Journal of
Ecology 1993,
81, 465-476
- relativeimportance
Comparativeplantdemography
of
life-cycle
components
to thefiniterateof increasein
woodyand herbaceousperennials
JONATHAN SILVERTOWN, MIGUEL FRANCO,* IRENE PISANTYt &
ANA MENDOZA*
Departmentof Biology, Open University,
Milton Keynes MK7 6AA, UK,
*Centrode Ecologia, UniversidadNacional Autonomade Me'xico,04510 Me'xicoDF, Me'xicoand
tFacultad de Ciencias, UniversidadNacional Autonomade Me'xico,04510 Me'xicoDF, Me'xico
Summary
1 Stage projection(Lefkovitch)matricesfor 21 species of woody plants and 45
or comherbaceousperennialswere extractedfromthe plantdemographicliterature
piled frompublisheddata.
1, recruitment
of seeds to the
2 Each matrixwas dividedintosix regionsrepresenting:
of seedlingsor juveniles fromcurrentseed production;3,
seed pool; 2, recruitment
in stage;
due to plantsdecreasingin size or reverting
clonal growth;4, retrogression,
5, stasis,(survivalfromone yearto thenextin the same stageclass); 6, progression
to laterstageclasses.
3 Matrixanalysiswas used to calculatethefiniterateof increaseX foreach population
in thematrices.Elasticities
and to calculatetheelasticitiesof each transition
coefficient
were summedwithineach of the six regionsof thematrixto give measures(E1 - E69
of each componentof the lifecycle to X and fitness.
respectively)of the importance
4 Herbs as a group differedsignificantly
from woody plants in most of these
was more important
in herbsthanwoody plants.
components.Seedling recruitment
occurredonlyin herbs,particularly
thosewitha tuber.Stasis occurred
Retrogression
in woodyplants.Progressionwas more
in nearlyall species,butwas mostimportant
in almostall species.
thanfecundity
important
matrices
fromcorrelation
5 Trade-offs
amonglifecycle componentsweredetermined
of r (= ln X) and elasticitiesE1 - E6 forthe whole sample and forherbsand woody
withelasticitiesforfecundity
plantsseparately.
As a whole,r was positivelycorrelated
(E1 + E2) and growth(E3 + E6) and negativelycorrelatedwithsurvival(E4 + E15).In
and clonal growthwere negativelycorrelated.
clonal herbs,fecundity
6 The divisionof elasticitiesinto threemajor components(growth,G = E3 + E6;
F = E1 + E2; and survival,L = E4 + E5) allowed us to constructtriangular
fecundity,
plots in G-L-F space. This was done separatelyfor iteroparousforestherbs,
iteroparousherbsfromopen habitats,semelparousherbsand woody plants.Each of
thesefourgroupsoccupieda distinctpositionin G-L-F space. Withinwoodyplants,
with the lowest
habitatsoccupied the end of the distribution
shrubsof fire-prone
survivalelasticity.
of distinctecological
7 It is arguedthatthedemographic
approachto theclassification
betweenlife historyand habitat.
groupsoffersnew insightsintotherelationship
evoluKeywords:clonal growth,elasticityanalysis,Lefkovitchmatrix,life-history
retrogression,
stasis,trade-off
recruitment,
tion,matrixanalysis,progression,
Journalof Ecology 1993, 81, 465-476
Introduction
The comparativemethodhas a long traditionin biology, particularlyin evolutionarystudies (Harvey
& Pagel 1991), and is the modus operandi of a significant contemporaryschool of plant ecology
(Grime et al. 1988). The methodis foundedon the
principle that similar environmentsexert similar
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
466
Comparative
plant
demography
selectiveforceson different
species, leadingto convergentevolution and adaptive patternsthat transcend taxonomic boundaries. Dissimilar environmentsexertdifferent
selectiveforcesthatmay lead
to the evolutionarydivergenceof relatedtaxa.
Since the pioneeringstudyof threeRanunculus
species by Sarukhain& Harper (1973), the demographyof wild plants has oftenbeen analysed on a
comparativebasis, albeit usually forsmall numbers
of related taxa (e.g. Schaffer & Schaffer 1977;
Newell, Solbrig & Kincaid 1981; Angevine 1983;
Kawano et al 1987; Fone 1989; Young 1990;
Boutin & Harper 1991). Wider comparisons between largernumbersof unrelatedtaxa should allow greatergeneralizationabout the evolutionary
forces that shape plant life history.However, before any such exercise can be tackled we must
establish a meaningfulmethod of comparison for
species with life cycles as differentas, for example, Linum catharticum,a short-livedsemelparous
herb and Sequoia sempervirens,a clonal tree of
renownedsize and longevity.
The life cycle of a plant can be described by a
life-cycle graph (Hubbell & Werner 1979), from
which a population projectionmatrixmay be derived (Caswell 1989). The projectionmatrixallows
the quantitativedemographicdata thatdescribe the
life cycle of a population with age or stage structure to be representedin a standardformat.The
contributionthat an average individual belonging
to an age, size or stage class (say j), makes in a
predefinedtime interval(t to t+]) to anotherclass
(say i; where i takes the values 1, 2, ..., j, ..., k) is
expressed as a coefficient(aij) of a square matrix
(A) whose numberof rows and columns is equal to
the number of classes chosen (k). Populations
where the individuals are grouped in age classes
are describedby a Leslie matrix(afterLeslie 1945,
1948), wherethe only non-zeroelementsare on the
first row (fecundities = alj) and on the first
subdiagonal (survivorship= aij,-1). When individuals are classified in size or stage classes, any
elementof thematrixmay be positivebecause each
class may potentially(if not biologically) contribute to any other. This is known as a Lefkovitch
matrix(Lefkovitch1965). In mostplantsfecundity,
growthand survivorshipare closely relatedto individual size or stage of growthand are only loosely
related to chronological age, so Lefkovitchmatrices tendto be moreappropriate,and are moreoften
used, than Leslie matrices. Dual classificationby
age and stage is possible using a Goodman matrix
(Goodman 1969), but is rarelyused (but see van
Groenendael & Slim 1989, Law 1983).
Analysis of populationprojectionmatricesprovides a range of measures of population structure
and behaviourthataffordcomparisonbetweenspecies (Caswell 1989). First,analysis of a population
projectionmatrixyields the finiterate of increase
X, which may be used as a measure of fitnessfor
organismspossessing a particularset of traitsin a
particularenvironment.Secondly, matrix analysis
yields the stable age or stage distributionand a
vector of reproductivevalues. These are of interest
in themselves(J. Silvertown& M. Franco, unpublished), and may also be used to calculate the
elasiticity eij of each element aij in the matrix.
Elasticity is a measure of the sensitivityof X to
small changes in aij, standardizedto allow for the
fact that elements aij representingsurvival probabilities can only range between zero and one,
wheras an ai1 representingfecunditycan have any
value at all. If sij is the sensitivityof element aij,
then the elasticityof the elementis:
e.. = (a./X) x si.
Elasticityis a measure of the relative change in
the value of X in response to small changes in the
value of a matrixelement,and it is also a measure
of an element's contributionto fitness(de Kroon,
van Groenendael& Caswell 1986). Elasticities sum
to unity,and may be summed across selected regions of a matrixin order to compare the relative
importanceof, say, fecunditywith the importance
of growth.Caswell (1986) made such a comparison
for Lefkovitch matrices of five tree species and
found that the probabilityof remainingin a size
class was generally more importantthan that of
growinga size class or of fecundity.This was not
so forDipsacus sylvestris(a semelparousherb),and
he concluded that 'These patternsdeserve further
study'.
In a recent comparative sttudy,Silvertown,
Franco & McConway (1992) used elasticityanalysis
of matricesfor 18 herb species to test for a correspondence between demographic measures of
growth, survival and fecundityand measures of
and Ruderal (CSR) staCompetitive,Stress-tolerant
tus accordingto Grime's classification(Grime et al.
1988). No correspondencewas found. Enright &
Watson (1992) made a similarcomparisonforseven
trees and a herb,but theirsample was too small to
permitany firmconclusions.
It is an axiom of life-historytheorythat tradeoffs between differentlife historyparameters,in
particular between reproduction,growth and survival, constrainlife-historyevolution. The evolutionaryconstraintscreatedby such trade-offsshould
lead to negative correlationsamong the elasticity
values representingdifferent
componentsof the life
cycle. In particular,one would expect a trade-off
between fecundity and survival, with fecundity
more importantto short-livedherbs and survival
more importantto long-lived trees. Among clonal
plants one might expect a trade-offbetween the
importanceof vegetativereproductionand the importanceof sexual reproduction.
In this studywe use elasticityanalysis of matrix
projectionmodels for a sample of 45 herbs and 21
woody species to determinethe contributionof dif-
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
467
J. Silvertown
et al.
ferentcomponentsof the life cycle to X in plantsof
widely contrastinglife history.This sample is large
and ecologically diverse enough for us to test for
correlationbetween the importance(elasticity) of
life historycomponents and habitat. This is the
ultimatetest of utilityin any comparativestudyof
life historyand has not been applied to the results
of elasticity analysis before. If this approach to
comparative plant demography is successful it
should help us understandthe relationshipbetween
life history and the habitat templet (Southwood
1977, 1988).
Methods
A comprehensivesurveyof the literatureon plant
demography(Franco & Silvertown1990) was used
to identifystudiesof perennialsthatpresenteddata
in the formof a populationprojectionmatrix(43
cases), or which supplied enough informationto
permitus to constructa projectionmatrixfor the
population(s)ourselves(23 cases). Matricesforspecies studiedat more than one site or in more than
one year were averagedto give one matrixper species per study.In one case (Araucaria hunsteinii)
matricesfordifferent
populationscould not be averaged because stage classificationsdifferedbetween
sites. In this case the populationparameterswere
calculatedseparatelyforeach matrixand theparameters averaged, using the geometricmean of X, to
obtaina single species' estimate.Most authorsgave
annual estimatesof the coefficientsa... When this
was notthecase we standardizedthematrixto apply
to a projectionintervalof one year.
Caswell (1989, p. 49) identified an error in
population projection matrices for plants that we
foundto be frequentin the literature.A proportion
of the seeds of manyplantspass fromproductionto
germinationin underone year, so seeds should not
appear as a separate stage in matrixmodels that
have a projectionintervalof one year unless there
is a long-term(supra-annual)seed pool. Even when
a supra-annual seed pool exists, a proportionof
recruitsfromseed will enterthe populationwithout
passing throughit. The many studies which have
not allowed for this give an underestimateof X
because an artificialseed pool delays recruitment.
We correctedfor this error,which in some cases
meant the disappearance altogetherof a seed categoryappearingin thepublishedmatrixfora population.
Matrices were analysed by the power method
(Caswell 1989, p. 79). Here we report only the
resultsconcerningthe finiterate of increase of the
population(X) or its naturallogarithm,the intrinsic
rate of population increase (r), and the elasticity
(ei]) of the differentelementsof the matrix.Each
of the 66 matrices(Table 1) was divided into six
regions, each representinga differentpart of the
life cycle. The regions,shown in Fig. 1, were:
1 recruitment
of seeds to the seed pool;
2 recruitment
of seedlingsor juveniles fromcurrent
seed production;
3 clonal growth;
4 retrogression
due to plantsdecreasingin size during the year or revertingfroma floweringstateto a
vegetativeone or becomingdormant;
5 stasis, or survivalfromone yearto thenextin the
same stage class;
6 progressionto later stage classes.
Elasticities e.. were summed withineach of the
six regionsto give totals foreach life-history
process that are termed E1-E6, respectively.For the
purpose of the presentanalysis E1+E2 collectively
representfecundity(F), E4+E5 collectively represent survival (L), and E3+E6 collectively represent
growth(G). Not all matricescontainedall six components and the relevantmatrixelements in published matrices were not always in the positions
shown in Fig. 1. Care was taken to assign each
elasticitycoefficientto its biologicallycorrectcomponent,regardlessof its actual position in the matrix.
Trade-offs between the differentlife history
componentswere soughtby compilinga Spearman
rank correlationmatrix for r, E1 - E6, F, L, G.
Variables E1 - E6, F, L, G are directlyor indirectly
dependenton each otherbecause elasticitiessum to
unity. Some negative correlations among these
variables are thereforeto be expected. However,
which variables are negatively and which positivelycorrelated,and to some extentthe strengthof
negative correlations,is determinedby biological
trade-offs.The significanceof correlationsbetween
elasticities was determinedusing a randomization
test (Manly 1991) thatallowed for the mathematical constraintsthatcould produce spuriouscorrelation.
For the whole sample and forherbs and woody
plants separately,each observed correlationcoeffiYear t
seed
Stage
seedling
iii
iv
seed
1
seedling
2
+a
iii ___
ivI
v
I
I~~~
v
3
iv----r - - v----r
---r--
-X
6
Fig. 1 The six regions of the stage projectionmatrix: 1,
seed production;2, seedlingrecruitment;
3 clonal growth;4,
retrogressionto a previous stage or size; 5, stasissurvivorship
withinthe same class; 6, Pprogressionto later
stages.
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
Table 1 Finite rate of increase X and summed elasticity values in six components E, - E6 of the stage projection matrices for 66 species of
herbs, shrubs and trees. n = dimension of the matrix.
Species
El
E2
E3
E4
E
E6
n
Herbs
1. Agropyronrepens'
2. Allium monanthum'
3. Anthyllisvulneraria2
4. Arisaema serratum
5. Arisaema triphyllum3
6. Armeria maritima2
2.963
1.588
1.416
0.991
1.073
1.458
0.0001
0
0.1306
0
0.0122
0
0.0003
0.0003
0.2347
0.0680
0.0691
0.1225
0.2302
0.2395
0
0.1050
0.0661
0
0
0.0613
0
0
0
0
0.4910
0.4416
0.0727
0.2640
0.6533
0.2258
0.2773
0.2572
0.5621
0.5630
0.1995
0.6517
6
7
4
19
7
11
7. Calathea ovandensis'
8. Calochortus albus
9. Calochortus obispoensis
10. Calochortus pulchellus
11. Calochortus tiburonensis
12. Chamaelirium
luteum3
13. Cleome droserifolia2
14. Clintonia borealis'
15. Cynoglossum officinale2
16. Danthonia sericea3
17. Daucus carota2
18. Digitalis purpurea2
1.550
1.542
1.023
1.115
1.156
1.004
1.118
1.128
1.064
1.196
1.367
11.815
0
0
0
0
0
0
0.0358
0
0
0
0
0.0397
0.2659
0.1875
0.0411
0.0859
0.0811
0.0279
0.0333
0
0.3148
0.1087
0.2736
0.4375
0
0.0067
0.0253
0.0288
0.0040
0
0
0.1754
0
0
0
0
0.0353
0
0
0
0
0.2801
0
0
0
0.0456
0
0
0.2677
0.4048
0.8314
0.6629
0.7570
0.2958
0.5753
0.6459
0.0557
0.4260
0.1791
0.0059
0.4312
0.4011
0.1022
0.2224
0.1579
0.3961
0.3557
0.1787
0.6295
0.4197
0.5473
0.5169
4
4
3
4
3
24
15
3
3
6
3
4
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
2.322
0.936
1.427
1.548
1.001
1.018
1.335
1.012
1.270
1.237
2.159
0.976
1.038
0.996
1.035
0.767
1.142
1.158
0.0659
0
0
0
0
0
0.0934
0.0014
0
0
0
0
0
0.0750
0
0
0
0
0.0015
0.0224
0.0054
0.2761
0.0437
0.0220
0.1147
0.0015
0.2840
0.3238
0.9417
0.0176
0.3204
0
0.0778
0.2678
0.4055
0.0045
0
0.2478
0.1929
0
0.1742
0.0770
0
0.0716
0.1900
0
0
0.0844
0
0
0.1346
0
0.0116
0.1891
0.2773
0.0560
0.1070
0
0
0.1051
0
0
0
0
0
0
0.0369
0
0.0152
0
0
0
0.0506
0.2089
0.3761
0
0.3547
0.5145
0.3156
0.8498
0.1640
0.0285
0
0.7853
0.3865
0.5606
0.3565
0
0.1659
0.5831
0.6047
0.4649
0.3186
0.7239
0.4274
0.2814
0.4763
0.0758
0.3620
0.6477
0.0584
0.1127
0.2561
0.3644
0.4159
0.7322
0.4171
0.2232
6
13
8
4
13
8
4
4
3
3
3
3
7
6
6
4
3
4
37. Potentilla anserina3
38. Ranunculus acris'
0.883
1.206
0
0.0767
0.0022
0.2097
0.1902
0.0217
0
0
0.5166
0.3073
0.2910
0.3847
6
4
39. Ranunculus bulbosus'
1.345
0.2219
0.0481
0
0
0.2383
0.4918
3
40. Ranunculus repens'
0.498
0.0586
0.0025
0.0169
0
0.7853
0.1367
4
1.030
0
0.1482
0
0.0228
0.3192
3
0.803
0.997
1.484
0
0
0.0854
0.2012
0.0330
0.0947
0.971
1.009
0
0
1.014
1.246
1.609
0.992
2.995
Dipsacus sylvestris
Disporum sessile'
Disporum smilacinuml
Echium vulgare2
Erythronium
japonicum'
Fritillaria meleagris2
Gentiana pneumonanthe2
Hieraciumfloribundum2
Hypochoeris radicata
Isatis tinctoria2
Linum catharticum2
Narcissus pseudonarcissus3
Ophrys sphegodes'
Panax quinquefolium3
Pedicularis furbishiae
Picris hieracoides2'3
Plantago coronopus2'3
PodophyllumpeltatuM2'3
41. Scabiosa columbaria2'3
42. Seneciointegrifolius2'3
43. Senecio jacobaea2
44. Swallenia alexandrae2
45. Viola fimbriatula'
Trees and shrubs
46. Alnus incana3
47. Araucaria cunninghamii
48. Araucariahunsteinii"3
49. Astrocaryummexicanum3
50. Avicennia marina'
51. Banksia ericifolia2
52. Betula nana
53. Calluna vulgaris'
54. Carnegiea gigantea2
55. Cassia nemophila'
56. Fagus grandifolia'
57. Iriartea deltoidea3
58. Nothofagus
fusca3
59. Pentaclethra
macroloba'
60. Petrophile
pulchella2
61. Pinuspalustris'
62. Podococcusbarteri'
63. Psidiumguajava'
64. Rhopalostylis
sapida
65. Sequoia sempervirens'
66. Vaticahainanensis'
1.446
1.020
0.540
1.207
0.939
1.081
1.006
1.002
1.643
0.998
1.013
0.994
1.007
0.992
1.000
0.5098
3
Mortimer(1984)
Kawano et al (1987)
Sterk (1975), Sterk et al. (1982)
Kinoshita (1987)
Bierzychudeck (1982)
Lefebvre &
Chandler-Mortimer(1984)
Horvitz & Schemske (1986)
Fiedler (1987)
Fiedler (1987)
Fiedler (1987)
Fiedler (1987)
Meagher (1982)
Hegazy (1990)
Pitelka et al. (1985)
Boorman & Fuller (1984)
Moloney (1988)
Verkaar & Schenkeveld (1984)
van Baalen (1982),
van Baalen & Prins (1983)
Caswell (1989)
Kawano et al. (1987)
Kawano et al. (1987)
Klemow & Raynal (1985)
Kawano et al. (1987)
Zhang (1983)
Chapman et al. (1989)
Thomas & Dale (1975)
de Kroon et al. (1987)
Farah et al. (1988)
Verkaar & Schenkeveld (1984)
Barkham (1980)
Waite & Hutchings (1991)
Charron & Gagnon (1991)
Menges (1990)
Klemow & Raynal (1985)
Waite (1984)
Sohn & Polikansky (1977), Rust
& Roth (1981)
Eriksson (1987, 1988)
Sarukhan & Harper (1973),
Sarukhan (1974), Harper (1977)
Sarukhan & Harper (1973),
Sarukhan (1974), Harper (1977)
Sarukhan & Harper (1973),
Sarukhan (1974), Harper (1977)
Verkaar & Schenkeveld (1984)
Widen(1987)
0.0775
0
0.0457
0
0
0
0
0.3941
0.3999
0.6770
0.0991
0.5223
4
4
14
Forbes (1977)
Pavlik & Barbour (1988)
Solbrig et al. (1988)
0
0.0078
0.0615
0
0
0
0.7411
0.9412
0.1974
0.0510
5
10
Huenneke & Marks (1987)
Enright& Watson (1991)
0.0081
0
0.0755
0
0.0853
0
0.0974
0.0728
0
0.2021
0
0
0
0.1421
0.0008
0
0
0
0
0
0.9031
0.6350
0.3875
0.6740
0.2029
0.0889
0.2676
0.4642
0.1840
0.5089
14
6
9
4
6
0
0.0479
0
0
0.0006
0.0439
0.0078
0.0324
0
0
0
0
0
0
0
0
0.0024
0.3707
0.0235
0.1275
15
12
4
6
0
0
0
0
0.0600
0
0
0
0
0
0
0.1940
0.0116
0.0084
0.0091
0.0985
0.0057
0.0081
0.0020
0.0081
0
0.0219
0.0119
Source
0
0
0
0
0
0.0404
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.0444
0.8679
0.2519
0.9281
0.9969
0.5375
0.9687
0.8402
0.9696
0.8946
0.3645
0.9649
0.8191
0.9767
0.9440
1
0.7885
0.0603
0.0221
0.0963
0.4770
0.0294
0.1325
0.0213
0.0478
0
0.1896
7
4
14
9
8
6
12
8
5
12
Enright(1982)
Pinieroet al. (1984)
Burns & Ogden (1985)
Bradstock & O'Connell (1989)
Ebert & Ebert (1989)
Barclay-Estrup& Gimingham
(1975), Mallik et al. (1984),
Scandrett& Gimingham (1989)
Steenbergh & Lowe (1977, 1983)
Silander (1983)
Harcombe (1987)
Pinard (1992)
Enright& Ogden(1979)
Hartshorn
(1975)
Bradstock& O'Connell(1989)
Plattet al. (1988)
Bullock(1980)
Somarriba(1988)
Enright& Watson(1992)
Namkoong& Roberds(1974)
Hu (1988)
'Matrixgivenby thesource,butmodifiedor corrected
forthisstudy.2Matrixcompiledforthisstudyfromdata in thesource.3Matrix
used in this
studywas obtainedby averagingmatricesgivenin thesource.
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
469
J. Silvertown
et al.
cient was tested against a distributionof expected
values of the statisticgeneratedfroma null model.
The null models contained the same number of
species as each sample (66, 45, 21, respectively)
and were based on the observedelasticitiesof each
sample in order to preservebiological realism. In
each null model, observed values of the six
elasticitieswere independenetlypermutatedamong
species and then standardizedto sum to unityfor
each species. A correlationmatrixwas thencalculated forthe model. This was repeated5000 times
for each sample to generatea frequencydistribution of correlationcoefficientsagainst which observed values were tested. The test was conservative (i.e. prone to type II error)because null models were generatedfromthe observed data.
Because some species lack certain elasticities
(e.g. non-clonal species lack E3 and species with
no seed dormancylack El), spurious correlations
could be created by including all species in all
correlations.To avoid this,cases of zero values in
El - E6 were treated as missing obervations, so
sample sizes (and degrees of freedom)were determined pairwise withinthe correlationmatrix.
Because F + L + G = 1 thereis a mathematical
constraintamong these variables, but biological
constraintsdeterminewhichspecies occur wherein
the space definedby them. The 66 species in the
study were plotted in a triangularordinationfor
each of fourgroups: iteroparousherbs fromclosed
habitats (forest herbs), iteroparousherbs of open
habitats,semelparousherbs and woody species.
Results
COMPARISON
OF
WOODY
PLANTS
AND
HERBS
The parameterscalculated for each populationare
shown in Table 1. Althoughthe intrinsicrate of increase (r) varied greatlywithineach sample it differed at the 5% level between woody plants and
herbs (Table 2).
Table 2 A comparisonof themean values of r, elasticities
E6 and G, L, F forherbsand woodyplants.Differences
between the two groups were tested by Mann-Whitney
U-test
E-
Herbs
r
El
E2
E3
E4
Es
E6
G
L
F
Woody plants
n
mean (SD)
45
13
43
25
11
42
45
45
45
45
0.225
0.069
0.149
0.105
0.095
0.402
0.381
0.439
0.398
0.163
(0.451)
(0.060)
(0.175)
(0.083)
(0.096)
(0.246)
(0.184)
(0.183)
(0.256)
(0.175)
n
21
5
17
4
0
21
20
21
21
21
mean (SD)
P <
0.090
0.055
0.038
0.061
0.785
0.168
0.172
0.785
0.044
0.05
0.81
0.01
0.29
(0.315)
(0.030)
(0.053)
(0.060)
(0.235)
(0.165)
(0.170)
(0.235)
(0.074)
-
0.001
0.001
0.001
0.001
0.001
El. A supra-annualseed pool existed in 13/45herb
populationsand 5/21woodyplants.In onlytwo cases
did theseed pool contribute
above 10% to changesin
X (Anthyllisvulneraria and Ranunculus bulbosus;
Table 1) and thedifference
betweenherbsand woody
plants was not significant(Table 2).
E2. Seedlingrecruitment
occurredin all buttwo herb
populationsand in 17/21woodyplants(Table 1). The
importance of seedlings varied greatly between
herbs, reaching over 40% in the facultatively
semelparousperennialDigitalis purpureaand 94% in
the semelparousbiennial Linum catharticum.Digitalis purpureaalso had by farthe largestvalue of X
in the data set (11.815) whileLinumcatharticumoccupied fifthplace (k = 2.159). The importanceof
seedlingrecruitment
among woody plantswas highest in the heathlandshrubCalluna vulgaris (20%),
but 12 herbshad highervalues of E2 and the difference betweenthe two life formswas significant
(P <
0.01, Table 2). Calluna vulgarisalso had the highest
k among woody plants (2.995).
E3. Clonal growth was recorded in 25/45 herb
populationsand in 4/21woodyplants(Table 1, Table
2). Values were highestin Disporumsessile (0.2478)
and Allium monanthum(0.2395), two bulbiferous
woodland herbs,and Agropyronrepens (0.2302), a
persistentrhizomatousweed. The two woody plants
with the highestvalues of E3 were the dwarfarctic
shrubBetula nana and the shrubAlnus incana. No
seed or seedling recruitment
was recordedin either
species, but theirclonal growthelastictieswere only
0.1421 and 0.0615, respectively.Nine of the 25
clonal herbshad values of E3 > 0.14. Clonal growth
was not significantlydifferentbetween herbs and
woody plants (Table 2).
was sometimesdifficult
E4. Retrogression
to separate
from clonal growthin published matrices. It was
absentfromwoody plants,but definitely
occurredin
eleven herbs, including an orchid (Ophrys sphegodes) and five species in the Liliaceae (Allium
Chamaeliriumluteum,Disporumsessile,
monanthum,
D. smilacinum,Fritillaria meleagris).
E5. Stasis occurred in all species except Echium
vulgare, Linum catharticumand Picris hieracoides
which are all short-livedsemelparous perennials.
Values of E5 were particularly
high in woody plants,
reachinga value of one in the very long-livedtree
Sequoia sempervirens(Table 1). The differencebetweenherbsand woody plantswas highlysignificant
(Table 2).
E6. Progressionwas more importantthan seed or
in all species, with only two
seedling recruitment
exceptions:the short-lived,semelparous,biennial to
perennial herb Linum catharticum,and the orchid
Ophryssphegodes.In general,progressionwas more
importantin herbsthan woody plants (Table 2).
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
470
Comparative
plant
demography
Overall, growth(G) and fecundity(F) were significantlymore importantin herbs than woody plants
and the reversewas truefor survival(L) (Table 2).
1.51.0
a$
CORRELATION
BETWEEN
ELASTICITIES
OF
.~0.5
0
PARAMETERS
LIFE-CYCLE
Spearmanrank correlationswere calculated for the
whole data set (Table 3) and for herbs and woody
plants separately (Tables 4 and 5, respectively).
positivecorrelationbetween
There was a significant
the intrinsicrate of increase r and the elasticityof
fecundity(F, Table 3). This was especially strongin
woody plants(Table 5, Fig. 2), butthecorrelationin
herbs (Table 4) depended entirelyupon a single
outlierwitha high value of r. Seedling recruitment
fromthe seed pool (El)
(E2) ratherthanrecruitment
was responsible for this relationship.Significant
negative correlationsof similar strengthoccurred
between survival(L) and r and between stasis (E.)
and r for all threedata sets. Growthelasticity(G)
and r were positivelycorrelatedin woody plants (r
= 0.66, P < 0.0001, n =21), and in the sample as a
whole. Progression(E6) ratherthan clonal growth
(E3) was responsiblefor the correlationbetween r
and G, which was weaker than the correlationbetween r and E6 alone.
*
0.0
**
-0.5
-
-1.00.0
0.1
0.2
0.3
Fecundity
elasticity
Fig. 2 Relationshipbetweenthe intrinsicrate of population
increase (r) and the elasticityof fecundity(F) in woody
plants.
Seed recruitment(E1) was positively correlated
with seedling recruitment(E2), progression (E6),
and growth(G) and negativelycorrelatedwith survival (L) in the whole sample (Table 3). These
correlationswere weaker or not significantfor the
subsamples (Tables 4 and 5). Despite an overall
positive correlationbetweenE2 and G, the elasticity
of seedling recruitment
was significantly
negatively
correlatedwith the elasticityof the clonal compo-
Table 3 Spearmanrankordercorrelationmatrixforr (= In X), elasticitycomponentsEl - E6, fecundity(F = El + E2)9
survival(L = E4+ E5) and growth(G = E3+ E6) for66 species of herbsand woody plants.Values in italics are signifiP < 0.01. Except forcorrelationsinvolvingr, significancelevels were
cant P < 0.05, values in bold are significant
determinedby a randomizationtest.Pairwise sample sizes are shownin parentheses
r
0.22
El
E2 0.41
E3- 0.14
E 4 0.06
Es5- 0.55
ES6 0.43
F
0.51
L -0.53
G
0.39
El
(18)
(60)
(29)
(11)
(63)
(65)
(66)
(66)
(66)
E3
E2
0.55 (16)
- 0.75 (7)
(1)
- 0.63 (18)
0.70 (18)
0.72 (18)
-0.70 (18)
0.53 (18)
- 0.55 (26)
- 0.68 (11)
- 0.67 (57)
0.60 (60)
0.95 (60)
-0.76 (60)
0.45 (60)
Es
E4
- 0.20 (5)
- 0.15 (29)
0.07 (29)
-0.60 (29)
-0.12 (29)
0.46 (29)
- 0.21
0.02
-0.63
0.32
0.17
(11)
(11)
(11)
(11)
(11)
-0.95
-0.73
0.98
-0.94
E6
(62)
(63)
(63)
(63)
0.66 (65)
-0.89 (65)
0.94 (65)
F
L
-0.79 (66)
0.51 (66) -0.88 (66)
Table 4 Spearmanrankordercorrelationmatrixforr (= ln X), elasticitycomponentsE1- ES6,fecundity(F=E=+E2)9
P < 0.05, values in
survival(L = E4+E5) and growth(G = E3+E6) forherbsin the sample. Values in italics are significant
P < 0.01. Except forcorrelationsinvolvingr, significancelevels were determined
bold are significant
by a randomization
test.Pairwise sample sizes are shown in parentheses
r
0.11 (13)
El
ES2 0.26 (43)
ES3 - 0.03 (25)
E4 0.06 (11)
Es5 - 0.38 (42)
ES6 0.19 (45)
F
0.33 (45)
L - 0.38 (45)
0.16 (45)
G
E2
El
0.55 (12)
- 0.77 (6)
-
- 0.54
0.66
0.66
- 0.65
0.43
(1)
(13)
(13)
(13)
(13)
(13)
E3
- 0.55 (24)
-0.68
- 0.58
0.44
0.95
- 0.72
0.22
(11)
(40)
(43)
(43)
(43)
(43)
-0.20
- 0.22
0.12
-0.64
-0.18
0.54
(5)
(25)
(25)
(25)
(25)
(25)
- 0.21
0.02
-0.63
0.32
0.17
E6
Es5
E4
(11)
(11)
(11)
(11)
(11)
-0.91
-0.63
0.96
-0.85
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
(42)
(42)
(42)
(42)
0.49 (45)
- 0.79 (45)
0.89 (45)
F
L
- 0.74 (45)
0.24 (45)-0.75 (45)
471
J. Silvertown
et al.
(F = El + E2), survival
Table 5 Spearmanrankordercorrelationmatrixforr (= In X), elasticitycomponentsE, - E6, fecundity
P < 0.05, values in
(L = E4+ E5) and growth(G = E3+ E6) forwoodyplantsin the sample. Values in italics are significant
P < 0.01. Exceptforcorrelations
involvingr, significancelevels weredetermined
bold are significant
by a randomization
test.
Pairwise sample sizes are shownin parentheses
r
0.90
El
E2 0.88
E3 -0.80
Es5 -0.67
ES6 0.68
F
0.88
L - 0.67
G
0.66
El
(5)
(17)
(4)
(21)
(20)
(21)
(21)
(21)
E2
0.80 (4)
-(1)
-0.90 (5)
0.90 (5)
0.90 (5)
- 0.90 (5)
0.90 (5)
E3
-(2)
-0.90 (17)
0.90 (17)
1.00 (17)
- 0.90 (17)
0.90 (17)
0.20 (4)
- 0.40 (4)
- 0.95 (4)
0.20 (4)
- 0.20 (4)
-
1.00 (20)
(21)
1.00 (21)
1.00 (21)
-
w17
17
bt
19
9
1
17
X
0i4
0.6
0.4~~~~~~~~~~~~~~~~~~~~~~~4
0.8
0.2
1.0
0.8
0
0.2
0.4
0.6
L.
F
.0
G
10 0.4
1.0
1.0
0.8
20
1.0
/
04
3
0.4
-
0
0.2
L
0
0.22
0.8
0
0.6
0.4
0.6
(d)
.06
0.8
0.8
G
0
0.2
1.0
: .4
0
0.2
_
04
.-F
0.8
/
33\
31
4-F
(c)
6
27
0.2
1L0
0
3
38 428 1?47~~~~~~~~~~~35
%
\
- 1.00 (21)
0.2
0.8
0.2
0.6
- 0.66 (21)
0.64 (21)
G
1.0 0
(b)
0.8
F
E6
0.64 (20)
- 1.00 (20)
0.99 (20)
-0.66
G
1.0 0
(a)
F
Es
E4
0.2
0.
0.4
0.8
2504
0
0.6
1.5.
0.4
0.6
4
.6
4
F
62
04
F
02
5
36
of 66 perennialspecies in G-L-F space: (a) semelparousherbs,(b) iteroparousherbsof open habitats,(c)
Fig. 3 Distribution
iteroparousforestherbs,(d) woody plants.Species numberscorrespondto those in Table 1.
nentof growth(E3) in herbs (r = - 0.55, P < 0.05,
n = 24) and in the whole sample. The positive
relation between E2 and G was due to a strong
positive correlationbetween E2 and E6. E2 was
also negativelycorrelatedwith L and its componentsE4 and E5 althoughin herbsthe latterdid not
show significance.
The negative relationship between the
elasticities of sexual and clonal reproductionwas
manifestin a strong(P < 0.01) negativecorrelation
betweenfecundity(F = E1 + E2) and clonal growth
(E3) in both the whole sample and herbs,although
sample size was too small for woody plants
(P= 0.10, n= 4).
Retrogressionto previous stages (E4 ) had a
poor, non-significantcorrelationwith other variables. Woody plants did not have retrogression.
Stasis (E5) and progression (E6) were very
stronglynegativelycorrelatedwitheach other.Correlations between G, L and F are to be expected
because of the mathematicalconstraintreferredto,
but it is notable thatthe correlationbetweenfecundity and survival is a negative one while that
betweenfecundityand growthis positive (Table 3).
It is evident from the G-L-F triangularplots
thatmost populations had low fecundityelasticity
(Fig. 3). Nevertheless,the distributionof the 66
species is more or less continuous. Short-lived,
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
472
Comparative
plant
demography
semelparous herbs were distributedalong the G
axis (Fig. 3a). Although F varied from 0.07 for
Dipsacus sylvestristo 0.94 forLinum catharticum,
survivalelasticity(L) was always lower than0.33.
The high mortalityof seedlings and the absence of
a seed bank in Linum catharticummade it dependent on a high recruitmentrate. This species was
incorrectlyplaced along the L axis in a previous
paper (Silvertown,Franco & McConway 1992).
Iteroparous herbs of open habitats showed a
greatdeal more variationin the variables G, L and
F (Fig. 3b) but tendedto occupy the middleportion
of the trianglewith low to intermediatevalues for
F and L and intermediateG values. Five of them
(nos 9, 11, 26, 40 and 44), however, occurred
clumped near the L axis next to long lived trees
(see below). In particular,the high L value for
Ranunculus repens was due to seeds remainingin
the seed bank with a 'decay rate ... too slow to
detect...' (Sarukhan 1974). The otherfourplantsin
this group are characterisedby a bulbous (nos 9
and 11), stoloniferous(nos 26 and 40) or hummock-forming
(no. 44) habit.
Iteroparousforestherbswere scatteredalong the
survivorshipaxis fromL= 0.25 for Viola fimbriatula to L= 0.785 for Narcissus pseudonarcissus
(Fig. 3c). Plants in this group were characterized
by low-fecundityelasticity,the highestvalue being
F= 0.266 for Calathea ovandensis. Woody plants
tended to occupy the L cornerof the triangle(Fig.
3d). Their population growthrate depends heavily
on the survival of established adult individuals.
The four species in the lower range of survival
elasticityfor this group and which had highervalues of G and F (nos 51, 53, 55 and 60) are all small
shrubsof open, sometimesfire-pronehabitats.
Discussion
However ingeniouslydevised, a studythatattempts
to compare species thatrange fromSenecio to Sequoia is in danger of being somethingof a procrusteanexercise.How mightthishave affectedour
results? The dimensionalityof a matrix, or the
numberof stages into which a life cycle is divided,
will affectvalues of a,, and e... Althoughstatistical
rules of thumbhave been proposedto determinethe
appropriatedimensionalityof a projection matrix
(Vandermeer 1978; Moloney 1986), in practice it
has been a decisionbased on thebiologyof a species
(Caswell 1989). Even where we compiled matrices
ourselves, matrixdimensionalityin this studywas
largelydecided by the authorsof our data sources.
However,by aggregatingvalues of eJinto six components,each with a clear biological meaning,we
attemptedto iron out inaccuraciescaused by differing dimensionality.
Dimensionalityis importantin determiningthe
relativevalues of stasis and-progression.There was
a very strongnegative correlationbetween E5 and
E6, which is to be expected if these have a relativelyfixedsum. However, withinthe sum E5 + E6
the relative value of these variables in different
species may varyeitherforbiological reasons or as
an artifactof differingdimensionality.The more
dimensions in a matrix,the narrowerwill be the
limits which define each size class and the more
likely it is thatthe annual growthincrementof an
individual in a particularclass will take it out of
that size class at the next census. With increasing
dimensionalitythe diagonal matrixelementsaii will
become smaller and the subdiagonal elements
larger,causing an associated decrease in E5 and an
increase in E6. This artifactwill move individual
points in the G-L-F space to varyingdegrees. To
investigateits effectit is necessary to modifythe
dimensionalityof individual matrices and this in
turnrequires raw data on individual growthor at
least informationon the number of individual in
each stage class (stage distribution).This information was not usually available. Preliminaryanalyses
made by Enrightand Franco (unpublished) have,
however, shown thatfor long-lived woody species
dimensionalityeffectsare small withinthe range of
dimensionscommonlyused. An indicative test for
the occurrenceof this problemin our database may
be made. If the negativecorrelationbetweenE5 and
E6 is artifactualwe would expect a negative correlation betweenmatrixdimensionality(n) and E5. If
there is no such correlation,one can tentatively
attributesome biological significanceto the partitioning E5:E6. When treated separately, woody
plantsand herbsdid not show significantcorrelation
(Spearman) between E5 and n (herbs, S= - 0.06,
P = 0.720; woody plants, S = 0.02, P = 0.937).
However, when all species were lumped together,
the correlation was significant but positive
(S = 0.25, P < 0.05), i.e. given the range of values
for n in the dataset, long-lived woody plants have
high values of stasis. There may be a simple biological explantionof variationin E5 and E6. High
values of E5 are characteristicof woody plants and
high values of E6 are characteristicof herbs (Table
2). This makes intuitivesense and is confirmation
that our partitioningof elasticities has biological
meaningacross the fullrangeof plantlife historyin
our sample.
The distinctseparationof species into ecologically different
groups in G-L-F space (Fig. 3) provides a startingpoint to categorize patternsof demographyand life-historyin plants. Forest herbs
fall along the L-G axis; semelparous plants along
the F-G axis. Species lying along the L-G axis,
near the L = 1 vertex of the triangle,are mostly
(although not exclusively) woody plants of forest
habitats.Woody plants of open habitatslie towards
the centreof the trianglein the directionof the G
corner.Iteroparousherbs of open habitatare more
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
473
J. Silvertown
et al.
broadly scatteredbut this is to be expected given
the wide range of habitatstheyoccupy. Except for
the presenceof Linumcatharticum,the distribution
of our 66 perennialspecies in G-L-F space leaves
the region of the trianglewithF = 1 at its vertex
conspicuouslyempty.We would expect this region
to be occupied by annual species. With some exceptionsthen,ordinationin G-L-F space produces
a clear correspondencebetweenthe relativeimportance of the threemajor demographicparametersto
X and life formand habitat. This is an important
step towards linking a quantitativedescriptionof
life historywith the habitat templet (Southwood
1977, 1988).
The species in our study comprise both genet
populations(e.g. most of the trees) and rametpopulations (the clonal species). We have treatedthe
two kinds of population equivalently,although it
has been argued thata distinctionshould be made
between them because fitnessshould be measured
only at the level of the genet (Harper 1977). The
alternativeview is that ramet dynamics may be
used as an indirect measure of genet fitness
(Caswell 1985; de Kroon & van Groenendael1990;
Eriksson & Jerling1990), in which case the dominant eigenvalue, X, of a projectionmatrixmay be
used to measure fitnessin ramet as well as genet
populations. The validityof this approach is confirmedby our findingthat there is a correlation
between the elasticity of clonal growth and the
elasticity of fecundity in the demography of
ramets.
A negative correlationbetween elasticities implies a trade-offbetween the contributionsto
fitnessof the correspondingcomponentsof the life
cycle. However, it is importantto recognize that
this need not imply a precisely parallel trade-off
between the phenotypicvalues of two traits.It is
easiest to see the reason for this with an example.
Digitalis purpurea is a species thatproduces large
numbersof small seeds which can lie dormantfor
a long time in the seed pool. Only a small proportion of these seeds ever become seedlings (0.15%
per year), so one mightconclude, on the basis of
the numericalallocation of seeds betweendormant/
nondormantphenotypes,thatseed dormancymakes
a largercontributionto fitness(or is 'more important') in D. purpurea than in a species such as as
Ranunculus bulbosus with a smaller fractionof
dormantseed (45% germinationper year). In fact
this is incorrectand the elasticityforthe seed pool
(E1) is much greaterin R. bulbosus (0.2219) than
in D. purpurea (0.0397) (Table 1). The reason for
thisis simplythatdormantseeds make no contribution to fitnessunless they germinate,so the value
of a seed in the seed pool cannot be evaluated
withouttaking into account the germinationrate
and the restof the life cycle as well. In fact,this is
exactly what elasticitydoes (de Kroon, Plaiser &
van Groenendael 1987). It might be argued that
trade-offsbetween life-historytraits are better
measured by correlationsbetween elasticityvalues
than by correlations between trait values themselves, because the consequences for fitnesscan be
more directlyinterpretedin the former.
The literatureon the functionand evolutionary
significanceof clonal growthin plants has concentratedon its advantages,and on the costs and benefitsof clonal integrationwithlittleattentionto the
potential costs of clonality itself. It has been assumed thatthe evolutionof clonal growthis limited
by the long-termdisadvantagesthatare assumed to
operateagainst asexual reproductionin general,but
a short-termtrade-offbetween clonal growthand
sexual reproductionmust also occur. The negative
correlationbetween clonal growth elasticity (E3)
and fecundityelasticity (F) within the group of
clonal plants (Table 3) stronglysuggeststhatthere
is a trade-offbetweenthe contributions
to fitnessof
these two modes of reproduction.Furthermore,
therewas no correlationwhatsoeverbetween r and
E3, so thereis no evidence here eitherthat clonal
growthconfersan absolute fitnessadvantage.
The relativeimportanceof life-cycleparameters
to X is expected to vary with the value of X
(e.g.Caswell 1982), and the correlationswe found
between r (= ln X) and various elasticities confirm
this (Tables 3 and 4). The strongestcorrelationwas
between X and the value of F among woody plants
(Fig. 2). Using sensitivity analysis of model
populations Caswell (1982) found thatthe relative
importanceof fecundityincreased as X decreased,
whereas we found the reverse patternfor actual
populations.
The matricesused in this studywere stationary
ones, and thereforethe elasticities derived from
them project the relative contributionsof life historycomponentsto fitnessin an environmentthat
does not vary withtime and in which X is constant.
This may have a variety of effects. For species
which recruitonly infrequently,
our matricesmay
not portraythe full importanceof fecundityor a
seed pool to population dynamics.The importance
of a seed pool to fitness(E1) is very likely to be
because selection operates strongly
underestimated,
in favour of this characterwhen X varies (Cohen
1966; Silvertown1988; Venable 1990). The effects
of environmentalvariationcan be incorporatedin a
matrix approach to life history evolution (e.g.
Tuljapurkar1990).
This paper is only the firststep towardsa comparative demographyof plants. We have demonstrated that the approach can reveal meaningful
relationships between life history variables, between life historyand life form and between life
historyand habitat,but there is still much to do.
With a sample containingmore species it would be
possible to look for the influence of taxonomic
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
474
Comparative
plant
demography
constraintson demographicpatterns.We are also
acutely aware that demographic parameters for
most species varygreatlyin timeand in space, and
future studies should attemptto compare intraspecific patterns with interspecificones. Future
papers will look at this and othertopics in comparative plant demographyusing our dataset.
Acknowledgements
We are grateful to the British Council and
CONACyT, Mexico, for financial support. We
thank Ruben Perez-Ishiwara for technical assistance, Elena Alvarez-Buyllaforallowing us the use
of hermatrixanalysisprogram,J.BastowWilson for
the randomizationtests and James Bullock, Neal
Enright,Mike Gillman,Jan van Groenendael,Paul
Harvey,Irene Ridge, Tere Valverde and J. Bastow
Wilson forvaluable commentson the manuscript.
References
Angevine,M.W. (1983) Variationsin the demographyof
naturalpopulationsof the wild strawberries
Fragaria
vesca and F.virginiana.Journalof Ecology, 71, 959974.
van Baalen, J. & Prins,E.G.M. (1983) Growthand reproduction of Digitalis purpurea in differentstages of
succession.Oecologia, 58, 84-91
van Baalen, J. (1982) Germination
ecology and seed population dynamicsof Digitalis purpurea Oecologia 53,
61-67
Barkham,J.P. (1980) Population dynamics of the wild
daffodil(Narcissuspseudonarcissus).II. Clonal growth,
seed reproduction,
mortalityand the effectof density.
Journalof Ecology, 68, 607-633.
Bierzychudek,
P. (1982a) Life historiesand demography
of
shade-tolerant
temperateforestherbs: a review. New
Phytologist,90, 757-776.
Bierzychudek,P. (1982b) The demographyof Jack-in-the
pulpit,a forestperennialthatchanges sex. Ecological
Monographs,52, 335-351.
Boorman, L.A. & Fuller, R.M. (1986) The comparative
ecology of two sand dune biennials:Lactuca virosa L.
and CynoglossumofficinaleL. New Phytologist,69,
609-629.
Boutin,C. & Harper,J.L. (1991) A comparativestudyof
the populationdynamicsof fivespecies of Veronicain
naturalhabitats.Journalof Ecology, 79, 199-221.
Bradstock,R.A. & O'Connell, M.A. (1988) Demographyof
woody plantsin relationto fire:Banksia ericifoliaL.F.
and Petrophilepulchella (Schrad) R. Br. Australian
Journalof Ecology, 13, 505-518.
Bullock, S.H. (1980) Demographyof an undergrowth
palm
in littoralCameroon.Biotropica,12, 247-255.
Bums, B.R. & Ogden, J. (1985) The demographyof the
temperatemangrove(Avicenniamarina (Forsk.)Vierh.)
at it's southernlimitin New Zealand. AustralianJournal of Ecology, 10, 125-133.
Caswell, H. (1982) Life historytheoryand the equilibrium
statusof populations.AmericanNaturalist,120, 317339.
Caswell, H. (1985). The evolutionary
of clonal
demography
reproduction.Population Biology and Evolution of
Clonal Organisms,pp. 187-224. New Haven, Yale UniversityPress.
Caswell, H. (1986) Life cycle models forplants.Lectureson
Mathematicsin theLife Sciences, 18, 171-233.
Caswell, H. (1989) MatrixPopulationModels: Construction,
Analysis,and Interpretation.
SinauerAssociates,Sunderland, Mass.
Chapman,S.B., Rose, R.J.& Clarke,R.T. (1989) The behaviour of populations of the marsh gentian (Gentiana
pneumonanthe):a modellingapproach. Journal of Applied Ecology, 26, 1059-1072.
of northern
Charron,D. & Gagnon,D. 1991 The demography
populationsof Panax quinquefolium(Americanginseng)
Journalof Ecology, 79, 431-445.
Ebert,T.A. & Ebert, C.A. (1989) A methodfor studying
vegetationdynamicswhenthereare no obvious individuals: Virtual-populationanalysis applied to the tundra
shrubBetula nana L. Vegetatio,85, 33-44.
Enright,N. & Ogden, J. (1979) Applicationsof transition
matrixmodels in forestdynamics:Araucaria in Papua
New Guinea and Nothofagusin New Zealand. Australian
Journalof Ecology, 4, 3-23.
N.J.& Watson,A.D. (1992) Populationdynamicsof
Enright,
the nikaupalm,Rhopalostylissapida (Wendl. et Drude),
in a temperateforestrainforest
remnantnear Auckland,
New Zealand. New Zealand Journalof Botany,30, 2943.
Enright,N.J. (1982) The ecology of Araucaria species in
New Guinea. III. Populationdynamicsof sample stands.
AustralianJournalof Ecology, 7, 227-237.
Eriksson,0. (1986) Survivorship
and dynamics
reproduction
of rametsof Potentilla anserina on a Baltic seashore
meadow. Vegetatio,67, 17-25.
Eriksson,0. (1988) Rametbehaviourand populationgrowth
in the clonal herbPotentillaanserina. Journalof Ecology, 76, 522-536.
Eriksson,0. & Jerling,L. (1990) Hierarchicalselectionand
risk spreadingin clonal plants.Clonal growthin plants.
(eds J.van Groenendael& H. de Kroon),pp. 79-94. SPB
Academic Publishing,The Hague.
Farah,K.O., Tanaka, A.F. & West,N.E. (1988) Autecology
and populationbiology of dyerswoad (Isatis tinctoria).
Weed Science, 36, 186-193.
Fiedler,P.L. (1987) Life historyand populationdynamicsof
rare and common mariposa lillies (Calochortus Pursh:
Liliaceae). Journalof Ecology, 75, 977-995.
Fone, A.L. (1989) A comparativedemographicstudy of
annual and perennial species of Hypochoeris (Asteraceae). Journalof Ecology, 77, 495-508.
Forbes,J.C. (1977) Populationfluxand mortalityin a ragwort(Senecio jacobaea L.) infestation.Weed Research,
17, 387-391.
Franco,M. & Silvertown,J. (1990) Plantdemography:
What
do we know?EvolutionaryTrendsin Plants, 4, 74-76.
Goodman, L.A. (1969) The analysis of populationgrowth
whenthebirthratesand deathratesdependupon several
factors.Biometrica,25, 659-681.
Grime, J. P. (1977) Evidence for the existence of three
primarystrategiesin plantsand its relevanceto ecological and evolutionarytheory.AmericanNaturalist,111,
1169-1194.
Grime,J.P., Hodgson,J.G. & Hunt,R. (1988) Comparative
Plant Ecology. Unwin Hyman,London.
van Groenendael,J. & de Kroon,H. (1990) Clonal Growth
in Plants: Regulationand Function.SPB AcademicPublishing,The Hague.
van Groenendael,J.M. & Slim., P. (1988) The contrasting
dynamicsof twopopulationsof Plantago lanceolata classifiedby age and size. Journalof Ecology, 76, 585.
Harcombe,P. (1987) Tree life tables. Bioscience, 37, 557568.
Harper,J.L. (1977) PopulationBiology ofPlants. Academic
Press, London.
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
475
J. Silvertown
et al.
Hartshorn,G.S. (1975) A matrixmodel of tree population
dynamics.TropicalEcological Systems(ed. F.B. Golley
New York.
& E. Medina), pp. 41-51. Springer-Verlag,
Harvey, P.H. & Pagel, M.D. (1991) The Comparative
Method in EvolutionaryBiology. Oxford University
Press, Oxford.
Hegazy, A.K. (1990) Populationecology and implications
for conservationof Cleome droserifolia:a threatened
19, 269-282.
xerophyte.Journalof Arid Environments,
Horvitz,C.C. & Schemske,D.W. (1986) Seed dispersaland
environmentalheterogenietyin a neotropicalherb: a
model of populationand patch dynamics.Frugivores
and Seed Dispersal (eds A. Estrada& T.H. Fleming),pp.
170-186. Dr W. Junk,Dordrecht.
Hu, Y.J. & Wang,S.S. (1988) A matrixmodelof population
growthof dominanttropicalrain forestspecies Vatica
hainanensisin Hainan Island. Acta Ecologica Sinica, 8,
104-110.
Hubbell, S.P. & Werner,P.A. (1979) On measuringthe
intrinsicrateof increaseof populationswithheterogeneous life histories.AmericanNaturalist,113, 277-293.
Huenneke,L.F. &. Marks,P.L (1987) Stemdynamicsof the
shrubAlnus incana ssp. rugosa: transitionmatrixmodels. Ecology, 68, 1234-1242.
Hutchings,M. J. & Bradbury,I. K. (1986) Some ecological
perspectiveson clonal perennialherbs.Bioscience, 36,
178-182.
of temperate
Kawano, S. (1985) Life historycharacteristics
woodland plants in Japan.The Population Structureof
Vegetation(ed. J.White),pp. 515-549. Dr W. Junk,
Dordrecht.
Kawano, S., Takada, T., Nakayama, S. & Hiratsuka,A.
and lifehistoryevo(1987) Demographicdifferentiation
Patlutionin temperatewoodlandplants.Differentiation
ternsin higherplants (ed. K.M. Urbanska),pp. 153-181.
Academic Press,London.
Kinoshita,E. (1987) Sex changeand populationdynamicsin
Arisaema (Araceae) I. Arisaema serratum (Thunb.)
Schott.Plant Species Biology,2, 15-28.
Klemow, K.M. & Raynal,D.J. (1985) Demographyof two
facultativebiennial plant species in an unproductive
habitatJournalof Ecology, 73, 147-167
de Kroon,H., Plaiser,A., van Groenendael,J.M.& Caswell,
of demoH. (1986) Elasticity:the relativecontribution
graphicparametersto populationgrowthrate.Ecology,
67, 1427-1431.
de Kroon,H., Plaiser,A., & van Groenendael,J.M. (1987)
simulationof the populationdynamDensity-dependent
ics of a perennial grassland species, Hypochaeris
radicata. Oikos, 50, 3-12.
Law, R. (1983) A model for the dynamics of a plant
populationcontainingindividualsclassifiedby age and
size. Ecology, 64, 224-230.
A. (1984) Demographic
Lefevbre,C.& Chandler-Mortimer,
characteristics
of the perennialherbArmeriamaritima
on zinc-lead mine wastes. Journalof Applied Ecology,
21, 255-264.
Lefkovitch,L.P. (1965) The studyof populationgrowthin
organismsgroupedby stages.Biometrics,21, 1-18.
Leslie, P.H. (1945) On the use of matricesin certainpopulationmathematics.
Biometrika,33, 183-212.
noteson the use of matriLeslie, P.H. (1948) Some further
ces in certainpopulationmathematics.Biometrika,35,
213-245.
Mallik,A.U., Hobbs, R.J.& Legg, C.J. (1984) Seed dynamheath in north-eastern
ics in Calluna-Arctostaphylos
Scotland.Journalof Ecology, 72, 855-871.
Manly,B.F.J.(1991) Randomizationand MonteCarlo methods in biology.Chapman& Hall, London.
Meagher,T.R. (1982) The populationbiology of Chamaeliriumluteum,a dioecious memberof the lily family:
Two-sex populationprojectionsand stable population
structure.
Ecology, 63, 1701-1711.
Menges. E.S. (1990) Population viabilityanalysis for an
endangeredplant.ConservationBiology,4, 52-62
Moloney, K.A. (1986) A generalizedalgorithimfor determiningcategorysize. Oecologia, 69, 176-180.
Moloney,K.A. (1988) Fine-scale spatialand temporalvariation in the demographyof a perennial bunchgrass.
Ecology, 69, 1588-1598.
Mortimer,A.M. (1984) Populationecology and weed science Perspectiveson plant population ecology (eds R.
Dirzo & J. Sarukhan),pp.363-388. Sinauer,Sunderland,
Mass.
Namkoong,G.& Roberds,J.H. (1974) Extinctionprobabiliof redwoodforests
ties and the changingage structure
AmericanNaturalist,108, 355-368
Newell, S.J., Solbrig,O.T. & Kincaid, D.T. (1981) Studies
on the populationbiology of the genus Viola. III. The
demographyof Viola blanda and Viola pallens. Journal
of Ecology, 69, 997-1016.
Pavlick,B.M. & Barbour,M.G. (1988) Demographicmonitoringof endemic sand dune plants, Eureka Valley,
California.Biological Conservation,46, 217-242.
Pinard, M. (1993) Impacts of stem harvesting on
populationsof Iriartea deltoidea (Palmae) in an extractive reservein Acre, Brazil. Biotropica,25, 2-14.
M. & Sarukhan,J. (1984) A
Piniero,D., Martfnez-Ramos,
mexicanumand a senpopulationmodel of Astrocaryum
sitivityanalysisof its finiterate of increase.Journalof
Ecology, 72, 977-991.
Pitelka,L.F., Hansen,S.B. & Ashmun,J.W.(1985) Population biology of Clintonia borealis I. Ramet and patch
dynamics.Journalof Ecology, 73, 169-183
Platt,W.J.,Evans, G.W & Rathburn,S.L (1988) The populationdynamicsof a long-livedconifer(Pinuspalustris).
AmericanNaturalist,131, 491-525.
Rust,R.W. & Roth,R.R. (1981) Seed productionand seedling establishmentin the mayapple PodophyllumpeltatumL. AmericanMidland Naturalist,105, 51-60.
RanuncuSarukhan,J. (1974) Studieson plantdemography:
lus repensL., R.bulbosusL. and R.acris L. II. Reproductive strategiesand seed populationdynamics.Journalof
Ecology, 62, 151-177.
Sarukhan,J. & Harper,J.L. (1973) Studieson plantdemography:RanunculusrepensL., R.bulbosusL. and R.acris
L. I. Populationfluxand survivorship.
Journalof Ecology, 61, 675-716.
Scandrett,F. & Gimingham,C.H. (1989) A model of
Calluna populationdynamics;theeffectsof varyingseed
and vegetativeregeneration.
Vegetatio,84, 143-152.
Schaffer,W.M. & Schaffer,M.D. (1977) The adaptivesignificance of variations in reproductivehabit in the
Agavaceae. EvolutionaryEcology (eds B. Stonehouse&
C.M. Perrins),pp. 261-276. Macmillan,London.
Silander,J.A.,Jr(1983) Demographicvariationin the AustraliandesertCassia undergrazingpressure.Oecologia,
60, 227-233.
J.(1987) Introduction
to Plant PopulationEcolSilvertown,
ogy. LongmanScientific& Technical,Harlow,Essex.
Silvertown,J. (1988) The demographicand evolutionary
consequencesof seed dormancy.Plant PopulationEcology (eds A.J.Davy, M.J.Hutchings& A.R. Watkinson),
pp. 205-219. Blackwell ScientificPublications,Oxford.
Silvertown,J., Franco, M. & McConway, K. (1992) A
of Grime's triangle.Funcdemographicinterpretation
tional Ecology, 6, 130-136
Sohn, J.J.& Policansky,D. (1977) The costs of reproduction in the mayapplePodophyllumpeltatum(Berberidaceae). Ecology, 58, 1366-1374.
Soibrig,O.T., Sarandon,R. & Bossert,W. (1988) A densitydependentgrowthmodel of a perennial herb, Viola
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions
476
Comparative
plant
demography
fimbriatula.
AmericanNaturalist,137, 385-400.
Somarriba,E. (1988) Guava (Psidiumguajaya L.) treesin a
pasture:Populationmodel,sensitivity
analyses,and applications.Agroforestry
Systems,6, 3-17.
Southwood,T.R.E. (1977) Habitat,the templetforecological strategies?
JournalofAnimalEcology,46, 337-365.
Southwood,T.R.E. (1988) Tactics, strategiesand templets.
Oikos, 52, 3-18.
Steenbergh,W.F. & Lowe, C.H. (1977) Ecology of the
saguaro: II Reproduction,germination,establishment,
growthand survivalof the youngplant. National Park
Service ScientificMonographSeries. No.8. Washington
DC, US Government
PrintingOffice.
Sterk, A.A. (1975) Demographic studies of Anthyllis
vulnerariaL. in the Netherlands.Acta Botanica Neerlandica, 24, 315-337
Sterk,A.A., Duijkeren,A. van, Hogervorst,J. & Verbeek,
E.D.M. (1982) Demographicstudies of Anthyllisvulneraria L. in the Netherlands.II. Population density
fluctuationsand adaptationsto arid conditions,seed
and the influenceof the
populations,seedlingmortality,
biocenosis on demographicfeatures.Acta Botanica
Neerlandica,31, 11-40
Thomas,A.G. & H.M.Dale (1975) The role of seed reproductionin the dynamicsof establishedpopulationsof
Hieraciumfloribundum
and a comparisonwiththatof
vegetativereproduction.Canadian Journal of Botany,
53, 3022-3031
Tuljapurkar,S. (1990). Delayed reproduction
and fitnessin
variable environments.Proceedings of the National
Academyof Sciences of the USA, 87, 1139-1143.
Turkington,
R. & Aarsen,L.W. 1983. Hypochoerisradicata
L. Biological Flora of the BritishIsles. Journalof Ecology,71, 999-1022.
Venable,D. (1985) The evolutionary
ecologyof seed heteromorphism.AmericanNaturalist,126, 577-595.
Verkaar,H.J. & Schenkeveld,A.J. (1984) On theecologyof
short-lived
forbsin chalkgrasslands:Life-history
characteristics.New Phytologist,
98, 659-672.
Waite,S. & Hutchings,M. J. (1991) The effectsof different
managementregimes on the population dynamics of
Ophryssphegodes:analysisand descriptionusingmatrix
models. Population Ecology of TerrestrialOrchids (eds
T.C.E. Wells & J.Willems),pp. 161-175. SPB Academic
Publishing,The Hague.
Waite,S.J.(1984) Changes in the demographyof Plantago
coronopusat two coastal sites. Journalof Ecology, 72,
809-826
Widen,B. (1987) Populationbiologyof Senecio integrifolius
(Compositae),a rareplantin Sweden. NordicJournalof
Botany,7, 687-704.
Young, T.P. (1990) Evolution of semelparityin Mount
Kenya lobelias. EvolutionaryEcology, 4, 157-171.
Zhang,L. (1983) Vegetationecologyand populationbiology
of Fritillaria meleagris L. at the KungsangenNature
Reserve, Eastern Sweden. Acta Phytogeographica
Suecica, 73, 1-96.
Received30 August1992;
revisedversionaccepted 8 December 1992
This content downloaded on Wed, 6 Mar 2013 15:13:19 PM
All use subject to JSTOR Terms and Conditions