On the risk of extinction of a wild plant species through spillover of a biological control agent: Analysis of an ecosystem compartment model
Introduction
Invasive plant species pose a great problem to global agriculture and ecosystems, threatening valuable indigenous species and productivity in agricultural and natural systems (Callaway and Aschehout, 2000, Pimentel, 2002, Sheppard et al., 2003). Classical biological control, by introducing natural enemies from the native range, is widely regarded as a valuable method for managing invasive species (Ehler, 1998, Thomas and Willis, 1998, Pemberton, 2000). Classical biological control avoids the use of herbicides and can be highly cost-effective (Charudattan, 2001). Chalak-Haghighi et al. (2008) have recently shown that an insect herbivore (Apion onopordi) can increase the net present value obtained from pastures in New Zealand by reducing the growth rate of Californian thistle (Cirsium arvense).
Many authors have discussed the environmental risks of classical biological control (e.g. Thomas and Willis, 1998, Follett and Duan, 1999, Wajnberg et al., 2001). For example, natural enemies may attack non-target species. In order to assess this risk we need to understand the ecological dynamics of the biological control agent in the ecosystems where they are introduced, including their interactions with other species. These interactions include both local population interactions as well as spillover of enemies from one ecosystem compartment to another.
Many of the biological control agents introduced for pest control in agricultural areas can feed on alternative host plants in natural habitats and are likely to spill over from agricultural into natural systems (Henneman and Memmott, 2001, Symondson et al., 2002, Rand et al., 2006, Wirth et al., 2007). This spillover can result in important adverse consequences (Suarez et al., 1998, Cronin and Reeve, 2005, Rand et al., 2006). For instance, the weevil Rhinocyllus conicus, introduced for the biological control of Platte thistle (Cirsium canescens) in the United States, attacked a protected and rare relative, the Pitcher's thistle (Cirsium pitcheri) (Louda et al., 2003, Louda et al., 2005). Adult beetles of the corn rootworm (Diabrotica ssp.), which feed in agricultural land as larvae, spillover into tall-grass prairie causing damage to native plants (McKone et al., 2001). Thus, before introducing a herbivore to a managed system, it is important to consider potential spillover effects to the natural environment, resulting in attack on endangered or protected species in the natural environment.
Because ecological conditions of the managed and natural systems differ, a variety of plant species interactions can prevail in managed and natural systems. Thus, a herbivore may be able to build large populations in one compartment, spill over to another compartment, and affect species interactions and survival in this other compartment. There is a need for analysis of the conditions under which dispersal of a biological control agent from a managed to a natural system produces a spillover effect that is large enough to threaten biodiversity (Rand et al., 2006).
Here, we use a two compartment modelling approach to elucidate risks when releasing a biological control agent to a managed compartment that can spill over to another ecosystem compartment and attack a valuable indigenous species in this other compartment. We focus on the wild plant species’ risk of extinction. There have been some studies on two compartment model systems (Vellend et al., 2003). While compartmentalised ecosystem models appear a very suitable tool to study spillover and its effect on ecosystems, such models have, to the best of our knowledge, to date not been used to study extinction risks resulting from spillover.
We develop here a model consisting of two compartments, that represents key processes such as the interaction between a herbivore and its target and non-target plant species, dispersal of the herbivore between ecosystem compartments, and the competitive relationships between a non-target species and other species in a natural compartment. The objectives are to identify those system characteristics that enhance or mitigate the risk of extinction of the non-target plant species in the natural compartment, and to gain insight in the interrelationships between the different dynamic processes involved. In the next section the model system is described, followed by a mathematical analysis. Next, a numerical analysis is presented and finally, conclusions are drawn.
Section snippets
Description of the model system
For our analysis we model our system as two compartments: (1) a managed compartment where a herbivore (zm, numbers m−2) is introduced to control a pest weed (, shoots m−2), and (2) a natural compartment where the same herbivore species (here denoted as zn, numbers m−2) can attack a valuable wild plant species (species x, shoots m−2) (Fig. 1). The two herbivore populations are linked by dispersal, enabling the introduced species to spill over from one compartment to the other if the densities in
Mathematical analysis
Before conducting numerical analyses, the 5-dimensional system was analysed mathematically to obtain all of its equilibria and determine their stability. To facilitate mathematical analysis, the model was first non-dimensionalized, i.e. units were removed from the state variables as well as from the parameters by substitution of variables (Appendix A). This non-dimensionalization reduces the number of parameters from 13 (Table 1) to nine (system (A1)). Moreover, the combinations of original
Numerical analysis
For the numerical analysis, two equilibria are of particular interest: (1) equilibrium xiv in which all species coexist and (2) equilibrium x in which species x is extinct due to the combination of herbivore attack by zn and competition with y. A dynamic trajectory that starts from disturbance from the positive equilibrium xiv ending in equilibrium x is of special interest because it represents extinction of x, allowing us to investigate which parameter values would lead plant species x to
Comprehensive sensitivity analysis
A comprehensive local sensitivity analysis demonstrates the effect of all parameter values on the equilibrium densities of all state variables (Fig. 9). First, the relationship between percentage change from the default parameter values and the equilibrium density of plant species x is presented (Fig. 9A and B). The density of species x at equilibrium increases as x becomes a stronger competitor and herbivory on x decreases. Thus, on the one hand x is a strictly increasing function of
Discussion
This paper puts forward a theoretical model framework for analysing which factors contribute to extinction risk of a wild non-target plant species due to spillover of a herbivore introduced for biological control in agriculture. Extinction is enhanced by: (1) a large resident population of the herbivore in the agriculture compartment, which is the case at intermediate values of the attack rate on the target weed; (2) a high attack rate of the herbivore on the non-target wild species; (3) a high
Acknowledgments
We thank Dr. A.J.V. Rotteveel and T. Heijerman for helpful discussions on the parameter values. We acknowledge E. Hendrix and D. Pannell for their useful comments. We thank two anonymous reviewers for insightful comments.
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