Evaluating management interventions in small populations of a perennial herb Primula vulgaris using spatio-temporal analyses of point patterns

Evaluating management interventions in small

populations of a perennial herb Primula vulgaris using

spatio-temporal analyses of point patterns

Hans Jacquemyn1*, Patrick Endels2, Olivier Honnay1 and Thorsten Wiegand3

1Division of Plant Ecology and Systematics, University of Leuven, Arenbergpark 31, B-3001 Heverlee, Belgium;2Division of Forest, Nature and Landscape Research, University of Leuven, Celestijnenlaan 200E, 3001 Leuven,

Belgium; and 3UFZ Helmholtz Centre for Environmental Research – UFZ, Department of Ecological Modeling,

PF 500136, D-04301 Leipzig, Germany

Summary

1. In high-intensity agricultural landscapes, small landscape elements such as hedgerows, ditch

banks, and rows of pollard trees may represent the last refuge of many plant and animal species,

some of them being rare or even threatened with extinction. However, due to their small size and

low habitat quality, long-term population survival cannot be ascertained and often active manage-

ment is needed to maintain viable populations of species forced to survive in these small landscape

elements.

2. Population models are needed to assess the threats to species at risk and to evaluate alternative

management actions. Here, we present a methodology to evaluate management interventions using

spatio-temporal analyses of point patterns. We apply this method to several populations of prim-

rosePrimula vulgaris in Flanders, where it is rare and predominantly occurs along ditch banks.

3. The effects of ditch bank clearing on the establishment success of seedlings was investigated by

comparing spatial patterns of seedling recruitment, survival andmortality between populations that

were grazed and populations that were severely disturbed by mechanical clearing of ditch banks

followed by annual mowing. A total of 884 seedlings were mapped and monitored during 4

consecutive years (1999–2002).

4. In all populations, plants showed significant clustering, but in cleared sites only seedlings were

significantly clustered around adults. Spatial patterns of mortality varied according to the manage-

ment intervention. In grazed sites, mortality was almost random, whereas in cleared sites we found

clear evidence for strong negative density-dependent mortality. There was no evidence that the pres-

ence of adults affected survival of recruits in any of the sites studied.

5. Synthesis and applications. This study shows that the analysis of spatial point patterns

contributes to our understanding of the population dynamics of plant species occurring in different

environments. The approach can be broadly applied to other plant species to elucidate the processes

that determine the number of individuals that establish and persist into later life stages and will help

conservation managers to refine management strategies intended to conserve or restore plant

populations. In the case ofP. vulgaris, increasing the availability of microsites is most likely to result

in increased growth rates, as it results in increased recruitment and establishment of recruits.

Key-words: O-ring statistics, pair correlation function, point pattern analysis, Primula,

random mortality hypothesis, recruitment

Introduction

Inmost of north-western Europe, the intensification of agricul-

ture practices has forced many formerly widespread plant and

animal species to survive in semi-natural habitat remnants,

such as hedgerows, ditch banks, and rows of pollard trees (Sto-

ate et al. 2001; Robinson & Sutherland 2002). However, the

long-term survival of plant populations along small-landscape

elements cannot be guaranteed because of their small area and

low habitat quality (Kleijn & Verbeek 2000; Blomqvist et al.

2003). Specific management interventions are often needed to*Correspondence author. E-mail: [email protected]

Journal of Applied Ecology 2010, 47, 431–440 doi: 10.1111/j.1365-2664.2010.01778.x

� 2010 The Authors. Journal compilation � 2010 British Ecological Society

maintain viable plant populations in agricultural landscapes.

One way of evaluating changes in population viability after

intervention is to usematrix populationmodels (e.g.Brys et al.

2004; Pfeifer et al. 2006). These approaches, however, provide

little insight in the processes that determine why particular life

stages establish and survive into the next life stage and others

do not.

There are two contrasting explanations for the distribution

and abundance of individuals within a population (reviewed in

Turnbull, Crawley & Rees 2000; Clark et al. 2007; Poulsen

et al. 2007). The first states that the distribution of juveniles

and adults is primarily determined by the number of seeds that

are dispersed into a population. The alternative viewpoint is

that population size and the distribution of juveniles and adults

are primarily determined by the quality of suitable sites for

recruitment and the effect of density-dependent survival within

these sites. Recent meta-analyses of seed addition experiments

(Clark et al. 2007; Poulsen et al. 2007) have shown that supple-

mental addition of seeds to populations almost always results

in increased seedling recruitment, indicating that most plant

populations are seed limited. However, the effects of seed addi-

tion were relatively small and most seeds failed to recruit into

the seedling stage, suggesting that establishment limitation,

rather than seed limitation, is the most important factor

limiting the distribution and abundance of individuals (Clark

et al. 2007).

One way of investigating the relative importance of dispersal

and establishment processes in determining the distribution

and abundance in plant populations is the study of spatial

patterns in recruitment, survival andmortality, especially when

temporal changes in these patterns are analysed (e.g. Turnbull

et al. 2004).Whereas spatial patterns of seed arrival depend on

the mechanisms of seed dispersal, seed recruitment depends on

the interaction of multiple biotic and abiotic factors. Biotic

factors relate to seed competition, predation or pathogens,

whereas abiotic factors refer to gaps, resources or microsites

(Clark et al. 1999). Competitive interactions can be further

partitioned according whether they cause density-dependent

or density-independent mortality between seed arrival and

recruitment into a later life stage (Clark, Macklin & Wood

1998). Intra-specific competition can be intense, particularly

when seeds are strongly aggregated at small spatial scales

(Rees, Grubb & Kelly 1996; Turnbull et al. 2004). While

several mechanisms could generate this pattern, local seed

dispersal resulting in seedlings being clustered around adults or

seedlings clumped together at very high local densities, leading

to intra-specific aggregation is most likely for species with

limited dispersal capacities. This implies that patterns of seed

dispersal and the subsequent spatial arrangement of seedlings

within a population may largely determine patterns of growth

and mortality and thus may have important implications for

populationmanagement.

Few studies have investigated processes that determine the

number of individuals that establish and persist into later life

stages (but see Kenkel 1988; De la Cruz et al. 2008). In this

paper, patterns of seedling establishment were investigated in

several populations of the perennial Primula vulgaris by

comparing seedling recruitment, mortality and survival into

later life stages. In Flanders, the species is rare and occurs pre-

dominantly in small landscape elements that are subjected to

different disturbance regimes. Previous demographic research

using matrix models already showed that seed germination,

seedling establishment and survival were the most important

factors determining variation in growth rates (Endels et al.

2007). By examining changes in spatial patterns in natural pop-

ulations along ditch banks we aimed to investigate to what

extent density-dependent or density-independent mortality

between seed arrival and recruitment into a later life stage

determined seedling establishment success. The results of

this study may therefore not only contribute to a better

understanding of the driving forces (dispersal, competition and

management) that shape spatial patterns in plant populations,

but also allow conservation strategies to be refined. The

methodology should be widely applicable as a valuable

addition tomatrix populationmodelling.

Materials and methods

SPECIES

Primula vulgaris Huds. is a small, long-lived, herbaceous, diploid

perennial with a North Atlantic and Mediterranean distribution

(Jacquemyn et al. 2009). In Flanders, Belgium, it is considered a very

rare and declining species: only 89 populations, ranging in size from 1

to 1219 individuals, were found in 1999.Most populations (58 in total

or 68%) contained fewer than 50 individuals (Endels et al. 2002).

AlthoughP. vulgaris is regarded as a typical woodland species (Whale

1984) associated with newly opened gaps (Valverde & Silvertown

1995), most populations (85%) in Flanders occur on ditch banks

along hedgerows and forest edges (Endels et al. 2002). Plants flower

in early spring (March–May) and are mainly pollinated byHymenop-

tera (mostly bumblebees) andDiptera (Jacquemyn et al. 2009). Fruits

ripen around the middle of June and have an elaiosome, which is

attractive to ants and rodents who may actively harvest seeds and

disperse them across the landscape (Valverde & Silvertown 1995).

However, seeds usually fall directly to the ground in the immediate

vicinity of the mother plant (barochory; Cahalan & Gliddon 1985).

Vegetative spread is restricted and only occurs within very short

distances from the mother plant through production of lateral

rosettes. Although these individual rosettes can die off, individual

plants are relatively long-lived (10–30 years; Boyd, Silvertown &

Tucker 1990).

STUDY SITES AND DATA COLLECTION

During 1999–2002, population surveys of P. vulgariswere carried out

at four locations (Appendix S1). Two populations (G1 and G2) were

grazed, whereas the other two (MCL1 and MCL2) occurred at sites

that were cleared mechanically (with scraping of ditch banks and

partial removal of the vegetation) once every three years, followed by

annual mowing and removal of all litter in subsequent years.

Distances between the studied populations were small (0Æ5–2 km),

implying that they experienced similar climatic conditions. All sites

were visited once a year during spring at peak flowering (mid March

to early April). During each survey, all plants were mapped to the

nearest cm, enabling to locate each individual throughout the

sampling period and to locate mortality events within each site. In all

432 H. Jacquemyn et al.

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subsequent analyses, the following data were used. Adults were

defined as adults recorded in the 1999 census. Since there was little

adult turnover until 2002, we used the 1999 adult data in all cases.

Plants not present in the first (1999) census, but present in the 2000

census are recruits that were monitored for 3 years. In 2001 and 2002,

surviving and dead recruits were recorded. New recruits that origi-

nated after 2000were not considered in this analysis.

SPATIAL PATTERN ANALYSIS

We used the O-ring statistic (Wiegand&Moloney 2004) and the pair-

correlation function (Stoyan & Stoyan 1994) as summary statistics to

describe the spatial correlation structure of the bivariate point pat-

terns observed at our study site. Since there were no apparent hetero-

geneities in our study transects (Supporting Information Appendix

S1) we usedmethods for homogeneous point patterns.

The bivariate O-ring statistic for point patterns comprising type 1

and type 2 points (where, for example type 1may represent adult indi-

viduals and type 2 recruits) is the expected density of recruits in a ring

of radius r andwidth dw centred on an arbitrary adult plant (Wiegand

&Moloney 2004). The O-ring statistic has the intuitive interpretation

of a neighbourhood density and is especially sensitive to small-scale

effects (Wiegand & Moloney 2004; Illian et al. 2008). The bivariate

pair-correlation function g12(r) is the intensity normalized version of

O12(r), i.e., O12(r) = k2g12(r), where k2 is the intensity of recruits in

the study transect (i.e. the number of points of pattern 2 divided by

the area of the study plot; Stoyan & Stoyan 1994).We used the bivari-

ate O-ring statistic for analysis of the recruit-adult relationship where

the direct interpretation of a density is of interest, and the pair corre-

lation function for analysis of recruitmentmortality.

Because datawere collected at two replicate transects for eachman-

agement type, the results of the individual analyses of the two popula-

tions were combined into one overall test statistic by weighting the

contribution of each plot with the number of points of pattern 1 of

each plot (Riginos, Milton & Wiegand 2005; De Luis et al. 2008;

Illian et al. 2008). All analyses were done using the software

Programita (Wiegand & Moloney 2004; Wiegand et al. 2006, 2007b;

Wiegand, Gunatilleke & Gunatilleke 2007a). Details on the estima-

tors of the summary statistics and edge correction used in Programita

can be found inWiegand&Moloney (2004).

SIGNIF ICANCE OF PATTERNS AGAINST A NULL MODEL

The observed summary statistics were contrasted to that expected

under the specific null model chosen. Approximate (two-sided)

95% simulation envelopes for a given null model were created by

calculating for each distance r the 5th lowest and highest values

of the summary statistic from 199 Monte Carlo simulations of

the null model. This yields an approximate 5% error rate. Note

however that the simulation envelopes cannot be interpreted as

confidence intervals, given that the null hypothesis is tested

simultaneously at many scales, inflating the chance of type I

errors (Diggle 2003; Loosmore & Ford 2006; Illian et al. 2008).

We therefore examined the significance levels over a distance

interval of interest following the goodness-of-fit test proposed by

Diggle (2003). Under this test, both the observed pattern (i = 0)

and each of the simulated patterns (i = 1, …, 199) are reduced

to a single test statistic ui which represents the total squared devi-

ation between the observed pattern and the theoretical result

across the distances of interest (i.e. where the null model may be

rejected). The larger the rank of u0, the larger the departure of

the empirical summary statistic from that expected under the null

model. If the rank of u0 is larger than 190, the null hypothesis is

rejected at the distance interval of interest on a 5% level.

ANALYSES

Analysis 0: Univariate spatial patterns

We aimed to assess the univariate spatial structure of the spatial pat-

terns of adults and the three recruit cohorts to ascertain if the univari-

ate patterns were aggregated. To this end we compared our data

within each transect to a completely random pattern and used the O-

ring statistic as test statistic.

Analysis 1: Recruit-adult relationships

We sought to establish if the different recruit generations were

clustered around adults and if there were differences between

the two management interventions. We compared the bivariate

data to the null model of independence using the bivariate

O-ring statistic as test statistic and a toroidal shift as null model

(Goreaud & Pelissier 2003; Wiegand & Moloney 2004). This

null model preserves the spatial structures of both pattern, but

breaks the dependence between them. One way of achieving this

is by simulations that involve random shifts of the whole of

one component pattern (the recruits) relative to the other (the

adults). In practice, the rectangular study region is treated as a

torus where the upper and lower edges are connected and

the right and left edges are connected. Because the data for

population 2G comprised basically two transects (Appendix S1)

we analysed them separately.

Analysis 2: Recruit survival

We investigated the spatial structure in mortality of the recruits by

comparing the spatial pattern of surviving and dead recruits at years

2001 (and 2002) to the null model of random mortality (also called

random labelling; Goreaud & Pelissier 2003; Wiegand & Moloney

2004).

For each year (2001 and 2002) we know if a given recruit was

dead or alive. To identify the spatial structures in the process

that assigned a label ‘mortality’ to the recruits the framework of

‘marked point patterns’ is required (Goreaud & Pelissier 2003).

The fundamental question is to find out if the process that

distributed the label was a random process. A suitable null

model for this is ‘random labelling’. We used a Monte Carlo

implementation of random labelling that involves random re-sam-

pling of sets of n1 dead recruits from the total of (n1 + n2) dead

and surviving recruits, i.e. we randomly shuffle the label ‘dead’

among the recruits.

While the concept of random labelling is easy and intuitive, the test

statistics needed to test departures from random labelling are slightly

more complex because they need to be adapted to the specific ques-

tion asked. Conventional random labelling analyses only the two pat-

terns of dead and surviving plants (Goreaud & Pelissier 2003; De la

Cruz et al. 2008). In this case random labelling implies that

g1+2,1+2(r) = g11(r) = g22(r) = g12(r) = g21(r) where 1 symbolizes

dead individuals, 2 surviving, and 1 + 2 symbolizes the joint pattern

of dead and surviving individuals. This convenient property of ran-

dom labelling allows for construction of different test statistics based

on pair correlation functions. We used several specific test statistics,

each of which evaluates a different biological effect of the spatial

interactions that determinemortality.

Spatial population dynamics in Primula vulgaris 433

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Test of aggregation of dead plants with g11. We used the test

statistic g11(r) (i.e. univariate random labelling; Wiegand & Moloney

2004) to explore the patterns of recruit mortality. Under scramble

competition we expect that clumps of interacting recruits should die

together, thus dead recruits should be spatially aggregated (e.g.

Kenkel 1988). The test statistic g11(r) is especially tailored to detect

clustering of dead recruits: if g11(r) shows a positive departure from

the random labelling null model, dead recruits are significantly

clustered at scale r, conditionally on the joint pattern of dead and

surviving recruits.

Test of attraction vs. segregation of dead and surviving plants. We

used the test statistic g12(r) (Goreaud & Pelissier 2003) to explore

spatial patterns of recruit survival and mortality. Under two-sided

scramble competition negative interactions would be most

pronounced in areas of higher recruits density, leading eventually to

clumps of dead recruits which are spatially segregated from surviving

recruits. Conversely, one-sided contest competition leads to a

situation where suppressed ‘losers’ are located near its superior rivals.

Thus, in the language of point pattern analysis, dead recruits will be

‘attracted’ by surviving recruits (Kenkel 1988). The test statistic g12(r)

is tailored to detect correlation between dead and surviving recruits

(Goreaud & Pelissier 2003). Attraction (or segregation) between dead

and surviving recruits occurs if g12(r) shows positive (or negative)

departures from the random labelling null model.

Test of density dependent mortality. We developed the third test

statistic g1,1+2–g2,1+2 specifically to provide a direct test of density

dependent effects in mortality (see also Yu et al. 2009). This test

statistic compares the density of dead and surviving recruits (i.e.

1 + 2) around dead recruits (i.e. pattern 1) with the density of dead

and surviving recruits (i.e. 1 + 2) around surviving recruits (i.e.

pattern 2). The expected value of this test statistics is zero under

random labelling, but under density dependent mortality dead

recruits would occur preferentially y in areas with high pre-mortality

densities, i.e. g1,1+2 > g2,1+2. Conversely, recruits may show higher

survival probabilities in high-density situations. In this case, we

expect that surviving recruits would have more neighbours (i.e.

g1,1+2 < g2,1+2).

Test for additional pattern in dead recruits. To test for the presence

of an additional pattern in mortality (or survival) we used the

differences g21(r)–g22(r) and g12(r)–g11(r) as test statistics (Getzin et al.

2006). A value of g21(r)–g22(r) � 0 means that dead recruits (i.e.,

pattern 1) surround surviving recruits (i.e., pattern 2) at scale r in the

same way as surviving recruits surround surviving recruits. However,

if there was additional clustering within the dead recruits that is

independent from the pattern of surviving recruits (e.g. caused by

competition from adults or environmental conditions), this would

not be detected by the test statistic g21(r)–g22(r), but we would expect

g12(r)–g11(r) << 0. Thus, g21(r)–g22(r) reveals if surviving and dead

recruits follow the same overall pattern and g12(r)–g11(r) reveals if

there is an additional pattern within dead recruits that is independent

from the location of the surviving recruits (Watson, Roshier &

Wiegand 2007; Getzin et al. 2008).

Analysis 3: Survival of recruits vs. adults

To quantify the impact of adults on the survival of recruits we ask if

the probability of survival of recruits depends on the distance from

adult plants. The appropriate null model for this question is again

random labelling, but the test statistic needs to consider additionally

the impact of adults. The software Programita (Wiegand &Moloney

2004) provides an appropriate test statistics (e.g. Biganzoli, Wiegand

& Batista 2009; Xu et al. 2009), which was also independently

proposed byDe laCruz et al. (2008).We have adults plants (subscript

a), dead recruits (subscript 1) and surviving recruits (subscript 2). The

test statistic which estimates the probability of survival of recruits in

dependence on the distance r from adults (subscript a) is given by

pa;2ðrÞ ¼k2

ðk1 þ k2Þga;2ðrÞga;1þ2ðrÞ

eqn 1

where (k1 + k2) and k2 are the intensities of recruits and of the

surviving recruits, respectively, and ga,1+2(r) and ga,2(r) are the

bivariate pair correlation functions measuring the intensity

normalized neighbourhood density of surviving and dead recruits

(1 + 2) and surviving recruits (2), respectively, around adults (a).

The expectation of this test statistic under random labelling is

the overall probability of survival, i.e. number of surviving

recruits divided by number of recruits. In the case of negative

interactions exerted by adults at distance r (i.e. competition) we

expect a lower probability of survival, i.e. pa,2(r) < k2 ⁄ (k1 + k2),whereas positive interactions would be indicated by a higher

probability of survival in the proximity of heterospecific plants,

i.e. pa,2(r) > k2 ⁄ (k1 + k2).

Results

ANALYSIS 0 : UNIVARIATE SPATIAL PATTERNS

Both recruits and adults were clearly clustered for all

treatments (Fig. 1), which confirms the visual inspection of the

mapped patterns (Appendix S1). The patterns of adults were

relatively similar between the two treatments showing cluster

sizes of roughly 0Æ5 m (the O-ring statistic approached the

simulation envelopes at this scale), but the adult density was

six times higher under the grazing treatment. Recruits showed

extreme aggregation, especially under the mowing treatment,

with similar densities of approximately 5Æ5 recruits m)2.

ANALYSIS 1 : RECRUIT -ADULT RELATIONSHIPS

Recruits under the grazing treatment did not show any

aggregation to adults and the adult-recruit relationship did not

change from year 2000 to 2002 (Fig. 2a–c) except that the

recruit neighbourhood density decreased due to the recruit

mortality. However, under the mowing treatment in year 2000

there was a significant, positive association of recruits at

distances of 40 cm away from adults (Fig. 2d; Table 1). The

shape of the O-ring statistics indicates a (non-significant)

tendency of repulsion between recruits and adults at small

scales which changes to significant attraction at intermediate

scales (40 cm) and then disappears at larger scales. Recruit

morality from 2000 to 2001 changed the adult–recruit

relationship under themowing treatment substantially. Besides

a decrease in the neighbourhood density due to mortality, the

attraction at the 40 cm scale disappeared completely, yielding

independent patterns (Fig. 2e,f; Table 1). There was little

change between 2001 and 2002. Interestingly, the spatial

434 H. Jacquemyn et al.

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relationships of both treatments are similar at years 2001 and

2002.

ANALYSIS 2 : RECRUIT SURVIVAL

Mortality of recruits under the grazing treatment was almost

random, with the exception of a small scale aggregation of

dead recruits at year 2001 (Fig. 3a), an additional small-scale

pattern in dead recruits (Figs. 3d vs. e) and negative small-scale

density dependent effect (Fig. 3f). All three significant depar-

tures from the randommortality hypothesis are consistent with

small scale density dependent mortality under the scramble

type (although the tendency of segregation of dead and surviv-

ing recruits was not significant; Fig. 3c). However, in year 2002

recruit mortality was entirely random (Fig. 3g–l).

The 2001 mortality pattern under the mowing treatment

contrasted sharply with that under the grazing treatment. Due

to the extreme clustering of recruits (Supporting Information

Appendix S1, Fig. 1b–d), we observe strong departures from

random labelling in all test statistics (Figs. 4a–f; Table 1).

Dead recruits are clustered (Fig. 4a), surviving recruits are

more regular than the pre-mortality pattern (Fig. 4b), surviv-

ing and dead recruits are strongly segregated at scales up to

20 cm (Fig. 4c), there is a strong additional pattern in dead

recruits (Figs. 4d vs. e), and strong negative small-scale density

dependence in mortality (Fig. 4f). These departures from ran-

dommortality are consistent with density dependent mortality

of the scramble type. Curiously, the 2002mortality in themow-

ing treatment shows exactly the same characteristics as the

2001 mortality in the grazing treatment: a significant small

scale aggregation of dead recruits (Fig. 4g), an additional

small-scale pattern in dead recruits (Figs. 4j vs. k) and a

(weakly) significant negative small-scale density dependent

effect (Fig. 4l). Again, all three departures from random

labelling in year 2002 are consistent with small scale density

dependentmortality.

ANALYSIS 3 : SURVIVAL OF RECRUITS VS. ADULTS

There was no clear indication that adults influenced the sur-

vival of recruits although there was a tendency towards posi-

tive interactions: the probability of survival tended to be higher

in the neighbourhood of adults (Fig. 5b–d; Table 1). However,

at a scale of 40 cm, which was also the scale of maximal attrac-

tion of recruits around adults, the test statistic indicated a

weakly significant positive effect at approximately 40 cm,

slightly outside the simulation envelopes under the mowing

treatment for year 2001. This additional (weak) pattern in sur-

vival was also depicted by the test statistic g21(r) - g22(r) which

indicated additional aggregation of surviving recruits condi-

tionally on the pre-mortality pattern (Fig. 4e).

Discussion

SPATIAL CLUSTERING OF SEEDLINGS AND ADULTS

In plant populations, significant spatial structure (a departure

from complete spatial randomness) is the norm and plants in

mesic environments are commonly clustered together in

groups of conspecifics (Law et al. 2000). The results from our

study are similar to these general observations, as in all four

populations both adults and recruits showed significant spatial

clustering. Three major causes of spatial structure (aggrega-

tion or segregation) have been identified (Coomes et al. 1999):

MCL adults

0

5

10

15

20MCL recruits 00

1

10

100

1000

G adults

Spatial scale r [m] Spatial scale r [m] Spatial scale r [m] Spatial scale r [m] 0·0 0·2 0·4 0·6 0·8 1·0 0·0 0·2 0·4 0·6 0·8 1·0 0·0 0·2 0·4 0·6 0·8 1·0 0·0 0·2 0·4 0·6 0·8 1·0

O-r

ing

stat

istic

O(r

) [n

o pl

ants

m–2

]O

-rin

g st

atis

tic O

(r)

[no

plan

ts m

–2]

O-r

ing

stat

istic

O(r

) [n

o pl

ants

m–2

]O

-rin

g st

atis

tic O

(r)

[no

plan

ts m

–2]

0

10

20

30

40G recruits 00

1

10

100

1000

MCL surviving recruits 01

G surviving recruits 01

MCL surviving recruits 02

G surviving recruits 02

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 1. Analysis of the univariate spatial patterns of adults and recruits (00: recruits present in 2000, 01: surviving recruits in 2001; 02: surviving

recruits in 2002) under the two contrasting management treatments, grazing (G) and mowing plus clearing (MCL). The data were contrasted to

the null model of complete spatial randomness. The O-ring statisticO(r) giving the density of plants at distance r away from a typical plant of the

pattern (dots), simulation envelopes (black solid line) being the 5th lowest and highest values of theO-ring statistic taken from the 199 simulations

of null model, and the average O-ring statistic under the null model (grey solid line). Note the logarithmic scale of the y-axis for the recruit pat-

terns (b–d and f–h). The patterns are aggregated if the O-ring statistic is above the simulation envelopes.

Spatial population dynamics in Primula vulgaris 435

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(i) localized dispersal, (ii) intraspecific and interspecific interac-

tions, and (iii) local heterogeneity in topography, resource sup-

ply or background vegetation.

The first year after ditch banks were cleared, we found

strong spatial clustering of seedlings around adults (Fig. 2d),

indicating that most seeds germinate in the immediate vicinity

of the mother plant. Although strong clustering of seedlings

around adults is not necessarily direct evidence for limited seed

dispersal (Jacquemyn et al. 2007), previous studies using seed

traps to assess seed dispersal distances in P. vulgaris have

shown that it is usually restricted to a few centimetres or deci-

metres from maternal plants. Cahalan & Gliddon (1985), for

example, reported amean recruitment distance of 9Æ8 cm. Sim-

ilarly, Campagne et al. (2009) reported median dispersal dis-

tances of 10 and 25 cm in two populations in France. Because

ditch banks were cleared early in the season before plants had

set seed, creating favourable conditions for germination, it

seems plausible that establishment limitation was less impor-

tant in determining seedling recruitment in the cleared than in

the grazed sites. In the latter, the closed vegetation limited seed

germination to suitable microsites (most often small gaps or

small mounds of bare soil created by the digging activity of

molesTalpa europaea). As the location of these small-scale dis-

turbances is completely independent of the location of adult

plant, this explains why seedlings are not as tightly clustered

around adults in grazed sites as in the mown sites (Fig. 2a).

The fact that seedling densities were about six times higher in

the cleared sites also suggests that the availability of suitable

micro-sites was less limiting to seedling recruitment in the

cleared than in the grazed sites.

SEEDLING SURVIVAL , MORTALITY AND PERSISTENCE

INTO LATER LIFE STAGES

To explain species distribution and coexistence patterns, Jan-

zen (1970, 1971) and Connell (1971) proposed a model relating

G, 00

0

2

4

6

8

10

12

14 G, 01 G, 02

MCL, 00

Spatial scale r [m] Spatial scale r [m] Spatial scale r [m]

0·0 0·2 0·4 0·6 0·8 1·0 0·0 0·2 0·4 0·6 0·8 1·0 0·0 0·2 0·4 0·6 0·8 1·0

O-r

ing

stat

istic

O12

(r)

[no

plan

ts m

–2]

O-r

ing

stat

istic

O12

(r)

[no

plan

ts m

–2]

0

2

4

6

8

10

12

14 MCL, 01 MCL, 02

(a) (b) (c)

(d) (e) (f)

Fig. 2. Analysis of the recruit-adults relationship. Test of independence between the pattern of recruits in years 2000, 2001, and 2002 and the adult

pattern under the two contrasting management treatments grazing (G) and mowing plus clearing (MCL). The data were compared to toroidal

shift as null model. The bivariate O-ring statisticO12(r) giving the density of recruits at distance r away from a typical adults plant (dots), simula-

tion envelopes (black solid line) being the 5th lowest and highest values of theO12(r) taken from the 199 simulations of null model, and the aver-

age O12(r) under the null model (grey solid line). Recruits are significantly aggregated around adults if the O12(r) is above the simulation

envelopes.

Table 1. Results of goodness-of-fit tests. We used 199 Monte Carlo

simulations of a null model to assess significant departures of the

observed data from the null model. The table shows the rank of the

test statistic ui for the observed pattern (i = 0) within the simulated

patterns (i = 1, …, 199). If rank u0 > 190 the null model is rejected

at the distance interval of interest on a 5% level (*), and if

rank > 198 at a 1% level (**). The distance intervals were 0–1 m

(Figs 1, 2 and 5) and 0–30 cm (Figs 3 and 4)

Panel Fig 1 Fig 2 Fig 3 Fig 4 Fig 5

A 200** 90 199** 200** 164

B 200** 110 112 200** 168

C 200** 159 144 200** 118

D 200** 199** 199** 200** 120

E 200** 168 6 200**

F 200** 172 195* 200**

G 200** 137 200**

H 200** 109 119

I 97 124

J 89 200**

K 106 47

L 121 191*

436 H. Jacquemyn et al.

� 2010 The Authors. Journal compilation � 2010 British Ecological Society, Journal of Applied Ecology, 47, 431–440

MCL, 00–01

–500

–400

–300

–200

–100

0

MCL, 00–01

–500

–400

–300

–200

–100

0MCL, 00–01

0

50

100

150

200

MCL, 01–02

–150

–100

–50

0

50MCL, 01–02

–150

–100

–50

0

50

MCL, 00–01

–50

0

50

100

150

200

250

MCL, 01–02

Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]

–40

–20

0

20

40MCL, 01–02

0

20

40

60

80

100

MCL, 00–01

0

100

200

300

400

500

MCL, 01–02

0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3

g 11(r

)

g 22(r

)g 22

(r)

g 12(r

)g 12

(r)

g 12(r

)–g 11

(r)

g 12(r

)–g 11

(r)

g 21(r

)–g 22

(r)

g 21(r

)–g 22

(r)

g 1,1+

2(r)

–g2,

1+2(

r)g 1,

1+2(

r)–g

2,1+

2(r)

g 11(r

)

0

50

100

150

200

250

MCL, 00–01

0

50

100

150

200

MCL, 01–02

0

20

40

60

80

100

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)

Fig. 4. Analysis of survival for recruits under the mowing treatment. Conventions as in Fig. 3.

G, 00–01

g 12(r

)–g 11

(r)

g 12(r

)–g 11

(r)

g 21(r

)–g 22

(r)

g 21(r

)–g 22

(r)

g 1,1+

2(r)

–g2,

1+2(

r)g 1,

1+2(

r)–g

2,1+

2(r)

–30

–20

–10

0

10

20G, 00–01

–30

–20

–10

0

10

20G, 00–01

g 22(r

)g 22

(r)

g 12(r

)g 12

(r)

05

10152025303540

G, 01–02

–50–40–30–20–10

0102030

G, 01–02

–50–40–30–20–10

0102030

G, 00–01

–15–10–5

05

101520

G, 01–02

Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]Spatial scale r [m]

–15–10–505

101520

G, 01–02

0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·3 0·0 0·1 0·2 0·30·0 0·1 0·2 0·30

5

10

15

20

25

30

G, 00–01

g 11(r

)g 11

(r)

05

10152025303540

G, 01–02

0

20

40

60

80

G, 00–01

05

10152025303540

G, 01–02

0

5

10

15

20

25

30

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)

Fig. 3. Analysis of survival for recruits under the grazing treatment. We compared the spatial pattern of surviving (index 2) and dead recruits

(index 1) at years 2001 (00–01) and 2002 (01–02) with the null model of randommortality. We used different test statistics based on pair correla-

tion functions to test the random mortality null model; each test statistic depicts a different biological effect. The observed test statistics (dots),

simulation envelopes (black solid line) being the 5th lowest and highest values of the test statistic taken from the 199 simulations of null model,

and the average test statistic under the null model (grey solid line).

G, 00-01Pro

babi

lity

of s

urvi

val

0·0

0·2

0·4

0·6

0·8

1·0

G, 01-02

MCL, 00-01

Distance from adult [m]0·2 0·4 0·6 0·8 1·0 0·2 0·4 0·6 0·8 1·0

Pro

babi

lity

of s

urvi

val

0·0

0·2

0·4

0·6

0·8

1·0

MCLG, 01-02

Distance from adult [m]

(a) (b)

(c) (d)

Fig. 5. Probability of survival of recruits

depending on their distance from adults. We

compared the spatial pattern of surviving

(index 2) and dead recruits (index 1) at years

2001 (00–01) and 2002 (01–02) to the null

model of random mortality, but used a test

statistic that gives the probability of survival

pa,2(r) of recruits at distance r from adults

plants. The observed test statistics (dots),

simulation envelopes (black solid line) being

the 5th lowest and highest values of the test

statistic taken from the 199 simulations of

null model, and the average test statistic

under the randommortality null model (grey

solid line).

Spatial population dynamics in Primula vulgaris 437

� 2010 The Authors. Journal compilation � 2010 British Ecological Society, Journal of Applied Ecology, 47, 431–440

recruitment to distance from the parent plant. In their view,

predators or pathogens attracted to the reproductive adult or

high densities of seed or seedlings may hamper seedling

establishment in the immediate vicinity of the parent. Adult

conspecifics may also affect seedling survivorship through

competition for similar resource requirements (Leishman

1999). On the other hand, De la Cruz et al. (2008) found that

plants may have higher chances of survival in the direct

neighbourhood of adult plants in stressful environments due

to facilitation. In this case, the effects of abiotic factors, such as

soil moisture availability, are more important than density-

dependent processes for predicting the fate of individuals

(Fowler 1995).

However, there was no compelling evidence that adults

influenced the survival of recruits in the immediate neighbour-

hood in any of the studied populations, although there was a

slight tendency towards positive interactions. Predation or

pathogens are unlikely factors affecting the distribution of

P. vulgaris plants.Most mammals known to feed onP. vulgaris

(fallow deer Dama dama L., muntjac Muntiacus reevesi or

small mammals) mainly feed on the inflorescences (Tabor

1998; Rackham 1999), but they do little harm to the plants

themselves. Similarly, no fungi occurring on P. vulgaris are

known to cause substantial damage to the plants (reviewed in

Jacquemyn et al. 2009). The slight tendency to towards

positive interactions, on the other hand, might be related to the

fact that in the direct neighbourhood of adult plants seedlings

may be protected from drought through shade provided by the

leaves.

In the cleared sites there was clear evidence for strong

negative density-dependent mortality, whereas mortality of

recruits under the grazing treatment was almost random. In

the former, drought in summer due to slow vegetation recover

may have led to competition for limited water availability.

Because all recruits compete for the same resource, this effect

should therefore be most prevalent in high density phases

(Kenkel 1988). In contrast, densities of seedlings were much

lower in grazed sites and water availability was probably less

limiting due to higher vegetation cover. In this case, survival of

recruits was probably less dependent on competition for

available water and consequently we found only weakly

significant indications for negative density dependence in

mortality at scales<5 cm.

SPATIAL POINT PATTERN ANALYSIS AS A USEFUL

TOOL FOR THE STUDY OF RARE AND ENDANGERED

PLANT SPECIES

The heuristic power of the analysis of spatial patterns has been

widely acknowledged and spatial point pattern analyses

are widely used in ecological research (Law et al. 2009).

Surprisingly, they have only rarely been applied to the study of

rare or endangered plant species. Using a set of seven summary

statistics, we illustrate how this allows for a comprehensive

description and understanding of non-random effects in

mortality and can provide important information for the

management of rare plant species.

The test statistic g1,1+2 - g2,1+2 (Yu et al. 2009), which

compares the density of dead and surviving recruits (i.e.

1 + 2) around dead recruits (i.e. pattern 1) with that

around surviving recruits (i.e. pattern 2), provides a direct

test of density dependent effects in mortality. This is an

important advance since directly revealing density-depen-

dent effects is of great interest for ecological theory (Clark

et al. 1998). Mortality may also be caused by factors which

are independent of the overall distribution of recruits, for

example the presence of adults or plants of other species,

or by environmental differences. Contrasting the summary

statistic g21 - g22 with g12 - g11 allows assessing if recruit

mortality included such an additional effect independently

from the pattern of surviving recruits. Finally, detecting

the effects of a third pattern (e.g. adult plants or plants of

different species) on the probability of mortality has only

recently been addressed independently by De la Cruz et al.

(2008) using a summary statistic based on the K-function

and Biganzoli et al. (2009) and Xu et al. (2009) using a

summary statistic based on pair correlation functions. Here

we used the probability of survival at distance r away from

a typical adult plant as a summary statistic that is directly

interpretable.

Our results (Table 1) also showed that not all summary sta-

tistics depict existing departures from random mortality at the

same time, indicating that revealing specific biological effects

requires specific summary statistics. We thus recommend that

randommortality analyses should use a set of several summary

statistics simultaneously to gain a comprehensive understand-

ing on the nature of departures from the random mortality

hypothesis.

Conclusion

Earlier demographic studies on this species in these types of

habitats have stressed the importance of creating optimal

conditions for recruitment to increase population growth

rates (Endels et al. 2007). Our results confirmed that the

availability of suitable sites was the most important factor

determining seed germination and early establishment of

seedlings in the studied populations, but also highlighted

that high seed germination was associated with strong clus-

tering of seedlings followed by high mortality. Nevertheless,

the highest population growth rates of P. vulgaris were

observed at cleared sites (Endels et al. 2007), suggesting that

the frequency of ditch bank clearing should not be changed

drastically. In grazed sites, on the other hand, increasing the

size and number of suitable microsites will most likely result

in increased germination and seedling establishment and

eventually in increased population growth rates. Since many

populations along arable fields no longer receive any kind of

disturbance, these populations will inevitably decline, and

since 2000 several populations have already gone extinct

(Endels et al. 2007). The results from this study urge for the

re-introduction of these small-scale management practices,

as they increase germination, establishment and subsequent

survival of recruits. In the initial stage, this can be best

438 H. Jacquemyn et al.

� 2010 The Authors. Journal compilation � 2010 British Ecological Society, Journal of Applied Ecology, 47, 431–440

achieved by scraping of ditch banks, followed by annual

mowing (with removal of all litter) or grazing, provided that

a sufficient number of microsites are being constantly

created.

Acknowledgements

Wewould like to thank Rein Brys and Eric Van Beek for help during fieldwork

and two anonymous reviewers for constructive comments on an earlier version

of this paper.

References

Biganzoli, F., Wiegand, T. & Batista, W.B. (2009) Fire-mediated interactions

between shrubs in a South American temperate savannah.Oikos, 118, 1383–

1395.

Blomqvist, M.M., Vos, P., Klinkhamer, P.G.L. & ter Keurs, W.J. (2003)

Declining plant species richness of grassland ditch banks – a problemof colo-

nization or extinction?Biological Conservation, 109, 391–406.

Boyd,M., Silvertown, J. & Tucker, C. (1990) Population ecology of heterostyle

and homostyle Primula vulgaris: growth, survival and reproduction in field

populations. Journal of Ecology, 78, 799–713.

Brys, R., Jacquemyn, H., Endels, P., De Blust, G. & Hermy, M. (2004)

The effects of grassland management on plant performance and

demography in the perennial herb Primula veris. Journal of Applied

Ecology, 41, 1080–1091.

Cahalan, C.M. & Gliddon, C. (1985) Genetic neighbourhood sizes in Primula

vulgaris.Heredity, 54, 65–70.

Campagne, P., Affre, L., Baumel, A., Roche, P. & Tatoni, T. (2009) Fine-scale

response to landscape structure in Primula vulgaris Huds.: does hedgerow

network connectedness ensure connectivity through gene flow. Population

Ecology, 51, 209–219.

Clark, J.S., Macklin, E. &Wood, L. (1998) Stages and spatial scales of recruit-

ment limitation in southern Apalachian forests. Ecological Monographs, 68,

213–235.

Clark, J.S., Beckage, B., Camill, P., Cleveland, B., HillRisLambers, J., Lighter,

J., McLachlan, J., Mohan, J. & Wyckoff, P. (1999) Interpreting recruitment

limitation in forests.American Journal of Botany, 86, 1–16.

Clark, C.J., Poulsen, J.R., Levey, D.J. &Osenberg, C.W. (2007) Are plant pop-

ulations seed limited? A critique and meta-analysis of seed addition experi-

mentsAmericanNaturalist, 170, 128–142.

Connell, J.H. (1971) On the role of natural enemies in preventing competitive

exclusion in some marine animals and in rain forest trees. Dynamics of

Populations (eds P.J.D. Boer & G.R. Gradwell), pp. 290–310. Pudoc,

Wageningen.

Coomes, D.A., Rees, M. & Turnbull, L. (1999) Identifying aggregation and

association in fullymapped spatial data.Ecology, 80, 554–565.

De la Cruz, M., Romao, R.L., Escudero, A. & Maestre, F.T. (2008) Where do

seedlings go? A spatio-temporal analysis of seedling mortality in a semi-arid

gypsophyteEcography, 31, 1–11.

De Luis, M., Raventos, J., Wiegand, T. & Gonzalez-Hidalgo, J.C. (2008) Tem-

poral and spatial differentiation in seedling emergence may promote species

coexistence in Mediterranean fire-prone ecosystems. Ecography, 31, 620–

629.

Diggle, P.J. (2003) Statistical Analysis of Point Patterns, 2nd edn. Arnold, Lon-

don.

Endels, P., Jacquemyn, H., Brys, R., Hermy,M. &De Blust, G. (2002) Tempo-

ral changes in the population structure of primrose (Primula vulgarisHuds.)

in an agricultural landscape and implications for conservation. Biological

Conservation, 105, 11–25.

Endels, P., Jacquemyn, H., Brys, R. & Hermy, M. (2007) Genetic erosion

explains deviation from demographic response to habitat and year variation

in relic populations of the perennial Primula vulgaris. Journal of Ecology, 95,

960–972.

Fowler, N.L. (1995) Destiny-dependent demography in two grasses: a five-year

study.Ecology, 76, 2145–2164.

Getzin, S., Dean, C., He, F., Trofymow, J.A., Wiegand, K. & Wiegand, T.

(2006) Spatial patterns and competition of tree species in a Douglas-fir chro-

nosequence on Vancouver Island.Ecography, 29, 671–682.

Getzin, S., Wiegand, T., Wiegand, K. & He, F. (2008) Heterogeneity influences

spatial patterns and demographics in forest stands. Journal of Ecology, 96,

807–820.

Goreaud, F. & Pelissier, R. (2003) Avoiding misinterpretation of biotic

interactions with the intertype K12-function: population independence

vs. random labelling hypotheses. Journal of Vegetation Science, 14,

681–692.

Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. (2008) Statistical Analysis and

Modelling of Spatial Point Patterns. JohnWiley & Sons, Chichester.

Jacquemyn, H., Brys, R., Vandepitte, K., Honnay, O., Roldan-Ruiz, I. &

Wiegand, T. (2007) A spatially explicit analysis of seedling recruitment

in the terrestrial orchid Orchis purpurea. New Phytologist, 176, 448–

459.

Jacquemyn, H., Endels, P., Brys, R., Hermy, M. &Woodell, S.R.J. (2009) Bio-

logical flora of the British Isles: Primula vulgarisHuds. (P. acaulis (L.) Hill).

Journal of Ecology, 97, 812–833.

Janzen, D.H. (1970) Herbivores and the number of tree species in tropical for-

ests.AmericanNaturalist, 104, 501–528.

Janzen, D.H. (1971) Seed predation by animals. Annual Review of Ecology and

Systematics, 2, 465–492.

Kenkel, N.C. (1988) Pattern of self-thinning in jack pine: testing the random

mortality hypothesis.Ecology, 69, 1017–1024.

Kleijn, D. & Verbeek, M. (2000) Factors affecting the species composi-

tion of arable field boundary vegetation. Journal of Applied Ecology,

37, 256–266.

Law, R., Purves, D.W., Murrell, D.J. & Dieckmann, U. (2000) Causes and

effects of small-scale spatial structure in plant populations. Integrating Ecol-

ogy and Evolution in a Spatial Context (eds J. Silvertown & J. Antonovics),

pp. 21–44. Blackwell Science, London.

Law, R., Illian, J., Burslem, D.F.R.P., Gratzer, G., Gunatilleke, C.V.S.

& Gunatilleke, I.A.U.N. (2009) Ecological information from spatial

patterns of plants: insights from point process theory. Journal of Ecol-

ogy, 97, 616–628.

Leishman, M.R. (1999) How well do plant traits correlate with establishment

ability? Evidence from a study of 16 calcareous grassland species. New

Phylologist, 141, 487–496.

Loosmore, N.B. & Ford, E.D. (2006) Statistical inference using the G or K

point pattern spatial statistics.Ecology, 87, 1925–1931.

Pfeifer, M., Wiegand, K., Heinrich, W. & Jetschke, G. (2006) Long-term

demographic fluctuations in an orchid species driven by weather:

implications for conservation planning. Journal of Applied Ecology, 43,

313–324.

Poulsen, J.R., Osenberg, C.W., Clark, C.J., Levey, D.J. & Bolker, B.M. (2007)

Plants as reef fish: fitting the functional form of seedling recruitment. Ameri-

can Naturalist, 170, 167–183.

Rackham, O. (1999) The woods 30 years on: where have the Primroses gone?

Nature in Cambridgeshire, 41, 73–87.

Rees, M., Grubb, P.J. & Kelly, D. (1996) Quantifying the impact of competi-

tion and spatial heterogeneity on the structure and dynamics of a four-spe-

cies guild of winter annuals.AmericanNaturalist, 147, 1–32.

Riginos, C., Milton, S.J. & Wiegand., T. (2005) Context-dependent negative

and positive interactions between adult shrubs and seedlings in a semi-arid

shrubland. Journal of Vegetation Science, 16, 331–340.

Robinson, R.A. & Sutherland, W.J. (2002) Post-war changes in arable

farming and biodiversity in Great Britain. Journal of Applied Ecology,

39, 157–176.

Stoate, C., Boatman, N.D., Borralho, R.J., Rio Carvalho, C., de Snoo, G.R. &

Eden, P. (2001) Ecological impacts of arable intensification in Europe. Jour-

nal of EnvironmentalManagement, 63, 337–365.

Stoyan, D. & Stoyan, H. (1994) Fractals, Random Shapes and Point Fields.

Methods of Geometrical Statistics. Wiley, Chichester.

Tabor, R.C.C. (1998) The oxlip in Britain is its future in doubt?BritishWildlife,

10, 92–101.

Turnbull, L.A., Crawley, M.J. & Rees, M. (2000) Are plant populations seed-

limited?A review of seed sowing experimentsOikos, 88, 225–238.

Turnbull, L.A., Coomes, D., Hector, A. & Rees, M. (2004) Seed mass

and the competition ⁄ colonization trade-off: competitive interactions and

spatial patterns in a guild of annual plants. Journal of Ecology, 92,

97–109.

Valverde, T. & Silvertown, J. (1995) Spatial variation in the seed ecology of a

woodland herb (Primula vulgaris) in relation to light environment. Func-

tional Ecology, 9, 942–950.

Watson, D.M., Roshier, D.A. &Wiegand, T. (2007) Spatial ecology of a para-

sitic shrub: patterns and predictions.Austral Ecology, 32, 359–369.

Whale, D.M. (1984) Habitat requirements in Primula species.New Phytologist,

97, 665–679.

Wiegand, T. & Moloney, K.A. (2004) Rings, circles, and null-models for point

pattern analysis in ecology.Oikos, 104, 209–229.

Spatial population dynamics in Primula vulgaris 439

� 2010 The Authors. Journal compilation � 2010 British Ecological Society, Journal of Applied Ecology, 47, 431–440

Wiegand, T., Kissling, W.D., Cipriotti, P.A. & Aguiar, M.R. (2006) Extending

point pattern analysis to objects of finite size and irregular shape. Journal of

Ecology, 94, 825–837.

Wiegand, T., Gunatilleke, C.V.S. & Gunatilleke, I.A.U.N. (2007a) Species

associations in a heterogeneous Sri Lankan dipterocarp forest. American

Naturalist, 170, E77–E95.

Wiegand, T., Gunatilleke, C.V.S., Gunatilleke, I.A.U.N. & Okuda, T. (2007b)

Analyzing the spatial structure of a Sri Lankan tree species with multiple

scales of clustering.Ecology, 88, 3088–3102.

Xu, X., Harwood, T.D., Pautasso, M. & Jeger, M.J. (2009) Spatio-temporal

analysis of an invasive plant pathogen (Phytophthora ramorum) in England

andWales.Ecography, 32, 504–516.

Yu, H., Wiegand, T., Yang, X.H. & Ci, I.J. (2009) The impact of fire and

density-dependent mortality on the spatial patterns of a pine forest in the

Hulun Buir Sandland, Inner Mongolia, China. Forest Ecology and Manage-

ment, 257, 2098–2107.

Received 16 June 2009; accepted 12 January 2010

Handling Editor: Paul Lukacs

Supporting Information

Additional supporting information may be found in the online ver-

sion of this article.

Appendix S1. Location of adults (red dots) and recruits (black dots)

in four populations of Primula vulgaris located along ditch bank

habitats.

As a service to our authors and readers, this journal provides support-

ing information supplied by the authors. Such materials may be re-

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Technical support issues arising from supporting information (other

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