Skip to main content
Log in

Modelling the dynamics of invasion and control of competing green crab genotypes

  • ORIGINAL PAPER
  • Published:
Theoretical Ecology Aims and scope Submit manuscript

Abstract

Establishment of invasive species is a worldwide problem. In many jurisdictions, management strategies are being developed in an attempt to reduce the environmental and economic harm these species may cause in the receiving ecosystem. Scientific studies to improve understanding of the mechanisms behind invasive species population growth and spread are key components in the development of control methods. The work presented herein is motivated by the case of the European green crab (Carcinus maenas L.), a remarkably adaptable organism that has invaded marine coastal waters around the globe. Two genotypes of European green crab have independently invaded the Atlantic coast of Canada. One genotype invaded the mid-Atlantic coast of the USA by 1817, subsequently spreading northward through New England and reaching Atlantic Canada by 1951. A second genotype, originating from the northern limit of the green crabs European range, invaded the Atlantic coast of Nova Scotia in the 1980s and is spreading southward from the Canadian Maritime provinces. We developed an integrodifference equation model for green crab population growth, competition and spread, and demonstrate that it yields appropriate spread rates for the two genotypes, based on historical data. Analysis of our model indicates that while harvesting efforts have the benefit of reducing green crab density and slowing the spread rate of the two genotypes, elimination of the green crab is virtually impossible with harvesting alone. Accordingly, a green crab fishery would be sustainable. We also demonstrate that with harvesting and restocking, the competitive imbalance between the Northern and Southern green crab genotypes can be reversed. That is, a competitively inferior species can be used to control a competitively superior one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Baldwin PH, Schwartz CW, Schwartz ER (1952) Life history and economic status of the mongoose in Hawaii. J Mammal 33(3):335–356

    Article  Google Scholar 

  • Beverton RJ, Holt SJ et al (1957) On the dynamics of exploited fish populations. Fishery Invest, London 19(2):1–5339

  • Blakeslee A, McKenzie C, Darling J, Byers J, Pringle J, Roman J (2010) A hitchhikers guide to the maritimes: anthropogenic transport facilitates long-distance dispersal of an invasive marine crab to Newfoundland. Divers Distrib 16(6):879–891

    Article  Google Scholar 

  • Byers JE, Pringle JM (2008a) Going against the flow: how marine invasions spread and persist in the face of advection. ICES J Mar Sci 65(5):723–724

    Article  Google Scholar 

  • Byers JE, Pringle JM (2008b) Going against the flow: retention, range limits and invasions in advective environments. Mar Ecol Prog Ser 313:27–41

    Article  Google Scholar 

  • Canadian Science Advisory Secretariat (2006) Assessment of Eastern Nova Scotia (4VW) snow crab. DFO Can Sci Advis.Sec.Sci.Advis Rep 2006/027

  • Carlton JT, Cohen AN (2003) Episodic global dispersal in shallow water marine organisms: the case history of the European shore crabs Carcinus maenas and C. aestuarii. J Biogeogr 30(12):1809–1820

    Article  Google Scholar 

  • Cooper C, Hunt CD, Dingus C, Libby PS, Kirkbride G (2012) Assessing ballast treatment standards for effect on rate of establishment using a stochastic model of the green crab. Comput Ecol Softw 2(1):53–69

    Google Scholar 

  • Crooks JA (2002) Characterizing ecosystem-level consequences of biological invasions: the role of ecosystem engineers. Oikos 97(2):153–166

    Article  Google Scholar 

  • Department of Natural Resources USA (2013) Control methods (invasive species). http://dnr.wi.gov/topic/Invasives/control.html

  • Dewhirst S, Lutscher F (2009) Dispersal in heterogeneous habitats: thresholds, spatial scales, and approximate rates of spread. Ecology 90:1338–1345

    Article  PubMed  Google Scholar 

  • Grosholz ED (1996) Contrasting rates of spread for introduced species in terrestrial and marine systems. Ecology 77(6):1680–1686

    Article  Google Scholar 

  • Jamieson G, Foreman M, Cherniawsky J, Levings C (2002) European green crab (Carcinus maenas) dispersal: the Pacific experience. In: Paul AJ, Dawe EG, Elner R, Jamieson GS, Kruse GH, Otto RS, Sainte-Marie B, Shirley TC, Woodby D (eds) Crabs in cold water regions: biology, management, and economics. University of Alaska Sea Grant College Program AK-SG-02-01, pp 561–576

  • Kaluza P, Kölzsch A, Gastner MT, Blasius B (2010) The complex network of global cargo ship movements. J Roy Soc Interface 7(48):1093–1103

    Article  Google Scholar 

  • Kawasaki K, Shigesada N (2007) An integrodifference model for biological invasions in a periodically fragmented environment. Jpn J Ind Appl Math 24(1):3–15

    Article  Google Scholar 

  • Klassen GJ, Locke A (2007) A biological synopsis of the European green crab, Carcinus Maenas. Can Manus Rep Fish Aquat Sci 2818

  • Koch R (2003) The multicolored Asian lady beetle, Harmonia axyridis: a review of its biology, uses in biological control, and non-target impacts. J Insect Sci 3:1–16

    Article  Google Scholar 

  • 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 

  • League-Pike PE, Shulman MJ (2009) Intraguild predators: behavioral changes and mortality of the Green crab (Carcinus maenas) during interactions with the American lobster (Homarus americanus) and Jonah crab (Cancer borealis). J Crust Biol 29(3):350–355

    Article  Google Scholar 

  • Lewis MA, Li B, Weinberger HF (2002) Spreading speeds and linear determinacy for two-species competition models. J Math Biol 45:219–233

    Article  PubMed  Google Scholar 

  • Locke A, Klassen GJ (2007) Canadian science advisory secretariat, Department of Fisheries and Oceans: using the quantitative biological risk assessment tool (QBRAT) to predict effects of the European green crab, Carcinus maenas, in Atlantic Canada. Can Sci Advis Sec Res Doc 2007/077

  • Lowe S, Browne M, Boudjelas S, De Poorter M (2000) 100 of the world’s worst invasive alien species: a selection from the global invasive species database. Invasive Species Specialist Group, World Conservation Union (IUCN), Auckland, New Zealand. www.issg.org/booklet.pdf

  • Lutscher F, McCauley E, Lewis M (2007) Spatial patterns and coexistence mechanisms in systems with unidirectional flow. Theor Popul Biol 71:267–277

    Article  PubMed  Google Scholar 

  • Lutscher F, Nisbet RM, Pachepsky E (2010) Population persistence in the face of advection. Theor Ecol 3(4):271–284

    Article  Google Scholar 

  • Lutscher F, Pachepsky E, Lewis M (2005) The effect of dispersal patterns on stream populations. SIAM J Appl Math 65:1305–1327

    Article  Google Scholar 

  • Medlock J, Kot M (2003) Spreading disease: integro-differential equations old and new. Math Biosci 184(2):201–222

    Article  PubMed  Google Scholar 

  • National Oceanic and Atmospheric Administration USA (2012) Fish facts - blue crab. http://chesapeakebay.noaa.gov/fish-facts/blue-crab

  • Neubert MG, Caswell H (2000) Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations. Ecology 81(6):1613–1628

    Article  Google Scholar 

  • Ontario Ministry of Natural Resources (2014) Invasive species prevention, management and control. http://www.mnr.gov.on.ca/en/Business/Biodiversity/2ColumnSubPage/STDPROD_06 8705.html

  • Pickering T, Quijón PA (2011) Potential effects of a non-indigenous predator in its expanded range: assessing green crab, Carcinus maenas, prey preference in a productive coastal area of Atlantic Canada. Mar Biol 158(9):2065–2078

    Article  Google Scholar 

  • Pimentel D, Zuniga R, Morrison D (2005) Update on the environmental and economic costs associated with alien-invasive species in the United States. Ecol Econ 52(3):273–288

    Article  Google Scholar 

  • Pringle JM, Blakeslee AM, Byers JE, Roman J (2011) Asymmetric dispersal allows an upstream region to control population structure throughout a species range. P Natl Acad Sci 108 (37):15288–15293

    Article  CAS  Google Scholar 

  • Pringle JM, Wares JP (2007) Going against the flow: maintenance of alongshore variation in allele frequency in a coastal ocean. Mar Ecol Prog Ser 335:69–84

    Article  CAS  Google Scholar 

  • Roman J (2006) Diluting the founder effect: cryptic invasions expand a marine invader’s range. Proc Roy Soc B 273 (1600):2453–2459

    Article  Google Scholar 

  • Ropes JW (1968) The feeding habits of the green crab, Carcinus maenas (L.) Fish Bull 67(2):183–203

    Google Scholar 

  • Rossong M, Quijon P, Williams P, Snelgrove P (2011) Foraging and shelter behavior of juvenile American lobster (Homarus americanus): the influence of a non-indigenous crab. J Exp Mar Biol Ecol 403(1):75–80

    Article  Google Scholar 

  • Rossong M, Williams P, Comeau M, Mitchell S, Apaloo J (2006) Agonistic interactions between the invasive green crab, Carcinus maenas (Linnaeus) and juvenile American lobster Homarus americanus (Milne Edwards). J Exp Mar Biol Ecol 329(2):281–288

    Article  Google Scholar 

  • Rossong MA, Quijón PA, Snelgrove PV, Barrett TJ, McKenzie CH, Locke A (2012) Regional differences in foraging behaviour of invasive green crab (Carcinus maenas) populations in Atlantic Canada. Biol Invas 14(3):659–669

    Article  Google Scholar 

  • Ruiz A, Franco J, Villate F (1998) Microzooplankton grazing in the Estuary of Mundaka, Spain, and its impact on phytoplankton distribution along the salinity gradient. Aquat Microb Ecol 14(3):281–288

    Article  Google Scholar 

  • Samia Y, Lutscher F (2010) Coexistence and spread of competitors in heterogeneous landscapes. Bull Math Biol 72:2089–2112

    Article  PubMed  Google Scholar 

  • Say T (1818) An account of the Crustacea of the United States. J Acad Nat Sci Phila 1(2):95–101

    Google Scholar 

  • Smith H (1995) Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems. Amer Math Soc 33(2):174

    Google Scholar 

  • Thompson WJ (2007) Population-level effects of the European green crab (Carcinus maenas, L.) in an eelgrass community of the southern Gulf of St. Lawrence. M.Sc. Thesis, University of New Brunswick (Canada)

  • Volkov D, Lui R (2007) Spreading speed and travelling wave solutions of a partially sedentary population. IIMA J Appl Math 72(6):801–816

    Article  Google Scholar 

  • Walton W (2000) Mitigating effects of nonindigenous marine species: evaluation of selective harvest of the European green crab, Carcinus maenas. J Shellfish Res 19(1):634

    Google Scholar 

  • Weinberger H (1982) Long-time behavior of a class of biological models. SIAM J Math Anal 13(3):353–396

    Article  Google Scholar 

  • Weinberger HF, Lewis MA, Li B (2002) Analysis of linear determinacy for spread in cooperative models. J Math Biol 45(3):183–218

    Article  PubMed  Google Scholar 

  • Weinberger HF, Lewis MA, Li B (2007) Anomalous spreading speeds of cooperative recrusion systems. J Math Biol 55:207–222

    Article  PubMed  Google Scholar 

  • Williams P, Floyd T, Rossong M (2006) Agonistic interactions between invasive green crabs, Carcinus maenas (Linnaeus), and sub-adult American lobsters, Homarus americanus (Milne Edwards). J Exp Mar Biol Ecol 329(1):66–74

    Article  Google Scholar 

  • Wisconsin Department of Natural Resources (2012) Control methods. http://dnr.wi.gov/topic/invasives/control.html

Download references

Acknowledgments

The authors are grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC) and MITACS for project funding. Also, a special thank you to C. McCarthy, Kejimkujik National Park, for sharing unpublished results of green crab control experiments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lisa Kanary.

Appendices

Appendix A: Stability of the positive steady state

We prove that the unique positive steady state of the non-spatial model equation (1) is stable whenever it exists. The single-genotype non-spatial model is given by

$$ N_{t+1} \,=\,F(N_t) = \left(\frac{P_{m}}{1+\alpha_P N_t} + \frac{S_{m}}{1+\alpha_S N_t} \frac{R_{m}}{1+\alpha_R N_t} \right) N_t. $$
(32)

Model (32) possess the trivial equilibrium, and has a unique positive equilibrium provided P m + S m R m > 1 and at least one of α S , α P , α R is positive. The unique positive equilibrium satisfies the equation

$$ 1 - \frac{P_{m}}{1 + \alpha_p N^{*}} = \frac{S_{m}}{1+\alpha_S N^{*}} \frac{R_{m}}{1+\alpha_R N^{*}}. $$
(33)

It is stable when \(|F^{\prime }(N^{*})|<1\). Substituting, we calculate

$$\begin{array}{@{}rcl@{}} F^{\prime}(N^{*})&=& \frac{P_{m}}{(1 + \alpha_p N^{*})^2} + \frac{R_{m}\,S_{m}(1+\alpha_sN^{*})(1+\alpha_rN^{*}) - R_{m}\,S_{m}N^{*}(\alpha_s(1 + \alpha_rN^{*}) + \alpha_r(1 + \alpha_sN^{*}))}{(1 + \alpha_sN^{*})^2(1 + \alpha_r N^{*})^2}. \end{array} $$
(34)

which can be simplified by using Eq. 33 to

$$\begin{array}{@{}rcl@{}}F^{\prime}(N^{*}) &=& \frac{P_{m}}{(1 + \alpha_p N^{*})^2} + \left(1 - \frac{P_{m}}{1 + \alpha_p N^{*}}\right)\\ &&\times\left(1 - \frac{N^{*}\alpha_s}{1 + \alpha_sN^{*}} - \frac{N^{*}\alpha_r}{1 + \alpha_rN^{*}}\right). \end{array} $$
(35)

Since \(\frac {P_{m}}{1 + \alpha _p N^{*}} < 1,\) the first bracketed quantity in Eq. 35 is strictly positive and smaller than unity. The second bracketed quantity in Eq. 35 is between negative one and positive one. Therefore, \(|F^{\prime }(N^{*})| \leq 1,\) and the unique positive equilibrium is always stable. Note that, solutions near N may oscillate since the updating function in Eq. 32 is, in general, not monotone. However, it turns out that for our point-estimates listed in Table 1, the updating function in Eq. 32 is monotone.

Appendix B: Monotonicity and the joint spreading speed

We show that a change of variables turns the competitive system (7) into a cooperative system, and we discuss the similarities and differences with the work in Weinberger et al. (2002, 2007).

We can write the non-spatial competitive system as

$$\begin{array}{@{}rcl@{}} N_{t+1} &=& f(E_t) N_t \\ M_{t+1} &=& f(\rho E_t)M_t, \end{array} $$
(36)

where E t = N t + κ M t . If updating function Nf(N)N is monotone on [0,M ], then the domain [0,M ]2 is invariant for this system. While our updating function need not be monotone, it is monotone for the parameter ranges we found in the literature. The new variables u t = N t , and v t = M M t . satisfy the equations

$$\begin{array}{@{}rcl@{}} u_{t+1} &=& f(u_t + \kappa(M^{*} - v_t)) u_t := \mathcal{F}(u_t, v_t) \\ v_{t+1} &=& f(u_t + \kappa(M^{*} - v_t)) \\ &&+ M^{*}(1 - f(u_t + \kappa(M^{*} - v_t))) := \mathcal{G}(u_t, v_t). \end{array} $$
(37)

We verify that system (37) is cooperative. By definition (Smith 1995), system (37) is cooperative if

$$\frac{\partial \mathcal{F}}{\partial v} \geq 0, \qquad \frac{\partial \mathcal{G}}{\partial u} \geq 0.$$

Since \(f^{\prime }(E) < 0,\) we have

$$\begin{array}{@{}rcl@{}} \frac{\partial \mathcal{F}}{\partial v} &=& f^{\prime}(E)(-\kappa) \geq 0 \\\notag \frac{\partial \mathcal{G}}{\partial u} &=& f^{\prime}(E)(v - M^{*}) \geq 0, \ \text{if} \ v < M^{*}. \end{array} $$
(38)

Thus, we see that system (37) is cooperative in the biologically realistic region 0 ≤ uN , 0 ≤ vM .

The above results have implications for the spreading speed of the spatial system in Eq. 10. Weinberger et al. (2002, 2007) gave sufficient conditions under which the joint spreading speed of the two genotypes in a special case of system (10) exists, is linearly determinate and is given by the speed of the dominant invader. Namely, for P m = 0 and either α S = 1 and α R = 0 or vice-versa, system (10) is the one studied by Weinberger et al. (2002, 2007). The crucial part of the proof requires that the system can be transformed into a monotone system. In the general case, i.e. P m > 0 and α s α R > 0 the situation is unclear. For one, the operator is not compact. Secondly, the operator may not be monotone. Our numerical results suggest that the conclusions still hold, but the mathematical proof is a future challenge.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kanary, L., Musgrave, J., Tyson, R.C. et al. Modelling the dynamics of invasion and control of competing green crab genotypes. Theor Ecol 7, 391–406 (2014). https://doi.org/10.1007/s12080-014-0226-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12080-014-0226-8

Keywords

Navigation