Modelling mortality and dispersal: consequences of parameter

generalisation on metapopulation dynamics

Gwenaelle Mennechez, Sandrine Petit, Nicolas Schtickzelle and Michel Baguette

Mennechez, G., Petit, S., Schtickzelle, N. and Baguette, M. 2004. Modelling mortalityand dispersal: consequences of parameter generalisation on metapopulation dynamics.�/ Oikos 106: 243�/252.

Modelling dispersal is a fundamental step in the design of population viability analyses.Here, we address the question of the generalisation of population viability analysismodels across landscapes by comparing dispersal between two metapopulations of thebog fritillary butterfly (Proclossiana eunomia ) living in similar highly fragmentedlandscapes (B/1% of suitable habitat in 9 km2). Differences in dispersal patterns wereinvestigated using the virtual migration (VM) model, which was parameterised withcapture�/mark�/recapture data collected during several years in both landscapes. TheVM model allows the estimation of 6 parameters describing dispersal and mortality aswell as the simulation of dispersal in the landscapes. The model revealed largedifferences in the VM parameter estimates between the two landscapes andconsequently, simulations indicated differential rates of emigration and dispersalmortality. Furthermore, results from crossed-simulations i.e. simulations performed inone of the landscape but using parameter estimates from the other landscape emphasizethat dispersal parameters are very specific to each metapopulation and to theirlandscape. Hence, we urge conservation biologists to be cautious with such parametergeneralisations, even for the same species in comparable landscapes.

G. Mennechez, N. Schtickzelle and M. Baguette, Biodiversity Research Centre, Univ.Catholique de Louvain, Croix du Sud 4, BE-1348 Louvain-la-Neuve, Belgium(baguette@ecol.ucl.ac.be). �/ S. Petit, Centre For Ecology and Hydrology, MerlewoodResearch Station, Grange-over-Sands, Cumbria, UK, LA11 6JU.

All over the world, species face loss and fragmentation

of their natural habitats by human activities (Wilcox and

Murphy 1985, Saunders et al. 1991). In western Europe,

specialist species are now restricted to small remnants of

suitable habitat surrounded by a more or less hostile

matrix. In well known taxonomic groups like butterflies,

most specialist species have been shown to be dramati-

cally declining (Warren 1993, Van Swaay and Warren

1998, Maes and Van Dyck 2001). Nevertheless, such

species with narrow ecological requirements may persist

in fragmented landscapes as metapopulations, i.e. as-

semblages of local populations connected by dispersal

and potentially submitted to extinctions and recolonisa-

tions (Gilpin and Hanski 1991, Hanski and Gilpin 1997,

Hanski 1999).

The metapopulation paradigm is an operational

framework to predict the long-term persistence of

species living in highly fragmented landscapes (Hanski

et al. 1996, Hanski and Gilpin 1997, Baguette and

Stevens 2004). Different kinds of population viability

analysis (PVA) models (notably patch occupancy mod-

els, structured population models), currently developed

to assess the fate of endangered species in real conditions

or under different potential management plans, are

derived from metapopulation biology (Akcakaya and

Sjogren-Gulve 2000). The parameterisation of such

Accepted 2 December 2003

Copyright # OIKOS 2004ISSN 0030-1299

OIKOS 106: 243�/252, 2004

OIKOS 106:2 (2004) 243

models, and especially of the structured populations

models, is highly demanding in accurate estimates,

therefore requiring large and comprehensive empirical

data-sets on the focal species. For example, the analysis

of the viability of the bog fritillary Proclossiana eunomia

by Schtickzelle and Baguette (2004) is based on a long

term study in which a patchy population was monitored

during 11 consecutive years. Of course, it is unimagin-

able to extend such long term studies to masses of

endangered species and to all landscapes contexts. A

crucial question in conservation biology is therefore to

what extent models constructed for a specific species in a

particular landscape can be extrapolated to similar

landscapes or to related species (Wahlberg et al. 1996,

Rodriguez and Andren 1999, White 2000). Without

potential for a generalisation of models from one system

to another, we have to admit that their usefulness may be

limited in the more general perspectives of biodiversity

conservation. In this paper, we address this question of

the generalisation of PVA across landscapes by compar-

ing dispersal rates �/ a key parameter in the metapopula-

tion functioning �/ between two highly fragmented

landscapes.

Few attempts have been made to investigate differ-

ences in dispersal rates between metapopulation inhabit-

ing different landscapes (Mennechez et al. 2003). Surely,

such comparisons are not so trivial and require efficient

tools (Wahlberg et al. 2002). The virtual migration

model (VM) developed by Hanski et al. (2000) is a

multi-population model designed to estimate dispersal

and survival of individuals in metapopulations. This

model is well adapted to compare the functioning of

metapopulations since it allows the comparison of

movements (1) between species within the same network

of habitat patches or (2) within the same species between

different networks of habitat patches. The VM model

has already been used successfully to quantify the

dispersal rates in the bog fritillary butterfly as well as

their variation between sexes and across years (Petit et

al. 2001) and to compare metapopulation structure and

movements in five species of checkerspot butterflies

(Wahlberg et al. 2002).

Here we investigate differences in dispersal patterns of

P. eunomia between two highly fragmented landscapes of

the uplands of the Belgian Ardenne. We first parame-

terised the VM model using data collected in the two

landscapes during several years in order to estimate

dispersal and mortality. In a second step, dispersal was

simulated in both landscapes to obtain a general picture

of inter-patch movements, given their respective para-

meter estimates. Finally, using the parameter estimates

obtained in one landscape, we simulated dispersal and

survival in the other landscape, in order to assess

whether parameter generalisation will induce changes

in the prediction of dispersal pattern.

Material and methods

The species

In Belgium, the bog fritillary butterfly (Proclossiana

eunomia ESPER; Lepidoptera, Nymphalidae) is a spe-

cialist species living in a very restricted habitat (bogs and

unfertilised wet meadows) where its only host plant

Polygonum bistorta L. grows. Because of changes in

agricultural practices in the middle of the 20th century,

the spatial extent of this transitional habitat, which was

maintained by traditional agro-pastoral practices, has

been dramatically reduced (Baguette et al. 2003). Nowa-

days, suitable patches of habitat remain scattered along

rivers where they form networks supporting P. eunomia

metapopulations at the landscape scale (Neve et al.

1996). Besides the loss and fragmentation of wet hay

meadows, there is also the problem of their degradation

induced by the abandon of extensive management

practices. Bistort patches that represent an early transi-

tional stage are either unmanaged and progressively

invaded by nitrophilous vegetation and scrubs or over-

grazed or overcut. Previous studies have shown that

adult butterflies fly in one generation from late May to

early July with males emerging a few days before females

(protandry, Baguette and Neve 1994). Mating system is

polygynous and male mate-locating behaviour is patrol-

ling: males continuously fly looking for unmated females

(Baguette et al. 1996).

The landscapes

Our study of survival and dispersal parameters in

metapopulations of the bog fritillary was conducted on

the ‘‘Plateau des Tailles’’ upland (20�/20 km; 50814?N,

5847?E), southern Belgium. The selected landscapes,

Lierneux and Wibrin, have both a total area of 9 km2.

They were selected because they were (1) close to each

other (ca 10 km) and 2) located at the same altitude (ca

350�/400 m). The composition of these two landscapes

was typical of the Ardenne uplands i.e. a mosaic of

grasslands, Norway spruce (Picea abies Karst) planta-

tions and deciduous forests, although forests were more

widespread in Wibrin (68%) than in Lierneux (50%). The

proportion of suitable habitat for P. eunomia �/ wet

meadows with Polygonum bistorta �/ was similar in both

landscapes, i.e. less than 1% of the total area.

Habitat patch networks within the landscapes differed

from each other in the number of suitable patches as well

as in their spatial configuration (Fig. 1). The mean patch

size was similar in both landscapes (0.429/0.43 ha and

0.319/0.25 ha in Lierneux and Wibrin respectively) but

the mean proximity index �/ a measure of the degree of

habitat fragmentation which decreases when fragmenta-

tion increases (McGarigal and Marks 1994) �/ indicated

244 OIKOS 106:2 (2004)

that habitat fragmentation was slightly higher in Wibrin

(MPI�/9.9 vs MPI�/20.7 in Lierneux).

The capture�/mark�/recapture experiment

Capture�/mark�/recapture (CMR) experiments were car-

ried out in 1993, 1994 and 1997 in Lierneux and in 1999

and 2001 in Wibrin, following the same protocol. During

the flight season, patches were visited daily, weather

permitting. Within patches, encountered butterflies were

netted and marked with an individual number on the

underside of the left hind wing with a thin-point

permanent pen. For each (re)capture, we recorded the

butterfly mark, the date, the patch location and the sex

of the individual. Butterflies were immediately released

at the location of their capture.

The capture histories obtained from the CMR studies

were used as an input to the VM model and to calculate

population size. As inter-patch movements were very few

for females in Wibrin �/ due to lower capture probabil-

ities of females which is related to the mating behaviour

(Schtickzelle et al. 2002) �/ only males were taken into

account in the present analysis. Although CMR studies

were performed in different years in Lierneux and

Wibrin, results can really be compared between the

two landscapes. Indeed, there were no differences in

climatic conditions between the two landscapes (one-way

ANOVAs: for maximum temperature, P�/0.10 and for

insolation, P�/0.36).

Virtual migration model and data analysis

The VM model was developed by Hanski et al. (2000) to

describe survival and dispersal in metapopulations living

in networks of at least 10 patches. It was constructed

under some simple biological assumptions described in

previous papers (Hanski et al. 2000, Petit et al. 2001,

Wahlberg et al. 2002). Consequently, we only give here a

general outline of the biological model; more details �/

about the statistical model and the algorithm used for

the parameter estimation �/ are to be found in Hanski et

al. (2000).

The model is based on discretised histories of marked

butterflies with events occurring in the following order in

the course of a day time. First, consider a butterfly

within a habitat patch j. Its survival probability until the

next day or until it emigrates �/ whichever occurs first �/

is Fp. If the butterfly survives it may stay in the patch or

emigrate with the probability oj calculated as a power

function scaling the patch area Aj

oj�hA�zemj (1)

where h and zem are positive parameters that describe

the propensity to emigrate from a habitat patch of unit

size (�/1 ha in the present study) and the scaling of the

emigration to patch area respectively.

Next, if the butterfly emigrates, it may die or survive

to dispersal and reach another patch. The probability of

a individual to survive dispersal from patch j, Fmj, is

assumed to increase as a sigmoid function of the

Fig. 1. Patch networkconfiguration within thelandscapes of Lierneux (A) andWibrin (B). Patch networks arecomposed of 12 and 15 habitatpatches ranging from 0.04 to1.2 ha (totalling ca 5.04 ha ofsuitable habitat) and from 0.08to 1.05 ha (totalling ca 4.69 haof suitable habitat) in Lierneuxand Wibrin respectively.Suitable habitat patches(indicated in black) are locatedalong rivers.

OIKOS 106:2 (2004) 245

connectivity of patch j, Sj, as measured by the following

equation:

Fmj�S2

j

l� S2j

(2)

where l is a positive parameter �/ that corresponds to the

square of the population connectivity for which the

probability of surviving dispersal is equal to 0.5 �/ giving

an indication on the mortality during dispersal and

where Sj is calculated by:

Sj�X

k"j

e�adjk Azim

k (3)

In which djk is the Euclidian distance between patches j

and k, and a and zim are two other model parameters

(�/0). Parameter a weights the effect of the distance on

dispersal and zim is a constant scaling the dependence of

the immigration on the patch area.

Finally, the model assumes that individuals that

survive dispersal will immigrate into the potential target

patches depending on their relative contribution to the

connectivity of patch j. Consequently, the probability of

an individual leaving patch j to end up into patch k is:

cj;k�e�adjk A

zim

k

lSj

� Sj

(4)

Of course, these events recur in the subsequent time

intervals until the individual dies. Thus, in the following

time interval (e.g. day 2. . .) the same individual may or

not survive in the patch, (re-)emigrate and eventually

reach another patch. For each butterfly, it is possible to

compute the probabilities of the observed daily events

and the likelihood of the data set is calculated as the

product of the likelihood of individual capture histories.

To conclude, VM model has six parameters which

are estimated via maximum likelihood technique: mp

(�/1�/Fp), the daily patch mortality, h, the daily

propensity to emigrate from a 1-ha size patch, a, the

dependence of dispersal to distance, l, giving an

indication on mortality during dispersal, zem and zim

scaling respectively the dependence of emigration and

the immigration on patch area.

In order to obtain a general image of dispersal and

reduce the potential random effects due to limited

number of movements between patches in each year

(especially in Wibrin), to be able to compare mean

parameters between the two landscapes VM model was

parameterised using pooled yearly CMR data-sets for

Lierneux and for Wibrin separately: capture histories

were put end to end (Schtickzelle 2003, Schtickzelle and

Baguette 2003). This was possible as experimental

conditions are similar for all years: (1) sampling was

done only during favourable climatic conditions; (2) the

catch effort is kept as constant as possible and (3)

weather conditions (maximum temperature and insola-

tion) did not significantly vary between years for each

network (one-way ANOVA and Bonferroni mean com-

parisons: on the eight comparisons of weather variables,

only insolation 1993 and insolation 1994 are different at

the 0.05 level).

Since confidence intervals of the parameters are not

symmetrical, when comparing mean parameters, we

assumed as others (Wahlberg et al. 2002, Schtickzelle

and Baguette 2003) significant difference only if their

confidence limits do not overlap.

Simulations of inter-patch movements within

networks

Using the respective mean parameter estimates and

mean local population sizes (see below for the estimation

of population size), we simulated (with VM simulation

model) dispersal and mortality in Lierneux (Lierneux/

Lierneux simulations) and in Wibrin (Wibrin/Wibrin

simulations) to evaluate the potential difference between

the two landscapes. To allow comparisons between

predictions, CMR conditions were considered to be

similar in both landscapes; (1) all butterflies were

assumed to emerge the first day; (2) a 30-day period

was simulated with CMR experiment performed every

day. For each landscape, simulations were performed 10

times.

In a second step, we generated crossed-simulations i.e.

simulations (1) in Lierneux using parameter estimates

based on CMR data from Wibrin (Lierneux/Wibrin

simulations) and (2) in Wibrin using parameter estimates

based on CMR data from Lierneux (Wibrin/Lierneux

simulations) to evaluate the consequences of generalising

parameters from a metapopulation to another.

Results of VM simulations are notably given in terms

of (1) number of butterfly-days spent in and outside the

natal patch and (2) number of successful and unsuccess-

ful (i.e. leading to the death of the butterfly) dispersal

events.

Estimation of population size

Yearly population sizes were estimated using Con-

strained Linear Models methodology (CLM, Lebreton

et al. 1992, Schwarz and Seber 1999). CLM methodol-

ogy allows to fit regression models with various factors

on the 3 demographic parameters (survival 8, catch-

ability P and recruitment B). The best model is selected

by the way of the Akaike’s Information Criterion

modified for small samples (AICc: Burnham and

Anderson 1998) which makes a trade-off between the

fit of the model and its parsimony (in terms of number of

parameters). The best model gives the factors signifi-

cantly acting on demographic parameters as well as the

246 OIKOS 106:2 (2004)

estimates for these parameters and the total population

size.

Total population sizes for the core area of Lierneux

have already been estimated (Schtickzelle et al. 2002).

For Wibrin, data-sets did not contain enough recaptures

to allow model selection to be achieved, but good

parameter estimates could nevertheless be obtained by

using a biologically adequate model. We used the model

8 s�tlinps�1Bs�[tlin�tlin2] �/ where the daily survival de-

creases linearly through the flight period with a constant

sex difference, the catchability varies between days with a

constant sex difference and the recruitment rate follows a

parabola with males emerging, reaching their abundance

peak and dying before female (protandry) �/ as it has

been found to be the best description for the bog

fritillary (Schtickzelle et al. 2002) and a closely related

species with a similar ecology, the cranberry fritillary

Boloria aquilonaris (Baguette and Schtickzelle 2003).

For some patches, CMR data sets were insufficient to

obtain accurate estimates with the selected model. We

therefore estimated total population size by multiplying

the number of captured butterflies in the patch by a

conversion coefficient (Hanski et al. 1994). This coeffi-

cient was inferred from patches for which local popula-

tion size was calculated using CLM; it equals the

estimated number of individuals divided by the number

of individuals marked.

Results

CMR study and estimation of population sizes

The pooled data-set total to 632 marked individuals and

1061 recaptures in Lierneux and 172 marked individuals

and 446 recaptures in Wibrin. On average, the number of

recaptures per individual and the capture probability

estimated in the VM model were lower in Lierneux

(1.68 times; 0.479/0.04) than in Wibrin (2.59 times;

0.719/0.01); this does not prevent comparing the two

landscapes as VM parameter estimates are corrected for

capture probability (Hanski et al 2000).

Estimates of the total male metapopulation size varied

substantially between years in both landscapes (Fig. 2).

Despite the fact that the total area of suitable habitat

was similar in both landscapes (Fig. 1), butterfly density

was on average 2.5 times higher in Lierneux with 55.8

butterflies per ha of suitable habitat versus 21.2 butter-

flies per ha in Wibrin.

The CMR experiment revealed that butterflies moved

frequently between patches: the fraction of the number

of dispersal events/total number of recaptures �/ an

indicator of dispersal rate �/ was on average 0.20 (214/

1061) in Lierneux and 0.11 (49/446) in Wibrin. The

largest dispersal distance recorded during the study was

2.37 km (1993) in Lierneux and 5.13 km (2001) in

Wibrin.

VM parameters estimation and model goodness-of-

fit

To check the adequacy of the model with the data,

goodness-of-fit tests �/ based on comparison between

expected and observed numbers of immigration, emigra-

tion and residency events as described in Hanski et al.

(2000) �/ were performed for each patch. Of the 81

goodness-of-fit tests, only 9 (11%) revealed a significant

lack of fit, which suggested a globally good overall fit.

When a significant difference between the predicted and

observed number of emigrants and immigrants was

detected, the model always underestimated the dispersal

events (Table 1).

When comparing the mean parameter estimates

between the two landscapes (Fig. 3), it appears that

they all differed significantly (no overlap of confidence

intervals between the two sets of parameter estimates).

The daily propensity to emigrate from a patch of unit

size (h) was much higher in Lierneux than in Wibrin.

The effect of patch size on emigration, expressed by the

parameter scaling the emigration (zem), was significant in

both landscapes (i.e. significantly different from 0) but

roughly five times smaller in Lierneux than in Wibrin

(0.194 vs 1.032). As showed in Fig. 4, which illustrates

the probability of emigrating from patches as a function

of their size (Eq. 1), it means that males tended to

emigrate more from smaller patches in Wibrin than in

Fig. 2. Metapopulation size estimates for each year in Lierneuxand Wibrin.

Table 1. VM model goodness-of-fit tests for the numbers ofresidents, emigrants and immigrants in Lierneux and Wibrin.The table gives the patch codes for which there is a significantlack of fit. The difference between the predicted and observednumber of dispersal events is indicated in brackets (observed �/

predicted).

Lierneux Wibrin

Residents 2 (�/11), 4 (�/10) 3 (�/5)Emigrants 4 (�/12) 3 (�/2)Immigrants 3 (�/19), 6 (�/8) 2 (�/2), 7 (�/3)

OIKOS 106:2 (2004) 247

Lierneux; the reverse is true for large patches. The

immigration scaling (zim,) was significantly different

from 0 in both landscapes, which indicates that butter-

flies are more prone to immigrate into big patches than

into small ones. This effect of the receiver patch area on

immigration was much smaller in Lierneux (0.585 vs

2.426). Results also showed that the value of the

parameter describing the effect of distance on isolation

(a) was significantly higher in Lierneux: on average

butterflies tend to move shorter distances in Lierneux.

However, in both landscapes, the average range of daily

dispersal distances was more than several hundred

meters (inferred from a: 240 m in Lierneux and 470 m

in Wibrin). Butterflies in Lierneux have a lower prob-

ability of daily mortality within habitat patches (mp) than

in Wibrin while for the same patch connectivity, they

suffered a higher mortality when dispersing (Fig. 5).

Simulation of survival and dispersalSimulation of dispersal within the two landscapes using

their respective VM parameter estimates

Results of VM simulations are presented in Table 2.

Here, we compare results obtained for Lierneux/Lier-

neux and Wibrin/Wibrin simulations. The model pre-

dicted that the majority of butterfly-days was spent

inside the natal patch in both landscapes. However, the

proportion of butterfly-days spent outside the natal

patch was significantly higher in Lierneux (Mann-

Whitney test; U�/2, PB/0.001). The predicted number

of dispersal events was 7 times higher in Lierneux than in

Wibrin. Considering the mean metapopulation sizes

(estimated 275 in Lierneux and 103 in Wibrin), the

predicted mean number of dispersal events per indivi-

dual was 1.749/0.08 in Lierneux vs 0.669/0.08 in Wibrin.

The difference was significant (Mann-Whitney U-test;

U�/0, PB/0.001). The model also predicted a much

lower proportion of successful dispersal events in

Lierneux i.e. a higher mortality rate during dispersal

(Mann-Whitney U-test; U�/100, PB/0.001).

Crossed-simulations of dispersal within the two

landscapes

First, when running the model with the VM parameters

extrapolated from Wibrin using the patch configuration

etamitse rete

maraP

etamitse rete

maraP

etami tse rete

maraP

Lierneux Wibrin

0

0.2

0.4

0.6

0.8

1

Within-patch mortality, 1-φ

etamitse ret e

maraP

etamitse rete

maraP

etamitse rete

m ar aP

0

1

2

3

4

5

Distance dependence, α

Lierneux Wibrin

0

1

2

3

4

5

Scaling of immigration, ζim

0

0.1

0.2

0.3

0.4

0.5

Daily emigration rate , η

0

1

2

3

4

5

Scaling of emigration, ζem

0

0.2

0.4

0.6

0.8

1

Migration mortality, λ

Fig. 3. Comparison between Lierneux and Wibrin landscapesof mean VM parameter estimates (with 95% confidenceintervals) for P. eunomia males. See text for details on theseparameters.

Fig. 4. Daily probability of emigration as a function of patcharea for the Lierneux and Wibrin landscapes.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5

Lierneux

Wibrin

Patch connectivity (Sj)

la

sre

psi

d g

niru

d ytil

atro

m yli

aD

Fig. 5. Daily mortality of individuals emigrating from patchesas a function of patch connectivity, Sj, for the Lierneux and theWibrin landscapes.

248 OIKOS 106:2 (2004)

and the mean metapopulation size of Lierneux, simula-

tions indicated a much higher number of butterfly-days

spent in the system than with parameter estimates from

Lierneux (Lierneux/Lierneux vs Lierneux/Wibrin:

Mann-Whitney U-test; U�/100, PB/0.001, Table 2).

The model predicted also a higher proportion of

butterfly-days spent outside the natal patch (Mann-

Whitney U-test: U�/100, PB/0.001) but a lower number

of dispersal events (Mann-Whitney U-test: U�/86.5,

PB/0.006). In addition, simulations predicted a much

higher proportion of successful dispersal events (Mann-

Whitney U-test: U�/0, PB/0.001).

Secondly, when running the model with the VM

parameters extrapolated from Lierneux using the patch

configuration and the mean metapopulation size of

Wibrin, simulations predicted a lower number of butter-

fly-days spent in the system than with parameter esti-

mates from Wibrin (Wibrin/Wibrin vs Wibrin/Lierneux:

Mann-Whitney U-test; U�/98, PB/0.001, Table 2). The

model also predicted a lower proportion of butterfly-

days spent outside the natal patch (Mann-Whitney

U-test: U�/100, PB/0.001). While the predicted number

of dispersal events was significantly higher, the propor-

tion of successful dispersal events decreased significantly

(Mann-Whitney U-tests: U�/0, PB/0.001 and U�/100,

PB/0.001 respectively).

Discussion

We compared here dispersal and mortality of the bog

fritillary butterfly Proclossiana eunomia between two

fragmented landscapes of Belgian Ardenne using the

VM model. As our main objective was to test the

possibility to generalise dispersal between similar land-

scapes when constructing PVA models, the study land-

scapes were both (1) highly fragmented with similar

proportion of suitable habitat (less than 1% of suitable

habitat; albeit there was a difference in their fragmenta-

tion level, it remained slight), (2) located within the same

upland characterised by a agricultural land/forest matrix

and (3) close to each other to ensure similarity in

environmental and historical factors affecting P. euno-

mia populations. Furthermore, as the studies were

carried out in different years in Lierneux and Wibrin,

we made sure our comparison was valid by checking that

climatic conditions (maximum temperature and insola-

tion), which are known to affected strongly butterfly

movements (Shreeve 1992), were similar between the two

landscapes. It is worth noting that modelling studies

rarely take as many precautions when entering into the

model previously published parameter estimates i.e.

when using generalized parameter estimates (Wahlberg

et al. 1996, Thomas et al. 2002).

Similarities in dispersal pattern between fragmented

vs continuous landscapes

Our results show that all the six VM parameter estimates

are clearly different between Lierneux and Wibrin land-

scapes. However, comparisons with results obtained

under more continuous habitat conditions bring to light

some similarities in dispersal patterns between the two

fragmented landscapes (Mennechez et al. 2003, Schtick-

zelle and Baguette 2003). First, the dispersal propensity,

i.e. the daily propensity to emigrate from 1-ha patch is

much lower in fragmented landscapes. Secondly, the

emigration probability clearly decreases when patch size

increases in fragmented landscapes.

Using the same methodology, i.e. the VM model, we

estimated to 43% (vs less than 20% and 10% in Lierneux

and Wibrin respectively) the dispersal propensity of

P. eunomia in a continuous landscape totalling ca 45.5

ha of suitable habitat in 12 patches (G. Mennechez,

unpubl.). Furthermore, a recent study using ad hoc

Table 2. Results (mean9/SD, given 10 replicate simulations) of VM simulations in Lierneux and Wibrin landscapes using theirrespective mean population size (N) and the mean VM parameter estimates from Lierneux and Wibrin. The VM simulation modelcalculates the number of butterfly-days spent inside and outside the natal patch and the number of successful and unsuccessfuldispersal events.

Parameter values from: Landscape configuration

Lierneux (N�/275) Wibrin (N�/103)

Lierneux Wibrin Wibrin Lierneux

Number of butterfly-days spentin the natal patch 12089/72 13829/60 5419/78 4379/55outside the natal patch 7329/85 12539/78 1839/45 729/24in the system (i.e. total) 19409/88 26359/70 7249/95 5099/62

% butterfly-days spent outside the natal patch 389/3 489/2 259/5 149/4

Number of dispersal eventssuccessful 2109/6 1899/6 429/6 189/4unsuccessful 2699/5 19/5 269/5 1029/1total 4799/8 1909/8 689/8 1209/4

% successful dispersal events 449/5 999/5 629/5 159/3

OIKOS 106:2 (2004) 249

measures confirmed that dispersal in P. eunomia was

lower in the fragmented system (Mennechez et al. 2003):

39% of recaptures involved inter-patch movements in the

fragmented system instead of 64% in the more contin-

uous one. This reduction of dispersal propensity may be

explained in the light of the dispersal cost hypothesis:

due to predation risks and uncertainty to reach a

suitable patch when dispersing, individuals may be

reluctant to leave patch under highly fragmented condi-

tions. Recent behavioural analyses in P. eunomia sup-

ported this assumption (Schtickzelle and Baguette 2003).

Furthermore, we have also shown previously that

mortality experienced by dispersing individuals was

effectively higher in fragmented vs continuous land-

scapes (Schtickzelle and Baguette 2003, G. Mennechez,

unpubl.). Here, simulations confirmed the cost of dis-

persal in fragmented landscapes since only ca 40�/60% of

the dispersal events are successful, i.e. lead to an

immigration.

VM estimates also indicated here a significant effect of

patch size on emigration in both fragmented landscapes,

which confirms results obtained previously (Petit et al.

2001) in the Pres de la Lienne: emigration probability

decreases when patch size increases. Such relations were

shown in many other butterflies (Hill et al. 1996;

Kuussaari et al. 1996, Baguette et al. 2000). An

explanation often reported for the increasing emigration

rate with decreasing patch area is that butterflies are

more likely to encounter patch boundaries in small

patches and consequently to leave (Kuussaari et al. 1996,

Baguette et al. 2000). However, in a previous study we

showed that the effect of patch size on dispersal rates

depended on the fragmentation level of the landscape

(Mennechez et al. 2003): the comparison of dispersal

pattern between a highly fragmented landscape and a

continuous one revealed an effect of patch size on

dispersal rates in the fragmented landscape only. We

therefore suggest that differences in costs and benefits of

emigration from different patch size exist, leading to

area-dependant dispersal in fragmented landscapes: in

large patches, individuals may be reluctant to leave as

they find resources (nectar, mates. . .) while they may

take the risk of migrating from small patches where

resources are limited. Furthermore, these empirical

results match the predictions of the simulation model

of movement developed by some of us (Schtickzelle and

Baguette 2003): based on the behavioural difference

observed at patch boundary between landscapes with

contrasted level of fragmentation, we developed an

individual-based model that explores the relationship

between patch area, patch permeability and emigration

rate. The simulations showed that the value of zem

increases with habitat fragmentation. In other words,

the decrease in emigration rate with increasing patch

area is more pronounced in fragmented landscapes

where patch boundaries are less permeable to movement.

As a consequence of (1) patch area dependant

emigration and (2) the small size of suitable habitat

patches in both fragmented landscapes (mean patch

sizesB/1 ha), the global level of dispersal observed here

remains high in the two landscapes. Indeed, simulations

indicated that ca 25 to 40% of butterfly-days are spent as

immigrants in a new population. From earlier works on

movement pattern of P. eunomia within fragmented

landscapes, we already knew that the rate of inter-patch

movements was high in this specialist species, particu-

larly within the same river basin (Baguette and Neve

1994, Neve et al. 1996, Petit et al. 2001). Most exchanges

occurred between neighbour patches: the value of a-

parameter indicates that mean daily dispersal distances

were inferior to 500 m. By moving from patch to patch

scattered along rivers (stepping stone movements),

individuals may however travel long distances during

their lifetime. The longest travelled distance found

during this study was more than 5 km, meaning that

most patches within the networks were connected,

therefore allowing metapopulation dynamics and persis-

tence of the species in such a landscape.

Differences in dispersal and mortality patterns

between the two fragmented landscapes

Despite the above-mentioned similarities between the

two fragmented landscapes in comparison with contin-

uous landscapes, it appears that dispersal and mortality

patterns differed highly between Lierneux and Wibrin.

Concerning emigration, our results reveal that the

propensity to disperse was lower and the effect of patch

area on emigration higher in Wibrin, the more fragmen-

ted landscape. This is not surprising since h has been

shown to decrease and zem to increase with fragmenta-

tion (Schtickzelle and Baguette 2003, G. Mennechez,

unpubl.). However, we have to admit that the difference

in the fragmentation degree between the two landscapes

is very low and therefore this effect may need to be

qualified. Those two parameters affect the probability to

emigrate from patch (Eq. 1) and consequently a differ-

ential emigration rate is revealed by the VM model

between the two landscapes: simulations predicted 2.5

time less dispersal events in Wibrin than in Lierneux.

Density-dependence of dispersal which has been

demonstrated in other butterfly species (Kuussaari et al

1996, Brunzel 2002) might also be a likely explanation

for the difference in the dispersal patterns since, as we

pointed out earlier, butterfly densities were on average

2.5 times higher in Lierneux than in Wibrin. In P.

eunomia, Baguette et al. (1998) showed that at low

female density, males were more likely to move away

from patch in search of new mates. Since the probability

for a male to encounter a potential mate is very low in

smaller patches at low density �/ it was the case in

250 OIKOS 106:2 (2004)

Wibrin �/, the probability to leave such patches should

therefore be high. On the other hand, the relation

between densities and emigration could be inversed in

larger patches. At high densities �/ it was the case in

Lierneux*/the presence of many males could motivate

individuals to leave habitat patches: Petit et al. (2001)

showed a positive relationship between male movements

and population size. However, from our results it is not

possible to ascertain whether the observed difference is

purely attributable to landscape structure or to butterfly

densities.

Once dispersing, individuals moved longer distances

in Wibrin, which is probably related to differences in the

spatial configuration of patch network between the two

landscapes. They also encounter a lower risk of mortality

in Wibrin as indicated by the value of l (0.017 vs 0.803

in Wibrin and Lierneux respectively). Simulations pre-

dicted that only ca 40% of dispersal events lead to death

in Wibrin vs ca 60% in Lierneux where the connectivity

as measured by Sj is higher. Insofar as there is no clear

difference in the quality of the matrix between the two

landscapes (fertilized pastures/afforestation areas in both

cases), there is no obvious reason for such a differential

dispersal mortality. Possible explanations could lie on

difference in predation rates or in other sources of

mortality in the matrix.

Finally, immigration scaled significantly to area of

receiver-patch in both landscapes, butterflies tending to

immigrate more into large than into small patches.

However, area of receiver-patches affected more immi-

gration in Wibrin than in Lierneux. As for emigration,

this difference might be related to differences in frag-

mentation degree. In a more highly fragmented land-

scape, the effect of receiver-patch area on immigration is

probably stronger than in a less fragmented landscape,

butterflies having a real interest �/ in term of cost-

benefice �/ to settle and stay in a large patch where nectar

and mate resources are sufficient. Moreover, this effect

of fragmentation could be here reinforced by lower

butterfly densities recorded in Wibrin.

Consequences of generalising dispersal patterns

between landscapes

Simulation results were highly affected by either the

configuration of the patch network in which the model

was run or the set of parameter estimates used. First, the

size and the spatial arrangement of habitat patches

strongly constrained the emigration rate (function of hand Ai scaling by zem) and the survival during dispersal

(function of the connectivity and l). For example, the

VM parameter set from Wibrin resulted in 99% or 62%

of successful migrating events (i.e. 1% or 38% of death

during dispersal) according to the landscape configura-

tion used when running the model, Lierneux or Wibrin

respectively. Secondly, our results clearly show that

depending on the parameter set used to run the VM

model, i.e. generalised or not, simulation results were

significantly different. For the Lierneux patch config-

uration, simulations indicated that parameter general-

isation lead to an under-estimation of dispersal and to

an over-estimation of survival during dispersal. This is

related to the fact that VM parameters from Wibrin

expressed lower probabilities to leave patches and a

lower mortality during dispersal. On the contrary, for

the Wibrin patch configuration, simulations indicated

that parameter generalisation leads to an over estimation

of dispersal and an under estimation of survival during

dispersal. In other words, dispersal parameters seems

very specific to a particular metapopulation and to the

landscape in which it evolves. Hence, we have to face the

fact that generalisation of parameters in PVA models

may create a problem especially when it is conducted

between too dissimilar conditions. Conservation biolo-

gists can find themselves obliged to use best guesses of

demographic and dispersal parameters from the litera-

ture when constructing PVA, because of the lack of

required data (Conroy et al. 1995, Akcakaya 2000, White

2000). However, ‘‘incorrect parameter estimates will

result in unreliable model ouput’’ (Conroy et al. 1995).

To minimise such risk, we recommended to be rigorous

with (1) the environmental conditions under which the

estimation of parameters was performed �/ they have to

be as similar as possible to those under which the PVA

model will be conducted �/ and (2) the incorporation of

uncertainties in the data when building the model of

PVA as outlined notably by Akcakaya and Sjogren-

Gulve (2000).

Conclusion

Modelling dispersal is a fundamental step to the

construction of spatially-structured population viability

analysis models (Akcakaya 2000, Morris and Doak

2002). However, in some cases required data on dispersal

can not be available but in the literature. The message of

our paper is a call for caution with such parameter

generalisations, even within the same species between

comparable landscapes. We believe that the urgency to

provide efficient tools to predict endangered species

persistence in human-made landscapes must not drive

conservation biologists to make dangerous generalisa-

tions.

Acknowledgements �/ We thank Benedicte Gerard, GregoryPlace, Marc Dufrene, Gabriel Neve and Laurent Warge for fieldwork assistance. This work was supported by the EC fundedtraining and mobility of researchers network FRAGLAND(‘‘Survival and Evolution of Species in FragmentedLandscapes’’) and by a grant from the Office of Scientific,Technical and Cultural Affairs (Belgian Federal Government)(contract OSTC-SPSDII EV10/16A 2000�/2004). Butterfly

OIKOS 106:2 (2004) 251

capture licences and sites access were granted from theMinistere de la Region Wallonne. N.S. is ‘‘collaborateurscientifique du F.N.R.S.’’. This is contribution BRC030 of theBiodiversity Research Centre.

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