Population demographics and trade-offs to reproduction of an invasive and

noninvasive species of Rubus

Susan C. Lambrecht-McDowell1,3,* & Steve R. Radosevich21Environmental Sciences Program, Oregon State University, 321 Richardson Hall, Corvallis, OR 97331,USA; 2Department of Forest Science, Oregon State University, Corvallis, OR 97331, USA; 3Currentaddress: Department of Biological Sciences, San Jose State University, San Jose, CA 95192-0100, USA;*Author for correspondence (e-mail: slambrec@email.sjsu.edu; fax: +1-408-924-4840)

Received 2 January 2004; accepted 18 February 2004

Key words: density, elasticity, exotic, invasion, matrix model, non-native, Rubus

Abstract

Do trade-offs between growth and reproduction differ between an invasive and noninvasive plant speciesand how do such trade-offs relate to population demographics? To help address these questions, wecompared demographics for an invasive plant species, Rubus discolor, with a noninvasive congener, R.ursinus, in several populations of varying density. Removal of floral buds from reproductive canesincreased the size of juvenile canes that arose from clonal sprouting in R. ursinus, suggesting a trade-offbetween current reproduction and growth. Removal of floral buds had no effect on growth of R. dis-color. R. ursinus displayed trade-offs between reproduction (sexual and vegetative) and future growthbased on negative correlations between leaf area production and both clonal sprouting and seedling pro-duction during the previous year. R. discolor did not exhibit these trade-offs. Both species had high pop-ulation growth rates in low-density populations, but exhibited little or no growth in high-densitypopulations. A life table response experiment was used to determine the underlying cause for the effectof density on population growth. For R. ursinus, lack of population growth in high-density populationswas due primarily to increased mortality of clonally sprouting canes, while for R. discolor, it was due todecreased clonal cane production. Elasticity analysis revealed that clonal growth was more importantthan sexual reproduction for population growth of both species. However, elasticity values for sexualreproduction in R. discolor were greater in high- than low-density populations. This suggests anincreased reliance on sexual reproduction in populations that had reached stable sizes, which couldincrease the capacity of R. discolor to disperse to new sites. Elasticity analyses were also used to simulatethe efficacy of various control strategies for R. discolor. Control of this species could be attained byreducing clonal production within existing populations while reducing seed production to limit establish-ment of new populations.

Introduction

Invasiveness in plant species has been correlatedwith the ability to reproduce abundantly andgrow rapidly. Reproductive traits, such as thecapacity for both sexual and vegetative reproduc-

tion, an ability to self-fertilize, a lack of seed dor-mancy, and multi-seeded fruit, have been relatedto invasiveness because they confer the capacityto rapidly colonize a site, which is the first stageof the invasion process (Baker 1965; Bazzaz1986; Reichard and Hamilton 1997; Daehler

Biological Invasions (2005) 7: 281–295 � Springer 2005

1998; Sakai et al. 2001). Fast growth rates reflectrapid acquisition and allocation of resources,which enable a species to swiftly establish a pop-ulation following colonization. While life-historytheory predicts a trade-off between high repro-duction and growth rates (Stearns 1992), researchexamining growth, competitive ability, and repro-duction in purple loosestrife (Lythrum salicaria),a noxious wetland invader, suggests that not allinvasive plant species are subject to such trade-offs (Keddy et al. 1994). There is relatively littledirect experimental evidence or observationaldata examining the life-history trade-offs ofreproduction in invasive plant species.

The trade-offs between reproduction andgrowth are due to competition for limitedresources within an individual (Stearns 1992).The mechanisms underlying these trade-offs arephysiological, where reproductive effort may beexpressed as the amount of resources (e.g., car-bon) allocated to reproduction at the expense ofother functions (Geber 1990; Fox and Stevens1991; Stearns 1992). The consequences of alloca-tion to reproduction, along with the constraintsimposed by resource availability, are expressed atthe demographic level and are called the long-term or demographic costs of reproduction (Foxand Stevens 1991; Nicotra 1999). It is at this levelthat the costs of reproduction may be observedas a decrease of growth or increase of mortalityassociated with increased reproduction. The bal-ance among these demographic trade-offs ofreproduction ultimately determines the popula-tion growth rate for a species.

Theory predicts that high allocation ofresources to reproduction confers a competitiveadvantage during site colonization, but that allo-cation of resources should shift to vegetativegrowth after colonization to facilitate populationestablishment (Sakai et al. 2001). Thus, density-dependent shifts in resource allocation betweensexual reproduction and vegetative growth maybe expected. However, relatively little is knownabout density effects on population growth ratesof invasive plant species or how these effectscompare with those found in native species(Parker 2000). Even less is known about the spe-cific life-history factors that contribute to popula-tion growth at different densities as an invasionprogresses.

Demographic matrix analysis can be used toassess population growth and the factors that con-tribute to it and may have valuable managementapplications. For example, they can be used toidentify the most important life-history stage orprocess to the population growth of a species,information which can be used to guide decisionswith the objective of sustaining or increasing thepopulation size of rare species (e.g., Charron andGagnon 1991; Maschinski et al. 1997; Kaye et al.2001) or to target and decrease the population sizeof invasive species (e.g., Maxwell et al. 1988; Sheaand Kelly 1998; McEvoy and Coombs 1999; Par-ker 2000). A further application of demographicanalyses to invasive plant study is they can pro-vide valuable, but often ignored, insights into theconnection between theories of plant invasionsand quantitative field data, such as determiningwhether population growth remains constantthroughout the stages of invasion (Parker 2000).

The native, noninvasive R. ursinus Cham. andSchlect. (trailing blackberry) and the invasiveR. discolor Weihe and Nees (also R. procerus;Himalayan blackberry) are members of thesame sub-genus (Rubus), share many life-historycharacteristics, and often grow together in thesame sites in the Pacific Northwest UnitedStates (PNW). A recent study compared thereproductive effort between these species (McDo-well and Turner 2002). Reproduction in the non-invasive species was associated with decreasedleaf water status, causing early stomatal closure,and with decreased leaf nitrogen concentration,contributing to lower photosynthetic capacity.However, these physiological costs of reproduc-tion were not observed in the invasive Rubus.The objective of the current study is to examinethe implications of these physiological costsat the plant and population scales. We usedstage-based demographic models and field experi-ments and observations to address the follow-ing questions: (1) What are the demographictrade-offs between reproduction and growth andhow do they differ between an invasive speciesand a noninvasive congener? (2) How do thesetrade-offs affect the population demographics ofthese two species? and 3) How do populationdemographics influence invasiveness and poten-tial control strategies of R. discolor, the invasivespecies?

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Materials and methods

Study species

Rubus ursinus is native to the PNW. Its canestypically grow to about 3 m in length and pro-duce approximately 25 fruit per cane in a year(McDowell and Turner 2002). R. ursinus is con-sidered noninvasive in its native range, where thisstudy took place. R. discolor was first introducedto the PNW from Europe via India for fruit pro-duction (Kent 1988) and is considered an inva-sive plant species outside of its native rangebecause it can grow, reproduce, and proliferatefollowing introduction. Canes of R. discolor cangrow to 10 m in length and produce over 700fruit in a year (McDowell and Turner 2002).

Rubus ursinus and R. discolor share severalmorphological and ecological characteristics.They grow together in open to moderately shadysites at low- (sea-level) to mid- (~2000 m) eleva-tions in the PNW. Both species are described asbiennial/perennial, indicating that roots areperennial while above-ground canes live for twoyears. However, canes arising from seeds actuallydevelop for three years. Seeds germinate in thewinter or early spring and plants remain in aseedling stage for approximately one year. In thefollowing year, canes remain vegetative whilenearly all elongation occurs. In the spring of thethird season, the canes shed their leaves anddevelop lateral reproductive shoots. The entirecane senesces following reproduction. Both spe-cies have perennial rhizomes (below-groundstems) that can produce and simultaneously sup-port several clonally sprouted canes that emergeand grow as vegetative canes for one year andreproduce in the following year. Therefore, incontrast to the canes that arise from seeds, thecanes that arise clonally develop for only twoyears, but in both cases, the roots may be peren-nial. An additional form of clonal spread thatmay occur in both species, as in several other Ru-bus species, arises when the tip of a cane roots inthe soil, forming a new perennial root crown(Heslop-Harrison 1959). As with other species ofRubus, clonal spread from above-ground andbelow-ground structures may be very importantto the population growth of both of these species(Heslop-Harrison 1959; Baret et al. 2003)

Study site

All research was conducted within the McDon-ald-Dunn Research Forest near Corvallis, OR(44�40¢ N, 123�20¢ W, ~350 m elevation) whichreceives approximately 300 cm of rain annually,as measured at a nearby (~5 km) meteorologicalstation (Oregon Climate Service). In 1999, plotswere established around existing populations ofeach species in a recent clearcut for demographicmonitoring. Populations were selected to repre-sent either early population colonization (pre-sumed based on low density of the target species)or established populations (high density of thetarget species). Therefore, low-density popula-tions for both species were selected to haveapproximately 6–12 canes each while high-densitypopulations had approximately 45–55 canes each.To control for the same number of individualsper population between the species, plot sizes forR. discolor were larger than for R. ursinusbecause R. discolor canes are approximately twiceas large. Eight high- and low-density 5 · 5 mplots were established for R. discolor and sixhigh- and low-density 2 · 2 m plots were estab-lished for R. ursinus. Fewer populations wereselected for R. ursinus because there were fewerpopulations available of the appropriate densi-ties. In 2001, six additional plots were establishedaround populations of varying densities of eachspecies to be used for an experiment manipulat-ing sexual reproduction. All populations werelocated within 0.5 km of each other in a largeclearcut, with similar levels of irradiance andpotential access to equivalent resources.

Field and laboratory methods

We conducted one census of each population infall 1999. Two censuses of each population wereconducted per year in 2000 and 2001. At thosetimes, one census was done in the spring, beforegrowth of surrounding vegetation obscured theseedlings, and another was done in the fall, aftermost mortality of seedlings and canes occurred.In our initial census (1999), all canes were num-bered and tagged, and their position within eachplot was mapped. In subsequent censuses, wetagged and mapped new canes and recorded themortality of previously identified canes.

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During a census, canes were classified into oneof four stages based on Rubus life-history. Thesestages were seedling, canes, canev, or reproductivecanes (Figure 1). In this study, canes were definedas vegetative canes that had developed from seed-lings, while canev were vegetative canes that arosefrom either rhizome sprouting or tip-rooting ofreproductive canes. Reproductive canes developedfrom both canes and canev and had the potentialto produce both fruit and vegetative sprouts(canev). In the first census, canes and canev weredistinguished by their position relative to living orsenesced reproductive canes. Our ability to makethis distinction was validated by examining rootconnections in neighboring populations not usedin the study. In all subsequent censuses, canes andcanev were easily distinguished because all seed-lings were identified and labeled in a previouscensus. Over the course of this study, we followedthe fate of approximately 600 canes of each spe-cies. The nonparametric Kruskal–Wallis (KW)procedure was used to test for differences betweenthe demographic parameters, such as productionand survival rates of each life-history stage, forboth species at each density.

In spring 2001, floral buds were removed fromsix entire populations of each species to determinethe effects of current reproduction on currentgrowth. Prior to bud removal, average cane lengthwas measured to assess the degree of similaritybetween these six treatment and six control popu-lations. The control populations were randomlyselected from those used in the demographic analy-ses (three each from low- and high-density). Dueto the length and the arching, sprawling growth

form of Rubus canes, total cane length could beaccurately measured only by harvesting canes.Therefore, we removed three senesced reproductivecanes from each of the plots, which would notlikely affect the growth or survival of plantsremaining in the population. Average cane lengthper population was not significantly differentbetween control and treatment populations (Wilco-xon Signed Ranks Z ¼ 0.280, P ¼ 0.778 for low-density and Z ¼ 0.294, P ¼ 0.768 for high-densityR. ursinus; and Wilcoxon Signed Ranks Z ¼ 0.643,P ¼ 0.530 for low-density and Z ¼ 0.472,P ¼ 0.647 for high-density R. discolor) and, there-fore, the populations were considered similar priorto the floral manipulation. To test for the effect offloral bud removal on growth of canev, three ran-domly selected canev were removed from each ofthe control and manipulated populations in thefall. Total cane length of each canev was measuredin the field. Then, all leaves from each canev wereharvested, brought to the lab, and kept in coldstorage. Within ~48 h of harvesting, leaf area of allfoliage was determined using a video image recor-der and AgVision software (Decagon Devices, Pull-man, Washington). Three leaves per canev wererandomly selected, placed in a 65 �C oven for 48 h,and then weighed to the nearest 0.01 g. Specific leafarea (SLA; leaf area per unit leaf mass) was calcu-lated from these data. The non-parametric wilco-xon signed ranks (WSR) test was used to examinethe difference between growth parameters of fruit-removal and control populations because thesedata did not meet the assumptions for a parametricanalysis. Demographic and cane size parameters ofcontrol populations were used in a Pearson correla-

Figure 1. A conceptual transition matrix for R. ursinus and R. discolor showing possible transitions from one year (t) to the next

(t + 1). The dark shaded rectangles indicate the transitions (aij) associated with continuance in the same stage from one period to

the next, stippled rectangles indicate aij associated with cane production and development arising from vegetative sprouting (canev),

and hatched rectangles indicate aij associated with sexual reproduction and growth of canes originating from seeds (canes). Transi-

tions without shading were not observed.

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tion matrix to examine life-history trade-offsbetween years.

Demographic analyses

The observations made during our field censuseswere used to construct stage-based transitionmatrices with a time interval of one year usingthe four life-history stages previously describedfor the Rubus species. Separate transition matri-ces were constructed for each of the populationsover each of the transition intervals to follow theform of projection matrix models

nðtþ 1Þ ¼ A � nðtÞ

where n(t) is a vector of the number of individu-als in each of the four stages at time t, n(t + 1)is a vector of the number of individuals in eachstage at time t + 1, and A is a matrix of thetransition probabilities (aij). The aij for all transi-tions except seedling recruitment and canev pro-duction were calculated as the proportion ofindividuals in stage i at time t that contributed tostage j at time t + 1 (Figure 1). Occasionally, anindividual remained in stage i over a transitioninterval (Figure 1), although this was rare. Sev-eral possible transition probabilities did notoccur (e.g., seedlings in one year could notbecome reproductive canes in the following year)and were, therefore, entered as 0’s in the matrix.

Seedling recruitment and canev productionprobabilities were calculated as the number ofseedlings and canev, respectively, produced inone year relative to the number of reproductivecanes existing in the previous year. Our calcula-tion for seedling recruitment was based on theassumption that all seedlings germinated fromseeds produced during the previous year and notfrom the seed bank. This assumption was proba-bly reasonable based on the rapid disappearanceof Rubus seeds from the soil due to predation(Maxwell 1990; Kollmann et al. 1998) and thelow germination probability of seeds followingstorage (Amor 1974) or desiccation in the field(S. Lambrecht- McDowell, personal observation).

From each matrix, we calculated the finite rateof population growth, k, which is the dominanteigenvalue of A. We calculated an average transi-tion matrix for each species in both low- and

high-density populations over each transitioninterval. A value of k > 1 indicates a positivepopulation growth rate, k < 1 indicates the pop-ulation is decreasing in size, and k ¼ 1 indicatesa stable population size. We used an analyticalapproximation according to Caswell (2000, 2001)for the variance (V) of k where

VðkÞ �X

ij

X

kl

CovðaijaklÞ@k@aij

@k@akl

for each of these eight average matrices whereCov denotes the covariance between pairs oftransition probabilities (aij and akl) and ¶k/¶aij isa sensitivity term and denotes the effect of achange in aij on k. We used t-tests to determinethe significance of the difference between k inlow- and high-density populations over a transi-tion interval for each species and between thespecies and densities for each transition interval.

Given a difference in k between low- and high-density populations for both species, we used alife table response experiment (LTRE) to deter-mine the contribution (cij) of each transition tothe effect of population density on k (Levin et al.1996; Caswell 2000, 2001). The size of each cijrelative to other cij indicates the relative effect ofthat transition on the reduction in populationgrowth between low- and high-density popula-tions. In this manner, the LTRE can be used todetermine which transitions underlie the popula-tion-level effect of density. To calculate the cij foreach species, we first calculated an average transi-tion matrix for all populations at a given density.For R. ursinus, we averaged transitions fromboth transition intervals. However, for R. dis-color, we only used the transitions from the2000–2001 interval because we observed no effectof density on k over the 1999–2000 interval forthis species. We then calculated a matrix midwaybetween the high- and low-density populationmatrices for each species where values in themidway matrix were averages of the correspond-ing values from the mean low-density and meanhigh-density matrices. Finally, we estimated theeffect of density on k by calculating the cij ofeach vital rate using the difference between theaverage matrix elements of high- and low-densitypopulations and using the equation

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cij ¼ ðahighij � alowij Þ@k@aij

� �

where ðahighij � alowij Þ is the difference (dij) betweenthe transition values in the low- and high-densitymatrices and the ¶k/¶aij are the sensitivity termscalculated from the matrix midway between thehigh- and low-density matrices.

Elasticity analysis

The elasticity of each matrix element (eij) is ameasure of the proportional sensitivity of k toproportional changes in the aij (de Kroon et al.1986; de Kroon et al. 2000; Caswell 2001). Usingthe same average matrices generated for theLTRE, we calculated the eij for each aij as

eij ¼aijk@k@aij

for each of the four average matrices. The eij val-ues for a single matrix sum to 100% and, there-fore, it is possible to sum the eij for transitionsassociated with the same life-history process (e.g.,sexual reproduction or clonal growth) to com-pare the relative importance of each life-historyprocess to k (Silvertown et al. 1993; van Groen-endael et al. 1994; de Kroon et al. 2000). Usingthe transition matrix in Figure 1, we identifiedthe characteristic life-history processes for thetwo Rubus species, denoting each with a differenttype of shading. The eij of all transitions sharingthe same type of shading, and therefore, withinthe same life-history process, were added.

We used numerical manipulations of seedlingand canev production to assess the contributionof these transitions to k and to assess the impactof potential control strategies. For each of thefour average transition matrices, new k’s weredetermined by modifying the seedling recruitmenttransition value by differing proportions (from)90 to +50%), holding all other transition valuesconstant. Similar analyses were repeated formanipulations of the transition value for canevproduction. We also tested whether our assump-tion that all seedlings germinated from seeds pro-duced during the previous year by adding anadditional transition stage (seed) to the modeland calculating the change in k and elasticity val-ues for reproduction.

Results

Trade-offs between growth and reproduction

Flower removal from all reproductive caneswithin a population only slightly increased canelength production by canev for both species.Although the average cane length produced washigher for R. ursinus in the flower removal plotsrelative to the control plots, these differenceswere not statistically significant at a ¼ 0.05(Table 1; low-density WSR Z ¼ 1.244, P ¼ 0.095;high-density WSR Z ¼ 0.524, P ¼ 0.300). Aver-age cane length produced by canev was moresimilar between flower removal and control plotsof R. discolor (Table 1; low-density WSRZ ¼ 0.280, P ¼ 0.389; high-density WSRZ ¼ 0.105, P ¼ 0.459).

Table 1. Effects of floral bud removal on average cane length produced, leaf area produced per cane, and average specific leaf area

in both low- and high-density populations of R. ursinus and R. discolor.

R. ursinus R. discolor

Population density Control Floral bud removed Control Floral bud removed

Cane length produced (cm) Low 145.5 ± 23.2 228.2 ± 45.7 336.7 ± 54.1 404.5 ± 105.7

High 106.9 ± 16.5 133.9 ± 16.9 345.1 ± 41.9 475.4 ± 135.0

Leaf area produced (cm2) Low 319.6 ± 72.3* 615.0 ± 176.4* 3492.8 ± 713.9 3964.6 ± 939.0

High 156.0 ± 16.2 201.9 ± 20.2 2877.0 ± 623.2 4018.6 ± 1263.1

Specific leaf area (cm2 g)1) Low 162.1 ± 7.7* 116.5 ± 4.7* 88.8 ± 2.6 64.6 ± 4.0

High 130.6 ± 15.6 111.4 ± 6.4 87.1 ± 3.4 93.8 ± 2.2*

Values are the mean ± 1 SE.

* indicates a significant treatment effect at a = 0.05 according to the nonparametric Wilcoxon Signed Ranks test.

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In contrast to cane length, leaf growthresponded significantly to the flower removalexperiment. In low-density populations of R. ursi-nus, flower removal resulted in increased leaf area(Table 1; WSR Z ¼ 1.718, P ¼ 0.043) andreduced SLA (WSR Z ¼ 2.667, P ¼ 0.004) com-pared to control plots. There was a similarresponse in high-density populations of R. ursinus,but the differences were not significant at a ¼ 0.05(Table 1; leaf area WSR Z ¼ 1.363, P ¼ 0.087;SLA WSR Z ¼ 1.373, P ¼ 0.085). Flowerremoval had no statistically significant impact onleaf area produced per cane for R. discolor(Table 1; low-density WSR Z ¼ 0.280, P ¼ 0.389;high-density WSR Z ¼ 0.943, P ¼ 0.173), but didsignificantly increase SLA for high-density popu-lations (WSR Z ¼ 2.694, P ¼ 0.004; low-densityWSR Z ¼ 1.234, P ¼ 0.125).

Correlations between growth, reproduction,and demographic parameters reveal differencesbetween the species. For R. ursinus, leaf area pro-duced per canev was negatively correlated withboth the number of seedlings and the number ofcanev produced per reproductive cane in the pre-vious year (Table 2; P ¼ 0.028 and 0.050, respec-tively), while there was no such relationship forR. discolor (Table 2; P ¼ 0.385 and 0.695, respec-tively). There was a positive correlation betweenseedling and canes survival for both species(P ¼ 0.049 for R. ursinus and P ¼ 0.026 for

R. discolor). For R. discolor, there was a negativecorrelation between cane length and both seed-ling and canes survival (P ¼ 0.049 and P ¼ 0.007,respectively) and between leaf area and canes sur-vival (P ¼ 0.045) while there was a positive cor-relation between cane length production andcanes survival for R. ursinus (P ¼ 0.008). Leafarea and cane length were positively correlatedfor both species (P ¼ 0.003 for R. ursinus andP < 0.0001 for R. discolor).

Demographic patterns

Populations of the two Rubus species exhibiteddifferences in rates of clonal growth, sexualreproduction, and survival and advancement ofindividuals to the next stage of development. Thenoninvasive R. ursinus produced more seedlingsper m2 in both high- and low-density populationsthan the invasive R. discolor (Table 3; KWF ¼ 22.89, P < 0.0001), but the two species pro-duced a similar number of seedlings per repro-ductive cane (KW F ¼ 4.55, P ¼ 0.208). R.ursinus also produced more canev per m2 and perreproductive cane than R. discolor (Table 3; KWF ¼ 31.32, P < 0.0001 and F ¼ 12.04, P ¼ 0.007,respectively). Although R. discolor producedfewer seedlings and canev, its canev and canestended to have higher survival rates than R. ursi-nus (KW F ¼ 20.01, P < 0.001 and KW

Table 2. Pearson correlation values between demographic parameters of control populations of the noninvasive R. ursinus (upper

panel) and the invasive R. discolor (lower panel).

Year t

Canelength Leaf area Canevproduction

Seedling

production

Seedling

survival

Canessurvival

Canevsurvival

Leaf area 0.781** –

Canev production )0.183 )0.576* –

Seedling production )0.317 )0.630* 0.362 –

Seedling survival )0.006 )0.384 0.263 0.212 –

Canes survival 0.723** 0.313 )0.065 0.038 0.579* –

Canev survival )0.226 0.069 )0.796** )0.052 )0.073 )0.145 –

Year ðt + 1)

Leaf area 0.837** –

Canev production 0.347 0.242 –

Seedling production )0.111 )0.108 0.250 –

Seedling survival )0.516* )0.465 0.190 0.081 –

Canes survival )0.665** )0.523* 0.270 0.288 0.573* –

Canev survival 0.075 )0.147 0.309 0.509 )0.020 0.246 –

* Indicates a significant difference at a = 0.05 and ** indicates a significant difference at a = 0.01.

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F ¼ 6.22, P ¼ 0.102, respectively). Seedling sur-vival was similar between densities for a givenspecies (KW F ¼ 2.34, P ¼ 0.505).

Population growth

Rubus ursinus exhibited positive populationgrowth rates over both transition years in bothlow- and high-density populations (Figure 2).However, for high-density populations, k was veryclose to 1, suggesting that population size in theseestablished populations was fairly constant. The kin low-density populations was higher than thatof high-density populations over both transitionyears (t ¼ )2.144, P ¼ 0.034). The range in k forlow-density R. ursinus populations was 1.22–1.92and for high-density populations was 0.72–1.22.

The average population growth rate of R. dis-color was positive over both transition years inboth low- and high-density populations, exceptin high-density populations in 2000–2001 (Fig-ure 2). Like R. ursinus, R. discolor showed anapparently higher k in low-density populationsthan in high-density populations in 2000–2001(t ¼ )6.353, P ¼ 0.003), but in 1999–2000, k wasapproximately equal between the two populationdensities (t ¼ 0.705, P ¼ 0.262). Values of k forR. discolor ranged from 0.82 to 1.76 for low-den-sity populations and from 0.70 to 1.41 in high-density populations.

Population growth rates were similar betweenthe species. k was not significantly differentbetween the species over the 1999–2000 (t ¼ 0.437,P ¼ 0.402 for low-density and t ¼ 0.898,P ¼ 0.251 for high-density) or 2000-2001 transi-tion intervals (t ¼ 1.428, P ¼ 0.223 for low-densityand t ¼ 1.439, P ¼ 0.206 for high-density).

The LTRE revealed that the factors underlyingthe effects of density on k were different for eachof the species. The transition that contributes the

Table 3. Average demographic parameters ± 1 SE for the noninvasive R. ursinus and the invasive R. discolor.

R. ursinus R. discolor

Low density High density Low density High density

Seedlings (m)2) 2.0 ± 0.5a 3.6 ± 0.6b 0.3 ± 0.1c 0.7 ± 0.2c

Canev (m)2) 4.9 ± 0.7a 14.7 ± 0.7b 1.1 ± 0.2c 1.5 ± 0.1c

Seedlings per reproductive cane 1.1 ± 0.3a 0.5 ± 0.1a 0.3 ± 0.1a 0.5 ± 0.2a

Canev per reproductive cane 3.1 ± 0.6a 2.4 ± 0.3ab 1.4 ± 0.2bc 0.9 ± 0.2c

Seedling survival (%) 68 ± 16a 69 ± 9a 79 ± 9a 86 ± 7a

Canes survival (%) 41 ± 14a 26 ± 13a 58 ± 14a 72 ± 9a

Canev survival (%) 70 ± 7a 41 ± 4b 93 ± 4c 98 ± 2c

Values of the same parameter sharing letters are not significantly different at a = 0.05 as determined with the nonparametric Krus-

kal–Wallis procedure.

λ

1

2

1999-2000 2000-2001

λ

1

2

R. ursinus

R. discolor

High-densityLow-density

Figure 2. The finite rate of increase (k) for low- (open bars)

and high-density (shaded bars) populations of R. ursinus and

R. discolor over each one-year transition interval. Error

bars ¼ 1 SE as calculated using an analytical approximation

(discussed in the text).

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most to the density-dependent change in k foreach species has the largest cij. The cij for R. ursi-nus reveal that high population density causedreduced canev survival and, to a lesser degree,reduced canev production because the cij for thesetransitions were largest (Figure 3C). For R. dis-color, the reduction in k in high-relative to low-density populations was due to reduced canevproduction because this transition had the largestcij (Figure 3D). For R. ursinus, the transition ele-ments that yielded the largest dij between high-and low-density populations did not produce thelargest cij and, therefore, largest effect on k (Fig-ure 3). However, for R. discolor, the largest dijproduced the largest cij (Figure 3).

Elasticity analysis

Comparison of the summed elasticity values foreach life-history process indicated that clonalgrowth affected k relatively more than sexualreproduction for both species in both low andhigh population densities (Table 4). For R. ursi-nus, the contribution of clonal growth and sexualreproduction to k remained relatively constantbetween low- and high-density populations(Table 5). However, the relative importance of

sexual reproduction to k increased between low-and high-density populations of R. discolor. Thesummed elasticity values for sexual reproductionwere higher in R. discolor than R. ursinus, partic-ularly in high-density populations, (t ¼ 0.670,P ¼ 0.128 for low-density populations andt ¼ 1.728 and P ¼ 0.028 for high-density popula-tions). Similarly, clonal growth contributedslightly more to population growth in R. ursinusrelative to R. discolor (t ¼ )1.751, P ¼ 0.050 forlow-density populations and t ¼ )1.544,P ¼ 0.075 for high-density populations). Addingthe seed transition stage to the model reduced kfor both species at both densities, but not signifi-cantly (t ¼ 1.95, P ¼ 0.15 and t ¼ 0.37, P ¼ 0.73for R. discolor high- and low-density populations,respectively and t ¼ 1.89, P ¼ 0.16 and t ¼ 1.97,P ¼ 0.15 for R. ursinus high- and low-densitypopulations). For both species, the summed elas-ticity values for sexual reproduction increased inthe high-density populations, but not significantly(5% increase for R. discolor, t ¼ 0.53, P ¼ 0.63and 1% increase for R. ursinus, t ¼ 2.12,P ¼ 0.12). In low-density populations of bothspecies, the summed elasticity values for sexualreproduction decreased by a nonsignificantamount (4% decrease for R. discolor, t ¼ 0.96,

Transitions

Dif

fere

nce

s in

aij

-1.0-0.8-0.6-0.4-0.20.00.20.4

Transitions

Co

ntr

ibu

tio

ns

of

a ij

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

R. ursinus R. discolor

ss scs csr cvcv cvr rs rcvscs csr cvcv cvr rs rcv rrcscs

(A) (B)

(C) (D)

Figure 3. The differences (dij) between transition values (aij) from the mean low- and mean high-density populations of R. ursinus

(A) and R. discolor (B), and the contribution (cij) of each of those differences to the density-dependent change in population growth

(C and D). Abbreviations for transitions from one year to the next are ss (seedling to seedling), scs (seedling to canes), cscs (canesto canes), csr (canes to reproductive), cvcv (canev to canev), cvr (canev to reproductive), rs (seedling recruitment), rcv (vegetative cane

production), and rr (reproductive to reproductive).

289

P ¼ 0.41 and 2% decrease for R. ursinus,t ¼ 1.33, P ¼ 0.31). Therefore, we conclude thatour assumption that seeds produced in one yeargerminated in the following year did not signifi-cantly affect the results of our analyses.

For both species, changes in the average canevproduction transition value had a much largereffect on k than proportional changes in the aver-age seedling recruitment value, holding all othertransition values constant (Figure 4). For R. ursi-nus, reducing seedling recruitment by as much as90% had virtually no impact on k in both low-and high-density populations while even smallchanges in canev production had a proportion-ately larger effect on k. In low-density popula-tions of R. discolor, the proportional effects ofchanges in seedling recruitment and canev produc-

tion on k were similar to the effects observed inR. ursinus (Figure 4). However, in high-densitypopulations of R. discolor, changes to the seedlingrecruitment and to the canev production transi-tion value produced more similar effects on k.

Figure 5 shows the percent change in k given a50% change in either the canev production orseedling recruitment transition values for eachmatrix of each species while holding all othertransition values constant. For R. ursinus, a 50%reduction in seedling recruitment yielded a smallchange in k (always less than 10% change), whilea 50% change in canev production yielded a mini-mum 15% change in population growth (Fig-ure 5). For R. discolor, although a 50% change incanev production generally had a larger impacton k than a 50% change in seedling recruitment,the impact of these two transitions on k weremore similar to each other than their impacts onk of R. ursinus (Figure 5). With a 50% change inseedling recruitment, k changed by as much as14% while a proportional change in canev pro-duction changed k by as little as 7%.

Discussion

Trade-offs between growth and reproduction

The demographic trade-offs between currentsexual reproduction and growth of canev withina clone are more evident in the noninvasive

Table 4. Average summed elasticity values ± 1 SE for sexual

reproduction and clonal growth transitions of all low- and

high-density populations for each species over both transition

years. Transitions included in the sum for sexual reproduction

include those depicted with hatched lines in Figure 1, while

transitions included in clonal growth include those with dots

in Figure 1.

Mode of reproduction

Sexual Clonal

R. ursinus

Low density 14 ± 10 85 ± 10

High density 13 ± 6 81 ± 6

R. discolor

Low density 20 ± 8 71 ± 7

High density 32 ± 7 68 ± 8

Low density

Fin

ite

rate

of

incr

ease

,λ, f

or

R. u

rsin

us

0.75

1.00

1.25

1.50

1.75

2.00

High density

-1.0 -0.5 0.0 0.5 1.0

Proportional change in transition value (%)

-1.0 -0.5 0.0 0.5 1.0

Fin

ite

rate

of

incr

ease

,λ,f

or

R. d

isco

lor

0.50

0.75

1.00

1.25

1.50

1.75

(A) (B)

(C) (D)

Figure 4. The finite rate of increase (k) for a proportional change in the average transition value of seedling recruitment (circles)

and canev production (triangles) for R. ursinus in low- (A) and high-density (B) populations and for R. discolor in low- (C) and

high- (D) density populations.

290

R. ursinus than in the invasive R. discolor. Trade-offs between current growth and reproductionhave been observed in studies with natural andmanipulated levels of reproduction for noninva-sive species (Fox and Stevens 1991; Newell 1991;Ashman 1992; Nicotra 1999). However, little isknown about these trade-offs in an invasive plantspecies. The apparent trade-offs in R. ursinuswere driven by the physiological costs associatedwith reproduction, leading to relatively higherreproductive effort. A previous study of thesesame two species demonstrated that sexual repro-duction caused decreased foliar water status andphotosynthetic capacity in R. ursinus, leading toa reduction in annual carbon gain (McDowelland Turner 2002). These effects of reproduction

on carbon gain, however, were not apparent inR. discolor, thus explaining the apparent lack ofgrowth response to floral bud removal observedin this study.

In addition to the trade-off between currentgrowth and reproduction, plants may also exhibita negative relationship between current reproduc-tion and future growth and reproduction. If cur-rent and future reproduction draw on the samepool of resources, then current reproduction maydeplete available resources for future growth,flower, and fruit development (Stearns 1992).Furthermore, the negative effects of reproductionon current plant size may decrease a plant’scapacity to acquire resources in the future(Bloom et al. 1985) or limit the number of meris-tems that may develop into inflorescences (Geber1990). The negative correlation between leaf areaproduction per canev of R. ursinus in one yearand canev production in the following year sug-gests trade-offs may exist between generations inthe noninvasive Rubus because these two parame-ters, as components of clonally integrated canes,draw on the same pool of resources. Althoughthere is a negative correlation between leaf areaproduction in one year and seedling productionin the following, this correlation may be spuri-ous. In order for seedling production to have aneffect on resource allocation to leaf area produc-tion of canev, the seeds from which those seed-lings germinated must have been produced byreproductive canes clonally connected to theaffected canev. In this study, it was not possibleto determine the seed source of the germinatedseedlings.

The demographic trade-offs between growthand reproduction within and between generationswere not apparent in the invasive R. discolor. Itis possible that such life-history trade-offs are notapparent when resources are not limiting, whendifferent life-history functions are dependentupon separate resource pools, or when currentallocation does not affect the capacity of a plantto capture resources in the future (Geber 1990;Stearns 1992). The two Rubus species examinedin this study grow in the same open sites and,therefore, have potential access to equivalentresources. However, R. discolor is able to achievehigher photosynthetic rates per unit resourceinvestment of carbon, water, and nitrogen than

% c

han

ge

in λ

5

10

15

20

25

30

35

R2 = 0.874

Elasticity (%)

0 10 20 30 40 50

% C

han

ge

in λ

0

5

10

15

20

25

30

35

R2 = 0.983

R. ursinus

R. discolor

Figure 5. The percent change in the finite rate of increase (k)for a 50% proportional change in seedling recruitment (cir-

cles) and canev production (triangles) versus the elasticity

value (eij) for each fecundity and canev transition for each

matrix of R. ursinus and R. discolor. For R. ursinus,

k ¼ 1.06 + 0.49eij (P < 0.0001) and for R. discolor,

k ¼ 0.06 + 0.56eij (P < 0.0001).

291

R. ursinus (McDowell 2002). Therefore, resourceavailability may be more limiting to carbon gainin R. ursinus than in R. discolor. Furthermore,the lack of effect of reproduction on carbon gainin R. discolor highlights a possible mechanismunderlying the apparent lack of trade-offs for thisspecies (McDowell and Turner 2002).

Demographic patterns

Rates of production and survival of canes withinpopulations were different for the species. Thehigher rate of seedling and canev production byR. ursinus on a ground area basis is due, at leastin part, to the smaller size of R. ursinus canes;more small canes can grow in a given area thanlarge canes. However, R. ursinus also producedmore canev per reproductive cane, a value thatwas standardized for plant size. Although R. dis-color produced fewer canev, they had a highersurvival rate than the canev of R. ursinus. In fact,the noninvasive R. ursinus displayed a demo-graphic trade-off between canev production andsurvival, as evidenced by the negative correlationbetween these two parameters. For R. discolor,there was a positive, although not significant,relationship between canev production and sur-vival, suggesting there was no demographictrade-off between these two parameters.

Population growth and invasiveness

As plant populations become more dense, theyeventually reach the site carrying capacity andare subject to density-dependent limits on recruit-ment of new individuals. In short-lived speciessuch as Rubus, recruitment may be expected toplateau so that each year, the population merelyreplaces senescing canes. Clonal plants commonlyshow constant rates of mortality and recruitmentfollowing population establishment so that canevnumbers remain relatively constant (Cook 1985;Hartnett and Bazzaz 1985; Meyer and Schmid1999). For both Rubus species in this study, k ofthe high-density populations was approximatelyequal to 1, suggesting that the populations had,on average, reached a plateau in populationgrowth. Furthermore, k was higher in low- thanin high-density populations, with the exceptionof R. discolor over the 1999–2000 transition. This

pattern of population growth is similar to that ofother clonal plant species (Barkham 1980; Cook1985; Briske and Butler 1989) as well as that ofthe invasive, but non-clonal, Cytisus scoparius(Parker 2000), in response to increasing popula-tion density. The LTRE showed that for R. ursi-nus, the effect of density on k was due to areduction in canev survival with increasing popu-lation density, while in R. discolor, the differencewas due to a reduction in canev production.Reduced canev production, rather than increasedmortality, is a more commonly observed responseto increased population density in other clonalplant species (Cook 1985; Briske and Butler1989), perhaps because canev mortality generatesa resource cost for the entire clone. The mortalityof canev in R. ursinus was particularly pro-nounced over the 2000–2001 transition interval,along with mortality of other life-history stages,and may have arisen due to the colder than nor-mal conditions during the winter and much drierthan normal spring. R. discolor, which is moretolerant of seasonal and diurnal drought than R.ursinus (McDowell 2002; McDowell and Turner2002), may have been less adversely affected bythe climate over that transition interval.

The elasticity analysis revealed that life stagetransitions relating to canev production and sur-vival were relatively more important to popula-tion growth of both species than transitionsrelating to sexual reproduction. A reliance onpredominantly clonal spread over sexual repro-duction has been observed in other species of Ru-bus (Abrahamson 1975; Maxwell et al. 1993;Baret et al. 2003), as well as other plants thatreproduce both sexually and clonally (Cook1985). There are several advantages associatedwith the reliance on clonal growth for populationexpansion. Although canev production mayrequire an initial investment of more resourcesthan sexual reproduction, canev eventually con-tribute positively to the resource balance of theclone (Cook 1985), increase the capacity of theclone to recover from stresses such as defoliation(Price et al. 1992), and increase the potential forthe clone to access unevenly distributedresources, such as light and water (Stuefer et al.1996). Furthermore, production of canev enablesa clone to rapidly capture and dominate an area,competitively excluding other species (Pitelka and

292

Ashmun 1985). Finally, life history processeswith fewer transitions contribute relatively moreto population growth than those with more tran-sitions (de Kroon et al. 2000). Therefore, devel-opment of canev contributes more to populationgrowth of Rubus because it takes two years for areproductive cane to develop from clonal origins,while it takes three years for a reproductive caneto develop from seed.

Population growth rates within existing popu-lations were similar among the species acrossboth densities and transition intervals. Therefore,invasiveness of R. discolor may be due to agreater capacity for dispersal and establishmentof new populations than R. ursinus, whereinvasiveness is defined as the ability to rapidlycolonize sites, reproduce, and spread to new sitesoutside of the species’ previous range. We didnot explicitly measure dispersal or establishmentrates of new populations for these species, but wedid observe a relative increase of importance ofsexual reproduction with population density forR. discolor. This increase was due to seedlingsgerminating in locations within the high-densityplots that had not been previously colonized byclonal spread. The minimal physiological costsassociated with sexual reproduction for R.discolor (McDowell and Turner 2002) mean thatthe importance of sexual reproduction in popula-tions may increase without incurring negativeeffects on the current population. R. ursinusrelied almost entirely on clonal spread forpopulation growth and, therefore, had limitedpotential for dispersal.

Control of R: discolor

The elasticity analysis for R. discolor may be use-ful in determining methods for controlling thisspecies. In order to control invasive plant species,population growth needs to be lowered to belowk ¼ 1, so that population size will decrease. Onebiological control strategy suggested for severalother invasive plant species is to utilize predatorsor pathogens to reduce flower or seed develop-ment (Shea and Kelly 1998; McEvoy andCoombs 1999; Parker 2000). Seed predationcould reduce population growth of establishedpopulations of R. discolor by limiting dispersal,but only if seedling recruitment is reduced by at

least 70%. The most effective strategy for control-ling population growth for existing populationsof R. discolor would be to reduce canev produc-tion. The numerical simulations in this studyshowed that reducing canev production by as lit-tle as 30% could reduce population growth ade-quately to bring about eventual extinction ofexisting populations. Control methods thatinvolve mowing canes or applying herbicide tofoliage have proven relatively ineffective at con-trolling this species (reviewed in Hoshovsky2001), probably because such methods havefailed to adequately affect allocation to thebelowground portions of the plant. The mosteffective controls for this invasive Rubus includethe introduction of animals that graze canes tothe roots from which canev sprout (Amor 1974;Daar 1983) or the use of herbicides applied tocut or burned stems following fruit set (Hoshov-sky 2001). The effectiveness of this latterapproach is likely due to the translocation ofnutrients and, therefore, herbicides from repro-ductive canes to the roots prior to senescence.Such management tactics, in addition to reducingseedling recruitment to limit dispersal and estab-lishment of new populations, could be effective incontrolling established populations of this inva-sive species in the PNW.

Acknowledgements

The authors would like to acknowledge theMcDonald–Dunn Research Forest and CFIRPfor use of field sites. We thank B. Endress, R.Meilan, P. Muir, and three anonymous reviewersfor their comments on this manuscript. Thisresearch was funded by Sigma Xi Grant-in-Aidof Research, Northwest Science Research Fellow-ship, and the Graduate Women in Science VessaNotchev Fellowship to SCLM.

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