The University of Chicago Age-Specific Survivorship and Reproduction in Phlox drummondii Author(s): Wesley J. Leverich and Donald A. Levin Source: The American Naturalist, Vol. 113, No. 6 (Jun., 1979), pp. 881-903 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/2460310 Accessed: 11-05-2015 19:32 UTC

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Vol. 113,No. 6

The AmericanNaturalist

AGE-SPECIFIC SURVIVORSHIP AND REPRODUCTION PHLOX DRUMMONDII

June1979

IN

WESLEY J. LEVERICH* AND DONALD A. LEVIN The Universityof Texas at Austin,Austin,Texas 78712

The interestofecologistsin thedemographyofnaturalpopulationshas developed greatlysinceLotka (1925) used theEuler equationto describepopulationgrowthin termsof age-specific components.Theoreticianshave demonstrated thesignificance of life-history strategiesin determining reproductiveperformanceand growthof populations(e.g.,Cole 1954; Gadgil and Bossert1970; Emlen 1970; Schaffer1974a, and Gadgil 1975),and theinfluenceofdemographiccharacteristics 1974b; Schaffer upon the geneticstructureand evolutionarypotentialof populations(e.g.,MacArthur1961, 1962; Andersonand King 1970; King and Anderson1971; Charlesworth 1970, 1972). Althoughtheoryis well developed informationon life-history parametersof naturalpopulationsis meager. There are relativelyfew life tables for organismsother than man. The first completetables fornonhumanorganismswerethoseof Pearl and Parker(1921) for laboratorypopulationsof Drosophilamelanogaster. Deevey (1947) constructedlife tables fornaturalpopulationsof severalanimal species,includingDall mountain sheep (Murie 1944), a sessile rotifer(Edmondson 1945),a barnacle(Hatton 1938), and severalbirdtaxa. Sincethenlife-history data havebeenpublishedfora varietyof invertebrates (Birch1948; Leslie and Park 1949;Evans and Smith1952; Howe 1953; Lefkovitch1963; etc.)and vertebrates (Zweifeland Lowe 1966; Lowe 1969; Spinage 1972; Wilbur 1975; etc.). Only during the past decade has the study of plant lifetables receiveddue attention.Harper and White(1974) reviewedcontemporary studiesofsurvivorship in several Plantago species (Sagar 1959; Hawthorne 1973), Ranunculusspecies (Sarukhan and Harper 1973), Anthoxanthum odoratum(Antonovics1972),and in several otherperennialherbs.A fewresearchershave investigatedsurvivorship in woody perennials(e.g., Hett and Loucks 1971, 1976; Guittetand Laberche 1974; Yarrantonand Yarranton1975; etc.).Otherstudieshave revealedtheage structures of perennialplant populations (e.g., Kerster 1968; Levin 1973; Schaal 1974; Van Andel 1975),whichalso add to our knowledgeof survivorship in nature. Formal life-tableanalyses of natural populations of annual plants have been reportedonlyforSedumsmalliiand Minuartiauniflora (Sharitz1970).Exceptforthis exemplarystudy,our knowledge of the demographicfeaturesof annual plant populationsis fragmentary. thereare essentiallyno data concerning Furthermore, the age-specificfecunditiesof plants in natural populations.It is the details of * Presentaddress: Departmentof Botany,The Ohio State University, Columbus,Ohio 43210. Am. Nat. 1979. Vol. 113,pp. 881-903. n!C1979 by The Universityof Chicago. 0003-0147/79/1306-0007$00.81

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age-specificsurvivorshipand reproductionwhichbest elucidatethe dynamicsof theconsequencesofparticularlife populations,and theyare crucialto understanding are neededfromspeciesofa varietyofhabitsand histories.Completemeasurements habitatsbeforethe meritsand liabilitiesof divergentlifehistoriesin plantsmay be fullyassessed. In this reporta detailed lifetable is presentedfora naturalpopulationof the and featuresderivedfromsurvivorship Life-history annual herbPhlox drummondii. rate rate,theintrinsic data willbe discussed,includingthenetreproductive fecundity values. of increase,and age-specific reproductive Hook. (Polemoniaceae) is a conspicuous The winterannual Phlox drummondii elementof the springflora of south centralTexas. Withinits range the species typicallyoccursin discontinuouspopulationsofthousandsofindividuals.The plants to varietydrummondii of the populationin this studyare referred (sensuErbe and Turner1962). Seeds of Phlox drummondii germinatein late Novemberor earlyDecemberand exhibitslow vegetativegrowththroughthe wintermonths.Plants typicallybegin flowering profuselyin March,althoughsome fewindividualsmayfloweras earlyas late January.The plants show indeterminategrowthand flowering,and given rainfallplantswillcontinueto flowerthroughMay. The plantsare almost sufficient Individualflowerscan remainopen foras long as 8 completelyself-incompatible. days, providingabundant opportunityfor cross-pollination.The primarypollen vectoris thepipe-vineswallowtailbutterfly, BattusphilenorL. Thereare threeovules perflower, and althoughtheaverageseed setis lessthanthree,threeseedspermature capsule is common.The small seeds (ca. 1 x 3 mm) are disseminatedby explosive dehiscenceof the capsule, and can be scatteredas faras 5 m (Levin and Kerster fromseeds of ecological associates. 1968).The seeds are readilydistinguishable METHODS

The populationexaminedin thisstudyoccupiesapproximately 4 ha on an electric on the northernedge of Nixon, Gonzales County,Texas. cooperativeright-of-way The site is protectedfromcattle grazingand human disturbancebut not natural pests, providingoptimal conditionsfor monitoringa natural population. This populationis typicalof thoseoccurringin southcentralTexas. A sectionof the populationwas divided into 50 permanently markedquadrats, each 3 x 3 m,arrangedin an arrayof 10 rowsand fivecolumns.Withineach quadrat specificareas were reservedfor quadrat access, repeatedsoil samplingforseed, mapping,and plantsample removal. vegetativeand reproductive 8 cm,since Soil samplesforseed recoveryweretakento a depthofapproximately examinationrevealedthatmostPhloxseed was in thedetrituslayerofthesoil surface and none was found deeper than 5 cm. At each samplingepisode, fivesamples totaling929 cm2 were taken fromeach of the 50 quadrats, thus yieldingdata periodicallyon numberof seeds presentfrom250 samples totaling4.65 M2, or approximately1% of thestudyarea. Soil samplesweretakenforseed recoveryon May 29, July31, and September30, 1974,and February1, 1975.The sampleswere takento the lab and processedthroughnumbers12 and 18 U.S.A. standardtesting

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sieves to recoverthe size class of materialincludingPhlox seeds. This was sorted seeds wereremovedand counted. manually,and the P. drummondii To measure the dynamics of the vegetativeand reproductivephases of the population,individualseedlingswerelocated,mapped,and censusedat intervalsfor thedurationoftheirlives.This was accomplishedby placinga mappingframein the reservedarea withineach quadrat,locatingit withsteelpinsdrivenintothesoil,and recordingthecoordinatesofall seedlingcontainedin an area of929 cm2,equivalent to thearea sampledfortheseed population.Individualplantscould thenbe located fromtheircoordinatesduringeach subsequentcensusby replacingtheframeon the steel pins. The firstcensus of thissortwas takenon November29-30, 1974,a few days afterseedlingswerefirstdetected.Subsequentcensusesweretakenas indicated in the lifetable, and theywere made weeklyduringthe period of floweringand reproduction.In total, 190 individualplants were located in the 50 quadrats and observedfortheirlifedurations.Observationsrecordedduringthevegetativephase includednumbersofnodes,numbersofbranches,evidenceofdamagebyherbivores, and date offirstfloralbud appearance.Duringthereproductive phaseflowernumber was recordedat weeklyintervals, sinceflowerlifeis about 1 wk.Finally,thenumbers of capsules maturingin a given week were determined(the calyx recurvesafter dehiscenceand persistson the plant).Plants wererecordedas dead whentheywere leafless,dry, and brittle,and when subsequentexaminationshowed no sign of renewedgrowth. A greenhousestudyaccompaniedthefieldworkin orderto obtaininformation on the growthand reproductiveperformance of plantsunderuniformconditionsand freefromconstraintssuch as predation,drought,and disturbanceencounteredin naturalsituations.Plantsweregrownin individualcontainersfromseed ofthesame cohortas thatstudiedat Nixon. Theyweregivenadequate waterand nutrients, and maintaineduntilall had died. Plantswerethendried,weighed,and thetotalnumber of flowersproducedwas determinedby countingcalyces. RESULTS

The lifetableforthe 1974-1975generationofPhloxdrummondii at Nixon is given in table 1. The basic formused by Pearl and Miner (1935), Deevey (1947), Sharitz (1970),and othershas been adapted forthisstudy.A glossaryofthesymbolsused is providedin table 2. The data of the lifetable are summarizedin the survivorship curvein figure1. The semilogarithmic plot of figure1 indicatesinitialsurvivorshipas unity.The curve declines fairlyevenlyduringthe period of seed dormancy,then levels off somewhatduringthe period of growthand reproduction.Finally,the curvefalls sharplyin the period of seed set as the survivingplantsdie. The causes of mortalitycannot be completelydocumented,but thereis some indicationoftheirnature.Decline in numbersin theseed pool is due to theremoval ofindividuals,presumablyby granivores.Seed storedforseveralseasons,bothin the lab and in thefield,showsno loss ofviability.However,in thenaturalseed pool the numberof individualsremainingdeclinesat a fairlyconstantrate.At Nixon seed harvestingants wereobservedto take Phlox seeds,but onlyifpresentedwiththem;

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TABLE 1 LIFE TABLE FOR

Age Interval (days) x-x'

Lengthof Interval (days)

0- 63 ....... 63-124 ....... 124-184 ....... 184-215 ....... 215-231 ....... 231-247 ....... 247-264 ....... 264-271 ....... 271-278 ....... 278-285 ....... 285-292 ....... 292-299 ....... 299-306 ....... 306-313 ....... 313-320 ....... 320-327 ....... 327-334 ....... 334-341 ....... 341-348 ....... 348-355 ....... 355-362 .......

Phlox drummotidii AT

NIXON, TEXAS

No. No. Dying Surviving SurvivorDuring to Day x ship Interval

Average Mortality Rate Per Day

Mean Expectation ofLife(days)

Dx

Nx

lx

dx

qx

Ex

63 61 60 31 16 16 17 7 7 7 7 7 7 7 7 7 7 7 7 7 7

996 668 295 190 176 174 173 172 170 167 165 159 158 154 151 147 136 105 74 22 0

1.0000 .6707 .2962 .1908 .1767 .1747 .1737 .1727 .1707 .1677 .1657 .1596 .1586 .1546 .1516 .1476 .1365 .1054 .0743 .0221 .0000

328 373 105 14 2 1 1 2 3 2 6 1 4 3 4 11 31 31 52 22

.0052 .0092 .0059 .0024 .0007 .0004 .0003 .0017 .0025 .0017 .0052 .0009 .0036 .0028 .0038 .0107 .0325 .0422 .1004 .1428

122.87 104.73 137.59 137.05 115.72 100.96 85.49 68.94 62.71 56.78 50.42 45.19 38.46 32.36 25.94 19.55 13.85 9.90 5.58 3.50

TABLE 2 GLOSSARY OF SYMBOLS

x ...................

Age in days. (This designatesthe firstday of an interval.) The firstday of the intervalfollowingthe intervalof x. Lengthin days of the intervalbeginningwithday x. Numberof individualssurvivingto day x. Survivorship:theprobabilityan individualage zero willsurviveto day x. Numberof individualsdyingduringthe intervalbeginningwithday x. rateper day duringthe intervalbeginningwithday x. Averagemortality Mean expectationof lifeon day x, in days. Total numberof progenyproduced duringthe intervalbeginningwith day x. Superscriptsindicatethe basis of measurement, e.g., Boyule or

bx .....................

Averagenumberof progenyper individualduringthe intervalbeginning withday x. Superscriptsare as above. Contributionto Ro duringthe intervalbeginningwithday x. Net reproductiverate.Ro = E lxbx. The intrinsicrate of increase,from1 = lxbxex. Generationlength. The base of naturallogarithms;e = 2.71828 The naturallogarithmof x. The averagereproductive value per individualalive on day x.

xI ................... Dx . ................... Nx .................... lx ..................... dx ..................... qx ..................... Ex . ................... Bx ....................

seed

1xbx ................... Ro .................... r ................... T ................... e ................... In x ................... VX.....................

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REPRODUCTION

X in days 0

50

100

seed dormancy

150

200

I

F-vegetative germination

I

1.004

250

300

growth- flowering seed

350

setA

050-

lx 0.10005-

001

-100

-50

0 t5Q +100 % deviation from mean lifespan

+150

+200

at Nixon, Texas, 1974-1975.Age is inFIG. 1.-Survivorship curve for Phlox drummondii dicated both in days (day 0 = May 29, 1974) and as percentdeviationfrommean lifespan (= 122.87days).

otherinvertebrates and birdsmay take themalso. Because of theirsmall size and itis unlikely comparedto theseeds ofothermembersofthecommunity, infrequency thattheyare selectivelyremoved. Seedlingsshow a lower mortalityratethando individualsin the seed pool; this lower rate continuesuntilfinalsenescenceof the population.During the period of individualsis due to almostall damage to P. drummondii growthand reproduction, feedingby larvae and adults of a Chrysomelidbeetle,Disonychaalabamae.Most,if some degreeofdamage.Althoughcompletely not all, oftheplantsat Nixon suffered defoliatedplants oftenrecover,show renewedgrowth,and subsequentlyflower, about 37% of all plants ultimatelyfailed to recoverfollowingextensivebeetle damage. data wereconstructedfromtwo different FecundityschedulesforP. drummondii schedulebased on seed bases, seed productionand ovule production.The fecundity outputis givenin table 3, and thatbased on ovule productionis in table 4. The seed productionestimatesare based on total capsules maturedmultipliedby 2.787,the averagenumberofseedspercapsule (see table5). Ovule productionis based on three in tables3 and 4, the fecundity ovules per ovary.From the estimatesof age-specific

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TABLE 3 FECUNDITY

SCHEDULE x -

0-299 299-306 306-313 313-320 320-327 327-334 334-341 341-348 348-355 355-362

FOR Phlox drummondiiAT NIXON, TEXAS, BASED ON SEED PRODUCTION

X'

.......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... .......................... ..........................

seed BXee

N.,

seed bXee

.000 52.954 122.630 362.317 457.077 345.594 331.659 641.023 94.760 .000

996 158 154 151 147 136 105 74 22 0

.0000 .3394 .7963 2.3995 3.1904 2.5411 3.1589 8.6625 4.3072 .0000

lx,1

lb.,

1.0000 .1586 .1546 .1516 .1476 .1365 .1054 .0743 .0221 .0000

.0000 .0532 .1231 .3638 .4589 .3470 .3330 .6436 .0951 .0000 L=

2.4177

R0 = E lxbx = 2.42 (percapita)

In R0 r = 365 = 0.0024 (percapita perday) NOTE.-X -X' = age interval;Bseed = total no. of seeds producedduringinterval;Nx = no. surviving to day x; bseed = averageno. of seeds per individualduringinterval;lx= survivorship;lxbx= contribution to net reproductiverateduringinterval.

TABLE 4 FECUNDITY

SCHEDULE

AT NIXON, TEXAS, BASED ON OVULE FOR Phlox drummonidii

x-x 0-264 264-271 271-278 278-285 285-292 292-299 299-306 306-313 313-320 320-327 327-334 334-341 341-348 348-355 355-362

............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................ ............................

oxvule

Nx

0 123 573 696 729 663 756 609 579 369 285 177 0 0

996 172 170 167 165 159 158 154 151 147 136 105 74 22 0

bolvule .0000 .7151 3.3706 4.1678 4.4182 4.1698 4.7848 3.9545 3.8344 2.5102 2.0956 1.6857 .0000 .0000 .0000

PRODUCTION

bx

lIx 1.0000 .1727 .1707 .1677 .1657 .1596 .1586 .1546 .1516 .1476 .1365 .1054 .0743 .0221 .0000

.0000 .1235 .5753 .6988 .7319 .6657 .7590 .6114 .5813 .3704 .2861 .1777 .0000 .0000 .0000 L=

5.5813

R0 = E lxbx = 5.58 (percapita)

r = 365? 365

= 0.0047 (per capita per day)

= totalno. ofovules producedduringinterval;Nx = no. surviving -X' = age interval;Boxvule NOTE.-X = averageno. ofovulesper individualduringinterval;lx= survivorship, to day x; bovule lxbx= contribution to net reproductiverateduringinterval.

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TABLE 5 SEED PRODUCTION

PER CAPSULE SEEDS

CAPSULES

No.

Proportion

No.

Proportion

April 16, 1975 0 .................................... 1 ................................... 2 .................................... 3 .................................... 4 .................................... Total ............................... Mean no. seeds per capsule = 2.7867

7 1 24 177 2 .211

.033 .005 .114 .839 .009 1.000

0 1 48 531 8 588

.000 .002 .082 .903 .013 1.000

May 5, 1975 0 ................................... 1 .................................. 2 ................................... 3 ................................... 4 ................................... Total ............................... Mean no. of seeds per capsule = 2.7873

7 2 33 225 1 268

.026 .007 .123 .840 .004 1.000

0 2 66 675 4 747

.000 .003 .088 .904 .005 1.000

SEEDS PER CAPSULE

Pooled No. of capsules = 479 No. of seeds = 1,335 Mean no. seeds per capsule = 2.787

fecundity curvesin figure2 have been drawn.These graphicallyshow the relation and survivorship. betweenthe estimatesof age-specificfecundity The net reproductiverate Ro is the average numberof offspring producedper individualalive on day 0. This is givenby the expression

Ro = E 1xbx and estimatesof Ro based on bothseed productionand ovule productionare given schedulesin tables 3 and 4. The actual replacementratein this below the fecundity studyis based on seed production(sinceseeds are the individualswhichenterage class zero of the nextgeneration),and Rsed = 2.42. This value would indicatethat the populationwas increasingin numbersduringthe 1974-1975generation.Calcu= 5.58,whichis of ratefromovuleproductiongivesR7ovul' latingthenetreproductive course greaterthanrealizedpopulationgrowth. Witha discretegenerationorganism,Ro may be obtaineddirectlyfromthetotal numberof offspring dividedby the numberof individualsin theoriginalcohort(in about thiscase Ro = 2408/996= 2.42). However,thisshortcutobscuresinformation thedistribution of reproductionwithinthe generation;it is not obvioushow many individualsproducedhow manyseeds or,when.Figure3 is a plot of 1xb" values,the contributionsto Ro fromeach age class. The area under each curve shows the magnitudeof the corresponding Ro estimate.The lxbx curvefromseed outputdata

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THE AMERICAN NATURALIST

888 75

18

100 _

_

% deviation frommean lifespan 125 150

175

9

0

,

.16.14-

7

bx

X1\2-

-d

x

ovule

>

bXseed6

X.l

~~~~~bx 10

0~~~~~~~~~~~~~~~~~~~

> 08

0

\ 4 O

/

0~~~~~~~~

x 215

235

255

275

295

315

335

355

AGE (days)

at Nixon, Texas, 1975. The solid line= FIG. 2.-Fecundity curves for Phlox drummondii averageno. ofseedsproducedperindividualduringan interval(b"ed);thebrokenline= average no. of ovules producedper individualduringan interval(b?Xule).A portionof the survivorship curve(Ix),on an arithmetic axis,is shownforreference.

75

% deviation from mean lifespan 125 150 l l

100 l

175 l

-.8 -.7 -.6

Ix bx ovule

-.4

Ix bx

.2 .

xbxseed 215

235

255

275 295 AGE (days)

315

335

355

FIG. 3.-Distribution of the contributions to net reproductiverateduringage intervals(lxbx values).Open circles= lxbxvalues based on seed production;closed circles= lxbxvaluesbased on ovule production.

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shows that actual reproductionis not at all evenlydistributed, but that a larger portionof the totalvalue of Ro accrueslate in the generation. The intrinsicrate of increase,r,can be determined by solvingtheEuler equation, 1= of lb., erx dx, forr (Lotka 1925).However,in thisstudythemeasurements 1, and are from the within is generation of a single and there no current cohort, lx bX growthof the populationduringtheone generationspan; therefore theapproximation 1 = E lxbxe- is moreappropriate.If T is thelengthofgeneration, then,since rateforone generation, theabove expressioncan Ro = E lxbxis thenetreproductive r = (ln RO)/T. be rewritten The difficulties involvedin ascertainingan appropriatemeasureforT, such that Ro = erTis satisfiedin general,havebeendiscussedbyLaughlin(1965),Leslie (1966), and Caughley (1967). In this studywe are dealing with a case like Caughley's birth-pulse model,and have adopted a measureforT thatreflects themean interval betweenbirthof parentand offspring (afterAndrewartha and Birch1954; Laughlin 1965). This has been called cohortgenerationlength(T7)by Laughlin(1965) and is appropriatein thissinglecohortstudy. Among annual plants generationlengthis commonlytaken to be 1 yr, but extendeddormancycan give riseto age-structured seed pools and mean generation lengthsofgreaterthan1 yr.But,ifextendeddormancyis infrequent and germination of the seed pool is essentiallycomplete,generationlengthmay be taken as 1 yr withoutintroducing seriouserror.In thisstudyonlyabout 30 oftheoriginalcohort of seed remainedungerminated and undera survivorship regimelikethatdescribed above onlya fraction ofthesecould contribute to successivegenerations. Therefore, a generationlengthof 1 yrhas been used in calculatingr; thisis thecohortgeneration length.A slightlygreatervalue forT would decreasethe value of r onlynegligibly. rseed is Using actual seed productionforthe 1974-1975generationofP. drumondii, 0.0024 per day (see table 3). Using ovule productionas an index of reproductive capacityforthe generation,rovuleis 0.0047 per day (see table 4). These values both show the populationto be in a period of growthduringthe measuredgeneration. Values ofr musthave a timeunitspecified(in thiscase, perday) or theyhaveno use in comparison;r = 0.0024was establishedoveran entireyear,but it is reportedas a daily rate. The conceptofreproductive value was developedby Fisher(1930) to measurethe average contributionby an individualat a given age to the ancestryof future generations.Fisher'sreproductive value is givenby V =e1 x

ef

x 't=x

rtitbt,

wherevXis reproductive value at age x, and x and t are both age indices. The above expressionforreproductivevalue is based on a model of continuous growth,and the exponentialfunctionserx and e -rt weightthe value forchanging populationsize. However,because thedata in thisstudyare froma singlediscrete generationwhich is not experiencingcuuent growththe exponentialsmay be omitted(theirvalues would be zero). It is thusappropriateto examinethedistributionofabsolutereproductive value at each age,whichis givenbyvx= 1/1x Yt=x itbt. The values forvx(based on actual seed production)are plottedin figure4.

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% deviation from mean lifespan +50 +100 0

1C

--

+200

+150

I

0~~~~~~~~ 0 0)

c5-

0

50

060

150

200

250

300

350

AGE(days) FIG. 4.-Reproductive values v.,forPhlox drummondii at Nixon,Texas, 1974-1975.

and reproductiondata thusfardescribedare measurements The survivorship of the average performanceof the entirepopulation sample. Since the data were ofsurvivorship collectedforindividualplantsthedistribution and reproduction may be morefullyexamined.Of thoseindividualswhichgerminated, thegreatestproportion (about 45o%) produced no capsules at all. A small proportionproduced relatively manycapsules; thegreatestnumberofcapsulesproducedbyanyplantwas 45. The distribution ofactual reproduction by individualsis givenin figure5, where 0 thepercentage ofindividualsthateventuallyproduceda givennumberofcapsulesis shown.Only thoseindividualswhichgerminatedare includedhere;inclusionofall membersof the originalseed cohortwould greatlyexpand the zero class. Vigor of plantswas estimatedby the numberof nodes on the day of census.To examinethe relationbetweenearlyvigorand eventualreproduction, thenumberof 1 mo aftergermination) nodes on a plantat theDecember30 census(approximately was correlatedwiththe numberof capsules subsequentlymatured,and thecorrelation (r = .491) was verysignificant(P