Biological Invasions

, Volume 17, Issue 12, pp 3371–3381 | Cite as

Statistical issues with using herbarium data for the estimation of invasion lag-phases

  • R. J. Hyndman
  • M. B. Mesgaran
  • R. D. Cousens
Original Paper


Current methods for using herbarium data as time series, for example to estimate the length of the invasion lag phase, often make assumptions that are both statistically and logically inappropriate. We present an alternative statistical approach, estimating the lag phase based on annual rather than cumulative data, a generalized linear model incorporating a log link for overall collection effort, and piecewise linear splines. We demonstrate the method on two species representing good and poor data quality, then apply it to two data sets comprising 448 species/region combinations. Significant lags were detected in only 28 and 40 % of time series, a much lower level than the 95 and 77 % found in previous analyses of the same data. In a case with high quality data, a lag was concluded even though during the “lag” the locations of herbarium collections indicated that it was spreading rapidly at a continental scale. In species with few records, results were sensitive to the way in which zeroes were included. Overall, our method gives very good fit to the data, avoids unrealistic assumptions of other methods and gives more reliable estimates of confidence. However, given the poor representation of herbarium samples in the early stages of invasions and the fact that they do not constitute a structured survey of abundance, we warn against over-reliance on statistical analysis of such data to reach conclusions about the dynamics of invasions.


Lag phase Invasion Herbarium Statistical analysis 



We thank Sami Aikio and Ines Schonberger for supplying data from the Allan Herbarium (CHR), Dan Larkin for his mid-west USA data and Alison Vaughan, National Herbarium of Victoria (MEL), for supplying data from Australia’s Virtual Herbarium. We also thank Rod Randall for supplying a list of invasive species for Australia. We appreciate comments on a previous version of this paper by Richard Duncan, Sami Aikio and Dan Larkin, although we have only incorporated some of their suggestions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10530_2015_962_MOESM1_ESM.pdf (64 kb)
Supplementary material 1 (PDF 63 kb)
10530_2015_962_MOESM2_ESM.docx (28 kb)
Supplementary material 2 (DOCX 27 kb)


  1. Aagaard K, Lockwood J (2014) Exotic birds show lags in population growth. Divers Distrib 20:547–554CrossRefGoogle Scholar
  2. Aikio S, Duncan RP, Hulme PE (2010) Lag-phases in alien plant invasions: separating the facts from the artefacts. Oikos 119:370–378CrossRefGoogle Scholar
  3. Booth BD, Murphy SD, Swanton CJ (2011) Invasive plant ecology in natural and agricultural systems, 2nd edn. CABI, Cambridge, MassachusettsGoogle Scholar
  4. Cousens R, Mortimer M (1995) Dynamics of weed populations. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  5. Cousens R, Ades PK, Mesgaran MB, Ohadi S (2013) Reassessment of the invasion history of two species of Cakile (Brassicaceae) in Australia. Cunninghamia 13:275–290CrossRefGoogle Scholar
  6. Crooks JA, Soulé ME (1999) Lag times in population explosions of invasive species: causes and implications. In: Sandlund OT, Schei PJ, Viken A (eds) Invasive species and biodiversity management. Kluwer, Alphen aan den Rijn, pp 103–125CrossRefGoogle Scholar
  7. Daehler CC (2009) Short lag times for invasive tropical plants: evidence from experimental plantings in Hawai’i. PLoS ONE 4(2):e4462PubMedCentralCrossRefPubMedGoogle Scholar
  8. Davidson R, MacKinnon JG (2004) Econometric theory and methods. Oxford University Press, OxfordGoogle Scholar
  9. Delisle F, Lavoie MJ, Lachance D (2003) Reconstructing the spread of invasive plants: taking into account biases associated with herbarium specimens. J Biogeog 30:1033–1042CrossRefGoogle Scholar
  10. Dobson AJ (2008) An introduction to generalized linear models, 3rd edn. Chapman and Hall/CRC Press, Boca Raton, FloridaGoogle Scholar
  11. Dogra KS, Sood SK, Dobhal PK, Sharma S (2010) Alien plant invasion and their impact on indigenous species diversity at global scale: a review. J Ecol Nat Environ 2:175–186Google Scholar
  12. Ellstrand NC, Schierenbeck KA (2000) Hybridization as a stimulus for the evolution of invasiveness in plants? Proc Natl Acad Sci USA 97:7043–7050PubMedCentralCrossRefPubMedGoogle Scholar
  13. Fuentes N, Ugarte E, Kuhn I, Klotz S (2008) Alien plants in Chile: inferring invasion periods from herbarium records. Biol Invas 10:649–657CrossRefGoogle Scholar
  14. Gallagher RV, Beaumont LJ, Hughes L, Leishman MR (2010) Evidence for climatic niche and biome shifts between native and novel ranges in plant species introduced to Australia. J Ecol 98:790–799CrossRefGoogle Scholar
  15. Hobbs RJ, Humphries SE (1995) An integrated approach to the ecology and management of plant invasions. Conserv Biol 9:761–770CrossRefGoogle Scholar
  16. Holt RD, Barfield M, Gomlkiewicz R (2005) Theories of niche conservatism and evolution: could exotic species be potential tests? In: Sax DF, Stachowicz JJ, Gaines SD (eds) Species invasions: Insights into ecology, evolution, and biogeography. Sinauer, Sunderland, Massachusetts, pp 259–290Google Scholar
  17. Keller SR, Taylor DR (2008) History, chance and adaptation during biological invasion: separating stochastic phenotypic evolution from response to selection. Ecol Lett 11:852–866CrossRefPubMedGoogle Scholar
  18. Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77:2027–2042CrossRefGoogle Scholar
  19. Kowarik I (1995) Time lags in biological invasions with regard to the success and failure of alien species. In: Pyšek P, Prach K, Rejmánek M, Wade M (eds) Plant invasions—general aspects and special problems. SPB Academic Publishing, Amsterdam, pp 15–38Google Scholar
  20. Larkin DJ (2012) Lengths and correlates of lag phases in upper-Midwest plant invasions. Biol Invasions 14:827–838CrossRefGoogle Scholar
  21. Lee CE (2002) Evolutionary genetics of invasive species. Trends Ecol Evol 17:386–391CrossRefGoogle Scholar
  22. Lenda M, Skórka P, Knops JMH, Moroń D, Tworek S, Woyciechowski M (2012) Plant establishment and invasions: an increase in a seed disperser combined with land abandonment causes an invasion of the non-native walnut in Europe. Proc R Soc B 279:1491–1497PubMedCentralCrossRefPubMedGoogle Scholar
  23. Mack RN, Simberloff D, Lonsdale WM, Evans H, Clout M, Bazzaz FA (2000) Biotic invasions: causes, epidemiology, global consequences, and control. Ecol Appl 10:689–710CrossRefGoogle Scholar
  24. Mesgaran MB, Mashhadi HR, Alizadeh H, Hunt JR, Young KR, Cousens RD (2013) Importance of frequency distribution selection in hydrotime and hydrothermal time models of seed germination. Weed Res 53:89–101CrossRefGoogle Scholar
  25. Mihulka S, Pyšek P (2001) Invasion history of Oenothera congeners in Europe: a comparative study of spreading rates in the last 200 years. J Biogeog 28:597–609CrossRefGoogle Scholar
  26. Parker IM (2004) Mating patterns and rates of biological invasion. Proc Natl Acad Sci USA 101:13695–13696PubMedCentralCrossRefPubMedGoogle Scholar
  27. Pyšek P, Hulme PE (2005) Spatio-temporal dynamics of plant invasions: linking patterns to process. Écoscience 12:302–315CrossRefGoogle Scholar
  28. Pyšek P, Prach K (1993) Plant invasions and the role of riparian habitats: a comparison of four species alien to central Europe. J Biogeogr 20:413–420CrossRefGoogle Scholar
  29. Rodman JE (1986) Introduction, establishment and replacement of sea-rockets (Cakile, Cruciferae) in Australia. J Biogeogr 13:159–171CrossRefGoogle Scholar
  30. Sakai AK, Allendorf FW, Holt JS, Lodge DM, Molofsky J, With KA, Baughman S, Cabin RJ, Cohen JE, Ellstrand NC, McCauley DE, O’Neil P, Parker IM, Thompson JN, Weller SG (2001) The population biology of invasive species. Annu Rev Ecol Syst 32:305–332CrossRefGoogle Scholar
  31. The Council of Heads of Australasian Herbaria (1999) Australia’s Virtual Herbarium Accessed 19 April 2013
  32. Wangen SR, Webster CR (2006) Potential for multiple lag phases during biotic invasions: reconstructing an invasion of an exotic tree Acer platanoides. J Appl Ecol 43:258–268CrossRefGoogle Scholar
  33. Webber BL, Yates CJ, Le Maitre DC, Scott JK, Kriticos DJ, Ota N, McNeill A, Le Roux JJ, Midgley GF (2011) Modelling horses for novel climate courses: insights from projecting potential distributions of native and alien Australian acacias with correlative and mechanistic models. Divers Distrib 17:978–1000CrossRefGoogle Scholar
  34. Wells MJ (1974) Nassella trichotoma (Nees) Hack in South Africa. In: Proceedings of 1st National Weeds Conference of South Africa, pp 125–137Google Scholar
  35. Williamson M, Pyšek P, Jarosík V, Prach K (2005) On the rates and patterns of spread of alien plants in the Czech Republic, Britain, and Ireland. Écoscience 12:424–433CrossRefGoogle Scholar
  36. Wood SN (2006) Generalized additive models: an introduction with R. Chapman and Hall/CRC Press, Boca Raton, FloridaGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • R. J. Hyndman
    • 1
  • M. B. Mesgaran
    • 2
  • R. D. Cousens
    • 2
  1. 1.Department of Econometrics and Business StatisticsMonash UniversityMelbourneAustralia
  2. 2.School of BioSciencesThe University of MelbourneMelbourneAustralia

Personalised recommendations