Modelling the spread of European buckthorn in the Region of Waterloo

Abstract

Established invasive species, such as European buckthorn (Rhamnus cathartica), pose a challenging problem for land managers who must decide when and how to control them. In order to make an informed decision land managers need to be able to predict the spread of these invasive species at local scales and without the need for excessive sampling. Our approach uses a hybrid model, combining habitat suitability and the presence of the invasive in neighbouring cells to predict the probability of a cell being invaded over time. A generalized linear mixed-effects model was used to create a habitat suitability model and a spread model. The habitat suitability model predicts the presence of buckthorn based on environmental characteristics and the results are used in the spread model. The spread model indicates that the invasion of buckthorn is influenced by the suitability of habitat and the presence of buckthorn in neighbouring cells. The success of the spread model suggests that this approach can be used to create a spatiotemporally explicit model with limited sampling effort.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  1. Archibold OW, Brooks D, Delanoy L (1997) An investigation of the invasive shrub European buckthorn, Rhamnus cathartica L., near Saskatoon, Saskatchewan. Can Field Nat 111(4):617–621

    Google Scholar 

  2. Bahlai C, Sikkema S, Hallett RH, Newman J, Schaafsma A (2010) Modeling distribution and abundance of soybean aphid in soybean fields using measurements from the surrounding landscape. Environ Entomol 39(1):50–56

    CAS  Article  PubMed  Google Scholar 

  3. Bates D, Maechler M, Bolker B, Walker S (2014) lme4: linear mixed-effects models using Eigen and S4. R package version 1.1-7, http://CRAN.R-project.org/package=lme4

  4. Bhagwat SA, Breman E, Thekaekara T, Thornton TF, Willis KJ (2012) A battle lost? Report on two centuries of invasion and management of Lantana camara L. in Australia, India and South Africa. PLoS ONE 7(3):e32407

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  5. Bjornstad ON (2013) ncf: spatial nonparametric covariance functions. R package version 1.1-5. http://CRAN.R-project.org/package=ncf

  6. Bocedi G, Zurell D, Reineking B, Travis JMJ (2014) Mechanistic modelling of animal dispersal offers new insights into range expansion dynamics across fragmented landscapes. Ecography 37(12):1240–1253

    Article  Google Scholar 

  7. Brenning A (2012) Spatial cross-validation and bootstrap for the assessment of prediction rules in remote sensing: the R package ‘sperrorest’. In: IEEE international symposium on geoscience and remote sensing IGARSS, (in press)

  8. Burnham KM, Lee TD (2010) Canopy gaps facilitate establishment, growth, and reproduction of invasive Frangula alnus in a Tsuga canadensis dominated forest. Biol Invasions 12(6):1509–1520

    Article  Google Scholar 

  9. Catterall S, Cook AR, Marion G, Butler A, Hulme PE (2012) Accounting for uncertainty in colonisation times: a novel approach to modelling the spatio-temporal dynamics of alien invasions using distribution data. Ecography 35(10):901–911

    Article  Google Scholar 

  10. Chong J, Gruenke J, Dueck R, Mayert W, Woods S (2008) Virulence of oat crown rust [Puccinia coronata f. sp avenae] in Canada during 2002–2006. Can J Plant Pathol 30(1):115–123

    CAS  Article  Google Scholar 

  11. Cook A, Marion G, Butler A, Gibson G (2007) Bayesian inference for the spatio-temporal invasion of alien species. B Math Biol 69(6):2005–2025

    Article  Google Scholar 

  12. Craves JA (2015) Birds that eat nonnative buckthorn fruit (Rhamnus cathartica and Frangula alnus, Rhamnaceae) in Eastern North America. Nat Areas J 35(2):279–287

    Article  Google Scholar 

  13. Crawley MJ (2007) The R book. Wiley, Chichester, Hoboken

    Google Scholar 

  14. Derickx LM, Antunes PM (2013) A guide to the identification and control of exotic invasive species in Ontario’s hardwood forests. Invasive Species Research Institute, Algoma University, Algoma

    Google Scholar 

  15. Diggle PJ, Ribeiro PJ Jr (2007) Model based geostatistics. Springer, New York

    Google Scholar 

  16. DMTI Digital Elevation Model [computer file] (2011) Markham, Ontario: DMTI Spatial Inc

  17. Epanchin-Niell RS, Hastings A (2010) Controlling established invaders: integrating economics and spread dynamics to determine optimal management. Ecol Lett 13(4):528–541

    Article  PubMed  Google Scholar 

  18. ESRI (Environmental Systems Resource Institute) (2014) ArcGIS 10.2. ESRI, Redlands, California

  19. Evans JS, Oakleaf J, Cushman SA, Theobald D (2011) An ArcGIS Toolbox for Surface Gradient and Geomorphometric Modeling, version 1.01. Available: http://evansmurphy.wix.com/evansspatial. Accessed April 2014

  20. Fennell M, Murphy JE, Armstrong C, Gallagher T, Osborne B (2012) Plant spread simulator: a model for simulating large-scale directed dispersal processes across heterogeneous environments. Ecol Model 230:1–10

    Article  Google Scholar 

  21. Fitzgerald K, Gordon DM (2012) Effects of vegetation cover, presence of a native ant species, and human disturbance on colonization by Argentine ants. Conserv Biol 26(3):525–538

    Article  PubMed  Google Scholar 

  22. Fitzgerald K, Heller N, Gordon DM (2012) Modeling the spread of the Argentine ant into natural areas: habitat suitability and spread from neighboring sites. Ecol Model 247:262–272

    Article  Google Scholar 

  23. Fitzpatrick MC, Preisser EL, Porter A, Elkinton J, Ellison AM (2012) Modeling range dynamics in heterogeneous landscapes: invasion of the hemlock woolly adelgid in eastern North America. Ecol Appl 22(2):472–486

    Article  PubMed  Google Scholar 

  24. Godwin H (1936) Studies in the ecology of wicken fen: III. The establishment and development of fen scrub (carr). J Ecol 24(1):82–116

    Article  Google Scholar 

  25. Hastings A, Cuddington K, Davies K, Dugaw C, Elmendorf S, Freestone A et al (2005) The spatial spread of invasions: new developments in theory and evidence. Ecol Lett 8(1):91–101

    Article  Google Scholar 

  26. Heimpel GE, Frelich LE, Landis DA, Hopper KR, Hoelmer KA, Sezen Z et al (2010) European buckthorn and Asian soybean aphid as components of an extensive invasional meltdown in North America. Biol Invasions 12(9):2913–2931

    Article  Google Scholar 

  27. Higgins SI, Richardson DM, Cowling RM (1996) Modeling invasive plant spread: the role of plant-environment interactions and model structure. Ecology 77(7):2043–2054

    Article  Google Scholar 

  28. Holst KK (2014) gof: model-diagnostics based on cumulative residuals. R package version 0.9.1

  29. Hosmer DW, Lemeshow S (2000) Applied logistic regression. Wiley, New York

    Google Scholar 

  30. Hulme PE et al (2009) Will threat of biological invasions unite the European Union? Science 324:40–41

    CAS  Article  PubMed  Google Scholar 

  31. Jeschke JM, Strayer DL (2008) Usefulness of bioclimatic models for studying climate change and invasive species. Ann NY Acad Sci 1134:1–24

    Article  PubMed  Google Scholar 

  32. Knight KS, Kurylo JS, Endress AG, Stewart JR, Reich PB (2007) Ecology and ecosystem impacts of common buckthorn (Rhamnus cathartica): a review. Biol Invasions 9(8):925–937

    Article  Google Scholar 

  33. Kolar C, Lodge D (2001) Progress in invasion biology: predicting invaders. Trends Ecol Evol 16:199–204

    Article  PubMed  Google Scholar 

  34. Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77(7):2027–2042

    Article  Google Scholar 

  35. Kurylo JS, Knight KS, Stewart JR, Endress AG (2007) Rhamnus cathartica: native and naturalized distribution and habitat preferences. J Torrey Bot Soc 134(3):420–430

    Article  Google Scholar 

  36. Kurylo J, Raghu S, Molano-Flores B (2015) Flood tolerance in common buckthorn (Rhamnus cathartica). Nat Areas J 35(2):302–307

    Article  Google Scholar 

  37. Lin DY, Wei LJ, Ying Z (2002) Model-checking techniques based on cumulative residuals. Biometrics 58(1):1–12

    CAS  Article  PubMed  Google Scholar 

  38. Mack RN, Simberloff D, Lonsdale WM, Evans H, Clout M, Bazzaz FA (2000) Biotic invasions: causes, epidemiology, global consequences, and control. Ecol Appl 10:689–711

    Article  Google Scholar 

  39. Mascaro J, Schnitzer SA (2007) Rhamnus cathartica L. (common buckthorn) as an ecosystem dominant in southern Wisconsin forests. Northeast Nat 14(3):387–402

    Article  Google Scholar 

  40. McCay TS, McCay DH, Caragiulo AV, Mandel TL (2009) Demography and distribution of the invasive Rhamnus cathartica in habitats of a fragmented landscape. J Torrey Bot Soc 136(1):110–121

    Article  Google Scholar 

  41. Ontario Geologic Survey [computer file] (2010) Toronto, Ontario: Ontario Geologic Survey

  42. Ontario Geological Survey and Planning and Engineering Initiatives Limited (1998) Aggregate resources inventory of the Regional Municipality of Waterloo, townships of North Dumfries, Wellesley, Wilmot, and Woolwich and the cities of Cambridge, Kitchener, and Waterloo; Ontario Geological Survey, Aggregate Resources Inventory Paper 161, http://www.geologyontario.mndmf.gov.on.ca/mndmfiles/pub/data/imaging/ARIP161/ARIP161.pdf Accessed 12 Feb 2015

  43. Ontario Ministry of Natural Resources (2008b) Southern Ontario land resource information system (SOLRIS) land use data. Toronto, Ontario

  44. Ontario Ministry of Natural Resources, Science and Information Branch. SOLRIS Technical Team (2008a) Accuracy Assessment Report 2: SOLRIS Version 1.2 (April 2008 release). Peterborough, Ontario: 44p Available at: http://www.mnr.gov.on.ca/en/Business/LIO/

  45. Pearce J, Ferrier S (2000) Evaluating the predictive performance of habitat models developed using logistic regression. Ecol Model 133(3):225–245

    Article  Google Scholar 

  46. Pejchar L, Mooney HA (2009) Invasive species, ecosystem services and human well-being. Trends Ecol Evol 24:497–504

    Article  PubMed  Google Scholar 

  47. Pilcher C, Rice ME, Vagts T (2005) Economic impact of soybean aphid. Integrated Crop Management News. Paper 1464. http://lib.dr.iastate.edu/cropnews/1464. Accessed 10 April, 2015

  48. R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/

  49. Ragsdale DW, Landis DA, Brodeur J, Heimpel GE, Desneux N (2011) Ecology and management of the soybean aphid in North America. Annu Rev Entomol 56:375–399

    CAS  Article  PubMed  Google Scholar 

  50. Ranius T, Niklasson M, Berg N (2009) A comparison of methods for estimating the age of hollow oaks. Ecoscience 16(2):167–174

    Article  Google Scholar 

  51. Region of Waterloo (2011) Census bulletin: agriculture http://www.regionofwaterloo.ca/en/doingBusiness/resources/2011_Census_Bulletin_2_Agriculture.PDF Accessed 12 Feb 2015

  52. Regional Municipality of Waterloo Property Parcels [computer file] (2012) Toronto, Ontario: Teranet Incorporated

  53. Sala O, Chapin F, Armesto J, Berlow E, Bloomfield J, Dirzo R, Huber-Sanwald E, Huenneke L, Jackson R, Kinzig A, Leemans R, Lodge D, Mooney H, Oesterheld M, LeRoy Poff N, Sykes M, Walker B, Walker M, Wall D (2001) Global biodiversity scenarios for the year 2100. Science 287:1770–1774

    Article  Google Scholar 

  54. Simberloff D (2009) We can eliminate invasions or live with them. Successful management projects. Biol Invasions 11(1):149–157

    Article  Google Scholar 

  55. Simberloff D (2014) Biological invasions: what’s worth fighting and what can be won? Ecol Eng 65:112–121

    Article  Google Scholar 

  56. Smolik MG, Dullinger S, Essl F, Kleinbauer I, Leitner M, Peterseil J et al (2010) Integrating species distribution models and interacting particle systems to predict the spread of an invasive alien plant. J Biogeogr 37(3):411–422

    Article  Google Scholar 

  57. Thiele J, Markussen B (2012) Potential of GLMM in modelling invasive spread. CAB Rev Perspect Agric Vet Sci Nutr Nat Resour 7(16):1–10

    Google Scholar 

  58. United States Department of Agriculture (2008) Oat crown rust. http://www.ars.usda.gov/Main/docs.htm?docid=9919. Accessed 22 April 2015

  59. Urban MC, Phillips BL, Skelly DK, Shine R (2008) A toad more traveled: the heterogeneous invasion dynamics of cane toads in Australia. Am Nat 171(3):E134–E148

    Article  PubMed  Google Scholar 

  60. Vallet J, Beaujouan V, Pithon J, Roze F, Daniel H (2010) The effects of urban or rural landscape context and distance from the edge on native woodland plant communities. Biodivers Conserv 19(12):3375–3392. doi:10.1007/s10531-010-9901-2

    Article  Google Scholar 

  61. Venables WN, Ripley BD (2002) Modern applied statistics with S, 4th edn. Springer, New York

    Google Scholar 

  62. Vitousek PM, D’Antonio CM, Loope LL, Rejmanek M, Westbrooks R (1997) Introduced species: a significant component of human-caused global change. N Z J Ecol 21:1–16

    Google Scholar 

  63. Vittoz P, Engler R (2007) Seed dispersal distances: a typology based on dispersal modes and plant traits. Bot Helv 117(2):109–124

    Article  Google Scholar 

  64. Wilcove D, Rothstein D, Dubow J, Phillips A, Losos E (1998) Quantifying threats to imperiled species in the United States. Bioscience 48:607–616

    Article  Google Scholar 

  65. Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J R Stat Soc B 73(1):3–36

    Article  Google Scholar 

  66. Zuur A, Ieno EN, Walker N, Saveliev AA, Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, Berlin

    Google Scholar 

Download references

Acknowledgements

We are grateful to the property owners in the Region of Waterloo for allowing access to their lands. We also thank James McCarthy and Scott MacFarlane for their help in the design of the figure depicting the sampling region and areas.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sarah Endicott.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 306 kb)

Appendix 1: Extended model results

Appendix 1: Extended model results

See Fig. 6.

Fig. 6
figure6

Overview of modeling decisions. For descriptions of variable names see Tables 1 and 3.

Habitat suitability

The univariable logistic regressions indicated that all explanatory variables had a significant relationship (p < 0.25) with the presence of buckthorn, except for NearPropLine (distance to the nearest property line) and CTI (compound topographic index). Therefore NearPropLine and CTI were excluded from subsequent analyses.

The formula for the maximal model was:

$$Buckthorn\;Presence \sim Material + Permea + log10\left( {PatchDist + 1} \right) + Land\;Cover + Land\;Cover:Permea$$

where Material indicates surficial geology, Permea is permeability of the surficial material, PatchDist is the distance from the centre of a cell to the edge of the nearest wooded patch, and Land Cover is land cover class.

The maximal model failed because of collinearity between Material and Permea. Since the univariable logistic regressions indicated that the Silt level of Material did not fit well, Material was removed from the model. Additionally, the interaction term was removed at this point. Although a likelihood ratio test showed that the model with the interaction provided a better fit than the model without the interaction, the coefficient for the interaction term had an excessive standard error (−12.20 ± 240).

The model simplification indicated that the minimal acceptable model was a model that included Permea, PatchDist, and Land Cover as explanatory variables. The Wald test showed that all coefficients in the minimal acceptable model were significant, except the Swamp level of Land Cover and the Low level of Permea (Table 2). Based on the results of the leave-one-out cross-validation, the AUROC for this model was calculated to be 0.63, which is considered poor discrimination (Hosmer and Lemeshow 2000).

The correlograms for the minimal acceptable model showed that some spatial autocorrelation was present within sampling areas. To account for spatial autocorrelation, we tried including a spherical correlation structure term that produced a model with a range of 25 m and a nugget of 0.95. This model effectively produced the same coefficients as the model without the spatial autocorrelation term (coefficient estimates within one standard error from each other; results not shown). The correlograms of the Pearson residuals for the model with spatial autocorrelation term are very similar to the model without the spatial autocorrelation term. An exponential correlation structure was tested with similar results. Since the results did not indicate a substantial reduction in the Pearson residuals through inclusion of within sampling areas spatial correlation structure, the model without a spatial autocorrelation term was used for the remaining analyses.

Spread model

Visual investigation of the GAMs showing the relationships between the number of first and second order neighbours with buckthorn and the probability of buckthorn invasion, suggested a non-linear positive effect of the number of first order neighbour cells on the probability of buckthorn invasion. The largest change in invasion probability occurred when the number of first order neighbours with buckthorn increased from zero to one. Further increases of neighbour cells with buckthorn resulted in less pronounced changes to the invasion probability (Table 3). Neither the presence of second order neighbour cells with buckthorn nor their exact number had a significant effect (Table 3). Accordingly, to account for the positive effect of buckthorn presence in first order neighbours on buckthorn invasion probability, we introduced a binary variable of buckthorn presence in first order neighbour cells.

Habitat suitability and year also had significant effects on the probability of buckthorn invasion (Fig. 3). Using the explanatory variables mentioned above, the semivariogram for the spatial autocorrelation in the spread model showed the presence of weak (nugget-to-sill ratio of approximately 0.045:0.060) residual autocorrelation. Additionally, the semivariogram for the temporal autocorrelation indicated the presence of nonstationarity in the model residuals with respect to time. The GLM model coefficients were within one standard error of the GLMM coefficients so we were able to use the GLM to produce cumulative residuals to evaluate the GLMM model (results not shown). The cumulative residual plots showed that the observed cumulative residuals are in the expected range for all the variables but not for the model results (Fig. 4). The model presented good discrimination with an AUROC of 0.88.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Endicott, S., Drescher, M. & Brenning, A. Modelling the spread of European buckthorn in the Region of Waterloo. Biol Invasions 19, 2993–3011 (2017). https://doi.org/10.1007/s10530-017-1504-3

Download citation

Keywords

  • Hybrid model
  • Species distribution model
  • Spread model
  • Generalized linear mixed effects model
  • Invasion dynamics
  • Local scale management
  • R. cathartica