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A unifying gravity framework for dispersal

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Abstract

Most organisms disperse at some life-history stage, but different research traditions to study dispersal have evolved in botany, zoology, and epidemiology. In this paper, we synthesize concepts, principles, patterns, and processes in dispersal across organisms. We suggest a consistent conceptual framework for dispersal, which utilizes generalized gravity models. This framework will facilitate communication among research traditions, guide the development of dispersal models for theoretical and applied ecology, and enable common representation across taxonomic groups, encapsulating processes at the source and destination of movement, as well as during the intervening relocation process, while allowing each of these stages in the dispersal process to be addressed separately and in relevant detail. For different research traditions, certain parts of the dispersal process are less studied than others (e.g., seed release processes in plants and termination of dispersal in terrestrial and aquatic animals). The generalized gravity model can serve as a unifying framework for such processes, because it captures the general conceptual and formal components of any dispersal process, no matter what the relevant biological timescale involved. We illustrate the use of the framework with examples of passive (a plant), active (an animal), and vectored (a fungus) dispersal, and point out promising applications, including studies of dispersal mechanisms, total dispersal kernels, and spatial population dynamics.

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References

  • Alba-Lynn C, Henk S (2010) Potential for ants and vertebrate predators to shape seed-dispersal dynamics of the invasive thistles Cirsium arvense and Carduus nutans in their introduced range (North America). Plant Ecol 210:291–301. doi:10.1007/s11258-010-9757-2

    Google Scholar 

  • Allen MR (2007) Measuring and modeling dispersal of adult zooplankton. Oecologia 153:135–143. doi:10.1007/s00442-007-0704-4

    PubMed  Google Scholar 

  • Altizer SM, Thrall PH, Antonovics J (1998) Vector behavior and the transmission of anther-smut infection in Silene alba. Am Midl Nat 139:147–163. doi:10.1674/0003-0031(1998)139[0147:VBATTO]2.0.CO;2

    Google Scholar 

  • Armsworth PR (2008) Conditional dispersal, clines, and the evolution of dispersiveness. Theor Ecol 2:105–117. doi:10.1007/s12080-008-0032-2

    Google Scholar 

  • Aylor DE (2003) Spread of plant disease on a continental scale: role of aerial dispersal of pathogens. Ecology 84:1989–1997. doi:10.1890/01-0619

    Google Scholar 

  • Baker RR (1978) The evolutionary ecology of animal migration. Hodder & Stoughton, London

    Google Scholar 

  • Barrios JM, Verstraeten WW, Maes P, Aerts J-M, Farifteh J, Coppin P (2012) Using the gravity model to estimate the spatial spread of vector-borne diseases. Int J Environ Res Public Health 9:4346–4364. doi:10.3390/ijerph9124346

    PubMed Central  PubMed  Google Scholar 

  • Bauer S, Hoye BJ (2014) Migratory animals couple biodiversity and ecosystem functioning worldwide. Science 344:1242552. doi:10.1126/science.1242552

    CAS  PubMed  Google Scholar 

  • Berg RY (1983) Plant distribution as seen from plant dispersal—general principles and basic modes of plant dispersal. Sonderbände Naturwiss Ver Hamb 7:13–36

    Google Scholar 

  • Bharti N, Xia Y, Bjørnstad ON, Grenfell BT (2008) Measles on the edge: coastal heterogeneities and infection dynamics. PLoS ONE 3:e1941. doi:10.1371/journal.pone.0001941

    PubMed Central  PubMed  Google Scholar 

  • Bilton DT, Freeland JR, Okamura B (2001) Dispersal in freshwater invertebrates. Annu Rev Ecol Syst 32:159–181. doi:10.1146/annurev.ecolsys.32.081501.114016

    Google Scholar 

  • Black WR (2003) Transportation: a geographical analysis. Guilford, New York

    Google Scholar 

  • Bonte D, Hovestadt T, Poethke H-J (2010) Evolution of dispersal polymorphism and local adaptation of dispersal distance in spatially structured landscapes. Oikos 119:560–566. doi:10.1111/j.1600-0706.2009.17943.x

    Google Scholar 

  • Bossenbroek JM, Kraft CE, Nekola JC (2001) Prediction of long-distance dispersal using gravity models: zebra mussel invasion of inland lakes. Ecol Appl 11:1778–1788. doi:10.1890/1051-0761(2001)011[1778:POLDDU]2.0.CO;2

    Google Scholar 

  • Bowler DE, Benton TG (2005) Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics. Biol Rev 80:205–225. doi:10.1017/S1464793104006645

    PubMed  Google Scholar 

  • Broadbend SR, Kendall DG (1953) The random walk of Trichostrongylus retortaeformis. Biometrics 9:460–466. doi:10.2307/3001437

    Google Scholar 

  • Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465. doi:10.1038/nature0429

    CAS  PubMed  Google Scholar 

  • Bubb DH, Thom TJ, Lucas MC (2004) Movement and dispersal of the invasive signal crayfish Pacifastacus leniusculus in upland rivers. Freshw Biol 49:357–368. doi:10.1111/j.1365-2426.2003.01178.x

    Google Scholar 

  • Bullock JM, Kenward RE, Hails RS (eds) (2002) Dispersal ecology. Blackwell, Oxford

    Google Scholar 

  • Bullock JM, Shea K, Skarpaas O (2006) Measuring plant dispersal: an introduction to field methods and experimental design. Plant Ecol 186:217–234. doi:10.1007/s11258-006-9124-5

    Google Scholar 

  • Bullock JM, White SM, Prudhomme C, Tansey C, Perea R, Hooftman DAP (2012) Modelling spread of British wind-dispersed plants under future wind speeds in a changing climate. J Ecol 100:104–115. doi:10.1111/j.1365-2745.2011.01910.x

    Google Scholar 

  • Burgiel S, Foote G, Orellana M, Perrault A (2006) Invasive alien species and trade: integrating prevention measures and international trade rules. Center for International Environmental Law, Washington

    Google Scholar 

  • Campbell CL, Madden LV (1990) Introduction to plant disease epidemiology. Wiley, New York

    Google Scholar 

  • Caplat P, Cheptou P-O, Diez J, Guisan A, Larson BMH, Macdougall AS, Peltzer DA, Richardson DM, Shea K, van Kleunen M, Zhang R, Buckley YM (2013) Movement, impacts and management of plant distributions in response to climate change: insights from invasions. Oikos 122:1265–1274. doi:10.1111/j.1600-0706.2013.00430.x

    Google Scholar 

  • Carrasco LR, Mumford JD, MacLeod A, Harwood T, Grabenweger G, Leach AW, Knight JD, Baker RHA (2010) Unveiling human-assisted dispersal mechanisms in invasive alien insects: integration of spatial stochastic simulation and phenology models. Ecol Model 221:2068–2075. doi:10.1016/j.ecolmodel.2010.05.012

    Google Scholar 

  • Charnov EL (1976) Optimal foraging; the marginal value theorem. Theor Popul Biol 9:129–136

    CAS  PubMed  Google Scholar 

  • Clark JS, Lewis M, Horvath L (2001) Invasion by extremes: population spread with variation in dispersal and reproduction. Am Nat 157:537–554. doi:10.1086/319934

    CAS  PubMed  Google Scholar 

  • Clobert J, Ims RA, Rousset F (2004) Causes, mechanisms and consequences of dispersal. In: Hanski I, Gaggiotti OE (eds) Ecology, genetics and evolution of metapopulations. Elsevier, Burlington, pp 307–335

    Google Scholar 

  • Clobert J, Baguette M, Beton TG, Bullock JM (eds) (2012) Dispersal ecology and evolution. Oxford University Press

  • Cohen JE, Roig M, Reuman DC, GoGwilt C (2008) International migration beyond gravity: a statistical model for use in population projections. Proc Natl Acad Sci U S A 105:15269–15274. doi:10.1073/pnas.0808185105

    PubMed Central  CAS  PubMed  Google Scholar 

  • Côté H, Garant D, Robert K, Mainguy J, Pelletier F (2012) Genetic structure and rabies spread potential in raccoons: the role of landscape barriers and sex-biased dispersal. Evol Appl 5:393–404. doi:10.1111/j.1752-4571.2012.00238.x

    PubMed Central  PubMed  Google Scholar 

  • Cousens R, Dytham C, Law R (2008) Dispersal in plants: a population perspective. Oxford University Press

  • Dauer JT, Mortensen DA, VanGessel MJ (2007) Spatial and temporal dynamics governing long distance dispersal of Conyza canadensis. J Appl Ecol 44:105–114. doi:10.1111/j.1365-2664.2006.01256.x

    Google Scholar 

  • Dauer JT, Luschei EC, Mortensen DA (2009) Effects of landscape composition on spread of an herbicide-resistant weed. Landsc Ecol 24:735–747. doi:10.1007/s10980-009-9345-9

    Google Scholar 

  • De Moraes CM, Stanczyk NM, Betz HS, Pulido H, Sim DG, Read AF, Mescher MC (2014) Malaria-induced changes in host odors enhance mosquito attraction. Proc Natl Acad Sci U S A 111:11079–11084. doi:10.1073/pnas.1405617111

    PubMed Central  PubMed  Google Scholar 

  • Dieckmann U, Law R, Metz JAJ (eds) (2000) The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press

  • Diefenbach DR, Long ES, Rosenberry CS, Wallingford BD, Smith DR (2008) Modelling distribution of dispersal distances in male white-tailed deer. J Wildl Manag 72:1296–1303. doi:10.2193/2007-436

    Google Scholar 

  • Dingle H (1996) Migration: the biology of life on the move. Oxford University Press

  • Elven R (ed) (2005) Norsk flora. Det Norske Samlaget, Oslo

    Google Scholar 

  • Epanchin-Niell RS, Hastings A (2010) Controlling established invaders: integrating economics and spread dynamics to determine optimal management. Ecol Lett 13:528–541. doi:10.1111/j.1461-0248.2010.01440.x

    PubMed  Google Scholar 

  • Epanchin-Niell RS, Wilen JE (2012) Optimal spatial control of biological invasions. J Environ Econ Manag 63:260–270. doi:10.1016/j.jeem.2011.10.003

    Google Scholar 

  • Evans H, Oszako T (eds) (2007) Alien invasive species and international trade. Forest Res Inst, Warsaw

    Google Scholar 

  • Ferrari MJ, Bjørnstad ON, Partain JL, Antonovics J (2006) A gravity model for the spread of a pollinator-borne plant pathogen. Am Nat 168:294–303. doi:10.1086/506917

    PubMed  Google Scholar 

  • Finlay BJ (2002) Global dispersal of free-living microbial eukaryote species. Science 296:1061–1063. doi:10.1126/science.1070710

    CAS  PubMed  Google Scholar 

  • Fischer SF, Poschlod P, Beinlich B (1996) Experimental studies on the dispersal of plants and animals on sheep in calcareous grasslands. J Appl Ecol 33:1206–1222. doi:10.2307/2404699

    Google Scholar 

  • Forman RTT, Gordon M (1986) Landscape ecology. Wiley, New York

    Google Scholar 

  • García C, Jordano P, Godoy JA (2007) Contemporary pollen and seed dispersal in a Prunus mahaleb population: patterns in distance and direction. Mol Ecol 16:1947–1955. doi:10.1111/j.1365-294X.2006.03126.x

    PubMed  Google Scholar 

  • Gaylord B, Reed DC, Raimondi PT, Washburn L, McLean SR (2002) A physically based model of macroalgal spore dispersal in the wave and current-dominated nearshore. Ecology 83:1239–1251. doi:10.1890/0012-9658(2002)083[1239:APBMOM]2.0.CO;2

    Google Scholar 

  • Greene DF, Calogeropoulos C (2002) Measuring and modelling seed dispersal of terrestrial plants. In: Bullock JM, Kenward RE, Hails RS (eds) Dispersal ecology. Blackwell, Oxford, pp 3–23

    Google Scholar 

  • Greene DF, Johnson EA (1989) A model of wind dispersal of winged or plumed seeds. Ecology 70:339–347. doi:10.2307/1937538

    Google Scholar 

  • Hanski I (1996) Metapopulation dynamics: from concepts and observations to predictive models. In: Hanski I, Gilpin ME (eds) Metapopulation biology, genetics and evolution. Academic, Ecology, pp 69–91

    Google Scholar 

  • Hanski I, Ovaskainen O (2000) The metapopulation capacity of a fragmented landscape. Nature 404:755–758. doi:10.1038/35008063

    CAS  PubMed  Google Scholar 

  • Hastings A, Cuddington K, Davies KF, Dugaw CJ, Elmendorf S, Freestone A, Harrison S, Holland M, Lambrinos J, Malvadkar U, Melbourne BA, Moore K, Taylor C, Thomson D (2005) The spatial spread of invasions: new developments in theory and evidence. Ecol Lett 8:91–101. doi:10.1111/j.1461-0248.2004.00687.x

    Google Scholar 

  • Hein AM, Gillooly JF (2011) Predators, prey, and transient states in the assembly of spatially structured communities. Ecology 92:549–555. doi:10.1890/10-1922.1

    PubMed  Google Scholar 

  • Higgins SI, Nathan R, Cain ML (2003) Are long-distance dispersal events in plants usually caused by nonstandard means of dispersal? Ecology 84:1945–1956. doi:10.1890/01-0616

    Google Scholar 

  • Holden C (2006) Inching toward movement ecology. Science 313:779–782. doi:10.1126/science.313.5788.779

    CAS  PubMed  Google Scholar 

  • Hughes L, Dunlop M, French K, Leishman MR, Rice B, Rodgerson L, Westoby M (1994) Predicting dispersal spectra: a minimal set of hypotheses based on plant attributes. J Ecol 82:933–950. doi:10.2307/2261456

    Google Scholar 

  • Huijbers CM, Nagelkerken IN, Debrot A, Jongejans E (2013) Geographic coupling of juvenile and adult habitat shapes spatial population dynamics of a coral reef fish. Ecology 94:1859–1870. doi:10.1890/11-1759.1

    PubMed  Google Scholar 

  • Hulme PE, Bacher S, Kenis M, Klotz S, Kühn I, Minchin D, Nentwig W, Olenin S, Panov V, Pergl J, Pyšek P, Roques A, Sol D, Solarz W, Vilà M (2008) Grasping at the routes of biological invasions: a framework for integrating pathways into policy. J Appl Ecol 45:403–414. doi:10.1111/j.1365-2664.2007.01442.x

    Google Scholar 

  • Ims RA, Yoccoz NG (1996) Studying transfer processes in metapopulations; emigration, migration and colonization. In: Hanski IA, Gilpin ME (eds) Metapopulation biology. Ecology, genetics and evolution. Academic, Ecology, pp 247–264

    Google Scholar 

  • Ingimarsdóttir M, Caruso T, Ripa J, Magnúsdóttir OB, Migliorini M, Hedlund K (2012) Primary assembly of soil communities: disentangling the effect of dispersal and local environment. Oecologia 170:745–754. doi:10.1007/s00442-012-2334-8

    PubMed  Google Scholar 

  • Isard SA, Gage SH (2001) Flow of life in the atmosphere: an airscape approach to invasive organisms. Michigan State University Press

  • Isard SA, Gage SH, Comtois P, Russo JM (2005) Principles of the atmospheric pathway for invasive species applied to soybean rust. BioScience 55:851–861. doi:10.1641/0006-3568(2005)055[0851:POTAPF]2.0.CO;2

    Google Scholar 

  • Isard SA, Barnes CW, Hambleton S, Anatti A, Russo JM, Tenuta A, Gay DA, Szabo LJ (2011) Predicting soybean rust incursions into the North American continental interior in 2007 and 2008 using crop monitoring, spore trapping, and aerobiological modeling. Plant Dis 95:1346–1357. doi:10.1094/PDIS-01-11-0034

    Google Scholar 

  • Jackson JK, McElravy EP, Resh VH (1999) Long-term movements of self-marked caddisfly larvae (Trichoptera: Sericostomatidae) in a California coastal mountain stream. Freshw Biol 42:525–536. doi:10.1046/j.1365-2427.1999.00503.x

    Google Scholar 

  • Jansen PA, Hirsch BT, Emsens W-J, Zamora-Gutierrez V, Wikelski M, Kays R (2012) Thieving rodents as substitute dispersers of megafaunal seeds. Proc Natl Acad Sci U S A 109:12610–12615. doi:10.5441/001/1.9t0m888q

    PubMed Central  CAS  PubMed  Google Scholar 

  • Järemo J (2009) Evaluating spread of invaders from gravity scores—a way of using gravity models in ecology. Math Biosci 222:53–58. doi:10.1016/j.mbs.2009.08.008

    PubMed  Google Scholar 

  • Johansson V, Lönnell N, Sundberg S, Hylander K (2014) Release thresholds for moss spores: the importance of turbulence and sporophyte length. J Ecol 102:721–729. doi:10.1111/1365-2745.12245

    Google Scholar 

  • Jongejans E, Telenius A (2001) Field experiments on seed dispersal by wind in ten umbellifers (Apiaceae). Plant Ecol 152:67–78. doi:10.1023/A:1011467604469

    Google Scholar 

  • Jongejans E, Pedatella N, Shea K, Skarpaas O, Auhl R (2007) Seed release by invasive thistles: the impact of plant and environmental factors. Proc Roy Soc B: Biol Sci 274:2457–2464. doi:10.1098/rspb.2007.0190

    Google Scholar 

  • Jongejans E, Skarpaas O, Shea K (2008) Dispersal, demography and spatial population models for conservation and control management. Perspect Plant Ecol Evol Syst 9:153–170. doi:10.1016/j.ppees.2007.09.005

    Google Scholar 

  • Jongejans E, Allen MR, Leib AE, Marchetto KM, Pedatella NM, Peterson-Smith J, Rauschert ESJ, Ruggiero DC, Russo LA, Ruth LE, Sezen Z, Skarpaas O, Teller BJ, Warg LA, Yang S, Zhang R, Shea K (2011) Spatial dynamics of invasive Carduus thistles. In: Chan F, Marinova D, Anderssen RS (eds) MODSIM2011, 19th International Congress on Modeling and Simulation, pp. 2514–2520

  • Jongejans E, Silverman EJ, Skarpaas O, Shea K (2015) Post-dispersal seed removal of Carduus nutans and C. acanthoides by insects and small mammals. Ecol Res. doi:10.1007/s11284-014-1224-4

  • Jonsen ID, Myers RA, James MC (2006) Robust hierarchical state-space models reveal diel variation in travel rates of migrating leatherback turtles. J Anim Ecol 75:1046–1057. doi:10.1111/j.1365-2656.2006.01129.x

    PubMed  Google Scholar 

  • Jordano P, García C, Godoy JA, García-Castaño JL (2007) Differential contribution of frugivores to complex seed dispersal patterns. Proc Natl Acad Sci U S A 104:3278–3282. doi:10.1073/pnas.0606793104

    PubMed Central  CAS  PubMed  Google Scholar 

  • Katul GG, Porporato A, Nathan R, Siquiera M, Soons MB, Poggi D, Horn HS, Levin SA (2005) Mechanistic analytical models for long-distance seed dispersal by wind. Am Nat 166:368–381. doi:10.1086/432589

    CAS  PubMed  Google Scholar 

  • Kavathekar D, Mueller T, Fagan WF (2013) Introducing AMV (animal movement visualizer), a visualization tool for animal movement data from satellite collars and radiotelemetry. Ecol Inf 15:91–95. doi:10.1016/j.ecoinf.2012.12.005

    Google Scholar 

  • Kelly N, Cousens RD, Taghizadeh MS, Hanan JS, Mouillot D (2013) Plants as populations of release sites for seed dispersal: a structural-statistical analysis of the effects of competition on Raphanus raphanistrum. J Ecol 101:878–888. doi:10.1111/1365-2745.12097

    Google Scholar 

  • Koenig WD, Van Vuren D, Hooge PN (1996) Detectability, philopatry, and the distribution of dispersal distances in vertebrates. Trends Ecol Evol 11:514–517. doi:10.1016/S0169-5347(96)20074-6

    CAS  PubMed  Google Scholar 

  • Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77:2027–2042. doi:10.2307/2265698

    Google Scholar 

  • Krings G, Calabrese F, Ratti C, Blondel VD (2009) Urban gravity: a model for inter-city telecommunication flows. J Stat Mech Theory Exp L07003. doi: 10.1088/1742-5468/2009/07/L07003

  • Kuparinen A (2006) Mechanistic models for wind dispersal. Trends Plant Sci 11:297–301. doi:10.1016/j.tplants.2006.04.006

    Google Scholar 

  • Le Corff J, Horvitz CC (2005) Population growth versus population spread of an ant-dispersed neotropical herb with a mixed reproductive strategy. Ecol Model 188:41–51. doi:10.1016/j.ecolmodel.2005.05.009

    Google Scholar 

  • Leung B, Roura-Pascual N, Bacher S, Heikkilä J, Brotons L, Burgman MA, Dehnen-Schmutz K, Essl F, Hulme PE, Richardson DM, Sol D, Vilà M (2012) TEASIng apart alien species risk assessments: a framework for best practices. Ecol Lett 15:1475–1493. doi:10.1111/ele.12003

    PubMed  Google Scholar 

  • Leuven R, van der Velde G, Baijens I, Snijders J, van der Zwart C, Lenders H, bij de Vaate A (2009) The river Rhine: a global highway for dispersal of aquatic invasive species. Biol Invasions 11:1989–2008. doi:10.1007/s10530-009-9491-7

    Google Scholar 

  • Levin LA (2006) Recent progress in understanding larval dispersal: new directions and digressions. Integr Comp Biol 46:282–297. doi:10.1093/icb/icj024

    CAS  PubMed  Google Scholar 

  • Levin SA, Muller-Landau HC, Nathan R, Chave J (2003) The ecology and evolution of seed dispersal: a theoretical perspective. Annu Rev Ecol Evol Syst 34:575–604. doi:10.1146/annurev.ecolsys.34.011802.132428

    Google Scholar 

  • Lisovski S, Hewson CM, Klaassen RHG, Korner-Nievergelt F, Kristensen MW, Hahn S (2012) Geolocation by light: accuracy and precision affected by environmental factors. Methods Ecol Evol 3:603–612. doi:10.1111/j.2041-210X.2012.00185.x

    Google Scholar 

  • Long ES (2005) Landscape and demographic influences on dispersal of white-tailed deer. Intercollege Graduate Degree Program in Ecology. Pennsylvania State University, p. 104

  • Long ES, Diefenbach DR, Rosenberry CS, Wallingford BD, Grund MD (2005) Forest cover influences dispersal distance of white-tailed deer. J Mammal 86:623–629. doi:10.1644/1545-1542(2005)86[623:FCIDDO]2.0.CO;2

    Google Scholar 

  • Long ES, Diefenbach DR, Rosenberry CS, Wallingford BD (2008) Multiple proximate and ultimate causes of natal dispersal in white-tailed deer. Behav Ecol 19:1235–1242. doi:10.1093/beheco/arn082

    Google Scholar 

  • Long ES, Diefenbach DR, Wallingford BD, Rosenberry CS (2010) Influence of roads, rivers, and mountains on natal dispersal of white-tailed deer. J Wildl Manag 74:1242–1249. doi:10.1111/j.1937-2817.2010.tb01244.x

    Google Scholar 

  • Lowen AC, Mubareka S, Steel J, Palese P (2007) Influenza virus transmission is dependent on relative humidity and temperature. PLoS Pathog 3:e151. doi:10.1371/journal.ppat.0030151

    PubMed Central  Google Scholar 

  • MacIsaac HJ, Robbins TC, Lewis MA (2002) Modeling ships’ ballast water as invasion threats to the Great Lakes. Can J Fish Aquat Sci 59:1245–1256. doi:10.1139/F02-090

    Google Scholar 

  • Maher SP, Kramer AM, Pulliam JT, Zokan MA, Bowden SE, Barton HD, Magori K, Drake JM (2012) Spread of white-nose syndrome on a network regulated by geography and climate. Nat Commun 3:1306. doi:10.1038/ncomms2301

    PubMed  Google Scholar 

  • Marchetto KM, Jongejans E, Shea K, Isard SA (2010) Plant spatial arrangement affects projected invasion speeds of two invasive thistles. Oikos 119:1462–1468. doi:10.1111/j.1600-0706.2010.18329.x

    Google Scholar 

  • Marchetto KM, Jongejans E, Shea K, Auhl R (2012) Water loss from flower heads predicts seed release in two invasive thistles. Plant Ecol Divers 5:57–65. doi:10.1080/17550874.2012.667841

    Google Scholar 

  • Marchetto KM, Shea K, Kelly D, Groenteman R, Sezen Z, Jongejans E (2014) Unrecognized impact of a biocontrol agent on the spread rate of an invasive thistle. Ecol Appl 24:1178–1187. doi:10.1890/13-1309.1

    PubMed  Google Scholar 

  • Matthysen E (2005) Density-dependent dispersal in birds and mammals. Ecography 28:403–416. doi:10.1111/j.0906-7590.2005.04073.x

    Google Scholar 

  • Morales JM, Moorcroft PR, Matthiopoulos J, Frair JL, Kie JG, Powell RA, Merrill EH, Haydon DT (2010) Building the bridge between animal movement and population dynamics. Phil Trans Roy Soc B Biol Sci 365:2289–2301. doi:10.1098/rstb.2010.0082

    Google Scholar 

  • Mueller T, Olson KA, Dressler G, Leimgruber P, Fuller TK, Nicolson C, Novaro AJ, Bolgeri MJ, Wattles D, DeStefano S, Calabrese JM, Fagan WF (2011) How landscape dynamics link individual- to population-level movement patterns: a multispecies comparison of ungulate relocation data. Glob Ecol Biogeogr 20:683–694. doi:10.1111/j.1466-8238.2010.00638.x

    Google Scholar 

  • Muirhead JR, MacIsaac HJ (2011) Evaluation of stochastic gravity model selection for use in estimating non-indigenous species dispersal and establishment. Biol Invasions 13:2445–2458. doi:10.1007/s10530-011-0070-3

    Google Scholar 

  • Muirhead JR, Lewis MA, MacIsaac HJ (2011) Prediction and error in multi-stage models for spread of aquatic non-indigenous species. Divers Distrib 17:323–337. doi:10.1111/j.1472-4642.2011.00745.x

    Google Scholar 

  • Muller-Landau HC, Wright SJ, Calderón O, Condit R, Hubbell SP (2008) Interspecific variation in primary seed dispersal in a tropical forest. J Ecol 96:653–667. doi:10.1111/j.1365-2745.2008.01399.x

    Google Scholar 

  • Münzbergová Z, Herben T (2005) Seed, dispersal, microsite, habitat and recruitment limitation: identification of terms and concepts in studies of limitations. Oecologia 145:1–8. doi:10.1007/s00442-005-0052-1

    PubMed  Google Scholar 

  • Nathan R (2001) Dispersal biogeography. In: Levin SA (ed) Encyclopedia of biodiversity. Academic, San Diego, pp 127–152

    Google Scholar 

  • Nathan R (2003) Seeking the secrets of dispersal. Trends Ecol Evol 18:275–276. doi:10.1016/S0169-5347(03)00063-6

    Google Scholar 

  • Nathan R (2006) Long-distance dispersal of plants. Science 313:786–788. doi:10.1126/science.1124975

    CAS  PubMed  Google Scholar 

  • Nathan R (2007) Total dispersal kernels and the evaluation of diversity and similarity in complex dispersal systems. In: Dennis AJ, Schupp EW, Green RJ, Wescott DA (eds) Seed dispersal: theory and its application in a changing world. CABI, Wallingford, pp 252–276

    Google Scholar 

  • Nathan R, Getz WM, Revilla E, Holyoak M, Kadmon R, Saltz D, Smouse PE (2008) A movement ecology paradigm for unifying organismal movement research. Proc Natl Acad Sci U S A 105:19052–19059. doi:10.1073/pnas.0800375105

    PubMed Central  CAS  PubMed  Google Scholar 

  • Nathan R, Katul GG, Bohrer G, Kuparinen A, Soons MB, Thompson SE, Trakhtenbrot A, Horn HS (2011) Mechanistic models of seed dispersal by wind. Theor Ecol 4:113–132. doi:10.1007/s12080-011-0115-3

    Google Scholar 

  • Nathan R, Klein E, Robledo-Arnuncio JJ, Revilla E (2012). Dispersal kernels: review. In: Clobert J, Baguette M, Benton TG, Bullock JM (eds) Dispersal ecology and evolution. Oxford University Press, pp. 187–210

  • Newton I (1687) Philosophiæ Naturalis Principia Mathematica. London

  • Noti JD, Blachere FM, McMillen CM, Lindsley WG, Kashon ML, Slaughter DR, Beezhold DH (2013) High humidity leads to loss of infectious influenza virus from simulated coughs. PLoS ONE 8:e57485. doi:10.1371/journal.pone.0057485

    PubMed Central  CAS  PubMed  Google Scholar 

  • Ohashi K, Yahara T (1999) How long to stay on, and how often to visit a flowering plant? A model for foraging strategy when floral displays vary in size. Oikos 86:386–392

    Google Scholar 

  • Okubo A, Ackerman JD, Swaney DP (2001) Passive diffusion in ecosystems. In: Okubo A, Levin SA (eds) Diffusion and ecological problems: modern perspectives. Springer, New York, pp 31–106

    Google Scholar 

  • Ouborg NJ, Piquot Y, van Groenendael JM (1999) Population genetics, molecular markers and the study of dispersal in plants. J Ecol 87:551–568. doi:10.1046/j.1365-2745.1999.00389.x

    Google Scholar 

  • Pakeman RJ (2001) Plant migration rates and seed dispersal mechanisms. J Biogeogr 28:795–800. doi:10.1046/j.1365-2699.2001.00581.x

    Google Scholar 

  • Pazos GE, Greene DF, Katul G, Bertiller MB, Soons MB (2013) Seed dispersal by wind: towards a conceptual framework of seed abscission and its contribution to long-distance dispersal. J Ecol 101:889–904. doi:10.1111/1365-2745.12103

    Google Scholar 

  • Peterson-Smith J, Shea K (2010) Seedling emergence and early survival of Carduus spp. in three habitats with press and pulse disturbances. J Torrey Bot Soc 137:287–296. doi:10.3159/09-RA-070R1.1

    Google Scholar 

  • Petrovskii S, Morozov A (2009) Dispersal in a statistically structured population: fat tails revisited. Am Nat 173:278–289. doi:10.1086/595755

    PubMed  Google Scholar 

  • Petrovskii S, Mashanova A, Jansen VAA (2011) Variation in individual walking behavior creates the impression of a Lévy flight. Proc Natl Acad Sci U S A 108:8704–8707. doi:10.1073/pnas.1015208108

    PubMed Central  CAS  PubMed  Google Scholar 

  • Portnoy S, Willson MF (1993) Seed dispersal curves: behavior of the tail of the distribution. Evol Ecol 7:25–44. doi:10.1007/BF01237733

    Google Scholar 

  • Potapov A, Muirhead JR, Lele SR, Lewis MA (2011) Stochastic gravity models for modeling lake invasions. Ecol Model 222:964–972. doi:10.1016/j.ecolmodel.2010.07.024

    Google Scholar 

  • Ravenstein EG (1885) The laws of migration. J Roy Stat Soc 48:167–235. doi:10.2307/2979181

    Google Scholar 

  • Redbo-Torstensson P, Telenius A (1995) Primary and secondary seed dispersal by wind and water in Spergularia salina. Ecography 18:230–237. doi:10.1111/j.1600-0587.1995.tb00126.x/

    Google Scholar 

  • Ribbens E, Silander JA, Pacala SW (1994) Seedling recruitment in forests: calibrating models to predict patterns of tree seedling dispersion. Ecology 75:1794–1806. doi:10.2307/1939638

    Google Scholar 

  • Robinson SJ, Samuel MD, Lopez DL, Shelton P (2012) The walk is never random: subtle landscape effects shape gene flow in a continuous white-tailed deer population in the Midwestern United States. Mol Ecol 21:4190–4205. doi:10.1111/j.1365-294X.2012.05681.x

    PubMed  Google Scholar 

  • Ronce O (2007) How does it feel to be like a rolling stone? Ten questions about dispersal evolution. Annu Rev Ecol Evol Syst 38:231–253. doi:10.1146/annurev.ecolsys.38.091206.095

    Google Scholar 

  • Rothlisberger JD, Lodge DM (2011) Limitations of gravity models in predicting the spread of Eurasian watermilfoil. Conserv Biol 25:64–72. doi:10.1111/j.1523-1739.2010.01589.x

    PubMed  Google Scholar 

  • Roy JR (2004) Spatial interaction modelling. A regional science context. Springer, Berlin

  • Schippers P, Jongejans E (2005) Release thresholds strongly determine the range of seed dispersal by wind. Ecol Model 185:93–103. doi:10.1016/j.ecolmodel.2004.11.018

    Google Scholar 

  • Schupp EW, Jordano P, Gómez JM (2010) Seed dispersal effectiveness revisited: a conceptual review. New Phytol 188:333–353. doi:10.1111/j.1469-8137.2010.03402.x

    PubMed  Google Scholar 

  • Schurr FM, Bond WJ, Midgley GF, Higgins SI (2005) A mechanistic model for secondary seed dispersal by wind and its experimental validation. J Ecol 93:1017–1028. doi:10.1111/j.1365-2745.2005.01018.x

    Google Scholar 

  • Shea K (2007) How the wood moves. Science 315:1231–1232. doi:10.1126/science.1136096

    CAS  PubMed  Google Scholar 

  • Shea K, Amarasekare P, Kareiva P, Mangel M, Moore J, Murdoch WW, Noonburg EG, Parma A, Pascual MA, Possingham HP, Wilcox W, Yu D (1998) Management of populations in conservation, harvesting and control. Trends Ecol Evol 13:371–375. doi:10.1016/S0169-5347(98)01381-0

    CAS  PubMed  Google Scholar 

  • Shea K, Metaxas A, Young CR, Fisher CR (2008) Processes and interactions in macrofaunal assemblages at hydrothermal vents: a modelling perspective. In: Lowell RP, Seewald JS, Metaxas A, Perfit MR (eds) Magma to microbe: modeling hydrothermal processes at oceanic spreading centers. Am Geophys Union: Geophys Monogr, pp. 259–274

  • Shea K, Jongejans E, Skarpaas O, Kelly D, Sheppard A (2010) Optimal management strategies to control local population growth or population spread may not be the same. Ecol Appl 20:1148–1161. doi:10.1890/09-0316.1

    PubMed  Google Scholar 

  • Shurin JB, Cottenie K, Hillebrand H (2009) Spatial autocorrelation and dispersal limitation in freshwater organisms. Oecologia 159:151–159. doi:10.1007/s00442-008-1174-z

    PubMed  Google Scholar 

  • Skarpaas O, Shea K (2007) Dispersal patterns, dispersal mechanisms and invasion wave speeds for invasive thistles. Am Nat 170:421–430. doi:10.1086/519854

    PubMed  Google Scholar 

  • Skarpaas O, Shea K, Bullock JM (2005) Optimising dispersal study design by Monte Carlo simulation. J Appl Ecol 42:731–739. doi:10.1111/j.1365-2664.2005.01056.x

    Google Scholar 

  • Skarpaas O, Auhl R, Shea K (2006) Environmental variability and the initiation of dispersal: turbulence strongly increases seed release. Proc Roy Soc B Biol Sci 273:751–756. doi:10.1098/rspb.2005.3366

    Google Scholar 

  • Skarpaas O, Shea K, Jongejans E (2011) Watch your time step: trapping and tracking dispersal in autocorrelated environments. Methods Ecol Evol 2:407–415. doi:10.1111/j.2041-210X.2010.00086.x

    Google Scholar 

  • Skelsey P, With KA, Garrett KA (2012) Why dispersal should be maximized at intermediate scales of heterogeneity. Theor Ecol 6:203–211. doi:10.1007/s12080-012-0171-3

    PubMed Central  PubMed  Google Scholar 

  • Skuldt LH, Mathews NE, Oyer AM (2008) White-tailed deer movements in a chronic wasting disease area in South-Central Wisconsin. J Wildl Manag 72:115–1160. doi:10.2193/2006-469

    Google Scholar 

  • Smith DL, Lucey B, Waller LA, Childs JE, Real LA (2002) Predicting the spatial dynamics of rabies epidemics on heterogeneous landscapes. Proc Natl Acad Sci U S A 99:3668–3672. doi:10.1073/pnas.042400799

    PubMed Central  CAS  PubMed  Google Scholar 

  • Smith RF, Alexander LC, Lamp WO (2009) Dispersal by terrestrial stages of stream insects in urban watersheds: a synthesis of current knowledge. J N Am Benthol Soc 28:1022–1037. doi:10.1899/08-176.1

    Google Scholar 

  • Snäll T, O’Hara RB, Arjas E (2007) A mathematical and statistical framework for modelling dispersal. Oikos 116:1037–1050. doi:10.1111/j.2007.0030-1299.15604.x

    Google Scholar 

  • Snäll T, O’Hara RB, Ray C, Collinge SK (2008) Climate-driven spatial dynamics of plague among prairie dog colonies. Am Nat 171:238–248. doi:10.1086/525051

    PubMed  Google Scholar 

  • Soons MB, Bullock JM (2008) Non-random seed abscission, long-distance wind dispersal and plant migration rates. J Ecol 96:581–590. doi:10.1111/j.1365-2745.2007.0

    Google Scholar 

  • Stenseth NC, Lidicker WZ (eds) (1992) Animal dispersal: small mammals as a model. Chapman & Hall, London

    Google Scholar 

  • Stiles EW, White DW (1986) Seed deposition patterns: influence of season, nutrients, and vegetation structure. In: Estrada A, Flemming TH (eds) Frugivores and seed dispersal. Dr W Junk, Dordrecht, pp 45–54

    Google Scholar 

  • Stockmarr A (2002) The distribution of particles in the plane dispersed by a simple 3-dimensional diffusion process. J Math Biol 45:461–469. doi:10.1007/s002850200157

    PubMed  Google Scholar 

  • Sutherland GD, Harestad AS, Price K, Lertzman KP (2000) Scaling of natal dispersal distances in terrestrial birds and mammals. Conserv Ecol 4:16

    Google Scholar 

  • Sutrave S, Scoglio C, Isard SA, Hutchinson JMS, Garrett KA (2012) Identifying highly connected counties compensates for resource limitations when evaluating national spread of an invasive pathogen. PLoS ONE 7:e37793. doi:10.1371/journal.pone.0037793

    PubMed Central  CAS  PubMed  Google Scholar 

  • Takken W, Knols BGJ (1999) Odor-mediated behavior of Afrotropical malaria mosquitoes. Annu Rev Entomol 44:131–157. doi:10.1146/annurev.ento.44.1.131

    CAS  PubMed  Google Scholar 

  • Taylor LR (1986) Synoptic dynamics, migration and the Rothamsted insect survey. J Anim Ecol 55:1–38. doi:10.2307/4690

    Google Scholar 

  • Teller BJ, Campbell C, Shea K (2014) Dispersal under duress: can stress enhance the performance of a passively dispersed species? Ecology 95:2694–2698. doi:10.1890/14-0474.1

    Google Scholar 

  • Thomas RW, Hugget RJ (1980) Modeling in geography. A mathematical approach. Barnes & Noble, Totowa

    Google Scholar 

  • Thomson FJ, Moles AT, Auld TD, Kingsford RT (2011) Seed dispersal distance is more strongly correlated with plant height than with seed mass. J Ecol 99:1299–1307. doi:10.1111/j.1365-2745.2011.01867.x

    Google Scholar 

  • Travis JMJ, Mustin K, Bartoń KA, Benton TG, Clobert J, Delgado MM, Dytham C, Hovestadt T, Palmer SCF, Van Dyck H, Bonte D (2012) Modelling dispersal: an eco-evolutionary framework incorporating emigration, movement, settlement behaviour and the multiple costs involved. Methods Ecol Evol 3:628–641. doi:10.1111/j.2041-210X.2012.00193.x

    Google Scholar 

  • Tufto J, Engen S, Hindar K (1997) Stochastic dispersal processes in plant populations. Theor Popul Biol 52:16–26. doi:10.1006/tpbi.1997.1306

    PubMed  Google Scholar 

  • Turchin P (1998) Quantitative analysis of movement: measuring and modeling population redistribution in animals and plants. Sinauer, Sunderland

    Google Scholar 

  • Urban MC, Zarnetske PL, Skelly DK (2013) Moving forward: dispersal and species interactions determine biotic responses to climate change. Ann N Y Acad Sci 1297:44–60. doi:10.1111/nyas.12184

    PubMed  Google Scholar 

  • van der Pijl L (1982) Principles of dispersal in higher plants. Springer, Berlin

    Google Scholar 

  • van Noordwijk CGE, Jongejans E, Boeye J, Remke E, Siepel H, Berg MP, Bonte D (2014) A multi-generation perspective on functional connectivity for arthropods in fragmented landscapes. In: van Noordwijk CGE (PhD thesis) Through arthropod eyes. Gaining mechanistic understanding of calcareous grassland diversity. Radboud University Nijmegen, pp. 127–145

  • van Putten B, Visser MD, Muller-Landau HC, Jansen PA (2012) Distorted-distance models for directional dispersal: a general framework with application to a wind-dispersed tree. Methods Ecol Evol 3:642–652. doi:10.1111/j.2041-210X.2012.00208.x

    Google Scholar 

  • Vander Wall SB (1992) The role of animals in dispersing a “wind-dispersed” pine. Ecology 73:614–621. doi:10.2307/1940767

    Google Scholar 

  • von der Lippe M, Bullock JM, Kowarik I, Knopp T, Wichmann MC (2013) Human-mediated dispersal of seeds by the airflow of vehicles. PLoS ONE 8:e52733. doi:10.1371/journal.pone.0052733

    PubMed Central  PubMed  Google Scholar 

  • Wichmann M, Alexander MJ, Soons MB, Galsworthy S, Dunne L, Gould R, Fairfax C, Niggemann M, Hails RS, Bullock JM (2009) Human-mediated dispersal of seeds over long distances. Proc Roy Soc B Biol Sci 276:523–532. doi:10.1098/rspb.2008.1131

    Google Scholar 

  • Willson MF (1993) Dispersal mode, seed shadows and colonization patterns. Vessgetatio 107(108):261–280. doi:10.1007/BF00052229

    Google Scholar 

  • Xia Y, Bjørnstad ON, Grenfell BT (2004) Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. Am Nat 164:267–281. doi:10.1086/422341

    PubMed  Google Scholar 

  • Yang S, Ferrari MJ, Shea K (2011) Pollinator behavior mediates negative interactions between two congeneric invasive plant species. Am Nat 177:110–118. doi:10.1086/657433

    PubMed  Google Scholar 

  • Yates G, Boyce MS (2012) Dispersal, animal. In: Hastings A, Gross L (eds) Encyclopedia of theoretical ecology. University of California Press, pp. 188–192

  • Zhang R, Jongejans E, Shea K (2011) Warming increases the spread of an invasive thistle. PLoS ONE 6:e21725. doi:10.1371/journal.pone.0021725

    PubMed Central  CAS  PubMed  Google Scholar 

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Acknowledgments

We thank the Intercollege Graduate Degree Program in Ecology of the Pennsylvania State University for creating a stimulating environment where faculty and students from a wide range of disciplines meet and interact. We are grateful for the financial support from the Netherlands Organization for Scientific Research (NWO-meerwaarde grant 850.11.001 to EJ), the Norwegian Research Council (grant 161484/V10 to OS), and the US National Science Foundation (grants DEB-0315860 and DEB-0614065 to KS).

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Authors and Affiliations

  1. Department of Animal Ecology and Ecophysiology, Institute for Water and Wetland Research, Radboud University Nijmegen, PO Box 9100, 6500 GL, Nijmegen, The Netherlands

    Eelke Jongejans

  2. Norwegian Institute for Nature Research, Gaustadalléen 21, 0349, Oslo, Norway

    Olav Skarpaas

  3. Center for Infectious Disease Dynamics, Department of Biology, The Pennsylvania State University, 208 Mueller Laboratory, University Park, PA, 16802, USA

    Matthew J. Ferrari

  4. Department of Biology, Seattle Pacific University, 3307 3rd Ave W, Seattle, WA, 98119, USA

    Eric S. Long

  5. School of Natural Resources, University of Nebraska-Lincoln, 1400 R Street, Lincoln, NB, 68588, USA

    Joseph T. Dauer

  6. Department of Biology, Western Washington University, Bellingham, WA, 98225, USA

    Carrie M. Schwarz

  7. Department of Biological, Geological and Environmental Sciences, Cleveland State University, Cleveland, OH, 44115, USA

    Emily S. J. Rauschert

  8. Department of Plant Sciences, University of Wyoming, 1000 E. University Ave, Laramie, WY, 82071, USA

    Randa Jabbour

  9. Plant Sciences Department, The Pennsylvania State University, 422 ASI Building, University Park, PA, 16802, USA

    David A. Mortensen

  10. Department of Plant Pathology and Environmental Microbiology and Department of Meteorology, The Pennsylvania State University, 205 Buckhout Lab, University Park, PA, 16802, USA

    Scott A. Isard

  11. Western Pennsylvania Conservancy and Pennsylvania Fish and Boat Commission, 450 Robinson Lane, Bellefonte, PA, 16823, USA

    David A. Lieb

  12. Department of Entomology, University of Minnesota, 209 Hodson Hall, 1980 Follwell Ave., St. Paul, MN, 55108, USA

    Zeynep Sezen

  13. Department of Crop and Soil Science, Oregon State University, 109 Crop Science Building, Corvallis, OR, 97331, USA

    Andrew G. Hulting

  14. Department of Biology, The Pennsylvania State University, 208 Mueller Lab, University Park, PA, 16802, USA

    Katriona Shea

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Jongejans, E., Skarpaas, O., Ferrari, M.J. et al. A unifying gravity framework for dispersal. Theor Ecol 8, 207–223 (2015). https://doi.org/10.1007/s12080-014-0245-5

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