Small-scale spatial structure influences large-scale invasion rates

Adams T, Holland EP, Law R, Plank MJ, Raghib M (2013) On the growth of locally interacting plants: differential equations for the dynamics of spatial moments. Ecology 94:2732–2743 Binny RN, Haridas P, James A, Law R, Simpson MJ, Plank MJ (2016a) Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ 4:e1689 Binny RN, James A, Plank MJ (2016b) Collective cell behaviour with neighbour-dependent proliferation, death and directional bias. Bull Math Biol 78(11):2277–2301 Binny RN, Law R, James A, Plank MJ (2019) Living in groups: spatial-moment dynamics with neighbour-biased movements. Ecological Modelling, in press Binny RN, Plank MJ, James A (2015) Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias. J R Soc Interface 12:20150228 Bolker B, Pacala SW (1997) Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor Popul Biol 52(3):179–197 Bolker BM, Pacala SW (1999) Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal. Am Nat 153(6):575–602 Dieckmann U, Law R (2000) Relaxation projections and the method of moments. In: Dieckmann U, Law R, Metz JAJ (eds) The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, Cambridge, pp 412–455 Dieckmann U, Law R, Metz JAJ (2000) The geometry of ecological interactions: Simplifying spatial complexity. Cambridge University Press, Cambridge Ellner SP, Sasaki A, Haraguchi Y, Matsuda H (1998) Speed of invasion in lattice population models: pair-edge approximation. J Math Biol 36(5):469–484 Fernando AE, Landman KA, Simpson MJ (2010) Nonlinear diffusion and exclusion processes with contact interactions. Phys Rev E 81(1):011903 Godsoe W, Murray R, Plank MJ (2014) Information on biotic interactions improves transferability of distribution models. Am Nat 185(2):281–290 Hastings A, Cuddington K, Davies KF, Dugaw CJ, Elmendorf S, Freestone A, Harrison S, Holland M, Lambrinos J, Malvadkar U et al (2005) The spatial spread of invasions: new developments in theory and evidence. Ecol Lett 8(1):91–101 Hurford A, Cobbold CA, Molnár PK (2019) Skewed temperature dependence affects range and abundance in a warming world. Proc R Soc B 286:20191157 Johnston ST, Simpson MJ, Plank MJ (2013) Lattice-free descriptions of collective motion with crowding and adhesion. Phys Rev E 88(6):062720 Katul GG, Porporato A, Nathan R, Siqueira M, Soons MB, Poggi D, Horn HS, Levin SA (2005) Mechanistic analytical models for long-distance seed dispersal by wind. Am Nat 166(3):368–381 Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77(7):2027–2042 Law R, Murrell DJ, Dieckmann U (2003) Population growth in space and time: Spatial logistic equations. Ecology 84(1):252–262 Lewis MA (2000) Spread rate for a nonlinear stochastic invasion. J Math Biol 41(5):430–454 Lewis MA, Pacala S (2000) Modeling and analysis of stochastic invasion processes. J Math Biol 41 (5):387–429 Mahdi A, Law R (1987) On the spatial organization of plant species in a limestone grassland community. J Ecol 75:459–476 Maini PK, McElwain DLS, Leavesley DI (2004) Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng 10(3-4):475–482 Murrell DJ (2005) Local spatial structure and predator-prey dynamics: counterintuitive effects of prey enrichment. Am Nat 166:354–367 Murrell DJ, Dieckmann U, Law R (2004) On moment closures for population dynamics in continuous space. J Theor Biol 229(3):421–432 Murrell DJ, Law R (2000) Beetles in fragmented woodlands: A formal framework for dynamics of movement in ecological landscapes. J Anim Ecol 69(3):471–483 Murrell DJ, Law R (2003) Heteromyopia and the spatial coexistence of similar competitors. Ecol Lett 6 (1):48–59 Omelyan I, Kozitsky Y (2019) Spatially inhomogeneous population dynamics: beyond the mean field approximation. J Phys A Math Theor 52:305601 Pacala SW, Silander JA Jr (1985) Neighborhood models of plant population dynamics. I. Single-species models of annuals. Am Nat 125(3):385–411 Paradis E, Baillie SR, Sutherland WJ (2002) Modeling large-scale dispersal distances. Ecol Model 151 (2-3):279–292 Plank MJ, Law R (2015) Spatial point processes and moment dynamics in the life sciences: a parsimonious derivation and some extensions. Bull Math Biol 77(4):586–613 Plank MJ, Simpson MJ (2012) Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. J R Soc Interface 9(76):2983–2996 Purves DW, Law R (2002) Fine-scale spatial structure in a grassland community: quantifying the plant’s-eye view. J Ecol 90:121–129 Simpson MJ, Baker RE (2011) Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena. Physical Review E 83(5):051922 Sprague R, Godsoe W, Hulme PE (2019) Assessing the utility of aerial imagery to quantify the density, age structure and spatial pattern of alien conifer invasions. Biol Invasions 21(6):2095–2106 Sundberg S (2005) Larger capsules enhance short-range spore dispersal in Sphagnum, but what happens further away? Oikos 108(1):115–124 Surendran A, Plank MJ, Simpson MJ (2018) Spatial moment description of birth–death–movement processes incorporating the effects of crowding and obstacles. Bull Math Biol 80(11):2828–2855 Yokozawa M, Kubota Y, Hara T (1999) Effects of competition mode on the spatial pattern dynamics of wave regeneration in subalpine tree stands. Ecol Model 118(1):73–86