# Barnacles vs bullies: modelling biocontrol of the invasive European green crab using a castrating barnacle parasite

## Abstract

Invasive species raise concern around the globe, and much empirical and theoretical research effort has been devoted to their management. Integrodifference equations are theoretical tools that have been used to understand the spatiotemporal process of a species invasion, with the potential to yield insight into the possible biological control measures. We develop a system of integrodifference equations to explore the potential release of a castrating barnacle parasite *Sacculina carcini* to control spread and abundance of an invasive species, *Carcinus maenas*, the European green crab. We find that the parasite does not completely eradicate the green crab population, but has the potential to reduce its density. Our model suggests that the crab population is likely to outrun the spread of the parasite, causing two waves of invasion travelling at different speeds. By performing a sensitivity analysis, we investigate the effects of the demographic parameters on the speed of invasion. To conclude, we discuss the predicted outcomes for the European green crab, and other non-target hosts, of using the castrating barnacle as a biocontrol agent.

## Keywords

Invasive species Biological control Integrodifference equations SEI model Green crab*Carcinus maenas*

*Sacculina carcini*

## Notes

### Acknowledgments

The authors encountered the green crab biocontrol problem at the 2013 PIMS IGTC Mathematical Biology Summer School on The Mathematics Behind Biological Invasions. All authors thank the organizers, Mark Lewis and Thomas Hillen, for providing the opportunity to attend the program, and to Mark Lewis and Devin Goodsman for their guidance during model development. Thomas Hillen provided useful comments on a previous version of this manuscript. AWB was supported by an NSERC Discovery grant (to Mark Lewis) and by NSERC and Killam postdoctoral fellowships. AB was supported by an Alberta Innovates Graduate Scholarship and a PIMS Graduate Scholarship. NGM was supported by NSERC TRIA-Net.

## References

- Audet D, Davis D, Miron G, Moriyasu M (2003) Geographical expansion of a nonindigenous crab,
*Carcinus maenas*(L.), along the Nova Scotian shore into the southeastern Gulf of St. Lawrence, Canada. J Shellfish Res 22:255–262Google Scholar - Bateman AW, Neubert MG, Krkosek M, Lewis MA (2015) Generational spreading speed and the dynamics of population range expansion. Am Nat 186:362–375CrossRefPubMedGoogle Scholar
- Berrill M (1982) The life cycle of the green crab
*Carcinus maenas*at the northern end of its range. J Crustac Biol 2:31–39CrossRefGoogle Scholar - Byers J, Pringle J (2006) Going against the flow: retention, range limits and invasions in advective environments. Mar Ecol Prog Ser 313:27–41CrossRefGoogle Scholar
- Caswell H (2001) Matrix population models: construction, analysis, and interpretation. Sinauer Associates, SunderlandGoogle Scholar
- Cohen AN, Carlton J, Fountain M (1995) Introduction, dispersal and potential impacts of the green crab
*Carcinus maenas*in San Francisco Bay, California. Mar Biol 122:225–237Google Scholar - Day J (1935) The life history of
*sacculina*. Q J Microsc Sci 77:549–583Google Scholar - De-Camino-Beck T, Lewis M (2007) A new method for calculating net reproductive rate from graph reduction with applications to the control of invasive species. Bull Math Biol 69:1341– 1354CrossRefPubMedGoogle Scholar
- Fagan W, Lewis M, Neubert M, Van Den Driessche P (2002) Invasion theory and biological control. Ecol Lett 5:148– 157Google Scholar
- Fife PC, McLeod JB (1977) The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch Ration Mech Anal 65:335–361CrossRefGoogle Scholar
- Gharouni A, Barbeau MA, Locke A, Wang L, Watmough J (2015) Sensitivity of invasion speed to dispersal and demography: an application of spreading speed theory to the green crab invasion on the northwest Atlantic coast. Mar Ecol Prog Ser 541:135– 150CrossRefGoogle Scholar
- Goddard JHR, Torchin ME, Kuris AM, Lafferty KD (2005) Host specificity of
*Sacculina carcini*, a potential biological control agent of the introduced european green crab*Carcinus maenas*in California. Biol Invasions 7:895–912CrossRefGoogle Scholar - Grosholz ED (1996) Contrasting rates of spread for introduced species in terrestrial and marine systems. Ecol 77:1680–1686CrossRefGoogle Scholar
- Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42:599–653CrossRefGoogle Scholar
- Høeg JT (1995) The biology and life cycle of the
*Rhizocephala*(*Cirripedia*). J Mar Biol Assoc U K 75:517–550CrossRefGoogle Scholar - Høeg JT, Lützen J (1995) Life cycle and reproduction in the Cirripedia Rhizocephala. Oceanogr Mar Biol Annu Rev 33:427–485Google Scholar
- Kanary L, Musgrave J, Tyson R, Locke A, Lutscher F (2014) Modelling the dynamics of invasion and control of competing green crab genotypes. Theoretical Ecology 7:391–406CrossRefGoogle Scholar
- Kelley AL, de Rivera CE, Grosholz ED, Ruiz GM, Yamada SB, Gillespie G (2015) Thermogeographic variation in body size of
*Carcinus maenas*, the european green crab. Mar Biol 162:1625–1635Google Scholar - Klassen G, Locke A (2007) A biological synopsis of the european green crab,
*Carcinus maenas*. Can Manuscr Rep Fish Aquat Sci 2818Google Scholar - Kot M (1992) Discrete-time travelling waves: ecological examples. J Math Biol 30:413–436CrossRefPubMedGoogle Scholar
- Kot M, Lewis M, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecol 77:2027–2042Google Scholar
- Kristensen T, Nielsen AI, Jørgensen AI, Mouritsen KN, Glenner H, Christensen JT, Lützen J, Høeg JT (2012) The selective advantage of host feminization: a case study of the green crab
*Carcinus maenas*and the parasitic barnacle*Sacculina carcini*. Mar Biol 159:2015–2023CrossRefGoogle Scholar - Krkoṡek M, Ashander J, Frazer LN, Lewis MA (2013) Allee effect from parasite spill-back. Am Nat 182:640–52CrossRefPubMedGoogle Scholar
- Lafferty KD, Kuris AM (2009) Parasitic castration: the evolution and ecology of body snatchers. Trends Parasitol 25:564–572CrossRefPubMedGoogle Scholar
- Li B, Lewis MA, Weinberger HF (2009) Existence of traveling waves for integral recursions with nonmonotone growth functions. J Math Biol 58:323–338CrossRefPubMedGoogle Scholar
- Lui R (1989) Biological growth and spread modeled by systems of recursions. i. mathematical theory. Math Biosci 93:269– 295CrossRefPubMedGoogle Scholar
- Lutscher F, Pachepsky E, Lewis M (2005) The effect of dispersal patterns on stream populations. SIAM Rev 47:749–772CrossRefGoogle Scholar
- Marculis NG, Lui R (2016) Modelling the biological invasion of
*Carcinus maenas*(the european green crab). J Biol Dyn 10:140–163CrossRefPubMedGoogle Scholar - Messing RH, Wright MG (2006) Biological control of invasive species: solution or pollution? Front Ecol Environ 4:132–140CrossRefGoogle Scholar
- Moksnes P-O (2004) Interference competition for space in nursery habitats: density-dependent effects on growth and dispersal in juvenile shore crabs
*Carcinus maenas*. Mar Ecol Prog Ser 281:181–191CrossRefGoogle Scholar - Mouritsen KN, Jensen T (2006) The effect of
*Sacculina carcini*infections on the fouling, burying behaviour and condition of the shore crab,*Carcinus maenas*. Mar Biol Res 2:270–275CrossRefGoogle Scholar - Neubert M, Caswell H (2000) Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations. Ecol 81:1613–1628CrossRefGoogle Scholar
- Nicholson AJ, Bailey VA (1935) The balance of animal populations.—part i. In: Proceedings of the Zoological Society of London. Vol. 105. Wiley Online Library, pp 551–598Google Scholar
- Parker I (2000) Invasion dynamics of
*Cytisus scoparius*: a matrix model approach. Ecol Appl 10:726–743CrossRefGoogle 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 52:273–288CrossRefGoogle Scholar
- Pringle J (2011) Asymmetric dispersal allows an upstream region to control population structure throughout a species’ range. Proc Natl Acad Sci 108:15288–15293CrossRefPubMedPubMedCentralGoogle Scholar
- R Development Core Team (2015) R: a language and environment for statistical computingGoogle Scholar
- Ricker WE (1954) Stock and recruitment. J Fish Res Board Can 11:559–623CrossRefGoogle Scholar
- Secord D (2003) Biological control of marine invasive species: cautionary tales and land-base lessons. Biol Invasions 5:117–131CrossRefGoogle Scholar
- Taylor CM, Hastings A (2005) Allee effects in biological invasions. Ecol Lett 8:895–908CrossRefGoogle Scholar
- Thresher R, Werner M, Høeg J, Svane I, Glenner H, Murphy N, Wittwer C (2000) Developing the options for managing marine pests: specificity trials on the parasitic castrator,
*Sacculina carcini*, against the european crab,*Carcinus maenas*, and related species. J Exp Mar Biol Ecol 254:37–51CrossRefPubMedGoogle Scholar - Torchin ME, Lafferty KD, Kuris AM (2001) Release from parasites as natural enemies: increased performance of a globally introduced marine crab. Biol Invasions 3:333–345CrossRefGoogle Scholar
- Torchin ME, Lafferty KD, Kuris AM (2002) Parasites and marine invasions. Parasitology 124 (Suppl):S137–S151Google Scholar
- Wang M-H, Kot M, Neubert MG (2002) Integrodifference equations, allee effects, and invasions 44:150–168Google Scholar
- Waser AM, Goedknegt MA, Dekker R, McSweeney N, Witte JI, van der Meer J, Thieltges DW (2016) Tidal elevation and parasitism: patterns of infection by the Rhizocephalan parasite
*Sacculina*carcini in shore crabs*Carcinus maenas*. Mar Ecol Prog Ser 545:215–225Google Scholar