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Relative importance of density-dependent regulation and environmental stochasticity for butterfly population dynamics

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Abstract

The relative contribution of density-dependent regulation and environmental stochasticity to the temporal dynamics of animal populations is one of the central issues of ecology. In insects, the primary role of the latter factor, typically represented by weather patterns, is widely accepted. We have evaluated the impact of density dependence as well as density-independent factors, including weather and mowing regime, on annual fluctuations of butterfly populations. As model species, we used Maculinea alcon and M. teleius living in sympatry and, consequently, we also analysed the effect of their potential competition. Density dependence alone explained 62 and 42% of the variation in the year-to-year trends of M. alcon and M. teleius, respectively. The cumulative Akaike weight of models with density dependence, which can be interpreted as the probability that this factor should be contained in the most appropriate population dynamics model, exceeded 0.97 for both species. In contrast, the impacts of inter-specific competition, mowing regime and weather were much weaker, with their cumulative weights being in the range of 0.08–0.21; in addition, each of these factors explained only 2–5% of additional variation in Maculinea population trends. Our results provide strong evidence for density-dependent regulation in Maculinea, while the influence of environmental stochasticity is rather minor. In the light of several recent studies on other butterflies that detected significant density-dependent effects, it would appear that density-dependent regulation may be more widespread in this group than previously thought, while the role of environmental stochasticity has probably been overestimated. We suggest that this misconception is the result of deficiencies in the design of most butterfly population studies in the past, including (1) a strong focus on adults and a neglect of the larval stage in which density-dependent effects are most likely to occur; (2) an almost exclusive reliance on transect count results that may confound the impact of environmental stochasticity on butterfly numbers with its impact on adult longevity.

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References

  • Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Akademiai Kiado, Budapest, pp 267–281

  • Andrewartha HG, Birch LC (1954) The distribution and abundance of animals. University of Chicago Press, Chicago

    Google Scholar 

  • Anton C, Musche M, Hula V, Settele J (2008) Myrmica host-ants limit the density of the ant-predatory large blue Maculinea nausithous. J Insect Conserv 12:511–517

    Article  Google Scholar 

  • Arnyas E, Bereczki J, Toth A, Pecsenye K, Varga Z (2006) Egg-laying preferences of the xerophilous ecotype of Maculinea alcon (Lepidoptera: Lycaenidae) in the Aggtelek National Park. Eur J Entomol 103:587–595

    Google Scholar 

  • Arnyas E, Bereczki J, Toth A, Varga K, Pecsenye K, Tartally A, Kövics G, Karsa D, Varga Z (2009) Oviposition preferences of Maculinea alcon as influenced by aphid (Aphis gentianae) and fungal (Puccinia gentianae) infestation of larval host plants. Ecol Entomol 34:90–97

    Article  Google Scholar 

  • Baguette M, Schtickzelle N (2006) Negative relationship between dispersal distance and demography in butterfly metapopulations. Ecology 87:648–654

    Article  PubMed  Google Scholar 

  • Batáry P, Körösi A, Örvössy N, Kövér S, Peregovits L (2009) Species-specific distribution of two sympatric Maculinea butterflies across different meadow edges. J Insect Conserv. doi:10.10070s10841-008-9158-1

  • Bauerfeind SS, Fischer K (2008) Maternal body size as a morphological constraint on egg size and fecundity in butterflies. Basic Appl Ecol 9:443–451

    Article  Google Scholar 

  • Bellows TS (1981) The descriptive properties of some models for density dependence. J Anim Ecol 50:139–156

    Article  Google Scholar 

  • Benton TG, Plaistow SJ, Coulson TN (2006) Complex population dynamics and complex causation: devils, details and demography. Proc R Soc Lond B 273:1173–1181

    Article  Google Scholar 

  • Bonelli S, Crocetta A, Barbero F, Balletto E (2005) Oviposition behaviour in the myrmecophilous butterfly Maculinea alcon (Lepidoptera: Lycaenidae). In: Settele J, Kuhn E, Thomas JA (eds) Studies in the ecology and conservation of butterflies in Europe. Species ecology along a European gradient: Maculinea butterflies as a model, vol 2. Pensoft, Sofia, pp 65–68

    Google Scholar 

  • Brooks T (2000) Conservation biology: living on the edge. Nature 403:26–29

    Article  PubMed  CAS  Google Scholar 

  • Burnham KP, Anderson DR (2001) Model selection and multi-model inference: a practical information-theoretic approach. Springer, New York

    Google Scholar 

  • Chan G, Chan KS, Stenseth NC, Lingjaerde OC (2004) Analyzing nonlinear population dynamics data. J Agric Biol Environ Stat 9:200–215

    Article  Google Scholar 

  • Chase MK, Nur N, Geupel GR (2005) Effects of weather and population density on reproductive success and population dynamics in a Song Sparrow (Melospiza melodia) population: a long-term study. Auk 122:571–592

    Article  Google Scholar 

  • Curnutt JL, Pimm SL, Maurer BA (1996) Population variability of sparrows in space and time. Oikos 76:131–144

    Article  Google Scholar 

  • Dempster JP (1983) The natural control of populations of butterflies and moths. Biol Rev 58:461–481

    Article  Google Scholar 

  • Dempster JP (1991) Fragmentation, isolation and mobility of insect populations. In: Collins NM, Thomas JA (eds) The conservation of insects and their habitats. Academic Press, London, pp 143–153

    Google Scholar 

  • Ehrlich PR, Breedlove DE, Brussard PF, Sharp MA (1972) Weather and the “regulation” of subalpine butterfly populations. Ecology 53:243–247

    Article  Google Scholar 

  • Elmes GW, Thomas JA (1992) The complexity of species conservation: interactions between Maculinea butterflies and their ant hosts. Biodivers Conserv 1:155–169

    Article  Google Scholar 

  • Elmes GW, Wardlaw JC, Thomas JA (1991) Larvae of Maculinea rebeli, a large blue butterfly, and their Myrmica host ants: wild adoption and behaviour in ant-nests. J Zool Lond 223:447–460

    Article  Google Scholar 

  • Elmes GW, Clarke RT, Thomas JA, Hochberg ME (1996) Empirical tests of specific predictions made from a spatial model of the population dynamics of Maculinea rebeli, a parasitic butterfly of red ant colonies. Acta Oecol 17:61–80

    Google Scholar 

  • Figurny E, Woyciechowski M (1998) Flowerhead selection for oviposition by females of the sympatric butterfly species Maculinea teleius and M. nausithous (Lepidoptera: Lycaenidae). Entomol Gen 23:215–222

    Google Scholar 

  • Fromentin JM, Myers RA, Bjornstad ON, Stenseth NC, Gjosaeter J, Christie H (2001) Effects of density-dependent and stochastic processes on the regulation of cod populations. Ecology 82:567–579

    Article  Google Scholar 

  • Glinka U, Settele J (2005) The effect of ant communities and spatial pattern for Maculinea nausithous. In: Settele J, Kuhn E, Thomas JA (eds) Studies in the ecology and conservation of butterflies in Europe. Species ecology along a European gradient: Maculinea butterflies as a model, vol 2. Pensoft, Sofia, p 72

    Google Scholar 

  • Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil Trans R Soc B 115:513–585

    Article  Google Scholar 

  • Griebeler EM, Seitz A (2002) An individual based model for the conservation of the endangered Large Blue Butterfly, Maculinea arion (Lepidoptera: Lycaenidae). Ecol Model 156:43–60

    Article  Google Scholar 

  • Grill A, Cleary DFR, Stettmer C, Bräu M, Settele J (2008) A mowing experiment to evaluate the influence of management on the activity of host ants of Maculinea butterflies. J Insect Conserv 12:617–627

    Article  Google Scholar 

  • Hassell MP (1975) Density-dependence in single-species populations. J Anim Ecol 44:283–295

    Article  Google Scholar 

  • Hassell MP, Lawton JH, May RM (1976) Patterns of dynamical behaviour in single-species populations. J Anim Ecol 45:471–486

    Article  Google Scholar 

  • Hawkins BA, Holyoak M (1998) Transcontinental crashes of insect populations? Am Nat 152:480–484

    Article  PubMed  CAS  Google Scholar 

  • Hochberg ME, Thomas JA, Elmes GW (1992) A modelling study of the population dynamics of a large blue butterfly, Maculinea rebeli, a parasite of red ant nests. J Anim Ecol 61:397–409

    Article  Google Scholar 

  • Hochberg ME, Clarke RT, Elmes GW, Thomas JA (1994) Population dynamic consequences of direct and indirect interactions involving a large blue butterfly and its plant and red ant hosts. J Anim Ecol 63:375–391

    Article  Google Scholar 

  • Hovestadt T, Mitesser O, Elmes GW, Thomas JA, Hochberg ME (2007) An evolutionarily stable strategy model for the evolution of dimorphic development in the butterfly Maculinea rebeli, a social parasite of Myrmica ant colonies. Am Nat 169:466–480

    Article  PubMed  Google Scholar 

  • Hurvich CM, Tsai C (1989) Regression and time series model selection in small samples. Biometrika 76:297–307

    Article  Google Scholar 

  • Johnson JB, Omland KS (2004) Model selection in ecology and evolution. Trends Ecol Evol 19:101–108

    Article  PubMed  Google Scholar 

  • Johst K, Drechsler M, Thomas J, Settele J (2006) Influence of mowing on the persistence of two endangered large blue butterfly species. J Appl Ecol 43:333–342

    Article  Google Scholar 

  • Kemp DJ, Rutowski RL (2004) A survival cost to mating in a polyandrous butterfly, Colias eurytheme. Oikos 105:65–70

    Article  Google Scholar 

  • Kolzsch A, Saether SA, Gustafsson H, Fiske P, Hoglund J, Kalas JA (2007) Population fluctuations and regulation in great snipe: a time-series analysis. J Anim Ecol 76:740–749

    Article  PubMed  Google Scholar 

  • Kuras T, Benes J, Konvicka M (2000) Differing habitat affinities of four Erebia species (Lepidoptera : Nymphalidae, Satyrinae) in the Hruby Jesenik Mts, Czech Republic. Biologia 55:169–175

    Google Scholar 

  • Larsson S, Ekbom B, Bjorkman C (2000) Influence of plant quality on pine sawfly population dynamics. Oikos 89:440–450

    Article  Google Scholar 

  • Legendre P, Legendre L (1998) Numerical ecology. Elsevier, Amsterdam

    Google Scholar 

  • Lewellen RH, Vessey SH (1998) Modeling biotic and abiotic influences on population size in small mammals. Oecologia 113:210–218

    Article  Google Scholar 

  • Liebhold A, Koenig WD, Bjornstad ON (2004) Spatial synchrony in population dynamics. Annu Rev Ecol Evol Syst 35:467–490

    Article  Google Scholar 

  • Lima M, Marquet PA, Jaksic FM (1998) Population extinction risks of three Neotropical small mammal species. Oecologia 115:120–126

    Article  Google Scholar 

  • Maes D, van Dyck H, Vanreusel W, Cortens J (2003) Ant communities (Hymenoptera: Formicidae) of Flemish (north Belgium) wet heathlands, a declining habitat in Europe. Eur J Entomol 100:545–555

    Google Scholar 

  • Maes D, Vanreusel W, Talloen W, Van Dyck H (2004) Functional conservation units for the endangered Alcon Blue butterfly Maculinea alcon in Belgium (Lepidoptera, Lycaenidae). Biol Conserv 120:229–241

    Article  Google Scholar 

  • McKilligan N (2001) Population dynamics of the Cattle Egret (Ardea ibis) in south-east Queensland: a 20-year study. Emu 101:1–5

    Article  Google Scholar 

  • Meyer-Hozak C (2000) Population biology of Maculinea rebeli (Lepidoptera: Lycaenidae) on chalk grasslands of Eastern Westphalia (Germany) and implications for conservation. J Insect Conserv 4:63–72

    Article  Google Scholar 

  • Mouquet N, Belrose V, Thomas JA, Elmes GW, Clarke RT, Hochberg ME (2005a) Conserving community modules: a case study of the endangered lycaenid butterfly Maculinea alcon. Ecology 86:3160–3173

    Article  Google Scholar 

  • Mouquet N, Thomas JA, Elmes GW, Clarke RT, Hochberg ME (2005b) Population dynamics and conservation of a specialized predator: a case study of Maculinea arion. Ecol Monogr 75:525–542

    Article  Google Scholar 

  • Musche M, Anton C, Worgan A, Settele J (2006) No experimental evidence for host ant related oviposition in a parasitic butterfly. J Insect Behav 19:631–643

    Article  Google Scholar 

  • Nicholson AJ (1933) The balance of animal populations. J Anim Ecol 2:131–178

    Article  Google Scholar 

  • Nowicki P, Richter A, Glinka U, Holzschuh A, Toelke U, Henle K, Woyciechowski M, Settele J (2005a) Less input same output-simplified approach for population size assessment in Lepidoptera. Popul Ecol 47:203–212. doi:10.1007/s10144-005-0223-2

    Article  Google Scholar 

  • Nowicki P, Settele J, Thomas JA (2005b) Woyciechowski M (2005b) A review of population structure of Maculinea butterflies. In: Settele J, Kuhn E, Thomas JA (eds) Studies in the ecology and conservation of butterflies in Europe. Species ecology along a European gradient: Maculinea butterflies as a model, vol 2. Pensoft, Sofia, pp 144–149

    Google Scholar 

  • Nowicki P, Witek M, Skórka P, Settele J, Woyciechowski M (2005c) Population ecology of the endangered butterflies Maculinea teleius and M. nausithous, and its implications for conservation. Popul Ecol 47:193–202. doi:10.1007/s10144-005-0222-3

    Article  Google Scholar 

  • Nowicki P, Witek M, Skórka P, Woyciechowski M (2005d) Oviposition patterns in the myrmecophilous butterfly Maculinea alcon Denis and Schiffermuller (Lepidoptera: Lycaenidae) in relation to characteristics of foodplants and presence of ant hosts. Pol J Ecol 53:409–417

    Google Scholar 

  • Nowicki P, Pepkowska A, Kudlek J, Skórka P, Witek M, Settele J, Woyciechowski M (2007) From metapopulation theory to conservation recommendations: lessons from spatial occurrence and abundance patterns of Maculinea butterflies. Biol Conserv 140:119–129. doi:10.1016/j.biocon.2007.08.001

    Article  Google Scholar 

  • Nowicki P, Settele J, Henry P-Y, Woyciechowski M (2008) Butterfly monitoring methods: the ideal and the real world. Isr J Ecol Evol 54:69–88

    Article  Google Scholar 

  • Parmesan C, Matthews J (2005) Biological impacts of climate change. In: Groom M, Meffe GK, Carroll CR (eds) Conservation biology, 3rd edn. Sinauer Assoc, Sunderland, pp 333–374

    Google Scholar 

  • Patterson BR, Power VA (2002) Contributions of forage competition, harvest, and climate fluctuation to changes in population growth of northern white-tailed deer. Oecologia 130:62–71

    Google Scholar 

  • Pickens BA (2007) Understanding the population dynamics of a rare, polyvoltine butterfly. J Zool 273:229–236

    Article  Google Scholar 

  • Pollard E (1988) Temperature, rainfall and butterfly numbers. J Appl Ecol 25:819–828

    Article  Google Scholar 

  • Pollard E, Lakhani KH, Rothery P (1987) The detection of density dependence from a series of annual censuses. Ecology 68:2046–2055

    Article  Google Scholar 

  • Raimondo S, Turcani M, Patocka J, Liebhold AM (2004) Interspecific synchrony among foliage-feeding forest Lepidoptera species and the potential role of generalist predators as synchronizing agents. Oikos 107:462–470

    Article  Google Scholar 

  • Ranta E, Lundberg P, Kaitala V, Laakso J (2000) Visibility of the environmental noise modulating population dynamics. Proc R Soc Lond B 267:1851–1856

    Article  CAS  Google Scholar 

  • Rothery P, Newton I, Dale L, Wesolowski T (1997) Testing for density dependence allowing for weather effects. Oecologia 112:518–523

    Article  Google Scholar 

  • Roy DB, Rothery P, Moss D, Pollard E, Thomas JA (2001) Butterfly numbers and weather: predicting historical trends in abundance and the future effects of climate change. J Anim Ecol 70:201–217

    Article  Google Scholar 

  • Salvidio S (2007) Population dynamics and regulation in the cave salamander Speleomantes strinatii. Naturwissenschaften 94:396–400

    Article  PubMed  CAS  Google Scholar 

  • Schönrogge K, Wardlaw JC, Thomas JA, Elmes GW (2000) Polymorphic growth rates in myrmecophilous insects. Proc R Soc Lond B 267:771–777

    Article  Google Scholar 

  • Schtickzelle N, Baguette M (2004) Metapopulation viability analysis of the bog fritillary butterfly using RAMAS/GIS. Oikos 104:277–290

    Article  Google Scholar 

  • Schtickzelle N, Choutt J, Goffart P, Fichefet V, Baguette M (2005) Metapopulation dynamics and conservation of the marsh fritillary butterfly: population viability analysis and management options for a critically endangered species in Western Europe. Biol Conserv 126:569–581

    Article  Google Scholar 

  • Schwarz CJ, Arnason AN (1996) A general methodology for the analysis of capture-recapture experiments in open populations. Biometrics 52:860–873

    Article  Google Scholar 

  • Schwarz CJ, Seber GAF (1999) Estimating animal abundance: review III. Stat Sci 14:427–456

    Article  Google Scholar 

  • Settele J, Kuhn E, Thomas JA (eds) (2005) Studies in the ecology and conservation of butterflies in Europe. Species ecology along a European gradient: Maculinea butterflies as a model, vol 2. Pensoft, Sofia

    Google Scholar 

  • Sibly RM, Barker D, Denham MC, Hone J, Pagel M (2005) On the regulation of populations of mammals, birds, fish, and insects. Science 309:607–610

    Article  PubMed  CAS  Google Scholar 

  • Sinclair ARE, Pech RP (1996) Density dependence, stochasticity, compensation and predator regulation. Oikos 75:164–173

    Article  Google Scholar 

  • Stenseth NC, Saitoh T, Yoccoz NG (1998) Frontiers in population ecology of microtine rodents: a pluralistic approach to the study of population ecology. Res Popul Ecol 40:5–20

    Article  Google Scholar 

  • Sutcliffe OL, Thomas CD, Djunijanti P (1997) Area-dependent migration by ringlet butterflies generates a mixture of patchy population and metapopulation attributes. Oecologia 109:229–234. doi:10.1007/s004420050077

    Article  Google Scholar 

  • Thomas JA (1995) The ecology and conservation of Maculinea arion and other European species of large blue butterfly. In: Pullin AS (ed) Ecology and conservation of butterflies. Chapman and Hall, London, pp 180–197

    Google Scholar 

  • Thomas JA (2005) Monitoring change in the abundance and distribution of insects using butterflies and other indicator groups. Phil Trans R Soc B 360:339–357

    Article  PubMed  CAS  Google Scholar 

  • Thomas JA, Elmes GW (1998) Higher productivity at the cost of increased host-specificity when Maculinea butterfly larvae exploit ant colonies through trophallaxis rather than by predation. Ecol Entomol 23:457–464

    Article  Google Scholar 

  • Thomas JA, Settele J (2004) Butterfly mimics of ants. Nature 432:283–284

    Article  PubMed  CAS  Google Scholar 

  • Thomas JA, Wardlaw JC (1992) The capacity of a Myrmica ant nest to support a predacious species of Maculinea butterfly. Oecologia 85:87–91

    Article  Google Scholar 

  • Thomas JA, Munguira ML, Martin J, Elmes GW (1991) Basal hatching by Maculinea butterflies eggs: a consequence of advanced myrmecophily? Biol J Linn Soc 44:175–184

    Article  Google Scholar 

  • Thomas JA, Elmes GW, Wardlaw JC (1993) Contest competition among Maculinea rebeli larvae in ant nests. Ecol Entomol 18:73–76

    Article  Google Scholar 

  • Thomas JA, Clarke RT, Elmes GW, Hochberg ME (1998a) Population dynamics in the genus Maculinea (Lepidoptera: Lycaenidae). In: Dempster JP, McLean IFG (eds) Insect population dynamics in theory and practice. Symposia of the Royal Entomological Society, 19. Chapman and Hall, London, pp 261–290

    Google Scholar 

  • Thomas JA, Elmes GW, Wardlaw JC (1998b) Polymorphic growth in larvae of the butterfly Maculinea rebeli, a social parasite of Myrmica ant colonies. Proc R Soc Lond B 265:1895–1901

    Article  Google Scholar 

  • van Swaay CAM, Nowicki P, Settele J, van Strien AJ (2008) Butterfly monitoring in Europe: methods, applications and perspectives. Biodivers Conserv 17:3455–3469. doi:10.1007/s10531-008-9440-2

    Article  Google Scholar 

  • Warren MS (1992) Butterfly populations. In: Dennis RLH (ed) The ecology of butterflies in Britain. Oxford University Press, Oxford, pp 73–92

    Google Scholar 

  • Watt AD, Woiwod IP (1999) The effect of phenological asynchrony on population dynamics: analysis of fluctuations of British macrolepidoptera. Oikos 87:411–416

    Article  Google Scholar 

  • Watt WB, Chew FS, Snyder LRG, Watt AG, Rothschild DE (1977) Population structure of pierid butterflies. I. Numbers and movements of some montane Colias species. Oecologia 27:1–22

    Article  Google Scholar 

  • White GC, Burnham KP (1999) Program MARK: survival estimation from populations of marked animals. Bird Study 46:120–138

    Article  Google Scholar 

  • Williams CK, Ives AR, Applegate RD (2003) Population dynamics across geographical ranges: time-series analyses of three small game species. Ecology 84:2654–2667

    Article  Google Scholar 

  • Williams DW, Liebhold AM (2000) Spatial scale and the detection of density dependence in spruce budworm outbreaks in eastern North America. Oecologia 124:544–552

    Article  Google Scholar 

  • Wilson RJ, Roy DB (2009) Population structure and dynamics (including metapopulations). In: Settele J, Shreeve T, Konvicka M, van Dyck H (eds) Ecology of butterflies in Europe. Cambridge University Press, Cambridge (in press)

  • Witek M, Sliwinska E, Skórka P, Nowicki P, Settele J, Woyciechowski M (2006) Polymorphic growth in larvae of Maculinea butterflies, as an example of biennialism in myrmecophilous insects. Oecologia 148:729–733. doi:10.1007/s00442-006-0404-5

    Article  PubMed  Google Scholar 

  • Witek M, Sliwinska E, Skórka P, Nowicki P, Wantuch M, Vrabec V, Settele J, Woyciechowski M (2008) Host ant specificity of large blue butterflies Phengaris (Maculinea) (Lepidoptera: Lycaenidae) inhabiting humid grasslands in East-central Europe. Eur J Entomol 105:871–877

    Google Scholar 

  • Wynhoff I (2001). At home on foreign meadows. The reintroduction of two Maculinea butterfly species. PhD thesis. Wageningen University, Wageningen

  • Zeng Z, Nowierski RM, Taper ML, Dennis B, Kemp WP (1998) Complex population dynamics in the real world: modeling the influence of time-varying parameters and time lags. Ecology 79:2193–2209

    Google Scholar 

  • Zonneveld C (1991) Estimating death rates from transect counts. Ecol Entomol 16:115–121

    Article  Google Scholar 

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Acknowledgments

Butterfly sampling was performed with the permission of the Italian Ministry for Environment, Territory and Sea, and was partly funded by the Parks Planning Department for the Piedmont Region. Silvia Ferretti, Andrea Crocetta, Camilla Colombo, Alessandra Rosso, Luca Pietro Casacci, Lisa Camerin and Marco Gherlenda helped in the fieldwork. The data analysis was conducted within the financial framework of the European Commission projects EuMon (FP6 contract no. 006463) and SCALES (FP7 contract no. 226852). We are grateful to Christine Richards for improving the English of the manuscript.

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Nowicki, P., Bonelli, S., Barbero, F. et al. Relative importance of density-dependent regulation and environmental stochasticity for butterfly population dynamics. Oecologia 161, 227–239 (2009). https://doi.org/10.1007/s00442-009-1373-2

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