M ratios (H5) in the K than defoliatedstand "were able to flyin an upward direc- in the G plots because H5 is spatiallydensity-depen- tion [thismust have been an exodus flight]soon after dent. Thus, Hg and H5 cancelled each other's effects emergence."In 1982, in a severelydefoliated fir stand on the intergenerationrate of change in egg density near Fredericton,New Brunswick,we (E. Eveleighand (R1), which is the sum Hg + H5 (Eq. 2). As a result, T. Royama,personal observations) confirmed that many populations in these plots peaked (or R1 zeroed) at mothscaught in theirexodus flightshad laid verylittle more or less the same year (about 1953). If this had of theircomplement of eggs. Because of the favorable not been the case (i.e., if the H5's were not density- weatherin the 1982 season, the rate of emigrationwas dependentin space) the population oscillationin these high.No immigrationoccurred in the sample area, and two groups of plots would have been offphase. consequentlythe E/M ratioh5 was < 15 (i.e., H5 < 2.6). Lack of temporaldensity-dependence in E/M ra- I will now discuss the rate of emigrationin a low- tio.-The within-plotrelationship between H5t (log E/M densitysituation. If high densityand consequent de- ratio) and N5t(log moth density),which is analogous foliationnecessarily induce a high rate of emigration, to thebetween-plot relationship in Fig. 15, is theregres- one mightconversely expect a low rate of emigration sion of Ht on N5tin a given plot (Fig. 16). Only in Fig. froma plot of low densityand littledefoliation. How- 16a (G plots) is H5tinversely correlated with N5t, and ever, this does not seem to be the case in the Green even that relationshipis not as clear as the between- River data. The rate of emigrationappears to have plotrelationship in Fig. 15. As a generalrule, the spatial been unexpectedlyhigh in the two lowestdensity plots density-dependenceof a population parameter does in 1955 and 1956 (Fig. 15); my explanationfor this is notimply that its temporalseries is necessarilydensity- as follows. dependent(Royama 1981a). Unlike Fig. 15, however, Suppose emigrationwas negligiblein a low-density the regressionsin Fig. 16 do not provide insightinto plot (the null hypothesis)and local moths laid on av- the relationships,because a correlationin trend be- erage 60-90% of their eggs in the plot due to moth tween the time series is indistinguishablefrom a cor- mortality(Appendix 2). Because of littledefoliation, relationin fluctuationafter trends are removed. the mean fecundityof local moths (Jj) is ; 100 eggs. We have therequired time-series information in Fig. Then, the value of fpt in Eq. 4 is 60 to 90. If the 9. It shows thatthe seriesof H5t(graph c) has no trend densityof local moths (n5) and the E/M ratio (h5) in thatis correlatedwith the increasingtrend followed by theplot are known,then, under the above assumptions, thedecreasing trend in the seriesof N1t (log eggdensity, we can calculate an expectednumber of eggs(per unit graph d), and one mightsuppose that the E/M ratio foliagearea) laid by immigrants(f2p2m) by using Eq. (H5t) is temporally density-independent.Curiously, 4; i.e., f2p2m= n5(H5 - fiPl). however,H5t does show a clearinverse correlation with There is a set of six plots in 1955 and 1956 in which N1tduring the period between 1950 and 1957, when the E/M ratio was well above the potentialfecundity N1tfluctuated at a plateau withouttrend. This corre- of local moths(Fig. 15), whichsuggests that these plots lation between H5tand N1tis the cause of the inverse received immigrants.In the two lowest-densityplots, correlationin Fig. 16a because N5t(log moth density December1984 SPRUCE BUDWORM 443

7 Then, the populations in which the immigrantsorigi- - a *. nate and the populations that receive them are likely 6 - . 00 to be in phase. It follows that,in a given year t, the 5 _ number of immigrantsmt and the number of local moths n5tare likelyto be positivelycorrelated, and, by 4 0 0 * Eq. 4, thiscorrelation tends to nullifythe dependence, in 3LO trend,of H5t on N5, 2_ The life-tabledata fromthe Green River Projectdid not encompass even one full cycle of population os- _ II I cillation,and we do not know if E/M ratios increased in the K plots afterthe recoveryof the forestfrom the 1950 budworm outbreak,as it mighthave if healthy 0 3 b foliageinduced netimmigration. A seriesof E/M 0 ratios * mightshow a trendif the relativelevel of densitygrad- ually changesbetween the local population and one in which immigrantsoriginate. Temporal changes in the 2 0 .0 0 E/M ratio would also be dependent on the degree of synchronyin populationoscillations between localities withinthe reach of moth dispersal. In my view, the -5 -4 -3 -2 -I 0 1 2 3 4 5 densitydependence of the E/M ratio will not show clearlyin time series forthe above reasons; hence, for log moth density, N5t most practical purposes, I treat the series of H5t as FIG. 16. Observedrelationships between log eggs/moth densityindependent. (E/M) ratio (H5t) and log moth density(N5,) at fourseparate plotsover several years. a. PlotsG4 (t = 1945 to 1958; 0) Generationsurvival rate and G5 (t = 1946 to 1957; *). b. Plots K1 = (t 1951 to 1958; In this section,I analyze generationsurvival in 0) and K2 (t = 1951 to 1957; 0). two ways (first,by stagesurvival rates and, second,by mortalityfactors) to findstage survival and mortalityfactors that cause population oscillation. Stage divisions at the end of generationt) is correlatedwith N1, (log are eggs,young larvae (L1 to L2), old larvae (L3 to L6), egg densityat the beginningof the generation). and pupae. Mortalityfactors to be examined are dis- However, Fig. 16a includes data when N1, (hence, persal losses in young larvae, parasitism,predation, N5,) was eitherincreasing or decreasing.Such a trend food shortage,weather influence,and a complex of in densityconsiderably weakens the inverse correlation disease and undeterminedmortality (which I call the withthe log E/M ratio because the latterhas no trend. "fifthagent") in old larvae. The correlationis even worse in Fig. 16b than in Fig. I findthat survival of old larvae is the main driving 16a because moth densitywas steeplydeclining in the forceof population oscillation. Survival of younglar- K plots duringthe period observed (cf. Figs. 6f and vae, thougha significantcontributor to generationsur- 7f). vival, does not cause the basic oscillation. Both egg But, why is log E/M ratio (H5,) correlatedwith log and pupal survival rates have a minor influenceon egg density(N,,) only when N1,has no trend?This is, generationsurvival. I findthe evaluation of mortality in fact,an interestingproperty of a stochasticprocess, factorsmore difficultthan the evaluation of stage sur- in whichthe inversecorrelation, unlike the one in Fig. vival rates,because of insufficientdata on mortality. 15, does not implydensity dependence. I have shown However, by eliminationI deduce thata combination (Royama 198 la) that,even if H5, is a series of com- of parasitismand the "fifthagent" is the most likely pletelyindependent random numbers,hence, without cause of population oscillation. trendand independentof N1t,H5, would still show an inversecorrelation with N1, only in an intervalin which Analysisby stage survivalrates N,, has no trend (Appendix 3). Thus, the observed In Figs. 4 to 7, generationsurvival (Hg, graph i) is relationship(Fig. 9c and d) makes sense if we assume partitionedinto H1 (egg survival,graph a), H2 (young that the E/M ratio in a given plot is densityindepen- larval survival,graph b), H3 (old larval survival + ear- dent. I now need only to explain why the time series ly part of pupal survival;graph c), and H4 (latterpart of E/M ratiosbehaves as thoughit is densityindepen- of pupal survival,graph d). The patternof fluctuations dent. in H1 and H4 is almost identicalamong plots. In every The originof the majorityof immigratingmoths is plot, H4 contributedslightly to the decliningtrend in within100 km oflanding sites (Greenbank et al. 1980), Hg, while H1 did not. Both H1 and H4, however,were and Fig. 2 suggeststhat local budworm populations such minor contributorsto Hg that I will not discuss within such distances must be oscillatingin unison. them furtherin this paper. 444 T. ROYAMA Ecological Monographs Vol. 54, No. 4 situationdoes not apply to the K plots,where the H3's -3 NG4 are much higherthan in the G plots but the H2's are more or less the same as H2 in G4. I will returnto this point. The curious compensations between survival of young(H2) and old (H3) larvae resultfrom the variation in the timingof sample collections.Usually, in a life table, the end of one stageconstitutes the beginningof -4 h_ the next stage, so the calculated survival rate in one - -53 ' G5 stage is not independent of that in the other stage; correlatedwith each other. %OI -6 generally,they are inversely I call this "stage-framingbias" in a life table. As shown in Table lb, the survivals of young and old larvae weredetermined by sampling(1) thenumber - of first-instarlarvae successfullyhatched, (2) the num- X 5 ber of larvae sampled when most larvae were in the third to fourthinstars, and (3) all pupae and pupal ? -6- cases found at the time of 60-80% moth emergence. The timingof sample collectiondoes not much influ- f3K K2 ence the estimation of (1) and (3), because egg and -4_ pupal cases remain attached to foliage for a while. However,the midpointsamples (2) were collectedjust _5_ whena comparativelyheavy mortality began to deplete -6 I,&[ . II,, 94648 50 52 54 56 58

Generation year 40 - 1951 30 FIG. 17. Yearlyfluctuations in thelog total survival rate oflarvae (H2 + H3) in plotsG4, G5, Kl, and K2. 0-- 0 20 - indirectestimates; see Introduction:Graphed Life Tables.

? - L4 L. Survival of both young larvae (H2) and old larvae (H3) contributedthe most to the yearlyvariation in >, ~~~~~~~P generationsurvival (Hg). However, a decliningtrend C in H3 was the cause of the same trendin Hg, whereas .> 303 - ~- + 1952 H2 did not show such a trend,as is clear in plots G4 - Eo 20 < and G5 (Figs. 4 and 5). As already discussed, the decliningtrend in Hg in the 1950s is the decreasingpart X03: lo 2-L3 of its oscillation. Therefore,I conclude that H3 is the L3L L m 2 ~~~4L5. L6 drivingforce of population oscillation.Only in plot K2 did H2 show an apparentlydecreasing trend (Fig. 7b), but I do not take this short-termtrend to be the de- 50 - -__+ creasingsection of an oscillation. 1954 - Now notice a tendencyfor H3 to fluctuateabout its 40 downward trendbut in the opposite directionto H2, 30 _ as typicallyexemplified in theG4 data; comparegraphs 20 - b (H2) and c (H3) in Fig. 4. As a result,fluctuations in 10 H3 about its trendtended to cancel those in H2, so that 0 -- o L3 L3 L - the sum H2 + H3 revealed an almost smooth down- 4L5 ward trend(Fig. 17), except forthe occasional dips in H3 mentionedabove. of old larvae (H3) in the G plots not The survival May June July Aug. onlycompensates for fluctuations in survivalof young larvae (H2), but also tendsto counteractthe mean level FIG. 18. Decreasein populationdensity (number/M2 of of H2. Thus, H2 tended to be higherin plot G5 (Fig. foliage)from second-instar (L2) to pupal(P) stageson selected treesin plotG4 in threeyears. The arrowsindicate the dates 5b) than in plot G4 (Fig. 4b), while the reverse was ofL3-sampling in theplot in eachyear. Adapted from Miller truefor H3 (Figs. 4c and 5c). Consequently,the sums, (1955: Fig. 2) and his unpublisheddata (MaritimesForest (H2 + H3)'s, are similarin the two plots (Fig. 17). This ResearchCentre). December 1984 SPRUCE BUDWORM 445

to the level at which H2 = -1 (or 37% survival). Be- cause annual larval developmentwas recordedin only G2 q 2 one plot, and not even in the same plot each year,the -10 -10 true mid-date between the two peak dates in a given plot could be in errorby a few days. Despite this,we see a good matchin thepatterns of fluctuationbetween H2 and the relativetiming of samplingin most plots, revealinga clear influenceof stage framing. Partitioninginto young and old larval stages is de- 01~~~~~~0 sirablein budwormlife-table studies because the types of mortalitychange distinctlybetween the two stages. IE I I ,I I , 10r t 2 However, withouta techniqueto estimatereliably the . G0 4 -0> numberof larvae that successfullymolt into the third -br~~~~~~~- instar,bias in framingthe consecutive stages is prac- ticallyunavoidable. Nevertheless,from the relationsin Fig. 19 we could %_ -1 t1 KI '?'m I reduce the stage-framingbias and adjust survival of young larvae to the developmentallystandard time, the mid-datebetween peaks ofthird and fourthinstars. l l l l l l -3 Im C ~ ~ ~ ~ 500~94 ~ ~ 52~ s4I q5 -30 KI0 > 0 -

G2 I I I -2 _ 948 505254565 -

Generation year

II- -I L FIG. 19. Comparison between log survival rate in young larvae(H2,@*, scaled on theright) and thetiming of L3-sam- 0 plingrelative to the mid-datebetween peaks of third-and fourth-instars(0). Relativetiming is measuredas deviation in days(scaled on theleft); a negativedeviation indicates a ? -I - relativelyearlier sampling, and viceversa. Zero deviation of a samplingdate was arbitrarily matched, on thevertical scale, withH2 = -1 and differencesin the level of matching differ fromplot to plot.For details, see Analysisby Stage Survival 0 -2 _ Rates. so 0r I KKI the larval population everyday (Fig. 18). Therefore,a 4) -I - comparativelyearly midpoint sampling would tend to E overestimatethe survival of young larvae (H2) and 0 - underestimatethe survivalof old larvae (H3), and vice versa. To demonstratethis, in each yearbetween 1948 and K2 1958 I took the mid-date between the peaks of the River thirdand fourthinstars observed near the Green - field stationwhere the G plots clustered(see Point 2 -2 in Area 1 in Fig. 1.1 of Morris 1963a). The deviations of the actual dates sampled in each plot fromthese 1948 50 52 54 56 58 mid-datesare shown in Fig. 19 (0). A negativedevia- Generation year tion indicatesearlier sampling, and vice versa. Devia- FIG. 20. Estimatedlog younglarval survival (H2). Ob- tions are comparedwith the H2's (0) takenfrom graph servedH2 was adjustedto themid-date between the peaks of b of Figs. 4-7. For convenience of comparison,zero- thirdand fourthinstars. For themethod of adjustment,see deviation of a samplingdate was arbitrarilymatched Appendix4. 446 T. ROYAMA Ecological Monographs Vol. 54, No. 4 Fig. 20 shows a resultof one such adjustment(details stantial differencesin the physical structureof these in Appendix 4), thoughlack of exact phenologicalin- stands (see Table 4.1 in Morris 1963a). The distinctly formationin individualplots makes it difficultto adjust higherH2's in plot G5 wereprobably due to the earlier the mean level of H2. average samplingdates, as already discussed. The adjustedlog survivalrates in younglarvae (H2's) Loss of young larvae during dispersal was consis- do not show a decliningtrend in most plots,and even tentlyhigh in all years(Miller 1958); thoughnot a cause where theydo (e.g., G4), the trendis too weak to ac- of population oscillation,this could be a major factor count forthe decreasingtrend in H2 + H3 in Fig. 17. determiningthe level about which the population os- Thus, althoughthe method of adjustmentis quanti- cillates.However, as faras I am aware, no reliabledata tativelycrude, it is adequate to demonstratethat the existon whetherthe rate of larval dispersalloss differs survivalrate of younglarvae is unlikelyto be a major among differentforest types. source of population oscillation. It follows that the main cause of the oscillationmust lie in the mortality Mortalityof old larvae.- of old larvae. 1. Parasitism.-Several hymenopterousand dipter- ous parasitoids attack spruce budworm larvae at dif- Analysisby mortalityfactors ferentstages (Miller 1955, Miller and Renault 1976). Mortalityof young larvae.-Miller (1958) showed The two most common wasps, Apantelesfumiferanae thatmost of the mortalityin younglarvae occurs dur- (Braconidae) and Glyptafumiferanae (Ichneumoni- ingdispersal in the falland the spring.Other mortality dae), attack the first-and second-instarbudworm lar- (e.g., mortalitywithin hibernacula, or mortalitydue to vae in thelate summer,and thesecond-generation wasps failureto spin hibernacula,to loss of hibernacula,or emergeand kill theirhosts in the followingsummer, to diapause-freedevelopment) was eitherminor or did when thehost larvae are at theirfourth or laterinstars, not varymuch from year to yearor fromstand to stand. though these parasitized larvae develop much more Many larvae drop on silk threads, and some are slowlythan unparasitizedones. The rate of parasitism carriedaway by air currentsduring fall dispersal (when by these species can be determinedaccurately by rear- theyare searchingfor overwintering sites) and during ing larvae that have been collected fromhibernacula springmigration from the hibernaculato feedingsites. beforespring emergence. Dropping on silk mightbe triggeredby contact with Other parasitic wasps (e.g., Meteorus trachynotus other larvae or by other tactile stimuli,but mostlyit [Braconidae]and severaltachinid flies) attack the third- seems to be a reactionto light(Wellington and Henson to fifth-instarlarvae, and adultparasitoids emerge from 1947, Henson 1950). Then, dispersal in younglarvae the sixth-instarlarvae or pupae. M. trachynotusoften mustbe largelyindependent of population density. This leaves hoststhat stay alive fora while,but neverpupate is consistentwith the lack of trend in H2 that was (E. Eveleigh and T. Royama, personal observations). discussed in the precedingsection, but disagreeswith Therefore,accurate estimationsof parasitismby these Mott's (1963) earlier analysis, in which average sur- species would require frequentsampling. Sampling at vival rates of young larvae exhibited an apparently intervalsof -7-10 d, supplementedby graphical in- hyperbolicinverse relationship with density (Mott 1963: terpolation(Miller 1955: Figs. 2, 3), probablyunder- Fig. 9.2). However, in Mott's more detailed Fig. 9.5, estimates parasitism. Keeping this in mind, I have in whichindividual data pointsare plotted,the inverse shown Miller's results on annual parasitism (by all relationshipin the averages can be seen to be heavily parasitoids) in Table 3, part of which has been pub- dependent on one single outlier at the lowest end of lished (Miller 1963b: Table 34.1). Also, letting100p the densityspectrum. In addition, Mott's data points be the percentage parasitism in Table 3, I plotted in his Fig. 9.5 were scatteredwidely and were influ- 100(1 - P)% in log scale over generation'yearin Fig. enced by the framingbias already noted. Thus, there 21. is no firmevidence of density-dependentsurvival of The number 1 - p is the proportionof old larvae younglarvae. that escaped parasitism,of which, let us say, 1 - q Mott (1963) and Morrisand Mott (1963) concluded proportionsurvived fromall other mortalityfactors. that the survival of young larvae was dependent on The overall survival rate of old larvae (H3) is then some physicalcharacteristics of the stand, such as stand approximately density,foliage thickness, stand continuity,and level H3 = log(l - p) + log(l - q) (5) of defoliation,that influencethe larvae's chances of landingon suitablefeeding sites. For instance,dispersal (Miller 1963b, Royama 1981b). Therefore,the graphs loss could be less in denserstands, and vice versa (see in Fig. 21 are the contributionsof parasitism to log Figs. 9.1 and 29.1 and Table 29.1 in Morris 1963a). survival of old larvae (H3) in the four sample plots. Unfortunately,data on this were not explicit,so there Comparingthe graphsin Fig. 21 withthe correspond- is no way to reassess theirconclusion. Rather,existing inggraphs of totallarval survival(H2 + H3) in Fig. 17, data (Fig. 20) reveal no clear heterogeneityin the level we see thatthe declining trend in log(l - p) is not large of H2 among plots G2, G4, Ki, and K2, despite sub- enough to account for the same but steeper trendin December 1984 SPRUCE BUDWORM 447

TABLE 3. Percentparasitism (all parasitoids) in old larvae.*

Year Plot 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 G4 13 10 18 6 19 12 41 47 36 52 33 38 25 48 G5 8 16 6 21 17 19 39 37 52 36 41 K . 8 20 18 25 19 16 35 K2 16 29 19 26 18 34 * Data fromMiller (1 963b: Table 34.1) and his unpublisheddata (on fileat the Maritimes Forest Research Centre,Fred- ericton,New Brunswick,Canada).

H2 + H3. In otherwords, parasitismalone cannot be There is no obvious difference,and we cannotattribute a major source of the declining trend in generation the loss in the exposed group to bird predation. survival rate and, hence, cannot be by itselfa main From the above observations,I deduce that birds cause of the observed population oscillation. took a substantialnumber of budwormlarvae and pu- 2. Predation.-Major predatorsare small insectiv- pae when insect density was high, and ignored this orous birds, such as warblersof the familyParulidae, source of food when the insect was scarce. This is in and a complex of invertebrates,predominantly spiders accord with the theoryof predation by profitability: (Morris 1963c). The rate of predation was not ade- birds tend to pay more attentionto a more profitable quatelyquantified in the Green River Project (nor, for (usually more abundant) source of food but tend to thatmatter, in any publishedworks on the sprucebud- rejectan unprofitable(usually scarce) source (Royama worm, as far as I am aware); nevertheless,I deduce 1970, 1971). Predationunder this mechanism is prob- thatpredation is unlikelyto be a primarycause of the ably a first-orderdensity-dependent process (i.e., de- budwormpopulation oscillations. pendenton preydensity in thecurrent generation only) Mitchell (1952) analyzed gizzard contentsof some thatdoes not generatean oscillationin a predator-prey songbirds over 2 yr(1949 and 1950) of highbudworm interactionsystem (Royama 1981a). For bird preda- densityin a Maine spruce-firforest. His resultsshowed tion to be a primarycause of a population oscillation, thatseveral species ofbirds consumed budworm larvae it must be at least a second-orderdensity-dependent and pupae in varyingdegrees (Mitchell 1952: Table 1), process; that is, the rate of predation must be depen- of which about a dozen species (Mitchell 1952: Table dent on the initial prey density,both of the current 2) contained the budworm in substantialproportions generationand of the previous generation.For birds (in volume) of their stomach contents.On the other thisis unlikely,because theydo not multiplyeffectively hand, a series of experimentsby Miller and Renault (1981) over 5 yr(1959-1963) of low budwormdensity in the Green River area, in which caged and uncaged G4 larvae wereused, has shownlittle sign of bird predation on the insect. 600 In the experimentsby Miller and Renault, second- instarlarvae were collected and individually"replant- ed" in threegroups on practicallybudworm-free bal- o100 G5 sam firbranches. The larvae of one group were com- - X 60 - pletelyprotected from predation and parasitismin cages . 00 35 coveredwith very fine nylon mesh, though some small predatorswere occasionally caged withthe larvae and x I KI some larvae were alreadyparasitized. A second group 60 of larvae, placed in a cage withcoarse wire mesh, was protectedonly frombirds and largeinvertebrate predators. In a third group, each larva was placed on a markedbut branch. Each 100I- K2 completelyexposed planted 60 - larva in all groupswas frequentlyinspected and its fate 35 - recordeduntil it disappeared, was found dead on the I I l l l I foliage,or survivedto themoth stage (or leftthe empty 194648 50 52 54 56 58 pupal case on the branch in the exposed and semiexposed groups). I have summarized the resultsin Fig. Generation year 22. FIG. 21. Yearlyvariations in theproportion of larvae un- Needless to say, bird predation should show as a parasitized,100(1 - P)%, plottedon a logscale, p beingtotal differencein the "disappeared" category(graph a) be- proportionof old larvaeparasitized; lOOp% is givenin Ta- tween the exposed (@) and semiexposed (0) groups. ble 3. 448 T. ROYAMA Ecological Monographs Vol. 54, No. 4 dependence of a predatorpopulation need not neces- X 50 a sarilyimply a second-orderdensity-dependent process, @ 40 * as would be necessaryto induce the budworm oscil- : o a. 30 lation. 0. 20 - (0 x It is unlikelythat breedingpopulations of birds in- X a 0Xo X X crease throughhigh reproductivesuccess in the previous yearin responseto highbudworm density. Mook ? o 20 x (1963) foundthat birds did nottake the small budworm 501b larvae beforethe sixthinstar. Only 10% (presumably, l 40 - x in numbers)of the larvae found in the gizzards were l 44 O 30l fifthor youngerinstars. This implies thatthe birds fed C~~~~~~~~~~' on budwormseffectively for only a fewweeks, at most, each season. It is hardlyconceivable thatyear-to-year changes in breedingbird populations could be deter- v 0 20 - i * the abundance of a particulartype X 10 - x ? ? mined primarilyby *Q ? I ~~~C~~~~~~~~I X X of food thatcould be utilizedeffectively for only a few weekseach year.A highbudworm density might assure 0.N a high nestingsuccess in some bird species, but is un- , 20020- * likelyto assure highfledgling survival, for by the time .0~~~ the young become independent,they can no longer utilize this once-abundantsource of food. A similarargument applies to omnivorous inverte- . E 100 , 0 ? 'C ' bratepredators that utilize a narrowrange of preysize. I I 1 0 ~ ~ Budworms rapidlydevelop in size duringthe season, 1959 60 61 62 63 and the lengthof the period duringwhich a predator Year species can utilize budworms is undoubtedlylimited. Perhaps,few predator species depend entirelyon bud- FIG. 22. Resultsof thecage experimentsby Millerand worms throughouttheir life cycle, and so few,if any, Renault(1981). Proportionsof larvae that a. disappeared;b. respondreproductively to budwormabundance. In fact, had beenparasitized, percentage of werefound dead; and c. Renault and Miller (1972) have shown that some spi- theinitial numbers of third-instar larvae in graphd. x fine- meshcages, 0 coarse-meshcages, and * openbranches. ders(e.g., of genus Dictyna) could consumemany young (mainlysecond-instar) budworm larvae, but the species compositionand densityof spidersstayed remarkably in numbersfrom one yearto the next,as the budworm constantduring their 8-yr study, confirming the earlier does. conclusionof Loughton et al. (1963) thatspiders showed Some bird species were reportedto be more abun- littlechange in densityduring the 1950s. dant duringbudworm outbreaksthan at other times Predation,though unlikely to be a primarycause of (Kendeigh 1947, Morris et al. 1958, Gage and Miller budwormpopulation oscillations,may nonethelessin- 1978). But many otherspecies, thoughfeeding on the fluencethe mean level ofthose oscillations. Little quan- budwormwhen it was abundant(Mitchell 1952), either titativeinformation on this subject is available, how- did not noticeably change in abundance, or became ever. even less abundant at high budworm density.On the 3. Food shortage.-If budworms kill a large pro- whole, therewere only twice as many birds of all in- portion of trees in a stand, the budworm population sectivorous species during outbreaks in some Green per unit area of the stand mustdecrease as well. How- River studyplots in the 1950s as therewere duringa ever,tree mortality did not necessarilyimply a decline period in the 1960s afteroutbreaks there (Gage and in survivalof old larvae (H3) in the Green River study, Miller 1978). A change in the bird population of this because survivalwas measuredby the reductionin the magnitudewould have had littleeffect on thebudworm numberof larvae per unitfoliage surface area on living population, which changed much more drastically. trees. Moreover, a correlation in abundance between the In his laboratorystudies, Miller (1977) found that budworm and some birds could be coincidental. In- nearly90% of the total food consumptionby a larva consistentresponses to changes in budworm density occurredafter it became sixth instar.Thus, even the by many bird species (Morris et al. 1958, Gage and total consumptionof current-yearshoots at veryhigh Miller 1978) that fed on budworms at high density budwormdensity, and the subsequentfeeding on older (Mitchell 1952) supportthis idea. Some of the corre- foliage,would occur only towardthe end of the larval lation could have been due to the fact that birds re- stage.Food shortageoften retards larval development distributedthemselves in responseto local differences or produces small female moths with reduced fecun- in budworm density.However, such spatial density- dity,but does not necessarilyproduce weak larvae or December 1984 SPRUCE BUDWORM 449 cause mortalityamong larvae, unless reinforced by other factors,such as diseases (discussed later). When highdensities of second- or third-instarlarvae I10 are mininginto buds, current-yearshoots can be totally 4 15-V destroyedwell beforethe larvae reach theirfinal stage *20- of feeding(Blais 1979). However, each larva in these ao 25 - earlystages eats so littlethat very heavy defoliationof the current-yearshoots and subsequent serious food 30 - shortagesoccur infrequently and onlyat extremelyhigh O323 0 larval densities. Moreover, even in this extremecir- 22 - a. cumstance,the larvae can still survive at the expense E 21- of body size and fecundity,as was observed on Cape 20 -A Breton Island, Nova Scotia, in 1977 and 1978 (Piene - et al. 1981). A. W. Thomas (personal communication) o 19 observed that mothsthat were produced fromstarved 18 - larvae could be as small as one-fifthof the normal 17- weightbut stillnot show any noticeableweakness and 301- seem as vigorousas those produced fromwell-fed lar- * 40- vae. Probably,budworms maintain their physiological 50_- vigorat the expense of body size to cope with a high- c densitysituation as 10 E 60_ lasting long as yrand occurring L, , I ,, .I , ..I ... as frequentlyas once every 30-40 yr. 1945 50 55 60 65 70 Duringthe late 1950s, the survivalof old larvae (H3) was still much higherin the heavily damaged K plots Year than in the littledamaged G plots (Figs. 4-7). Never- FIG. 23. Yearly fluctuationsin precipitation(inverted theless,the populations in all plots declinedin parallel. scale),mean daily maximum temperature, and mean daily Evidently,food shortagewas neithera primarynor a minimumrelative humidity (inverted scale) between 1 June and 15 at universal cause of population decline. This is not an July theGreen River field station. Horizontal line in eachgraph indicates average. isolated observation. All populations in New Bruns- wick declined in the late 1950s and early 1960s (Fig. 2) regardlessof defoliationand tree mortalityat the influenceon the survivalof feedinglarvae, as was pre- standlevel. Thus, budwormoutbreak cycles cannot be viously thought. adequately explained by habitat destruction-regener- As alreadyshown, fluctuations in the survivalof old ation cycles,as postulatedin thetask-force report (Bas- larvae (H3) about the downward trend of the 1950s kerville 1976). were influencedby the timingof the sample collection 4. Influenceof weather.-Some earlier analyses at the beginningof the stage concerned. Eliminating (Wellingtonet al. 1950, Greenbank 1956, 1963a, Mor- framingbias by combining H3 with H2 results in a ris 1963b) yieldeda climatic-controlhypothesis: a dry, smootherdeclining trend, particularly in plot G4 (Fig. warm summerfavors the developmentof the feeding 17). If the survival of larvae was much influencedby larvae, and so a series of favorableyears allows pop- weather,the compensationof H2 and H3 is incompre- ulationsto increase.(A wet,cool summerproduces the hensible. Althoughtemperature and precipitationex- opposite result.)Greenbank (1956 [Fig. 2], 1963a [Fig. hibit a patternof oscillation if smoothed by taking 3.2]) took 4- or 5-yrmoving averages of the average moving averages, the larvae in the Green River area precipitationand the average daily range of tempera- could notpossibly respond to thesmoothed (by moving ture in June and July(the intervalcovering a major average) patternof the average weatherover the prov- part of the larval feedingperiod in the northernpart ince and ignorethe detailed, much more irregularyear- of New Brunswick)and showed an on-average dry, ly fluctationat the Green River station(Fig. 23), where warmperiod between 1945 and 1949, an intermediate therewas no consistentdry, warm period between 1945 conditionbetween 1950 and 1955, and an on-average and 1949. wet, cool period between 1956 and 1960. The pattern In fact,fluctuations in log larval survivalrates (H2 + appeared to coincide withthe rise and fallof budworm H3; Fig. 17) are notwell correlatedwith weather records populationsin theprovince over the same period.There in Fig. 23. Althoughsurvival in plot G5 between 1951 were also several on-averagedry, warm years around and 1957 is vaguelycorrelated with mean daily max- 1910, which coincided with the well-knownoutbreak imum temperature,this is probablycoincidental. First, of the same period (see Fig. 3). However, anothersuch the distinctlylow survival rate in G5 in 1951, which favorableperiod around 1925 was associated withlow coincided with a low mean temperaturefor that year, populationsin theprovince. After careful examination, was likelya local phenomenonrather than an effectof I have foundno evidence thatweather has much of an the prevailingwet, cool weatherof that year,because 450 T. ROYAMA Ecological Monographs Vol. 54, No. 4 23 -

,22 - - 30_ E 21 -0-4 4W 0 o1

19 ~~~~~0 (U 18 70~

1946 48 50 52 54 56 58 60 62 64 66 68 70 Year FIG.24. Comparisonbetween the yearly fluctuation in meandaily maximum temperature (0) duringthe larval feeding period,1 Juneto 15July and the fluctuation inmean daily minimum relative humidity (0, invertedscale) during the estimated mothperiod (cf. Fig. 12) in lateJuly to earlyAugust, recorded at theGreen River field station. it did not influencethe survivalin plot G4. Conversely, ally between 15 May and 30 June.In the Green River the even worse weatherin 1950 did not have any ad- studyarea, the development is 2 wk behind many verse effecton survivalin any plot, includingG2. Fur- otherparts of the province.Therefore, the period over thermore,an intensivestudy by daily samplingin 1977 which the average temperaturewas calculated in Fig. at a firstand near Fredericton (data on fileat Maritimes 25 is adjusted accordingly.One of the bases for the Forest Research Centre) revealed an extremelyhigh adjustmentis the phenologyof springbudbreak in bal- larval survival rate, despite the unusually wet, cool sam fir,shown as a contourmap in Fig. 26. summerof thatyear. Over the period covered by the temperaturerecords To compare survival rate and weatherover a much in Fig. 25, therewere fourknown province-wideout- longerperiod, we can use the yearlyfluctuation in the break periods at about the times indicated by the ar- log rate of change in larval density(R3) shown in Fig. rows (cf. Fig. 3). As we see, thereis no particularpat- 8. Simple correlationshows some degreeof association tern, such as a succession of warmer summers, betweenthe temperaturefluctuation in Fig. 23 and the associated with the initiationof these outbreaks.Fur- secondaryfluctuations in R3 about its basic oscillation. ther,to comparewith the argument of the earlierwork- This association, however, does not imply a causal ers alreadycited, I took as an example the 5-yrmoving relationship.As alreadyshown, the secondaryfluctua- averagesin the Chathamweather data ofFig. 25, which tion in R3 is due largelyto a fluctuationin the log E/ by themselves cannot be distinguishedfrom a pure M ratio (H5), which is determinedin the moth stage random seriesby a simple runtest. The resultantmov- in late Julyand earlyAugust, and which shows a good ing-averageseries (Fig. 27) tends to oscillate because correlationwith mean daily minimumrelative humid- of positive autocorrelationsthat do not exist in the ityduring that period. There happened simplyto be a originalseries (details in Appendix 5). Again, thereis very good correlationbetween the mean daily maxi- no particularassociation of the fouroutbreaks with the mum temperatureduring the feedingperiod in Juneto "smoothed" weatherchanges, except fora vague ten- the early part of Julyand the mean daily minimum dencyfor some yearsof on-averagecooler weatherfol- relativehumidity during the moth period in late July lowing an outbreak that mighthave been associated to earlyAugust (Fig. 24). withthe decline ofthe budworm population. This point Another example of spurious relation is a coinci- will be discussed in the section on the "fifthagent." dence in trendbetween mean daily minimumrelative (Oscillations could be created artificiallyby taking humidity(Fig. 23; inverted for ease of comparison) movingaverages of a pure random series of numbers; and R3 (Fig. 8) between 1953 and 1970. However, the it could be misleading to compare such an artificial two series do not agree at all in the previous outbreak oscillationwith a population oscillation[see Appendix period between 1946 and 1952. 5].) Fig. 25 shows the annual fluctuationin mean daily In his key-factoranalysis, Morris (1 963b) foundthat maximumtemperature during the approximateperiod therehas been a consistentupward trend since themid- of larval feedingin various parts of New Brunswick 1920s in mean daily maximum temperature(recorded fromas many stations as had records for the 1870s in theCity of Edmundston, 50 km southof the Green onward. The larval feedingperiod differsamong the River station)during the main partof the larval feeding areas where the weatherstations are located (see Fig. period, which in the Green River area usually falls 26). Usually, budwormsdevelop in the province ear- between 1 Juneand 15 July(Morris 1963b: Fig. 18.2). liest around Fredericton,where most larvae feed usu- I find the association to be spurious, however. The December 1984 SPRUCE BUDWORM 451

Sussex region; in Bathurst,there was even a slightly decliningtrend (Fig. 25). Nevertheless,the population trendwas much the same everywhere(Fig. 2). 2025- . / VAX:V\FJrMVJ':" '."V\\J I have arguedthat weather is unlikelyto be a direct cause of budwormpopulation oscillationsand, hence, of outbreaks.However, my argumentsdo not exclude possible weatherinfluences on larval survival. For in- 25-20 stance,late frost,which is not infrequentin New Bruns- wick, mightkill buds and thus cause high mortality among young larvae, thoughI have seen no concrete evidence. Near the northernlimit of the budworm, such as at higherelevation on the Gasp6 Peninsula in Quebec, accumulatedheat unitsmay be insufficientin some years for complete larval development (Blais 2525 1958). Conspicuous dips in the survival rate of old 20- larvae (Fig. 17) mightindicate some localized weather hazards, because the dips were sporadic, did not coincide in years among plots, and leftno effecton survival in the followinggeneration. Weather might also act throughthe efficacyof diseases. I shall discuss this in the followingsection. 25- 5. Thefifthagent. -The last of the mortalityfactors .20 to be discussed is a complex of viral and protozoan diseases and "death fromunknown causes." Neilson (1963) found microsporidiosesand granu- losis to be the most prevalentprotozoan and viral diseases, respectively,in the Green River area. Otherviral diseases, such as nuclear and cytoplasmicpolyhedro- ses, and bacterialand fungaldiseases were infrequent. Between 1954 and 1958, Neilson (1963) collected 20[ I weeklysamples of budwormlarvae in plot K2, beginning fromthe thirdinstar and lastinguntil 80% pupation, reared each collection of larvae in the labora- toryfor 1 wk, and examined dead larvae fordiseases. He foundno apparentsymptoms of disease in a large proportionof larvae thatdied in the laboratory.More- 1880 1900 1920 940 1960 1980 over, because all pathogens that were identifiedby Neilson were of low virulence,it is not certainif those Year

FIG. 25. Yearlyfluctuations in themean daily maximum Green _-i\Dalhousie temperatureduring the approximate period of larval feeding, River. 1114 sincethe late 1800s in variouslocations in New Brunswick. *e15-18 r 0 >Bathurst Fromtop: Fredericton (15 May to 30 June),Sussex (15 May Edmundston 11-14 to 30 June),Chatham (15 Mayto 30 June),Chatham (25 May 15-18 to 10 July),Bathurst (Dalhousie, -----;20 May to 5 Grand July),Grand Falls (15 Mayto 30 June),Edmundston (1 June Falls Chatham to 15 July),Saint John (1 Juneto 15 July).Data are taken 7-10 fromthe MonthlyRecord, meteorological observations in easternCanada, Canada Departmentof the Environment. The arrowsin thetop graphindicate the occurrence of four 36 province-wideoutbreaks of the spruce budworm taken from Frederion J12 Fig. 3. 516 7-0 Saint John upward trendin temperaturesduring the feedingperiod, used in Morris's analysis,was due to an upward trendin Julytemperatures. In many partsof the prov- FIG. 26. Phenocontoursof New Brunswick,numerals rep- ince, the budwormlarvae should have completedtheir resentingdifferences in timingof springbudbreak of balsam fir,Abies balsamea, in days later than that in Fredericton. feedingby the end of June,and thereis no such trend Unpublishedmap by Forest Insect and Disease Survey(Mar- in the temperaturesof May and June, except in the itimes Forest Research Centre). 452 T. ROYAMA Ecological Monographs Vol. 54, No. 4

0)1

? 202{ E 19 _ I I I I I I 9 I I I I I 1888 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Year FIG. 27. Five-yearmoving averages of the seriesof mean dailymaximum temperatures from 15 May to 30 Junein Chatham,New Brunswick(Fig. 25), showingan oscillationcaused by positive autocorrelations in the moving-average series, notexisting in theoriginal series. Arrows indicate four province-wide spruce budworm outbreaks taken from Fig. 3. pathogens actually killed the larvae bearing them. right-handside of Eq. 5 in which q now representsthe Therefore,I treatthis inadequately understoodcom- fifth-agentmortality. Note that the combined effectis plex of mortalityfrom diseases and unknowncauses the union p + q - pq ratherthan the simple sum p + as one category,the "fifthagent, or Neilson's syn- q, because thepq proportionof larvae could have been drome." parasitizedas well as "diseased" (fordetails, see Roy- For several reasons,it is unlikelythat the fifthagent ama 198 lb). occurredonly duringlaboratory rearing. First, spruce Clearly, the gross field mortality(l00qj) and the budwormlarvae are well knownamong entomologists combined (union) parasitism and fifthagent are not as easy to rearin thelaboratory, and, ofcourse, Neilson only in the same magnitudefor the stages concerned; took the ulmost caution in rearinghis larvae. Second, theiryearly fluctuations are also similar.In otherwords, Neilson took weekly samples, reared the larvae indi- thegross field mortality in K2 in thoseyears was mostly viduallyfor 1 wk,and obtained consistentresults. The attributableto parasitismand the fifthagent. (The cal- third and most interestingreason is a similarityin culatedunion of thesetwo factorssometimes exceeded frequencybetween total fieldmortality and the com- the 100q. values, because the factorswere estimated bination of fieldparasitism and fifth-agentmortality independently.)Since I have raised all conceivable in Neilson's study. This suggeststhat the fifthagent mortalityfactors and have eliminatedunlikely causes, was also operatingin the field. the fifthagent combined with parasitismwould seem In Tables 4 and 5, I list gross fieldmortality (l00q. to be the only possible drivingforce of oscillationsin of the lifetables) and parasitismas well as fifth-agent the budwormpopulation. mortality,as determinedby Neilson in samples taken Currently,E. Eveleigh and I are conductingvery fromplot K2; Table 4 is forold larvae, and Table 5 is intensivefield studies in a firstand heavilyinfested by for pupae. The gross mortality,1 00q, in Table 4 is budwormnear Fredericton.So far,we have foundthat relatedto the survival of old larvae, H3 in Fig. 7c, by mortalityin feedinglarvae has been almost totallyat- q_ = 1 - exp(H3). In the last column of each table, I tributableto the 50-60% parasitism,which has been have combined parasitismand the fifthagent by the increasingonly slowly in the last 3 yr. This rate of parasitism,though higher than those observed in the TABLE 4. Totalstage mortality (100q_), parasitism, and mor- Green River area duringthe 1950s (Table 3), is not talitydue to thefifth agent, in old larvaefrom plot K2 in highenough to reduce the budwormpopulations. The GreenRiver area. operation of another agent is essential for the populations to decline fromthe currentoutbreak level. Unionof parasitism? Some diseases, like typical insect parasitoids, can and fifth build up over several generationsas the host popula- Year IOOq* ParasitismtFifth agentt agent tion increases,to induce a host-diseaseoscillation (An- Percentage derson and May 1979), thoughthe role of diseases in 1954 69 19 54 63 thebudworm system is not as certainas theAnderson- 1955 31 26 14 36 May model. Potentiallyimportant microbials in the 1956 57 18 76 80 1957 87 1611 49 57 spruce budworm are summarized in Dimond (1974) 1958 84 34 66 78 and Burke(1980), but the roles of microbialsin ending * a budwormoutbreak have not log(l -q_) = H3 in Fig. 7. been documented.Some t Same as in Table 3 (bottomrow). species of Microsporidia,though of low virulence,are : Sum of"total diseased" and "unknown"determined by common protozoan parasites of budworm that have laboratoryrearing in Neilson(1963: Table 38.5). the propertiesof a second-order ? Union= p + q - pq, wherep = proportionparasitized density-dependent and q = proportionsuccumbing to thefifth agent. mortalityfactor because theyspread by oral transmis- 11Substituted for by the KI data. sion among feedinglarvae withina season, and then December 1984 SPRUCE BUDWORM 453

TABLE 5. Same as Table 4 but forthe pupal stage. correlatedwith the fluctuationin H5 (see Analysis of life-tabledata: climaticinfluence on E/M ratio). Thus, Union of the R3's distinctlyabove the smoothed trend line in parasitism and fifth Fig. 8 (marked with arrows) indicate moth invasions Year l 00q* Parasitismt Fifthagent agent in those years. Clearly,invasions were frequent,and 1954 42 18 20 34 theyseem to be as frequentduring the decreasing phase 1955 26 5 17 22 of the population oscillation as duringthe increasing 1956 42 9 30 37 phase. (The graphafter 1972 in Fig. 8 is not a reliable 54 4 35 51 1957 indicatorof invasions, because it is based on the av- * - log(l qx) = H4 in Fig. 7. erageegg-mass density determined from small samples t C. A. Miller (MaritimesForest Research Centre,personal taken fromsample points scatteredover a wide area; communication). the averages probably do not give resolutionas high as did intensivesampling at a particularplot.) are transmittedtransovarially to the next generation It is particularlyimportant to note that duringthe (Thomson 1958). Thomson (1960) and Wilson (1973, decliningphase in plot G4 the population increased 1977) observed steadyincreases in therate of infection each springfollowing a moth invasion the previous by Microsporidia over several generationsduring the fall,as in 1954, 1957, and 1961 (Fig. 1), but that the 1950s and 1970s in Uxbridge,Ontario. The host pop- invasions did not reversethe overall decliningpopu- ulations,however, were not monitoredquantitatively lation trend,even when the local food supplywas still in eitherstudy. plentiful(for further discussion, see Synthesis:ampli- In his experiment,Neilson (1963) found that both tude of oscillationsand outbreakfrequency). In view diseased and "undiseased" deaths were inverselycor- of the facts that the population trend was the same relatedwith rearing temperature, and thatthe effectof over wide areas (Fig. 2) and thatgains of extraeggs in temperaturewas greateron starvedlarvae thanon well- a local population (as in G4, Fig. 8) were far more fedones. These resultsare not necessarilyinconsistent frequentthan occurrencesof outbreaks,the idea that withthe apparent lack of relationshipbetween the field moth invasions initiateoutbreaks is not as attractive survival of larvae and the weatherpattern, which has as I once thought(Royama 1977, 1978). alreadybeen discussed. If populationoscillation is due SYNTHESIS OF BUDWORM POPULATION to second-orderdensity-dependent factors, the influ- DYNAMICS ence of density-independentagents that are not a cause ofpopulation oscillation might not show clearlyin sim- Translatingthe resultsof the foregoinganalyses into ple correlation(Royama 1981a). a simple time-seriesmodel allows me to explain the Anotherpossibility for "unknown causes" thatNeil- followingfeatures of spruce budworm population dy- son (1963) consideredwas intrinsicphysiological vigor, namics: synchronyof oscillations between local pop- which decreases with increasing population density ulations,frequency and spread of outbreaks,regularity (Franz 1949, Chitty 1960, Wellington1960) through and irregularityof populationcycles, and maintenance endocrinological, behavioral, or genetic changes of local density-dependentpopulation oscillationsun- (Christianand Davis 1964, Pimentel1968, Krebs 1971). der perturbationfrom moth dispersal. No positive evidence forthese mechanismshas been I consideran idealized situationin whichbasic prob- reportedfor budworm population dynamics as far as abilistic properties of population processes do not I am aware, thoughthe possibilitycannot be excluded. change in time, so that even a very simple model, necessitatedfrom our limitedknowledge, can provide Frequencyof mothinvasions insight.We can make the above idealized situation Some ecosystemmodels (e.g., Petermanet al. 1979) compatible with actual population processes by care- have assumed thatif food (foliage)is plentiful,spruce fullyselecting the spatial unitsin whichwe definepop- budworm outbreaks can be "triggered"by mass in- ulations. vasions of egg-carryingmoths fromoutside, because If we were to consider the population process in a the invaders upset the assumed endemic equilibrium very small foreststand, we would findthat a severe state of local populations. However, this assumption outbreak mightdestroy the stand, and the budworm is not substantiatedby the Green River data. populationwould thenbecome extinct.Subsequent re- In plot G4, extra eggs gained fromimmigrants (in- generationand growthof a new foreststand would not dicated by E/M ratios much greaterthan the mean ensurethe stationarityof the local population process. potentialfecundity) occurred in 1946, 1947, 1949, 1953, Moreover,we have littleknowledge of the influenceof 1955, and 1956 (Fig. 10, top graph). The high value forestregeneration processes on the growthof a bud- of R3 (the log rate of change in larval density)in Fig. wormpopulation. If, on the otherhand, we considered 8 forthe years 1956-1972 indirectlyindicates the gain too largea geographicalarea, thenenvironmental het- of extra eggs,because the secondaryfluctuation in R3 erogeneity,such as differencesin weather patterns, about its principaloscillation (smooth curve) is highly would probablybe too high forsimple models to de- 454 T. ROYAMA Ecological Monographs Vol. 54, No. 4 scribe the population processes without undesirable ably chosen. Simulationsthat use this model demon- complications. strateMoran's idea. Thus, I consider populations in areas large enough In Fig. 28, I generatedthree sample series by Eq. 7 that changes in some local stands withineach area in with the same ao and a, values that are conveniently one way over time are compensated forby changesin chosen for simulations. The density-independentz's the other way in other stands withinthe same area. in each series are uncorrelated(zero autocorrelations) Therefore,the average characteristicsof the area as a randomnumbers, uniformly distributed in theinterval whole do not change drasticallyin time. An area as (-0.5, 0.5). The series a and b are startedwith an large as one block on the map in Fig. 2 is probablya identicalinitial state (N1, N2), but the z's are indepen- convenientsize formy argument(though a fewlarge- dentlygenerated and so are uncorrelatedbetween the scale outbreaks,such as the recentone on Cape Breton two series. These series simulate a situationin which Island, Nova Scotia, may destroyforests over a much two local populations that have a common density- largerarea). I also consider that budworm densityis dependent(endogenous) structureare under mutually measured on the foliageof living trees,so as to avoid independentclimatic (exogenous) influences.We see a complicationsarising from the effectof treemortality. strongresemblance in theircyclic patterns due to their common endogenousstructure, but thepopulations do A simplemodel not oscillate in unison,because of the independentex- Let us approximatethe dynamicsof budwormpop- ogenous influences.They come into synchronyocca- ulations by a second-orderdensity-dependent process sionally,but only by coincidence. of the generalform Seriesc in Fig. 28 has the same endogenousstructure (identicala-parameter values) as the othertwo series. Rt =J(N, N, 1) + zt, (6) The distributionof the density-independentz, termis where Nt is the log population densityof the tth gen- also the same as in the othertwo series,except that zt eration(it need not specifythe stage),and zt is the net in seriesc is correlatedwith zt in seriesb; thecorrelation effectof all density-independentfactors involved dur- coefficientis t0.7. Althoughseries b and c werestarted ing the tth generation.Rt = Nt+ - Nt, as in Eq. 3. I completelyout of phase, theycame into phase quickly, now equate the functionf in Eq. 6 to the density- and remained in phase thereafter.This suggeststhat dependent component of the log generationsurvival local budworm populations that oscillate indepen- rate (Hg) in Eq. 2, and equate the log E/M ratio (H5), dently(due to density-dependentgeneration survival) combined with the temperature-dependentefficacy of can be synchronizedunder the influenceof nonoscil- the fifthagent, to major elements of the density-in- lating but correlatedweather (among localities) that dependentterm z. governs the E/M ratio and, probably,the efficacyof Because the functionf in Eq. 6, which is probably the fifthagent. Well-correlatedweather patterns over nonlinear,is difficultto determinefrom our limited New Brunswickare exemplifiedby the annual fluctua- knowledge,I furthertake a linearapproximation of the tions in temperatureshown in Fig. 25. Nonetheless,a functionfor simulation purposes; thatis, I use the lin- degree of asynchronyalways exists between series b ear second-orderautoregressive model and c. This is analogous to an increase in budworm populationsin thesoutheastern corner that was slightly Rt= aONt + aIN,1 + zt, (7) earlierthan in northernareas of New Brunswick(Fig. in which ao and a, are constant. Note that the log 2). survival rate (Hg) is nonpositive,but the above linear approximation might violate this constraint.There- Amplitudeof oscillations and fore,I restrictmost of my argumentsto a qualitative outbreakfrequency level, so as to remainwithin the realm of this approx- The simulated populations in Fig. 28 cycle fairly imation. regularly,because their second-orderdensity dependence yields periodic autocorrelations.However, the Synchronizedpopulation oscillations and amplitude of an oscillation varies considerablyfrom therole of climate cycle to cycle under the influenceof the density-in- Moran (1953), in his statisticalanalysis of the Can- dependentz term.An oscillation that happens to ex- ada lynx (Lynx canadensis) cycles,proposed the idea ceed the dottedline in each graphof Fig. 28 represents that density-independentclimatic influences,if corre- a hypotheticaloutbreak. We see then that the occur- lated betweenlocalities, could synchronizelocal pop- renceof outbreaksgreatly depends on the random na- ulations that are oscillatingindependently because of tureof the E/M ratio as a major elementof the z term. factorsintrinsic to each population. This important The periodicityof the autocorrelation functions (cor- idea, however, did not attractmuch attentionfrom relogram)of a stationaryautoregressive time series is ecologists.As reviewedin Royama (1977, 1981a), the knownto be uninfluencedby temporallyuncorrelated autoregressivemodel of Eq. 7 can generateoscillations exogenousperturbations (zt in Eq. 7). This impliesthat of various lengths,if the values forao and a, are suit- theaverage length of a local budwormpopulation cycle December1984 SPRUCE BUDWORM 455 is determinedby thedensity-dependent larval survival, a not by the E/M ratio fluctuatingat random fromyear to year. Frequent, high E/M ratios can enhance the amplitude of an oscillation to an outbreak level, but only when the population is in an upswingphase of a cycledue to highlarval survival.High E/M ratioswould not,however, readily reverse the population trend, once larval survivalhas starteddecreasing; high E/M ratios were observed in 1954, 1957, and 1961 on plot G4, b but the population decreased, nevertheless(Fig. 1). z Thus, the seed of an outbreaklies in the intrinsicden- sity-dependentstructure, most likelyin the survivalof old (feeding)larvae, while moth invasions (high E/M C ratios) act only as fertilizers,so to speak. thatnot all peaks in the seriesb and c in Fig. Notice 0 28 exceeded an outbreaklevel simultaneously,and that outbreaks happened to occur more often in series b than in series c. In otherwords, even if the phases of population oscillations are well synchronizedamong C localities,the amplitudes need notbe correlatedas well. Further,outbreaks happened to occur more regularly in the latterhalf of series b than in the earlier half. These resultsin the simulationmay explain differences in the outbreakfrequency across easternCanada from Ontario to Newfoundland,such as the fairlyregular occurrencesof outbreaksin the past few centuriesin 0 50 100 150 200 250 300 New Brunswickand Quebec (Fig. 3) and the rather Generation, t sporadic ones in otherregions (Blais 1965). FIG.28. Simulatedsecond-order density-dependent pop- lesson of the simulations A particularlyinstructive ulationoscillations. In each series,300 points(N1, N2, . . . is thatan alternationbetween intervalsof regularand N300)are generatedby Eq. 7 (R, = a0Nt+ a1N11 + z1) with sporadic outbreaks does not necessarilyimply some ao = 0.80 anda, = -0.89. Initialconditions are (N1 = 1,N2 = fundamentalchanges in the environmentalconditions 2) in both series a and b, and (N1 = -1, N2= -2) in series z's in eachseries are temporally uncorrelated random in the structureof the population processes.Simply, c. The or numbersdistributed uniformly in theinterval (-0.5, 0.5). z, the random variationin the E/M ratio alone can cause in seriesb is uncorrelatedwith z, in seriesa, butis correlated such alternationsin population cycles.There is a pos- withz, in seriesc. Dottedline in each graphrepresents a sibility,though not highlycredible, that the nonlinear hypotheticaloutbreak level. For detailedexplanations, see Role process of the actual budworm population dynamics Synthesis:Synchronized Population Oscillations and the ofClimate. may exhibitstable oscillations,such as limit cycles. If so, a rathermore regularoccurrence of outbreakscould be expectedthan from the present simulations, because ulations were in theirtroughs by the early 1960s, and the simple linear model employed here is unable to started increasingagain thereafterjust about every- generatelimit cycles. wherein New Brunswick.However, in the centralregion (i.e., blocks B3, B4, C3, C4, and C5 in Fig. 2) the Initiationand spreadof outbreaks troughpopulations were somehow maintained at much Sprucebudworm infestation maps in easternCanada higherlevels than in any otherareas of the province. (Brown 1970, Kettela 1983) mightappear to support Consequently,when all populations in the province a widespreadnotion that outbreaks begin at a fewscat- increased again in the early 1970s, an outbreaklevel teredpoints, or 'epicenters,'then spread outwards,in- was reached in the centralregion sooner than in sur- festing surroundingareas through moth dispersal. roundingregions. The troughsof the southeasternpop- However, Stehr(1968) considered,in addition to the ulations (blocks A4, A5, B5, and B6 in Fig. 2) were above notion, a second possibilitythat an epicenter just as low as those of the populations in the north- mightbe "merelythe spot at which a general and al- western corner, but the southeastern populations readywidespread population surfacesfirst," but he ad- somehow increasedslightly earlier and reachedan out- mittedthat "we actuallydo not know today which of break level sooner. On infestationmaps, these areas these radicallydifferent structures applies to the epi- mightlook like "epicenters." centersof the spruce budworm." To summarize,although moth immigrationsmight Close inspection of the egg-masssurvey map (Fig. acceleratethe increase in local populations and create 2) supportsthe second interpretation.Budworm pop- outbreaksearlier or more frequently,moth dispersal 456 T. ROYAMA Ecological Monographs Vol. 54, No. 4 is unlikelyto act like a vector carryingan infectious In thissection, I discuss (1) Morris'skey-factor mod- disease. Rather,dispersal acts like a fertilizerto stim- el, (2) Watt's (1963) analysis of old (large) larvae, and ulate the seed of an outbreak(survival of local larvae) (3) the concept of dichotomousendemic and epidemic that has already startedgrowing in everylocality. budwormpopulations, or the double-equilibriumthe- oryof outbreakprocesses. I use my notationsthrough- Maintenanceof density-dependent population out. oscillationsunder perturbations frommoth dispersal Morris's key-factormodel A comparison between the simulated populations The key-factormodel of Morris (1 963b) is a linear, (Fig. 28) and egg-massfluctuations (Fig. 2) reveals a first-orderautoregression, a special case of Eq. 7 in subtle but importantdifference, namely that the sec- which a, = 0. Morrisused the log initialdensity of old ondary fluctuationsabout the principal oscillation in larvae (N3 in Table 1), regressedN3,+I on N3t,and the actual populationslook like sawteethas compared estimated the coefficientof N3, (ao in Eq. 7) by least with the smootherappearance of the simulated pop- squares to obtain do = -0.24. He then foundthat the ulations. Errors from small samples in the egg-mass residuals,as estimatesof the z's, werehighly correlated surveymay contributeto the sawtooth-likesecondary withthe mean daily maximum temperature,T (in 0F) fluctuations,but these fluctuationsmay primarilybe a between 1 Juneand 13 July,when much larval feeding resultof strongperturbations from moth dispersal. occurs in the Green River area. Based on this regres- Using the autoregressivemodel (Eq. 7), we can sim- sion, Morris formulatedhis key-factormodel: ulate strongperturbations from moth dispersal by a R3t =-0.24N3t + 0.18Tt - 10.99. (8) largevariance of z. Changes in the variance,however, influencethe amplitudes of oscillationsbut do not pro- Using the temperaturerecords from the City of Ed- duce sawtooth-likefluctuations (Royama 1979). Eq. 7 mundstonsince 1925, Morris's backward simulation can produce rapid fluctuationsin densityif the a-pa- with Eq. 8 yielded an oscillation that peaked around rametervalues are changed,but this tends to obscure the late 1940s and more or less coincided with the the oscillatorypattern of population cycles.The N's in observed outbreakof that period (Fig. 18.2 in Morris Eq. 7 are local population densities, so the density 1963b). dependence of the model is maintained only by local The apparentinfluence of Tt on R3t in Eq. 8 is spu- factorssuch as the parasitoid complex, which is un- rious, however,for two reasons. First,as discussed in likelyto migratewith dispersing budworm moths. Un- Analysis:influence of weather,the rise and fallin tem- der this assumption,the model would not produce the peraturesrecorded in Edmundston duringthe above desired effect. period did not occur everywherein the province,ex- If, however, the density-dependentoscillations in cept in Sussex, over the two centuries(Fig. 25) and budworm populations are caused largelyby the fifth cannot explain the province-widebudworm oscilla- agent, the situation can be quite different.The fifth tions (Figs. 2 and 3). Second, as discussed in Analysis: agent,be it of disease or of physiologicalorigin, would influenceof weather,R3 was only indirectlycorrelated travel with its carriers,the dispersingmoths. If local with T, because: (1) T was correlatedwith the mean populations oscillate in unison, under the mechanism dailyminimum relative humidity during the moth sea- discussed in Synthesis:synchronized population oscil- son (Fig. 24), (2) the mean daily minimum relative lations and the role of climate, the incidence of the humidityinfluenced the log E/M ratio H5 (Fig. 11), fifthagent should coincide among these populations. and (3) H5 was correlatedwith R3 (Figs. 9 and 13). Then,the exchange of moths,carrying the agent, among Morris himselfwas not satisfiedwith the simulated local populations can cause sawtooth-likesecondary patternof oscillation in his Fig. 18.2 (Morris 1963b), fluctuationswithout much influencingthe basic oscil- and so proposed an alternative double-equilibrium lation caused by the density-dependentprocess of the theory.To discuss this theory,however, I must first populations as a whole. review Watt's (1963) analysis of survival of old (his large) larvae, because his resultserved as supportfor COMMENTS ON SOME OTHER ANALYSES AND Morris's theory. THEORIES There are two major problems with analyses by Watt's analysis earlier authors: theirtreatment of density-dependent Watt(1963: Fig. 10.4) regressedthe log survivalrate population parametersas firstorder, and of autore- H3 (log of his SL) on log densityN3 (log of his NL). gressive-typedensity-dependent population processes Data taken frommany studyplots in the Green River as regressionsof independentparameters. These can area were pooled in his analysis. He then divided the seriouslymislead ifthe processesanalyzed are, in fact, densityspectrum into six intervals,calculated the av- second or higher order (Royama 1977, 1981a); the erage survivalrate in each interval,and fitteda regres- concept of high-orderdensity dependence was not sion curve throughthese averages (Fig. 10.5 in Watt known 20 yr ago. 1963). Watt found"a tendencyfor SL to increasewith December 1984 SPRUCE BUDWORM 457

comprisedfractions of many such oval trajectoriesbe- cause in no one plot did observationscover one whole 00 OLe population cycle. >0 In many plots, observationswere made roughlybe- tween peak and troughdensities. As a result,the data 0) fromthese plots formedthe lower rightquarter of an

Cy$O oval trajectory.These includedplots K1 and K2, which 0: had extremelyhigh peak densities.These data points comprise an upper section of the densityspectrum in log density Watt'sFig. 10.4. In otherplots, observations were made FIG. 29. A schematicillustration of therelationship be- several years afterpeak density,when low survival tweenthe survival of "large larvae" and their initial densities rates were accompanied by medium to low densities, in Watt's(1963) Fig. 10.5. For explanations,see Synthesis: so that theirdata points formeda bottom section of Watt'sanalysis. the oval trajectories.These comprise the medium to lowersections of the densityspectrum in Watt's figure. NL up to about NL = 120, afterwhich SL falls again." Onlyin two plots,G4 and G5, did observationsinclude This curious density-dependentrelationship resulted the increasingphase of oscillations,so that theirdata fromfitting a first-ordermodel to a second-orderpro- points formedall but the lower leftquarter of the oval cess and pooling time-seriesdata taken from many trajectories.Thus, average survivalrates in theseplots differentplots. were comparativelyhigh. Their data points comprise As I have deduced, budworm populations oscillate a middle to upper part of the densityspectrum in the because the survivalrate of old larvae oscillates.Need- figure. less to say, the survival rate tends to be highestat I have idealized the above situation in Fig. 29. It medium densitieswhen the population is fastincreas- would be misleadingto draw a singleregression curve ing, and lowest when it is collapsing. Survival is in- throughthe data points pooled withoutregard to the termediateboth when the population is aroundits peak cyclicsurvival of larvae. Populations in differentplots and when it is around its trough.Thus, with an oscil- did not oscillate with similar amplitudes. In the K lating second-orderpopulation process, H3, plotted plots, for example, peak densitieswere very high be- against N3,in time-seriesdata froma given plot tends cause the larval survivalwas somehow veryhigh dur- to yield an oblong circularpattern, though somewhat ingthe population increase. In theG plots,on the other irregularbecause ofrandom factors. Since Wattpooled hand, the larval survival rates were not as high, and all data taken from many study plots, his Fig. 10.4 peak densitiesstayed comparatively low. Thus, higher survivalrates produce higherpeak densities,and then

1OO

Co 0=

"E50

31. ~~~~~.l

1945 1950 1955 1960 1965 1970 1975 1980

Generationyear

FIG. 30. The same as Fig. 1, but density(number/M2 of foliage)is plottedon a linear scale. 458 T. ROYAMA Ecological Monographs Vol. 54, No. 4 some second-orderdensity-dependent mortality fac- fromendemic to epidemic statesoccurs when weather torseventually reduce the survival rate. Thus, the cause- favors larval survival duringthe feedingstage. Con- and-effectrelation is reversed between Watt's inter- versely,a transitionfrom epidemic to endemic states pretationand mine. in the model is dependent on heavy defoliationand resultantfood shortage.However, as I have argued in Dichotomyof endemic and detail, the survival of feedinglarvae does not seem to epidemicpopulations: the respond sensitivelyto weatherchanges (unless, possi- double-equilibriumtheory bly, the larvae are "diseased"), and food shortageis A first-orderdensity-dependent process, i.e., a, = 0 not a universalcause of population decline. in Eq. 7, willnot cause thepopulation to oscillateunless Third,Morris considered that his reproductioncurve the density-independentfactors involved, z in Eq. 7, along the 450 line was of the same formas the survival- oscillate (Royama 1981a). Thus, fittinga first-order densitycurve of Watt's Fig. 10.5; both curvesrise first model to an oscillatorydata serieswill necessarilyyield and then fall as densityincreases. Morris argued that an oscillatoryseries of residuals and would lead one Watt's curve did not rise toward the lower end of the to look for some oscillatorydensity-independent fac- densityspectrum only because the data did not include tors. sufficientlylow densitysituations. However, as already Morris (1963b) noted that his key-factormodel discussed, Watt's curve does not implya causal effect with oscillatingtemperature did not adequately sim- of densityon survival and, therefore,is irrelevantto ulate an endemic stateof budworm populations during the question of shape in Morris's reproductioncurve. the 1930s. Therefore,while stillmaintaining his mod- Thus, there is no reason to assume the dichotomy el's first-orderproperties, Morris nonlinearized it in of endemic and epidemic equilibrium states nor to such a way that a curvilinearregression of N,+1 on N, build a model on that assumption. My hypothesisof (knownas Ricker's [1954] reproductioncurve) crosses a second-orderdensity-dependent process with only the 450 line (on which N,+1 = N,) at two points from one equilibriumpoint is consistentwith the evidence above (Fig 18.3 in Morris 1963b), formingtwo locally and more parsimonious for describingthe dynamics stable equilibriumpoints. In betweenthese two points of sprucebudworm populations. thereproduction curve crosses the 450 line frombelow. This is an unstable equilibriumpoint, or a "release" ACKNOWLEDGMENTS point,above whichthe population increasesto the up- Manypeople from the Canadian Forestry Service contrib- to thecompletion of this paper. If the population overshoots, uted,directly and indirectly, per equilibrium point. Alloriginal members of the Green River Project provided the an epidemic or an outbreakmay result.However, after life-tabledata. In particular,Charles A. Millerand David 0. years of defoliationand subsequentdestruction of the Greenbank,both now retired,freely shared their first-hand forest,the population recedes to a lower level, where knowledgeand experience.Anthony W. Thomasspent his it is again withinthe endemic equilibrium region. Mor- timein frequentand involved discussions with me during the and also providedsome of his unpublished be last fewyears ris consideredthat the endemic equilibriumcould data. Discussionswith Jacques Regniere resulted in thedis- maintainedby predators(e.g., birds and spiders) and coveryof the framingbias in estimatingsurvival rates in parasitoids. However, he thoughtthat even the com- youngand old larvae.Harold Piene and David A. MacLean bined effectof these natural enemies would not stem providedinformation on theimpact of budworm defoliation EdwardG. Kettelaprovided his egg-mass increaseof budworm populations under a series on thehost trees. a rapid data. GrahamPage, Eldon Eveleigh,David MacLean,and offavorable weather conditions, and, hence,that "pop- TonyThomas read the manuscript. I owe MichaelL. Rosen- ulation release" would occur sooner or later. I once zweig,University of Arizona, Stuart L. Pimm,University of supportedthis theoryand even generalized it to the Tennessee,and an anonymousreferee thanks for their com- second-orderlevel (Royama 1977, 1978), but after ments.Finally, I thankDonald Strongfor his mostuseful adviceon improvingthe manuscript. carefulexamination, I have abandoned the idea forthe followingthree reasons. LITERATURE CITED First,the apparentexistence of an endemic statebe- Anderson,R. M., andR. M. May. 1979. Populationbiology tweenthe two recentoutbreaks in theGreen River area ofinfectious diseases. Nature (London) 280:361-367. is mainlydue to poor data resolutionat low densities Balch,R. E., andF. T. Bird. 1944. A diseaseof the European when these are plottedon a linear scale (Fig. 30). The sprucesawfly, Gilpinia hercyniae (Htg.), and its place in same data, when plotted on a logarithmicscale (Fig. naturalcontrol. Science in Agriculture25:65-80. Baskerville,G. 1976. Reportof the task-force for evaluation 1), give higherresolution and show no clear sign of an ofbudworm control alternatives, prepared for the Cabinet endemicequilibrium; the population simplydecreased Committeeon EconomicDevelopment, Province of New and then increasedwithout any sign of negativefeed- Brunswick.Department of Natural Resources, Fredericton, back. There is no reason to believe that this Green New Brunswick,Canada. River situationwas exceptionalamong thelow-density Blais,J. R. 1953. Effectsof thedestruction of thecurrent year'sfoliage of balsamfir on thefecundity and habitsof situationsbetween outbreaks over the past two cen- flightof the spruce budworm. Canadian Entomologist 85: turies(reconstructed in Fig. 3). 446-448. Second, Morris's model assumes that a transition 1958. Effectsof defoliation by spruce budworm on December 1984 SPRUCE BUDWORM 459

radialgrowth at breast height of balsam fir and white spruce. America.Information Report DPC-X-14, Canadian For- ForestryChronicle 34:39-47. estryService, Ottawa, Ontario, Canada. * 1962. Collectionand analysisof radial growth data Kendeigh,S. C. 1947. Birdpopulation studies in theconif- fromtrees for evidence of past spruce budworm outbreaks. erousforest biome during a sprucebudworm outbreak. On- ForestryChronicle 38:474-484. tarioDepartment of Lands and Forests,Division of Re- . 1965. Sprucebudworm outbreaks in thepast three search,Biological Bulletin Number 1. centuriesin theLaurentide Park, Quebec. Forest Science Krebs,C. J. 1971. Geneticand behavioralstudies on fluc- 11:130-138. tuatingvole populations.Pages 243-256 in P. J.den Boer 1968. Regionalvariation in susceptibilityofeastern and G. R. Gradwell,editors. Proceeding of theadvanced NorthAmerica forests to budworm attack based on history studyinstitute on dynamicsof numbersin populations ofoutbreaks. Forestry Chronicle 44:17-23. (Oosterbeek,1970). PUDOC, Wageningen,The Nether- 1979. Rate of defoliationof balsamfir in relation lands. to sprucebudworm attack and timingof spray application. Loughton,B. G., C. Derry,and A. S. West. 1963. Spiders CanadianJournal of Forest Research 9:354-361. and the sprucebudworm. In The dynamicsof epidemic Brown,C. E. 1970. A cartographicrepresentation ofspruce sprucebudworm populations. Entomological Society of budwormChoristoneura fumiferana (Clem.) infestation in Canada Memoir31:249-268. easternCanada, 1909-1966. Canadian ForestryService McKnight,M. E. 1968. A literaturereview of thespruce, PublicationNumber 1263:1-4. western,and 2-year-cyclebudworms. United States Forest Burke,J. M. 1980. A surveyof micro-organismsinfecting ServiceResearch Paper RM44. a sprucebudworm population. Pages 1-9 in Information Miller,C. A. 1955. A techniquefor assessing spruce bud- ReportFPM-X-37, Environment Canada, Canadian For- wormlarval mortality caused by parasites. Canadian Jour- estryService, Forest Pest Management Institute, Sault Ste. nal ofZoology 33:5-17. Marie,Ontario, Canada. 1957. A techniquefor estimating the fecundity of Chitty,D. 1960. Populationprocesses in thevole and their naturalpopulations of the spruce budworm. Canadian Jour- relevanceto generaltheory. Canadian Journal of Zoology nal ofZoology 35:1-13. 38:99-113. 1958. The measurementof sprucebudworm pop- Christian,J.J., and D. E. Davis. 1964. Endocrines,behavior ulationsand mortalityduring the firstand secondlarval and populations.Science 146:1550-1560. instars.Canadian Journal of Zoology 36:409-422. Dimond,J. B. 1974. Statusof microbialsfor control of 1963a. The analysisof the fecundity proportion in sprucebudworm. Proceedings of Symposium on the Spruce theunsprayed area. In The dynamicsof epidemicspruce Budworm.United States Forest Service Miscellaneous Pub- budwormpopulations. Entomological Society of Canada lication1327:97-102. Memoir31:75-87. Franz,J. 1949. Uber die genetischenGrundlagen des Zu- 1963b. Parasitesand thespruce budworm. In The sammenbruchseiner Massenvermehrung aus inneremUr- dynamicsof epidemicspruce budworm populations. En- sachen.Zeitschrift fuir angewandte Entomologie 3:228-260. tomologicalSociety of Canada Memoir31:228-244. Gage,S. H., andC. A. Miller. 1978. A long-termbird census 1977. The feedingimpact of sprucebudworm on in sprucebudworm-prone balsam firhabitats in north- balsamfir. Canadian Journal of Forest Research 7:76-84. westernNew Brunswick.Information Report M-X-84, Miller,C. A., D. C. Eidt,and G. A. McDougall. 1971. Pre- Departmentof Fisheriesand theEnvironment, Canadian dictingspruce budworm development. Canada Department ForestryService, Maritimes Forest Research Centre, Fred- ofFisheries and theEnvironment, Canadian Forestry Ser- ericton,New Brunswick,Canada. vice,Bimonthly Research Notes 27:33-34. Greenbank,D. 0. 195-6.The roleof climate and dispersal Miller,C. A., and T. R. Renault. 1976. Incidenceof para- in the initiationof outbreaksof the sprucebudworm in sitoidsattacking endemic spruce budworm (Lepidoptera: New Brunswick.1. The roleof climate. Canadian Journal Tortricidae)populations in New Brunswick.Canadian ofZoology 34:453-476. Entomologist108:1045-1052. 1963a. The developmentof theoutbreak. In The Miller,C. A., and T. R. Renault. 1981. The use ofexperi- dynamicsof epidemicspruce budworm populations. En- mentalpopulations to assessbudworm larval mortality at tomologicalSociety of Canada Memoir31:19-23. lowdensities. Information Report M-X-115, Environment 1963b. The analysisof moth survival and dispersal Canada,Canadian Forestry Service, Maritimes Forest Re- inthe unsprayed area. In The dynamicsof epidemic spruce searchCentre, Fredericton, New Brunswick,Canada. budwormpopulations. Entomological Society of Canada Mitchell,R. T. 1952. Consumptionof spruce budworms by Memoir31:87-99. birdsin a Maine spruce-firforest. Journal of Forestry50: Greenbank,D. O., G. W. Schaefer,and R. C. Rainey. 1980. 387-389. Sprucebudworm (Lepidoptera: Tortricidae) moth flight and Mook,L. J. 1963. Birdsand thespruce budworm. In The dispersal:new understandingfrom canopy observations, dynamicsof epidemicspruce budworm populations. En- radar,and aircraft. Entomological Society of Canada Mem- tomologicalSociety of Canada Memoir31:268-271. oir 110. Moran,P. A. P. 1953. The statisticalanalysis of the Ca- Henson,W. R. 1950. The meansof dispersal of the spruce nadianlynx cycle. II. Synchronizationand meteorology. budworm.Dissertation. Department of Forestry, Yale Uni- AustralianJournal of Zoology 1:291-298. versity,New Haven,Connecticut, USA. Morris,R. F. 1954. A sequentialsampling technique for Hudak,J., and A. G. Raske,editors. 1981. Reviewof the sprucebudworm egg surveys. Canadian Journal of Zoology sprucebudworm outbreak in Newfoundland-itscontrol 32:302-313. and forestmanagement implications, based on theCana- 1955. The developmentof techniquesfor forest dianForestry Service submission to the Newfoundland and insectdefoliators, with particular reference to the spruce LabradorRoyal Commission on forest protection and man- budworm.Canadian Journal of Zoology 33:225-294. agement.Information Report N-X-205, Newfoundland 1957. Theinterpretation ofmortality data in studies ForestResearch Centre, Canadian Forestry Service, De- on populationdynamics. Canadian Entomologist 89:49- partmentof theEnvironment, St. John's,Newfoundland, 69. Canada. ,editor. 1963a. The dynamicsof epidemicspruce Kettela,E. G. 1983. A cartographichistory of spruce bud- budwormpopulations. Entomological Society of Canada wormdefoliation from 1967 to 1981 in easternNorth Memoir31. 460 T. ROYAMA EcologicalMonographs Vol. 54, No. 4 * 1963b. The developmentof predictiveequations "dispersalof forestinsects: evaluation, theory and man- forthe spruce budworm based on key-factoranalysis. In agementimplications." Conference Office, Cooperative Ex- The dynamicsof epidemicspruce budworm populations. tensionService, Washington State University, Pullman, EntomologicalSociety of Canada Memoir31:116-129. Washington,USA. * 1963c. Predationand thespruce budworm. In The . 1981a. Fundamentalconceptsandmethodologyfor dynamicsof epidemicspruce budworm populations. En- theanalysis of animal population dynamics, with particular tomologicalSociety of Canada Memoir31:244-248. referenceto univoltinespecies. Ecological Monographs 51: Morris,R. F., W. F. Cheshire,C. A. Miller,and D. G. Mott. 473-493. 1958. The numericalresponse of avian and mammalian * 1981b. Evaluationof mortality factors in insectlife predatorsduring the gradationof the sprucebudworm. tableanalysis. Ecological Monographs 51:495-505. Ecology39:487-494. Stehr,G. 1968. On someconcepts in thepopulation biology Morris,R. F., and D. G. Mott. 1963. Dispersaland the ofthe spruce budworm. Proceedings of the Entomological sprucebudworm. In The dynamicsof epidemicspruce Societyof Ontario 99:54-56. budwormpopulations. Entomological Society of Canada Swaine,J. M., and F. C. Craighead.1924. Studieson the Memoir31:180-189. sprucebudworm (Cacoeciafumiferana Clem.). Canada De- Mott,D. G. 1963. The analysisof the survivalof small partmentof AgricultureTechnical Bulletin (new series), larvaein theunsprayed area. In The dynamicsof epidemic Ottawa,37. sprucebudworm populations. Entomological Society of Thomas,A. W.,S. A. Borland,and D. 0. Greenbank.1980. Canada Memoir31:42-53. Fieldfecundity of the spruce budworm (Lepidoptera: Tor- Neilson,M. M. 1963. Diseaseand thespruce budworm. In tricidae)as determinedfrom regression relationships be- The dynamicsof epidemicspruce budworm populations. tweenegg complement, fore wing length, and bodyweight. EntomologicalSociety of Canada Memoir31:272-287. CanadianJournal of Zoology 58:1608-1611. Outram,I. 1971. Aspectsof mating in thespruce budworm, Thomson,H. M. 1958. Some aspectsof the epidemiology Choristoneurafumiferana (Lepidoptera: Tortricidae). Ca- ofa microsporidianparasite of the spruce budworm, Chor- nadianEntomologist 103:1121-1128. istoneurafumiferana.Canadian Journal of Zoology 36:309- . 1973. Sprucebudworm moth dispersal project, 316. Chipman,N. B. 1973:morphometric and reproductive sta- 1960. Thepossible control of a budworminfestation tusof the spruce budworm moths. File Report,Maritimes by a microsporidiandisease. Canada Departmentof Ag- ForestResearch Centre, Fredericton, New Brunswick, Can- riculture,Ottawa, Bimonthly Progress Report 16(4): 1. ada. Tothill,J. D. 1922. Noteson theoutbreaks of spruce bud- Peterman,R. M., W. C. Clark,and C. S. Holling. 1979. The worm,forest tent caterpillar, and larch sawflyin New dynamicsof resilience:shifting stability domains in fish Brunswick.Proceedings of the Acadian Entomological So- and insectsystems. Pages 321-341 in R. M. Anderson,B. cietyfor 1922. 8:172-182. D. Turner,and L. R. Taylor,editors. Population dynamics: Watt,K. E. F. 1963. The analysisof thesurvival of large the20th symposium of the British Ecological Society, Lon- larvaein theunsprayed area. In The dynamicsof epidemic don,England. sprucebudworm populations. Entomological Society of Piene,H., D. A. Maclean,and R. E. Wall. 1981. Effectsof Canada Memoir31:52-63. sprucebudworm caused defoliation on thegrowth of bal- Wellington,W. G. 1960. Qualitativechanges in natural pop- samfir: experimental design and methodology. Information ulationsduring changes in abundance.Canadian Journal ReportM-X- 128, Environment Canada, Canadian Forest- ofZoology 38:289-314. ryService, Maritimes Forest Research Centre, Fredericton, Wellington, W. G., J. J. Fettes,K. B. Turner,and R. M. New Brunswick,Canada. Belyea. 1950. Physicaland biologicalindicators of the Pimentel,D. 1968. Populationregulation and genetic feed- developmentof outbreaksof thespruce budworm. Cana- back.Science 159:1432-1437. dianJournal of Research D 28:308-331. Renault,T. R., and C. A. Miller. 1972. Spidersin a fir- Wellington,W. G., and W. R. Henson, 1947. Noteson the sprucebiotype: abundance, diversity, and influence on spruce effectsof physical factors of the spruce budworm, Choris- budwormdensities. Canadian Journal of Zoology 50:1039- toneurafumiferana(Clem.). Canadian Entomologist 79:168- 1046. 170. Ricker,W. E. 1954. Stockand recruitment.Journal of the Wilson,G. G. 1973. Incidenceof microsporidiain a field FisheriesResearch Board of Canada 11:559-623. populationof spruce budworm. Canada Department of the Royama,T. 1970. Factorsgoverning the hunting behaviour Environment,Canadian Forestry Service, Bimonthly Re- and selectionof foodby the greattit (Parus majorL.). searchNotes 29:35-36. Journalof Animal Ecology 39:619-668. 1977. Observationson theincidence rates of No- * 1971. Evolutionarysignificance of predators're- sema fumiferana(Microsporidia) in a sprucebudworm sponseto local differencesin preydensity: a theoretical (Choristoneurafumiferana)(Lepidoptera: Tortricidae) pop- study.Pages 344-357 in P. J.den Boer and G. R. Gradwell, ulation.Proceedings of theEntomological Society of On- editors.Proceeding of the advanced study institute on dy- tario108:144-145. namicsof numbers in populations (Oosterbeek, 1970). PU- DOC, Wageningen,The Netherlands. . 1977. Populationpersistence and densitydependence.Ecological Monographs47:1-35. APPENDIX 1 1978. Do weatherfactors influence the dynamics of sprucebudworm populations? Canada Department of Fish- GENERALIZATIONOFEQ. 4 eries and Environment,Canadian ForestryService Bi- Migrationand mortalityof mothsoccur over the entire monthlyResearch Notes 34:9-10. adultperiod, say, k days.Also, the average number of eggs 1979. Effectof adultdispersal on thedynamics of carriedby a mothin anyone day tendsto decreasetoward local populationsof an insectspecies: a theoreticalinves- theend of the period, either because the average fecundity of tigation.Pages 79-93 in A. A. Berrymanand L. Safranyk, a mothtends to decreaseas its date of emergencegets later editors.Proceedings of thesecond IUFRO conferenceon in theseason, or becausea mothlays its eggs in batchesover December 1984 SPRUCE BUDWORM 461

severaldays, during which batch size decreases. The product APPENDIX 3 fip,is thentaken to be thescalar product of the two k-element "CORRELATION" BETWEEN E/M RATIO AND DENSITY vectorsfi and Pi, in whichthe Pth elementsoff and Pi are, respectively,the mean numberof eggsstill carried by the Consider a pair of consecutive points in the series of N1, mothsin theplot on day i and themean proportion of that (log egg density,Fig. 9d), e.g., N, and N,+1 (stage subscript numberlaid in the plot. The productyields the weighted one is dropped until needed). Take the differenceN,?1 - N, averageof the effectivepreemigration oviposition over the and writethis ANt,and furthertake the differenceof differ- k ences AN, - AN,, and writethis A2Nt,i.e., periodof k days,i.e., zf tip1i.The productf2p2m can likewise ill A2Nt= ANt- + N-1. (A 1) be takento be a matrixrepresentation ofthe weighted average Nt_=Nt-2N, k Now connect, by a line, N, 1 to N, and N, to N,+1 and observe if the line NN?+ 1 'swings' clockwiseor Af2p2m. Thus, this general situation can be representedby anticlockwise ill in relation to N, 1N,.A clockwise swing means that AN, is Eq. 4 withoutchanges in its form. less than AN,-,, or A2N, is negative;a positive A2N, indicates an anticlockwiseswing. Next, observe that as NN,+1 in Fig. 9d swingsclockwise or anticlockwise,the APPENDIX 2 correspondingseg- ment HtH+?1 in Fig. 9c tends to swing otherwise;a better MORTALITYOF MOTHSAND AVERAGE example is given in a simulationin Royama (198 la: Fig. 6). OVIPOSITIONRATE In other words, A2N, and A2H, tend to have opposite signs, A femalemoth normally lays its eggs over several days and, or the covariance betweenthem is negative.I show how this ifshe dies young, has moreunlaid eggs. Thomas et al. (1980) happens on the assumptionthat H5, (log E/M ratio)is a series collecteddead and dyingmoths on droptrays and examined of uncorrelatedrandom numbersgenerated independently of thenumber of eggs still retained by them. Collection was made N1,(log egg density)and of N5,(log moth density). dailyduring the moth period in 2 yrat three study plots. Since thefull complement of eggsof a femaleis highlycorrelated By the definitionh5, = nlt+l/n5tgiven in Table la, H5t = withher wing length, it is possibleto estimatethe proportion Nl t+ - N5. Then, H5t should be positivelycorrelated with of eggsalready laid by thedead females.Females that died Nlt+l, because H5t is independentof N5tby the above as- earlyin theseason had laid onlya fractionof their full com- sumption. Also, in Eq. A1, A2Nt contains Nt+1 - 2N, and plement,and theaverage proportion of eggslaid increased A2Ht likewise contains -2Ht + Ht-1. It followsthat the co- steadilyfor the 1st 10 d or so in eachseason. Only after 2 wk variance between A2Nt and A2Ht would be negative,unless or moreinto the moth season had mostof the dead females the covariance betweenNt+1 and Ht-1 is verylarge, which is laid mostof their full complement of eggs. In thethree plots, unlikely.This explains why H5tH5,t+land N1tN1,t+ltend to theaverage oviposition rates were 70, 80, and 90% of the swing opposite ways. But, if this happens all the time, it is potentialfecundity. The calculationdid notconsider moths, obvious that H5t is inverselycorrelated with Nlt when both ifany, that were preyed upon by birds, et cetera.The actual seriesfluctuate without trend, even thoughH5t was generated ovipositionrate could thereforebe even lower.Moreover, the completelyindependent of N1t. femalesthat died earlywere more to likely have emerged APPENDIX 4 locally, and the females that died later probably included immigrants.Therefore, even if no emigrationtook place, and ESTIMATION OF BIAS IN H2 in conjunctionwith bird predation, the effective oviposition Let "2 be an estimateof H2 adjusted to the zero deviation rateof the local females could be loweredto therange of 60- of the date sampled, and let Z(D) be the adjustmentterm, 80%. However,the rate would not be muchlower, because such that femaleslay ;50% oftheir eggs usually within 2 d aftermating (Outram1973), which occurs mainly within a dayof eclosion H2 = H2 + Z(D), (A2) (Outram 1971). Heavy mortalitywithin these firstfew days in which D is the deviation in days, shown as 0 in Fig. 19; ofadult life would be unusual. Z(O) = 0 by definition.We wish to estimate Z(D). One way

02 - E 0

(U (U 0 00~~~ 0 0

OA -2 . M 0 A~~~~~~~~~~~~

0~~~~~~~~~~~~ -4 -3 N

-15 -10 -5 0 5 10 15 20

D, relative timing of L3 sampling (days) FIG. Al. A graphicalmethod of calculating corrected survival rate of young larvae (H2) in Fig.20. D is therelative timing of L3 samplingin days(Fig. 19), and Z(D) is theadjustment term defined in Eq. A2 in Appendix4. For explanations,see Analysisby stage survival rates. 462 T. ROYAMA EcologicalMonographs Vol. 54, No. 4 to do thisis to regressH2 on D; thatis, to regressa 0 in Fig. froma completelyuncorrelated random series (hence, no trend) 19against the corresponding 0 in each plot. A regressioncurve tendsto exhibita patternof oscillation, known as theSlutzky was drawnby eyein Fig. Al. The regressionis curvilinear, effect.This is becausein an h-pointmoving-average series, presumablybecause the later the date in relationto theref- twopoints that are k pointsapart from each otherare posi- erencepoint (i.e., the mid-date between the peak L3 and L4 tivelycorrelated with each otherfor k < h, sincethey share stages),the steeperthe slope of populationdecline (cf. Fig. h - k pointsin theoriginal series in common.This tends to 18),and vice versa.This regressioncurve is takento be the resultin a tendencyfor the derived moving-average series to functionZ(D), so thatthe projection of thepoint for D = 0 stayon one sideof the mean level (set by the original uncor- on a verticalaxis gives Z(O) = 0. Thus,Z(D) forany given D relatedseries) for some time before crossing over to theother can be readon theright-hand axis in Fig.Al. H2 forthat D sideof the mean level. This tendency gives the impression of is thengiven by Eq. A2. an oscillatorypattern. However, the oscillations have no fixed periodicity. APPENDIX 5 Thebudworm oscillations, on theother hand, are more like A NOTE ON MOVING-AVERAGE SERIES a "stochasticallyperiodic" or "pseudoperiodic"density-de- A trendin a timeseries, if any, can be mademore apparent pendentprocess whose autocorrelation coefficients have a fixed by takingthe movingaverages of an appropriatelength, a periodicitywhen plotted against time lags; i.e., thedistance methodknown as smoothingor filtering.The methodis ef- betweentwo timepoints to be correlated.The patternof fectivein bringingout a truetrend. Caution is needed,how- oscillationgenerated by this mechanism (Fig. 28) givesa much ever,in employingthis method, because an artificialtrend more"regular" appearance than the moving-averageseries can be created.A seriesof h-pointmoving averages taken ofweather records (Fig. 27).