Theoretical Ecology

, Volume 11, Issue 3, pp 271–280 | Cite as

A flow network model for animal movement on a landscape with application to invasion

  • Rosalyn Rael
  • Caz Taylor


Animal movement, whether for foraging, mate-seeking, predator avoidance, dispersal, or migration, is a fundamental aspect of ecology that shapes spatial abundance distributions, genetic compositions, and dynamics of populations. A variety of movement models have been used for predicting the effects of natural or human-caused landscape changes, invading species, or other disturbances on local ecology. Here we introduce the flow network—a general modeling framework for population dynamics and movement in a metapopulation representing a network of habitat sites (nodes). Based on the principles of physical transport phenomena such as fluid flow through pipes (Pouiselle’s Law) and analogously, the flow of electric current across a circuit (Ohm’s Law), the flow network provides a novel way of modeling movement, where flow rates are functions of relative node pressures and the resistance to movement between them. Flow networks offer the flexibility of incorporating abiotic and biotic conditions that affect either pressures, resistance, or both. To illustrate an application of the flow network, we present a theoretical invasion scenario. We consider the effects of spatial structure on the speed of invasion by varying the spatial regularity of node arrangement. In the context of invasion, we model management actions targeting nodes or edges, and consider the effects on speed of invasion, node occupation, and total abundance. The flow network approach offers the flexibility to incorporate spatial heterogeneity in both rates of flow and site pressures and offers an intuitive approach to connecting population dynamics and landscape features to model movement.


Migration Dispersal Landscape modeling Metapopulations Migratory flow network Source-sink dynamics 


Funding information

Funding for this work was made available from the ByWater Institute at Tulane University and the National Science Foundation (BCS-1313703).

Supplementary material

12080_2018_373_MOESM1_ESM.pdf (73 kb)
(PDF 72.7 KB)


  1. Adriaensen F, Chardon J, De Blust G, Swinnen E, Villalba S, Gulinck H, Matthysen E (2003) The application of least-cost modelling as a functional landscape model. Landscape Urban Plan 64(4):233–247CrossRefGoogle Scholar
  2. Amarasekare P (2004) The role of density-dependent dispersal in source–sink dynamics. J Theor Biol 226(2):159–168CrossRefPubMedGoogle Scholar
  3. Amos JN, Bennett AF, Mac Nally R, Newell G, Pavlova A, Radford JQ, Thomson JR, White M, Sunnucks P (2012) Predicting landscape-genetic consequences of habitat loss, fragmentation and mobility for multiple species of woodland birds. PLoS One 7(2):e30,888CrossRefGoogle Scholar
  4. Armsworth PR (2002) Recruitment limitation, population regulation, and larval connectivity in reef fish metapopulations. Ecology 83(4):1092–1104CrossRefGoogle Scholar
  5. Barrios JM, Verstraeten WW, Maes P, Aerts JM, Farifteh J, Coppin P (2012) Using the gravity model to estimate the spatial spread of vector-borne diseases. Int J Environ Res Publ Health 9(12):4346–4364CrossRefGoogle Scholar
  6. Bascompte J, Solé RV (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. J Anim Ecol 65(4):465–473CrossRefGoogle Scholar
  7. Bossenbroek JM, Kraft CE, Nekola JC (2001) Prediction of long-distance dispersal using gravity models: zebra mussel invasion of inland lakes. Ecol Appl 11(6):1778–1788CrossRefGoogle Scholar
  8. Carroll C, Miquelle DG (2006) Spatial viability analysis of amur tiger panthera tigris altaica in the russian far east: the role of protected areas and landscape matrix in population persistencerstudio. J Appl Ecol 43(6):1056–1068. CrossRefGoogle Scholar
  9. Dingle H (2014) Migration: the biology of life on the move. Oxford University Press, USACrossRefGoogle Scholar
  10. Dingle H, Drake VA (2007) What is migration? Bioscience 57(2):113–121CrossRefGoogle Scholar
  11. Elliot NB, Cushman SA, Macdonald DW, Loveridge AJ (2014) The devil is in the dispersers: predictions of landscape connectivity change with demography. J Appl Ecol 51(5):1169–1178CrossRefGoogle Scholar
  12. Facon B, David P (2006) Metapopulation dynamics and biological invasions: a spatially explicit model applied to a freshwater snail. Am Nat 168:769–783. CrossRefPubMedGoogle Scholar
  13. Geritz SA, Gyllenberg M, Ondráċek P (2009) Evolution of density-dependent dispersal in a structured metapopulation. Math Biosci 219(2):142–148CrossRefPubMedGoogle Scholar
  14. Gilarranz LJ, Bascompte J (2012) Spatial network structure and metapopulation persistence. J Theor Biol 297:11–16CrossRefPubMedGoogle Scholar
  15. Grilli J, Barabás G, Allesina S (2015) Metapopulation persistence in random fragmented landscapes. PLoS Comput Biol 11(5): e1004,251CrossRefGoogle Scholar
  16. Hanski I (1999) Metapopulation ecology. Oxford University PressGoogle Scholar
  17. Hanski I, Ovaskainen O (2000) The metapopulation capacity of a fragmented landscape. Nature 404 (6779):755–758CrossRefPubMedGoogle Scholar
  18. Hill M, Caswell H (1999) Habitat fragmentation and extinction thresholds on fractal landscapes. Ecol Lett 2(2):121–127CrossRefGoogle Scholar
  19. Lande R (1987) Extinction thresholds in demographic models of territorial populations. Am Nat 130(4):624–635. CrossRefGoogle Scholar
  20. Leung B, Drake JM, Lodge DM (2004) Predicting invasions: propagule pressure and the gravity of allee effects. Ecology 85(6):1651–1660. CrossRefGoogle Scholar
  21. Marrotte R, Gonzalez A, Millien V (2014) Landscape resistance and habitat combine to provide an optimal model of genetic structure and connectivity at the range margin of a small mammal. Molecul Ecol
  22. Marrotte RR, Bowman J (2017) The relationship between least-cost and resistance distance. PloS one 12(3):e0174,212CrossRefGoogle Scholar
  23. Mateo-Sánchez MC, Balkenhol N, Cushman S, Pérez T, Domnguez A, Saura S (2015) Estimating effective landscape distances and movement corridors: comparison of habitat and genetic data. Ecosphere 6(4):1–16. art59CrossRefGoogle Scholar
  24. Matthysen E (2012) Multicausality of dispersal: a review. In: Clobert J, Baguette M, Benton TG, Bullock JM (eds). Dispersal Ecology and Evolution. Oxford University Press. pp 3–18Google Scholar
  25. McRae BH, Dickson BG, Keitt TH, Shah VB (2008) Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology 89(10):2712–2724. CrossRefPubMedGoogle Scholar
  26. 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. Philos Trans R Soc B: Biol Sci 365(1550):2289–2301CrossRefGoogle Scholar
  27. North AR, Godfray HCJ (2017) The dynamics of disease in a metapopulation: the role of dispersal range. J Theor Biol 418:57–65CrossRefPubMedPubMedCentralGoogle Scholar
  28. Parvinen K (2002) Evolutionary branching of dispersal strategies in structured metapopulations. J Math Biol 45(2):106–124CrossRefPubMedGoogle Scholar
  29. Peacock SJ, Bateman AW, Krkoṡek M, Lewis MA (2016) The dynamics of coupled populations subject to control. Theor Ecol 9(3):365–380CrossRefGoogle Scholar
  30. Peterman WE, Connette GM, Semlitsch RD, Eggert LS (2014) Ecological resistance surfaces predict fine-scale genetic differentiation in a terrestrial woodland salamander. Molec Ecol 23(10):2402–2413. CrossRefGoogle Scholar
  31. Potapov A, Muirhead JR, Lele SR, Lewis MA (2011) Stochastic gravity models for modeling lake invasions. Ecol Modell 222(4):964–972. CrossRefGoogle Scholar
  32. Sæther BE, Engen S, Lande R (1999) Finite metapopulation models with density–dependent migration and stochastic local dynamics. Proc R Soc London B: Biol Sci 266(1415):113–118CrossRefGoogle Scholar
  33. Silva JA, De Castro ML, Justo DA (2001) Stability in a metapopulation model with density-dependent dispersal. Bull Math Biol 63(3):485–505CrossRefPubMedGoogle Scholar
  34. Soares-Filho BS, Cerqueira GC, Pennachin CL (2002) Dinamicaa stochastic cellular automata model designed to simulate the landscape dynamics in an amazonian colonization frontier. Ecol Modell 154(3):217–235CrossRefGoogle Scholar
  35. Söndgerath D, Schröder B (2002) Population dynamics and habitat connectivity affecting the spatial spread of populations–a simulation study. Landsc Ecol 17(1):57–70CrossRefGoogle Scholar
  36. Spear SF, Balkenhol N, Fortin MJ, McRae BH, Scribner K (2010) Use of resistance surfaces for landscape genetic studies: considerations for parameterization and analysis. Molec Ecol 19(17):3576–3591. CrossRefGoogle Scholar
  37. Strevens CM, Bonsall MB (2011) Density-dependent population dynamics and dispersal in heterogeneous metapopulations. J Anim Ecol 80(1):282–293CrossRefPubMedGoogle Scholar
  38. Taylor CM, Laughlin AJ, Hall RJ (2016) The response of migratory populations to phenological change: a migratory flow network modelling approach. J Anim Ecol 85(3):648–659CrossRefPubMedGoogle Scholar
  39. Truscott J, Ferguson NM (2012) Evaluating the adequacy of gravity models as a description of human mobility for epidemic modelling. PLoS Comput Biol 8(10):e1002,699CrossRefGoogle Scholar
  40. Xia Y, Bjørnstad ON, Grenfell BT (2004) Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. Am Nat 164(2):267–281CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.ByWater InstituteTulane UniversityNew OrleansUSA
  2. 2.Department of Ecology and Evolutionary BiologyTulane UniversityNew OrleansUSA

Personalised recommendations