The rising introduction of invasive species through trade networks threatens biodiversity and ecosystem services. Yet, we have a limited understanding of how transportation networks determine spatiotemporal patterns of range expansion. This knowledge gap may stem from two reasons. First, current analytical models fail to integrate the invader's life-history dynamics with heterogeneity in human-mediated dispersal patterns. Second, classical statistical methods often fail to provide reliable estimates of model parameters, such as time and place of species introduction and life-history characteristics, due to spatial biases in the presence-only records and lack of informative demographic data. To address these gaps, we first formulate an age-structured metapopulation model that uses a probability matrix to emulate human-mediated dispersal patterns. The model reveals that an invader spreads radially along the shortest network path, such that the inter-patch network distances decrease with increasing traffic volume and reproductive value of hitchhikers. Next, we propose a hierarchical Bayesian statistical method to estimate model parameters using presence-only data and prior demographic knowledge. To show the utility of the statistical approach, we analyze zebra mussel (Dreissena polymorpha) expansion in North America through the inland commercial shipping network. Our analysis suggests that zebra mussels might have been introduced before 1981, indicating a lag of five years between time of introduction and first detection in late 1986. Furthermore, using our statistical model we estimated a one in three chance that they were introduced near Kingsville (Ontario, Canada), where they were first reported. We also find survival, fecundity, and dispersal during early life (1-2 years) play a critical role in determining the expansion success of these mollusks. These results underscore the importance of fusing prior scientific knowledge with observation and demographic processes in a Bayesian framework for conceptual and practical understanding of how invasive species spread by human agency.

Czech University of Life Sciences Prague Forestry and Wood Sciences 16500 Prague 6 Czech Republic

Department of Ecology and Evolution Biophore UNIL Sorge University of Lausanne Lausanne Vaud Switzerland 1015

Department of Integrative Biology The University of Texas at Austin Austin Texas USA 78712

Department of Physics Graduate Program in Bioinformatics and Biological Design Center Boston University Boston MA USA 02215

Department of Statistics and Data Sciences The University of Texas at Austin Austin Texas USA 78705

USDA Forest Service Northern Research Station Morgantown West Virginia USA 15349

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bioRxiv. 2024 Feb 12:2024.02.09.578762. doi: 10.1101/2024.02.09.578762. PubMed

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Bagnara M, Nowak L, Boehmer HJ, Schöll F, Schurr FM, and Seebens H. 2022. Simulating the spread and establishment of alien species along aquatic and terrestrial transport networks: A multi-pathway and high-resolution approach. Journal of Applied Ecology 59:1769–1780.

Banks NC, Paini DR, Bayliss KL, and Hodda M. 2015. The role of global trade and transport network topology in the human-mediated dispersal of alien species. Ecology Letters 18:188–199. PubMed

Bateman AW, Neubert MG, Krkošek M, and Lewis MA. 2015. Generational spreading speed and the dynamics of population range expansion. The American Naturalist 186:362–375. PubMed

Bellard C, Cassey P, and Blackburn TM. 2016. Alien species as a driver of recent extinctions. Biology Letters 12:20150623. PubMed PMC

Berliner LM 1996. Hierarchical Bayesian Time Series Models. Pages 15–22. Springer; Netherlands, Dordrecht.

Besson M, Alison J, Bjerge K, Gorochowski TE, Høye TT, Jucker T, Mann HM, and Clements CF. 2022. Towards the fully automated monitoring of ecological communities. Ecology Letters 25:2753–2775. PubMed PMC

Brockmann D, and Helbing D. 2013. The hidden geometry of complex, network-driven contagion phenomena. Science 342:1337–1342. PubMed

Buhle ER, Margolis M, and Ruesink JL. 2005. Bang for buck: Cost-effective control of invasive species with different life histories. Ecological Economics 52:355–366.

Carlton JT 2008. The zebra mussel

Carpenter B, Gelman A, Hoffman MD, Lee D, Goodrich B, Betancourt M, Brubaker MA, Guo J, Li P, and Riddell A. 2017. Stan: A probabilistic programming language. Journal of Statistical Software 76:1–32. PubMed PMC

Carrasco LR, Mumford J, MacLeod A, Harwood T, Grabenweger G, Leach A, Knight J, and Baker R. 2010. Unveiling human-assisted dispersal mechanisms in invasive alien insects: Integration of spatial stochastic simulation and phenology models. Ecological Modelling 221:2068–2075.

Casagrandi R, Mari L, and Gatto M. 2007. Modelling the local dynamics of the zebra mussel (

Caswell H 2001. Matrix Population Models. Sinauer; Sunderland, MA, USA.

Chapman DS, Makra L, Albertini R, Bonini M, Páldy A, Rodinkova V, Šikoparija B, Weryszko-Chmielewska E, and Bullock JM. 2016. Modelling the introduction and spread of non-native species: International trade and climate change drive ragweed invasion. Global Change Biology 22:3067–3079. PubMed

Colizza V, Barrat A, Barthélemy M, and Vespignani A. 2006. The role of the airline transportation network in the prediction and predictability of global epidemics. Proceedings of the National Academy of Sciences 103:2015–2020. PubMed PMC

Crooks JA 2005. Lag times and exotic species: The ecology and management of biological invasions in slow-motion. Ecoscience 12:316–329.

Cross CL, Wong WH, and Che T. 2011. Estimating carrying capacity of quagga mussels (

Crouse DT, Crowder LB, and Caswell H. 1987. A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68:1412–1423.

Dennis B 1989. Allee effects: population growth, critical density, and the chance of extinction. Natural Resource Modeling 3:481–538.

Diagne C, Leroy B, Vaissière A-C, Gozlan RE, Roiz D, Jarić I, Salles J-M, Bradshaw CJ, and Courchamp F. 2021. High and rising economic costs of biological invasions worldwide. Nature 592:571–576. PubMed

Dorazio RM, and Johnson FA. 2003. Bayesian inference and decision theory—A framework for decision making in natural resource management. Ecological Applications 13:556–563.

Engen S, Lande R, Sæther B-E, and Weimerskirch H. 2005. Extinction in relation to demographic and environmental stochasticity in age-structured models. Mathematical Biosciences 195:210–227. PubMed

Fenn-Moltu G, Ollier S, Caton B, Liebhold AM, Nahrung H, Pureswaran DS, Turner RM, Yamanaka T, and Bertelsmeier C. 2023. Alien insect dispersal mediated by the global movement of commodities. Ecological Applications 33:e2721. PubMed PMC

Fernald RT, and Watson BT. 2013. Eradication of zebra mussels (

Ferrari JR, Preisser EL, and Fitzpatrick MC. 2014. Modeling the spread of invasive species using dynamic network models. Biological Invasions 16:949–960.

Floerl O, Inglis G, Dey K, and Smith A. 2009. The importance of transport hubs in stepping-stone invasions. Journal of Applied Ecology 46:37–45.

Gautreau A, Barrat A, and Barthelemy M. 2008. Global disease spread: Statistics and estimation of arrival times. Journal of Theoretical Biology 251:509–522. PubMed

GBIF.org. 2022. Occurrence Download. The Global Biodiversity Information Facility.

Gelman A, Carlin JB, Stern HS, and Rubin DB. 1995. Bayesian Data Analysis. CRC Press, Boca Raton, FL.

Gelman A, Vehtari A, Simpson D, Margossian CC, Carpenter B, Yao Y, Kennedy L, Gabry J, Bürkner P-C, and Modrák M. 2020. Bayesian workflow. arXiv preprint arXiv:2011.01808.

Gippet JM, and Bertelsmeier C. 2021. Invasiveness is linked to greater commercial success in the global pet trade. Proceedings of the National Academy of Sciences 118:e2016337118. PubMed PMC

Goel N 2025. “A mechanistic statistical approach to infer invasion characteristics of human-dispersed species with complex life cycle. In Ecological Monographs (Version V1).” Zenodo. 10.5281/zenodo.14708765 PubMed DOI PMC

Griffiths RW, Schloesser DW, Leach JH, and Kovalak WP. 1991. Distribution and dispersal of the zebra mussel (

Hallatschek O, and Fisher DS. 2014. Acceleration of evolutionary spread by long-range dispersal. Proceedings of the National Academy of Sciences 111:E4911–E4919. PubMed PMC

Hebert PD, Muncaster B, and Mackie G. 1989. Ecological and genetic studies on

Hobbs NT, and Hooten MB. 2015. Bayesian Models: A Statistical Primer for Ecologists. Princeton University Press, Princeton, New Jersey.

Hoffman MD, and Gelman A. 2014. The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research 15:1593–1623.

Hooten MB, and Hefley TJ. 2019. Bringing Bayesian Models to Life. CRC Press, Boca Raton, Florida, USA.

Hooten MB, Wikle CK, Dorazio RM, and Royle JA. 2007. Hierarchical spatiotemporal matrix models for characterizing invasions. Biometrics 63:558–567. PubMed

Horvitz N, Wang R, Wan F-H, and Nathan R. 2017. Pervasive human-mediated large-scale invasion: Analysis of spread patterns and their underlying mechanisms in 17 of China’s worst invasive plants. Journal of Ecology 105:85–94.

Hu Y, and Zhu D. 2009. Empirical analysis of the worldwide maritime transportation network. Physica A: Statistical Mechanics and its Applications 388:2061–2071.

Hui C, and Richardson DM. 2017. Invasion Dynamics. Oxford University Press, Oxford.

Hulme PE 2009. Trade, transport and trouble: Managing invasive species pathways in an era of globalization. Journal of Applied Ecology 46:10–18.

Hunter CM, and Caswell H. 2005. The use of the vec-permutation matrix in spatial matrix population models. Ecological Modelling 188:15–21.

Iannelli F, Koher A, Brockmann D, Hovel P, and Sokolov IM. 2017. Effective distances for epidemics spreading on complex networks. Physical Review E 95:012313. PubMed PMC

Isaac NJ, van Strien AJ, August TA, de Zeeuw MP, and Roy DB. 2014. Statistics for citizen science: Extracting signals of change from noisy ecological data. Methods in Ecology and Evolution 5:1052–1060.

Jamieson-Lane A, and Blasius B. 2020. Calculation of epidemic arrival time distributions using branching processes. Physical Review E 102:042301. PubMed

Johnson LE, and Carlton JT. 1996. Post-establishment spread in large-scale invasions: Dispersal mechanisms of the zebra mussel

Johnson LE, and Padilla DK. 1996. Geographic spread of exotic species: Ecological lessons and opportunities from the invasion of the zebra mussel

Johnston A, Matechou E, and Dennis EB. 2023. Outstanding challenges and future directions for biodiversity monitoring using citizen science data. Methods in Ecology and Evolution 14:103–116.

Keevin TM, Yarbrough RE, and Miller AC. 1992. Long-distance dispersal of zebra mussels (

Keitt TH, and Abelson ES. 2021. Ecology in the age of automation. Science 373:858–859. PubMed

Kot M, Lewis MA, and vandenDriessche P. 1996. Dispersal data and the spread of invading organisms. Ecology 77:2027–2042.

Kulkarni VG 2016. Modeling and Analysis of Stochastic Systems. Chapman and Hall/CRC, London, U.K.

Lande R, and Orzack SH. 1988. Extinction dynamics of age-structured populations in a fluctuating environment. Proceedings of the National Academy of Sciences 85:7418–7421. PubMed PMC

Lefkovitch L 1965. The study of population growth in organisms grouped by stages. Biometrics 21:1–18.

Leslie PH 1945. On the use of matrices in certain population mathematics. Biometrika 33:183–212. PubMed

Lewis MA, Petrovskii SV, and Potts JR. 2016. The Mathematics Behind Biological Invasions. Springer, New York.

Lockwood JL, Cassey P, and Blackburn T. 2005. The role of propagule pressure in explaining species invasions. Trends in Ecology & Evolution 20:223–228. PubMed

Lowe S, Browne M, Boudjelas S, and De-Poorter M. 2004. One hundred of the world’s worst invasive alien species: A selection from the global invasive species database. Invasive Species Specialist Group, IUCN, Switzerland.

Ludyanskiy ML, McDonald D, and MacNeill D. 1993. Impact of the zebra mussel, a bivalve invader:

Lutscher F 2019. Integrodifference Equations in Spatial Ecology. Springer, Cham, Switzerland.

May RM 2004. Uses and abuses of mathematics in biology. Science 303:790–793. PubMed

McElreath R 2020. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. CRC Press, Boca Raton, FL.

Meyerson LA, and Mooney HA. 2007. Invasive alien species in an era of globalization. Frontiers in Ecology and the Environment 5:199–208.

Miller DA, Pacifici K, Sanderlin JS, and Reich BJ. 2019. The recent past and promising future for data integration methods to estimate species’ distributions. Methods in Ecology and Evolution 10:22–37.

Nalepa TF, and Schloesser DW. 2013. Quagga and Zebra Mussels: Biology, Impacts, and Control. CRC press, Boca Raton, Florida, USA.

Neal RM 2011. MCMC using Hamiltonian dynamics. Page 2 in Brooks S, Gelman A, Jones G, and Meng X-L, editors. Handbook of Markov Chain Monte Carlo. CRC Press, New York.

Neath AA, and Samaniego FJ. 1997. On the efficacy of Bayesian inference for nonidentifiable models. The American Statistician 51:225–232.

Neubert MG, and Caswell H. 2000. Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations. Ecology 81:1613–1628.

Padilla DK, Chotkowski MA, and Buchan LA. 1996. Predicting the spread of zebra mussels (

Pagel J, and Schurr FM. 2012. Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics. Global Ecology and Biogeography 21:293–304.

Pardieck KL, Z. LDJ Jr., A. M. VI, and M.-A. R. and Hudson. 2020. North American Breeding Bird Survey Dataset 1966—2019 in U.S.G.S., editor.

Peterson AT, Soberón J, Pearson RG, Anderson RP, Martinez-Meyer E, Nakamura M, and Araújo MB. 2011. Ecological Niches and Geographic Distributions. Princeton University Press, Princeton, New Jersey, USA.

Pollard E, Yates TJ, and Courtney SP. 1994. Monitoring butterflies for ecology and conservation: The British butterfly monitoring scheme. Ecology 75:1851.

Ricker WE 1954. Stock and Recruitment. Journal of the Fisheries Research Board of Canada 11:559–623.

Rvachev LA, and Longini IM Jr. 1985. A mathematical model for the global spread of influenza. Mathematical Biosciences 75:3–22.

Seebens H, Blackburn TM, Dyer EE, Genovesi P, Hulme PE, Jeschke JM, Pagad S, Pysek P, van Kleunen M, Winter M, Ansong M, Arianoutsou M, Bacher S, Blasius B, Brockerhoff EG, Brundu G, Capinha C, Causton CE, Celesti-Grapow L, Dawson W, Dullinger S, Economo EP, Fuentes N, Guenard B, Jager H, Kartesz J, Kenis M, Kuhn I, Lenzner B, Liebhold AM, Mosena A, Moser D, Nentwig W, Nishino M, Pearman D, Pergl J, Rabitsch W, Rojas-Sandoval J, Roques A, Rorke S, Rossinelli S, Roy HE, Scalera R, Schindler S, Stajerova K, Tokarska-Guzik B, Walker K, Ward DF, Yamanaka T, and Essl F. 2018. Global rise in emerging alien species results from increased accessibility of new source pools. Proceedings of the National Academy of Sciences 115:E2264–E2273. PubMed PMC

Seebens H, Briski E, Ghabooli S, Shiganova T, MacIsaac HJ, and Blasius B. 2019. Non-native species spread in a complex network: The interaction of global transport and local population dynamics determines invasion success. Proceedings of the Royal Society B 286:20190036. PubMed PMC

Shine R, Brown GP, and Phillips BL. 2011. An evolutionary process that assembles phenotypes through space rather than through time. Proceedings of the National Academy of Sciences 108:5708–5711. PubMed PMC

Simberloff D 2009. The role of propagule pressure in biological invasions. Annual Review of Ecology, Evolution, and Systematics 40:81–102.

Simini F, González MC, Maritan A, and Barabási A-L. 2012. A universal model for mobility and migration patterns. Nature 484:96–100. PubMed

Skellam JG 1951. Random dispersal in theoretical populations. Biometrika 38:196–218. PubMed

Solano A, Rodriguez SL, Greenwood L, Dodds KJ, and Coyle DR. 2021. Firewood transport as a vector of forest pest dispersal in North America: A scoping review. Journal of Economic Entomology 114:14–23. PubMed

Stouffer SA 1940. Intervening opportunities: A theory relating mobility and distance. American Sociological Review 5:845–867.

Thompson BK, Olden JD, and Converse SJ. 2021. Mechanistic invasive species management models and their application in conservation. Conservation Science and Practice 3:e533.

Turbelin AJ, Cuthbert RN, Essl F, Haubrock PJ, Ricciardi A, and Courchamp F. 2023. Biological invasions are as costly as natural hazards. Perspectives in Ecology and Conservation 21:143–150.

USGS. 2022. Dreissena polymorpha (Pallas, 1771): U.S. Geological Survey, Nonindigenous Aquatic Species Database. United States Geological Survey, Gainesville, FL.

van den Bosch F, Hengeveld R, and Metz JAJ. 1992. Analysing the velocity of animal range expansion. Journal of Biogeography 19:135–150.

Van den Bosch F, Metz JAJ, and Diekmann O. 1990. The velocity of spatial population expansion. Journal of Mathematical Biology 28:529–565.

Warziniack T, Haight RG, Yemshanov D, Apriesnig JL, Holmes TP, Countryman AM, Rothlisberger JD, and Haberland C. 2021. Economics of invasive species. Invasive Species in Forests and Rangelands of the United States: A Comprehensive Science Synthesis for the United States Forest Sector:305–320.

Wikle CK 2003. Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 84:1382–1394.

Williams PJ, and Hooten MB. 2016. Combining statistical inference and decisions in ecology. Ecological Applications 26:1930–1942. PubMed

Wolf F, Kirsch C, and Donner RV. 2019. Edge directionality properties in complex spherical networks. Physical Review E 99:012301. PubMed

Yee DA 2008. Tires as habitats for mosquitoes: A review of studies within the eastern United States. Journal of Medical Entomology 45:581–593. PubMed

Yemshanov D, McKenney DW, Pedlar JH, Koch FH, and Cook D. 2009. Towards an integrated approach to modelling the risks and impacts of invasive forest species. Environmental Reviews 17:163–178.

Zipf GK 1946. The P 1 P 2/D hypothesis: On the intercity movement of persons. American Sociological Review 11:677–686.

Zook B, and Phillips S. 2012. Uniform minimum protocols and standards for watercraft interception programs for dreissenid mussels in the western United States (UMPS). Pacific States Marine Fisheries Commission. Portland, OR. 77p.

A mechanistic statistical approach to infer invasion characteristics of human-dispersed species with complex life cycle