the control of emigration and its consequences for the survival of populations

Ecological Modelling 190 (2006) 443–453

The control of emigration and its consequencesfor the survival of populations

Thomas Hovestadt∗, Hans Joachim Poethke

Field Station Fabrikschleichach, University of Wurzburg, Glashuttenstraße 5, 96181 Rauhenebrach, Germany

Received 19 February 2004; received in revised form 11 March 2005; accepted 28 March 2005Available online 14 June 2005

Abstract

Dispersal is the key process enhancing the long-term persistence of metapopulations in heterogeneous and dynamic landscapes.However, any individual emigrating from a occupied patch also increases the risk of local population extinction. The consequencesof this increase for metapopulation persistence likely depend on the control of emigration. In this paper, we present resultsof individual-based simulations to compare the consequences of density-independent (DIE) and density-dependent (DDE)emigration on the extinction risk of local populations and a two-patch metapopulation. (1) For completely isolated patchesextinction risk increases linearly with realised emigration rates in the DIE scenario. (2) For the DDE scenario extinction risk isnearly insensitive to emigration as longs as emigration probabilities remain below≈0.2. Survival chances are up to half an orderof magnitude larger than for populations with DIE. (3) For low dispersal mortality both modes of emigration increase survivalof a metapopulation by ca. one order of magnitude. (4) For high dispersal mortality only DDE can improve the global survivalc sity andt

a systemw tly affecto©

K nt

1

b

(

9;

tionslula-nd

0

hances of the metapopulation. (5) With DDE individuals are only removed from a population at high population denhe risk of extinction due to demographic stochasticity is thus much smaller compared to the DIE scenario.

With density-dependent emigration prospects of metapopulations survival may thus be much higher compared toith density-independent emigration. Consequently, the knowledge about the factors driving emigration may significanur conclusions concerning the conservation status of species.2005 Elsevier B.V. All rights reserved.

eywords: Dispersal; Individual-based model (IBM); Population extinction; Metapopulation; Density-dependent; Density-independe

. Introduction

The analysis of dispersal and its consequences hasecome a major topic in various fields of ecology,

∗ Corresponding author. Tel.: +49 9554 92230; fax: +49 9554 367.E-mail address: [email protected]

T. Hovestadt).

e.g. evolution of life history (e.g.Ronce et al., 2000),species coexistence (e.g.Hastings and Gavrilets, 199Dieckmann et al., 1999; Hovestadt et al., 2000), or thesuccess of invasive species (e.g.Higgins et al., 2000). Ithas a special relevance in the study of metapopula(e.g. Levins, 1970; Hanski, 1994, 1998) as dispersais one of the two key-processes driving metapoption dynamics. However, most of the empirical a

304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2005.03.023

444 T. Hovestadt, H.J. Poethke / Ecological Modelling 190 (2006) 443–453

theoretical research in this field is focussed on thedocumentation and investigation of the consequencesof successful dispersal, i.e. immigration. Yet, the firststep in any dispersal event is emigration from an actualpopulation – and it is in no way secured that an emi-grant will ever arrive and successfully reproduce in anew population. Thus, the number of emigrants willin most circumstances exceed the number of immi-grants and dispersal will tend to reduce the average sizeof local populations, respectively, the realized popula-tion growth rate (cf.Kean and Barlow, 2000). Eventhough discussed (Hanski and Zhang, 1993; Thomasand Hanski, 1997), this effect has not been accountedfor in classical metapopulation modelling as nei-ther Levins (1970)nor Hanski (e.g.Hanski, 1999;Hanski et al., 2000; Ovaskainen and Hanski, 2003;but seeSchtickzelle et al., 2002or Ovaskainen, 2002)consider the dynamics of local populations in theirmodels. However, if we account for the emigrationinduced net-loss of individuals from local populationsthe question arises how this effect sets off against thebeneficial consequences of dispersal for population res-cue and patch (re-) colonisation (cf.Menendez et al.,2002).

Standard formulation of the dispersal process inmetapopulation models implicitly assumes a constantflow of emigrants from any occupied patch (Levins,1970), or a flow proportional to patch size, respec-tively, habitat capacity (cf.Hanski, 1999; Hanski etal., 2000; also Holt, 1985). However, empirical dataa also tion.A nceeA2 eM w,2( i eta ndeze ellea ed 97;L sky,2 02;A ce:H al.,2

et al., 2002). Especially high population densityis likely to be a trigger of emigration (directly orindirectly due to deteriorating resource availability)as the net benefit of dispersal (accounting for thecosts of dispersal, the reproductive chances whennot leaving, and the expected reproductive successwhen arriving somewhere else) will usually increasewith population density (Poethke and Hovestadt,2002).

Recently,Saether et al. (1999),Nachman (2000)andAmarasekare (2004)have developed models to explorethe effect of density-dependent emigration on metapop-ulation persistence. These papers give valuable insightsinto the effect of emigration on metapopulation sur-vival, but used a linear (Saether et al., 1999),respectively, an exponential function (Nachman, 2000;Amarasekare, 2004) to implement density-dependentregulation while a non-linear threshold function ismore likely to evolve (Travis et al., 1999; Poethkeand Hovestadt, 2002). Aamarasekares paper is alsolimited to source–sink systems while Saether et al., donot address the effect of dispersal mortality on modelpredictions.

In this paper, we analyse to what degree emigrationmay increase the risk of local population extinctionfor completely isolated patches and for a metapopula-tion consisting of two viable populations. We will useindividual-based simulations with density-dependentpopulation growth to investigate the effect of differentemigration rates on local and global extinction and toc t andd rsalm

2

2

hem d inP es uc-c s ofc hica ns.P g toH

s well as theoretical models indicate that individuften use certain cues as triggers for emigramong the factors known or assumed to influemigration are predation pressure (e.g.Dixon andgarwala, 1999; Weisser et al., 1999; Muller et al.,001; Bouwma et al., 2003; for opposing opinion (seichaud and Belliure, 2001; Woodward and Hildre002), social conflicts (e.g.Gerlach, 1998), patch sizeHill et al., 1996; Baguette et al., 1998; Gaggiottl., 2002; Leisnham and Jamieson, 2002; Menet al., 2002; Wahlberg et al., 2002; Schtickznd Baguette, 2003), or population density (positivependence:Denno et al., 1991; Rhainds et al., 19indberg et al., 1998; Semenchenko and Ostrov001; Brunzel, 2002a,b; Sutherland et al., 20ltwegg et al., 2003; inverse density-dependenerzig, 1995; Baguette et al., 1998; Crone et001; Lin and Batzli, 2001, implicitly in Bodasing

ompare the consequences of density-independenensity-dependent emigration under different dispeortalities.

. Model

.1. Population dynamics and dispersal

We will only present an abbreviated form of todel description here, more details can be founoethke and Hovestadt (2002). In our time-discretimulations we model the individual reproductive sess of annual organisms within local populationapacityK. This allows for the effects of demograps well as environmentally induced fluctuatioopulation growth is density-dependent accordinassell (1998):

T. Hovestadt, H.J. Poethke / Ecological Modelling 190 (2006) 443–453 445

Nt+1 = Ntλtst with st = 1

(1 + aNt)βand

a = Λ1/β − 1

K(1)

During each simulation cycle a patch-specific valuefor fertility λt is drawn from a log-normal distributionwith meanΛ and a standard deviationσ (environmen-tal stochasticity; cf.Lande et al., 1999). We assumeσ to be uncorrelated in space and time, which isnot always likely to be the case in real systems (seeSection4). To decide on the actual number of offspringproduced by each female a random number is drawnfrom a Poisson distribution with a mean value of 2λt

(demographic stochasticity). Offspring then matureinto adults (equal probability to become a male orfemale) with the density-dependent probabilityst

given in Eq.(1). After development individuals mayemigrate. Depending on the landscape, the emigrationscenario implemented (see below) and the dispersalmortalityµ, some emigrating individuals may arrive inanother patch. The decision to emigrate either occurswith a constant probabilitydi (density-independentemigration, in the following “DIE”) or with a prob-ability dependent on the actual population densityCt = Nt/K (density-dependent emigration, “DDE”).For the latter, emigration probability is calculatedby the following equation simplified fromPoethkeand Hovestadt (2002)for the case of equal patchc

d

T icha iesw ngi dt( ,i nsityp

2

pesw ac-i lity

may also be interpreted as a substitute for the distancebetween patches.

All patches were initialised withK individuals at thebeginning of each simulation run but the first five sim-ulation cycles were not used in any data analyses. In afirst set of experiments we ran 50,000 simulations forthe DIE and DDE scenario, respectively, over 100 timesteps with a single patch. For these simulations we ran-domly combined parameters drawn from the intervalsgiven inTable 1. For each simulation run it was notedwhether the population went extinct or not over thecourse of the simulation. The data were then analysedusing logistic regression technique (statistical packageGLM with binomial error,R Development Core Team,2003) to compare the contribution of variation in thesefactors to the overall extinction risk of the population.In the logistic regression we checked for linearity ofthe logit-transformed response. In case of the DDEscenario a linear model with respect to the dispersalthresholdpC was not adequate and we thus calculateda model withpC as a categorical variable (see furtherdetails in Section3).

In a next step we analysed the consequences offragmentation into two and four completely isolatedpatches for populations without emigration and for var-ious values of total patch capacity (1000 replicates foreach parameter combination). Maximum simulationtime was limited to 1000 time steps. For each simu-lation run we saved the moment of global extinction (ifit occurred) as well as the moment of first extinctionf la-t e tol earr tC fit-t el,i ond tch( an-n umea nceso thep

S

w ngu e

apacity:

p =

0 if Ct ≤ pC

1 − 1

Ct

pC if Ct > pC

(2)

he justification and derivation of this function, whllows for the evolution of ESS emigration strategith similar fitness for philopatric and dispersi

ndividuals, can be found inPoethke and Hovesta2002); also Metz and Gyllenberg (2001). Howevern the simulations presented here the threshold deC is implemented as a fixed parameter only.

.2. Setting of simulations and data evaluation

Simulations were carried out on simple landscaith only one or two habitat patches of equal cap

ty K. For the two-patch scenario dispersal morta

or a focal patch (local extinction). From the cumuive survival data we then estimated the mean timocal, respectively, global extinction using non-linegression (statistical package NLR,R Developmenore Team, 2003). For the one-patch scenario we

ed the parametertL of the negative exponential mod.e. the time until the fraction of surviving populatiropped to 1/e. For a system with more than one pan > 1) the decay function for the metapopulation cot be described by this model. However, if we assnegative exponential decay for the survival cha

f local populations we can estimate it by fittingarameterTn of the following equation:

G,t = 1 − (1 − e−t/Tn )n

(3)

hereSG,t is the fraction of metapopulations survivintil time t andn is the number of local patches. W


Table 1Parameter estimates of multiple logistic regression model for the effect of various population parameters on the extinction probability ofpopulations within 100 time steps

Population parameters Parameter range Regression coefficientb S.E. eb

(a) DIEFertility (Λ) 2–10 −0.895 0.009 0.443Competition (β) 0.5–3.5 −0.419 0.017 0.657Environmental stochasticity (σ) 0–5 1.083 0.013 2.954Habitat capacity (K) 5–100 −0.089 0.001 0.915Dispersal probability (di) 0–0.5 6.750 0.116 853.836

(b) DDEFertility (Λ) 2–10 −0.755 0.009 0.409Competition (β) 0.5–3.5 −0.254 0.017 0.776Environmental stochasticity (σ) 0–5 0.919 0.012 2.508Habitat capacity (K) 5–100 −0.089 0.001 0.915Dispersal threshold (pC) 1.1–1.2 0

1.0–1.1 0.014 0.065 1.0140.9–1.0 −0.055 0.065 0.9470.8–0.9 0.051 0.065 1.0530.7–0.8 0.044 0.065 1.0450.6–0.7 0.149 0.065 1.1610.5–0.6 0.345 0.065 1.4120.4–0.5 0.645 0.065 1.9050.3–0.4 1.099 0.065 3.0010.2–0.3 2.193 0.065 8.958

For each parameter the table gives the range of possible values (uniform intervals), the estimated regression coefficient and its standard error aswell as the valueeb, i.e. the change in the odds of extinction risk with a change of the population parameter by one unit. For both scenarios theanalyses are based on 50,000 simulation runs, each with a random combination of parameter values from the given range of values. (a) Resultsfor the scenario with density-independent emigration (DIE). (b) Results for the scenario with density-dependent emigration (DDE). As therewas evidence for a non-linear response to the dispersal thresholdpC, we grouped values into different categories. Values of coefficients printedin italic letters arenot significantly different from the reference categorypC [1.1. . . 1.2] at thep = 0.01 level. Note that a high dispersal thresholdpC implies a low emigration rate.

can then calculate the momenttG,n at which a fraction1/e of the metapopulations are still surviving by theequation:

tG,n = −Tn ln

(1 −

(1 − 1

e

)1/n)

(4)

We checked for the validity of a negative exponentialdistribution for the time to local extinction and founda very good agreement with this expectation.

Finally, we introduced emigration in a two-patchmetapopulation with different values for the dispersalprobabilitydi ∈ {0.0, 0.05,. . ., 0.5} (DIE), respectively,the dispersal thresholdpC ∈ {0.3, 0.4,. . ., 1.2} (DDE)as well as dispersal mortalityµ ∈ {1.0, 0.95, 0.9, 0.8,0.5, 0.1, 0.0}. For presentation, we will focus on a sce-nario with total patch capacityKT = 64, Λ = 3, σ = 1andβ = 1. With these parameter values we generatedreasonable population turnover rates, a prerequisite to

define a spatially structured population as a metapop-ulation. However, we checked for consistency of theresults also in scenarios withΛ = 5, σ = 3, and alsowith four patches with the same total patch capacity.An example for the population dynamics in the focalpatch for the DDE scenario can be seen inFig. 1.

3. Results

For the single patch scenario logistic regressionrevealed the expected strong effect of patch capacityand the population growth parametersΛ, σ andβ onthe extinction risk of the population. For the DIE sce-nario logistic regression also revealed a linear responseto the logit-transformed emigration probability withextinction risk substantially increasing over the rangeof values tested (Table 1a). Scaled to the range of valuestested, the effect ofdi (range 0–0.5) has about half the


Fig. 1. Example of a simulation run for the DDE-scenario in a two-patch scenario over a segment of 200 time steps. The lower panelshows the size of a local population before emigration and the numberof immigrants into the population during each time step as grey barsat the bottom. In the upper panel the values for the actual fertilityλt for each time step are shown. The population parameters wereΛ = 3,σ = 1,µ = 0.8,β = 1.0,KT = 64 andpC = 0.7. The arrow marksan episode of extinction and consecutive re-colonisation.

effect on extinction probability as the variation in patchcapacity (5–100) orΛ (2–10). For the DDE scenario anon-linear relationship between extinction risk and thedensity-thresholdpC emerged (Table 1b). The thresh-old had little effect on the extinction risk as long as itremained above a value of≈0.6 (cf.Fig. 2a). If we plotthe extinction risk over the observed mean emigrationrate we observe a uni-modal relationship with a peak atan emigration rate around 0.2 and the lowest extinction

risk at very high observable emigration rates (Fig. 2b).To understand this we have to keep in mind that in theDDE scenario emigration rates are an emerging prop-erty not only controlled by the emigration parameterpC

but also the parameters controlling population growth.In other words, in the DDE scenario high emigrationrates often signal “healthy” populations which tend toproduce surplus numbers of offspring and are thus notat a risk of extinction.

In the scenarios without emigration our simula-tions confirmed two well-known facts: the logarithmof the mean time to extinction increases linearly withtotal patch capacity (cf.Richter-Dyn and Goel, 1972;Gabriel et al., 1991; Hakoyama and Iwasa, 2005) andconsequently, a single large patch will survive longerthan two or four patches of the same total habitat capac-ity. Clearly, this conclusion would be altered if externalcatastrophes occasionally wipe out whole populationsregardless of patch capacity and actual population sizebut we do not consider such scenarios in this paper (seeSection4).

The importance of the demographic parameters (Λ,β, K) as well as environmental variability (σ) for pop-ulation extinction are well known (e.g.Richter-Dynand Goel, 1972; Lande, 1993). In this paper, we thusfocus on simulations runs with fixed values forKT = 64,Λ = 3,σ = 1 andβ = 1 in the two patch scenario. Theseparameters were chosen because they generated inter-mediate risks for local or global population extinction.

Fig. 2. Extinction risk for a single patch as a function of the emigration r theDDE scenario. Mean values and 95% CI intervals are calculated over i.e.andβ (seeTable 1). In all cases, the simulation time was 100 time step

thresholdpC (left) and the observed mean emigration rate (right) foall random combinations of the other population parameters,K, Λ, σ

s.


Fig. 3. Mean time to local extinction as a function of emigrationrate for completely isolated patches (dispersal mortalityµ = 1. Sepa-rate lines are plotted for the DIE and DDE scenario. The populationparameters wereΛ = 3,σ = 1,β = 1, KT = 64.

With complete isolation, the loss of an emigratingindividual cannot be compensated for by any immi-grants. Consequently, patch survival time is a decreas-ing function of emigration rate (Fig. 3). However, thereis a substantial difference between the DIE and DDEscenario. Particularly for intermediate emigration ratesDIE reduces population survival much more than DDE.For emigration rates between 0.15 and 0.35 persistencetime is approximately half an order of magnitude largerin the DDE compared to the DIE scenario.

If dispersal mortality is low, the loss of emigrants ismostly compensated by new immigrants. This rescue-effect may even over-compensate the negative effect ofemigration. Survival time of the metapopulation thusbecomes substantially larger (ca. 10-fold) with emi-gration, and the two scenarios do not lead to muchdifferent predictions (Fig. 4). However, the survivaltime of the metapopulation is still about half an orderof magnitude lower than that of a single patch with thesame total capacity. With dispersal mortality becominglarge, density-independent emigration will increase theextinction risk of the metapopulation, even at very lowemigration rates. In contrast, DDE still increases thesurvival times of the metapopulation by approximatelyhalf an order of magnitude. The latter conclusions arerather insensitive to changes in the dispersal thresh-old pC for 0.6≤ pC ≤ 1.2, i.e. realised emigration ratesbetween 0.05 and 0.20 (Fig. 4).

Fig. 4. Mean time to global extinction over emigration rate for ametapopulation with two patches with dispersal mortalityµ = 0.9and 0.1. Separate lines are plotted for the DIE and DDE scenario.Note that for the DDE scenario the observed mean emigration rateis an emergent property, which is also influenced by dispersal mor-tality. The population parameters wereΛ = 3, σ = 1, β = 1, KT = 64.Horizontal line is the survival time of the metapopulation withoutemigration.

Under DIE, populations usually experience anet-loss of individuals during migration even ifthe population size is already small (Fig. 5a). Thisincreases the risk of extinction due to environmentalor demographic stochasticity. In contrast, in theDDE-scenario populations never loose individuals byemigration as long as the population density is belowthe emigration thresholdpC but usually increase insize due to immigration (Fig. 5b). This effect willgreatly reduce the risk of local population extinction.

4. Discussion

The results of our simulations indicate that density-independent dispersal can only increase the survivalchances of a metapopulation if dispersal related costsare fairly low. However, if dispersal is not costly, evolu-tion of high inter-patch dispersal rates will be favoured(Heino and Hanski, 2001; Travis and Dytham, 1999;Poethke and Hovestadt, 2002). This will lead to avery high exchange of “migrants” between local pop-ulations and it is questionable whether such a patchypopulation should be declared a “metapopulation”(cf. Harrison, 1991; Doak and Mills, 1994; Nachman,


Fig. 5. Distribution of local population sizes before and after the migration phase in a two-patch metapopulation for the DIE (di = 0.15) scenario(left) and the DDE (pC = 0.7) scenario (right). The population parameters wereΛ = 3, σ = 1, β = 1, KT = 64 andµ = 0.8. Note that in the DDEscenario, populations below the threshold density (here 0.7× 32 = 22.4) are always as large or larger after dispersal than they were before(rescue-effect).

2000; Freckleton and Watkinson, 2002; Pannell andObbard, 2003). If dispersal becomes costly globalsurvivorship of the metapopulation will be highest ifindividuals do not emigrate at all. In this point, ourconclusion differs from those of other studies whichsuggest that a minimum amount of migration is alwaysrequired to increase metapopulation survival (Hanskiand Zhang, 1993; Saether et al., 1999; Nachman,2000; also Hakoyama and Iwasa, 2005). In contrastto these studies our simulations account for all threekinds of stochastic effects affecting (meta-) popu-lation survival: the demographic and environmentalstochasticity affecting local extinction but also for thestochastic nature of immigration. The abovementionedstudies all assume (infinitely) large number of patchesand global dispersal, which will lead (in equilibrium)to a constant influx in the number of immigrants. Apartfrom the study ofNachman (2000), these studies alsodo not account for demographic stochasticity.

With density-dependent emigration our resultsbecome completely different. In agreement withHanski and Zhang (1993)or Saether et al. (1999)we conclude that emigration will principally increasemetapopulation survival even under high dispersalmortality (it also increases mean persistence time oflocal populations in our simulations) but that too much

of it will eventually reduce metapopulation survival.Neither local nor global extinction risk is sensitive tochanges in the dispersal rate over a wide and presum-ably realistic range of values (0.05≤ de≤ 0.25). Inthis parameter range, predicted survival times for DDEare up to 10 times longer than for the DIE scenario.The predicted survival of a metapopulation may thuscritically depend on our knowledge about dispersalbehaviour; the use of standardized simulation toolslike SPOMSIM (Moilanen, 2004) should thus only beconsidered after careful examination of the underlyingmodel assumptions.

Because it tends to remove individuals alsofrom populations, which are already small density-independent emigration increases the risk of localextinction due to demographic stochasticity (cf.Menendez et al., 2002). This is different from thedensity-dependent emigration scenario where individ-uals are only removed from populations with a highpopulation density, especially, if we take into accountthe high value of the emigration thresholdpC likely toevolve under circumstances where dispersal is costly(cf. Poethke and Hovestadt, 2002). The increased riskof demographic extinction is thus completely avoided,but the occasionally large numbers of emigrantsproduced may rescue or re-colonise populations


even in distant patches. In a recent paper (Reed andLevine, 2004) classified the effects of various dispersalmechanisms on the dynamics of metapopulations.Taking DIE as the reference, DDE can clearly beclassified as a “local extinction inhibiting” mechanismin their terminology. The effects of DDE on rescueand colonization are more complicated (Hovestadt,unpublished) and will be discussed elsewhere but canprincipally range from “colonization inhibiting” to“colonization enhancing”.

The emigration threshold implemented in ourmodel is clearly responsible for the larger difference inextinction risk between DIE and DDE generated in oursimulations compared to the model ofSaether et al.(1999). It also distinguishes our model from the step-wise threshold model implemented in a model byJohstand Brandl (1997). In their model emigration abruptlyincreases beyond a certain threshold density leadingto an increase in population dynamics. In contrast, thespecific type of density-dependence implemented inour model emigration has a stabilizing effect on thedynamics of populations. Unfortunately, the modelimplemented byNachman (2000)does not allowseparating the effects of mean emigration rate as suchand the way it responds to population density. Thisexplains the rather surprising conclusion of Nachmanthat – at larger overall emigration rates – a negativelydensity-dependent is more likely to allow metapopula-tion persistence than the positively density-dependentemigration implemented in our simulations.

ter-n cies( ipeo on-s ivedb totalc tingf lityo ibe“ esaa ofe nt intc .,1 nalh rs on

local extinction characteristic for density-independentdispersal could surpass the benefits of re-colonisationas long as catastrophes remain rare.

We simulated environmental variability as inde-pendent in time and space (“white noise”). Even withthis condition strongly favouring metapopulationspersistence, the survival chances of a single largepatch turned out to be larger than that of severalsmaller patches of the same size. Evidently, the dis-crepancy should become even larger if we assume theenvironmental stochasticity to be spatially correlated(Johst and Drechsler, 2003; we verified this withour program), a phenomenon presumably not rare innature (cf.Ranta et al., 1999; Lundberg et al., 2000).The only situation where this may change could be ascenario with environmental fluctuations temporarilycorrelated within patches (“red noise”) but not inspace. In this situation a series of several bad yearsmight drive even a large patch to extinction (Iwasaand Mochizuki, 1988; alsoCaswell and Cohen, 1995),which could then be re-colonised from other patchesnot sharing its strain of bad luck.

A more important inference to be drawn from oursimulations is a partial justification of the simplifiedapproach implemented in the classical Levins–Hanskimetapopulation model. In this approach emigration isnot assumed to affect the extinction probability of thelocal population (cf.Hanski, 1999). Our simulationsshow that this is clearly not justified for the case ofdensity-independent emigration, i.e. the net-effect ofe andr n theo mi-g ba-b toe adei

thee tion( sb beenr tw ctedc 2)C ons( thee and r

In our simulations we have not included exal catastrophes or interactions with other spediseases, predators), which may eventually wut populations regardless of their actual size. Cequently, single large populations always survetter than a group of patches with the sameapacity. We believe that an approach accounor environmental variability as stochastic variabif population parameters will frequently descrreality” better than the introduction of catastrophs a size-independent external event (cf.Halleynd Iwasa, 1998). Nevertheless, the occurrencexternal catastrophes has been a critical argumehe SLOSS debate (seeOvaskainen, 2002) and suchatastrophes may in fact occur (cf.Thomas et al996), certainly for species inhabiting successioabitats (e.g.Stelter et al., 1997). However, even undeuch conditions the negative effect of emigration

migration on local extinction may be substantialeduce the chances of metapopulation survival. Other hand, with density-dependent emigration, eration hardly has an effect on local extinction proility, notably for the high dispersal thresholds likelyvolve. In this point, the assumption inherently m

n most metapopulation models is thus met.There are several observations, which indicate

xistence of negatively density-dependent emigracitations in Section1). Also, negative correlationetween patch size and emigration rate haveeported (e.g.Hill et al., 1996). A theoretical argumenhy the evolution of the latter pattern is to be expean be found inPoethke and Hovestadt (200.learly, increased emigration from small populati

an emigration Allee effect) is likely to increasextinction risk of small populations even further thensity-independent emigration would do (cf.Saethe


et al., 1999; Menendez et al., 2002). At the same time,any Allee-effect will reduce the chance of successfulre-colonisation by few individuals (e.g.Lande, 1998;Engen et al., 2003).

Evolutionary modelling (Olivieri and Gouyon,1997; Poethke and Hovestadt, 2002; Poethke et al.,2003) as well as the evidence collected on islands(Roff, 1990) suggest that emigration rates become lowas the costs of dispersal increase. Nevertheless, evenin this situation the emigration of an individual willincrease local extinction risk due to demographic rea-sons. Nowadays, landscapes are dramatically changingunder the influence of human activities. Species maythus “rely” on dispersal strategies not well adapted tothe actual situation. Even though species eventuallymanage to adapt to such new conditions ratherquickly (cf.Cody and Overton, 1996; Schtickzelle andBaguette, 2003; Mennechez et al., 2003), the net-lossof emigrating individuals may be of special concernin situations where the surrounding habitat does notpresent clear signals of a “hostile” environment orwhere populations became rapidly isolated and aproper reduction in the tendency to emigrate did not(yet) evolve.

Principally, knowledge about density-dependencehas a substantial effect on predicted survival chances of(meta-) populations. Wherever density-dependent emi-gration occurs, persistence time of populations may bean order of magnitude higher than predicted for a sys-tem with density-independent emigration (cf.Ruxtona utt reati

A

theE 1-0 lpfulc

R

A ionbarn

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nd Rohani, 1999). The collection of information abohe density-dependence of emigration is thus of gmportance for future conservation planning.

cknowledgements

Research in this project has been funded byC within the RTD project MacMan (EVK2-CT-2000126. We wish to thank Sven Jørgensen for his heomments to improve this manuscript.

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the control of emigration and its consequences for the survival of populations

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