Biological Invasions in Aquatic Systems: the Economic Problem

Biological invasions are recognised to be a problem of growing severity. Encompassing new human pathogens, weeds or pests in terrestrial systems, and dominant alien species in freshwater or marine aquatic systems, they are the second most important proximate cause of biodiversity loss worldwide. They also impose significant costs in terms of forgone output or costs of control in every major system except for pelagic marine systems. Coastal, coral reef, and estuarine systems are among the most vulnerable. This paper considers the economics of the problem in the context of a simple generic model of invasions and invasion control. It shows that the dynamical characteristics of the problem are driven not only by population dynamics but by the costs and benefits of ‘native’ and alien ‘invasive’ species. Most ecosystem types—terrestrial, freshwater, and marine—have been affected to a greater or lesser extent by biological invasions (Parker at al., 1999; Williamson, 1998, 2000). One of the best-known examples of a marine invasive species is in the Black Sea, where the establishment of the comb jelly Mnemiopsis leidyi has transformed the ecology of the system. The zebra mussel, Dreissena polymorpha, has had similar effects in freshwater systems in both Europe and America. It is now thought to have invaded about onethird of all freshwater aquatic environments in the United States (Williamson, 1996). These are only the most familiar examples, however, of a phenomenon that is rapidly growing with the widening and deepening of international markets in goods and services. The most severe costs of invasions may be due to their impact on local and global biodiversity (Glowka et al., 1994; Czech and Krausman, 1997; Wilcove et al., 1998), but they also impose significant costs in forgone output or defensive expenditure in a wide range of activities. Knowler (1999) and Knowler and Barbier (2000) have examined the role of Mnemiopsis in changing the cost of fishing effort in the Black Sea. Attempts have also been made to estimate the costs imposed by the green crab, Carcinus maenas, on the North Pacific Ocean fisheries (Cohen et al., 1995) and by the zebra mussel on industrial plants in both Europe and the USA (Khalanski, 1997). What makes the problem particularly interesting from an economic perspective is that it is usually an external effect of market transactions, and its control is a public good of a particularly intractable sort. The wider impacts of invasive species are ignored by those responsible for their introduction, establishment, or spread. These impacts may be localized and of relatively short duration, but they may also be widespread and have periodic, chronic, or potentially irreversible effects. Ecosystems vary in their natural susceptibility to invasion. Although pelagic marine systems appear to be least susceptible, mixed island systems and lake, river, and near-shore marine systems are especially vulnerable (Heywood, 1995). Of course, the probability of establishment of intentionally introduced species is higher than that of unintentionally introduced species simply because the former have been selected for their ability to survive in the environment where they are introduced (Smith et al., 1999) and may be introduced repeatedly (Enserink, 1999), but the probabil542 BULLETIN OF MARINE SCIENCE, VOL. 70, NO. 2, 2002 ity of both establishment and spread also depends on ways in which the environment is altered by human behavior. The best-understood source of marine invasions is the transfer of species in water ballast (Carlton and Geller, 1993), but marine invasions are frequently induced by changes in environmental conditions due to the effects of pollution. Among the most striking information reported by the Independent World Commission on the Oceans (1998) is that 77% of global marine pollution is now thought to derive from land-based sources either directly or through the atmosphere. Changing patterns of land use in watersheds have had major effects on flood regimes worldwide by changing in-stream flows. In some areas, increasing surface run-off due to deforestation has boosted the frequency and severity of floods. In others, increasing rates of water abstraction have had the opposite effect. Both pollution and changes in stream flows have altered estuarine and coastal ecosystems in ways that make them more susceptible to invasion. Many marine systems are characterized by multiple locally stable states. The characteristics and the economic value of such states may be very different. For example, sewage and fertilizer run-off has caused coral reefs with high diversity of fishes and other aquatic organisms to be flipped into a low-value state dominated by algae and otherwise low levels of aquatic diversity (Roberts, 1995). It turns out that biological invasions are frequently induced by changes of this sort. Terrestrial pollution is, for example, implicated in the susceptibility of the Black Sea to invasion by Mnemiopsis (Knowler and Barbier, 2000). Here, I consider biological invasions and their control as an economic problem. I identify the factors that determine whether a system affected by an invasion will experience a change of state. The control of biological invasions involves measures that increase or reduce the resilience of the system in either the ‘exclusion’ or the ‘invaded’ state. It is shown that the optimal level of the control is sensitive to the value of the system in either state, as well as to the costs of control. A MODEL OF BIOLOGICAL INVASIONS The generic problem of biological invasions involves four phases: the introduction, establishment, naturalization, and spread of a species outside its normal range (Williamson, 1996). In what follows these four phases are all subsumed under the spread of invasives. The process is held to be analogous to that of a virus entering and spreading within a host population (Delfino and Simmons, 2000). Indeed, the model is developed from the Kermack and McKendrick (1927) model behind epidemiological theory. Unlike those in epidemiological models, however, the state variables are measures of the space occupied by ‘invasive’ and ‘native’ species, rather than the population or biomass of those species. Because a biological invasion involves the occupation of habitat, it can be modeled as the growth of the space occupied by the invasive species. The problem will only be interesting if that space is otherwise occupied by species that yield a flow of goods or services. These will be referred to, for convenience, as ‘native’ species. The ‘invaded’ space is the space occupied or affected by alien invasive species, and the ‘native’ space is the space occupied by native species. For simplicity, the total space is assumed to be constant over the time horizon of interest. The state variables are denominated in terms of that space. They are the proportion of 543 PERRINGS: BIOLOGICAL INVASIONS IN AQUATIC SYSTEMS the total space occupied by native and invasive species, denoted x(t) and y(t) respectively. If a control program clears invasive species from some part of the total space, then x(t) + y(t) < 1. The rate of change in the space occupied by the invasive species is taken to be proportional to the product of the space occupied by the invasive and native species. This assumption implies that the spread of invasive species is proportional to the zone of contact between native and invasive species. As invasive species become established and begin to spread, the rate is low. It increases up to the point where the total space is split evenly between the native and invasive species and decreases again as the space occupied by the invasive species approaches the total space. The invasion rate, a, is taken to be a constant parameter in what follows, although I later consider the connection between the invasion rate and resource use. In general, the control of invasive species includes a number of options: exclusion, eradication, containment (control), mitigation, and adaptation. Exclusion implies the uses of measures such as quarantine, blacklists, or inoculation to prevent the introduction of potentially invasive species. Eradication is typically, but not always, an option only in the early stages of the spread of an invasive species. Containment implies the restriction of the space occupied by an invasive species. Mitigation and adaptation imply measures to accommodate the invasive species. In what follows these measures are collapsed into a single index of control, b(t), that is a measure of the effort committed to clearing the invasive species. The space occupied by invasive species is taken to be proportional to the product of the space occupied by natives and invasives. Similarly, the space cleared of invasives is taken to be proportional to the product of the space occupied by the invasive species and the space cleared of invasives. It is assumed that the space cleared of invasives can be returned to native species at some positive rate, the restoration rate, g. The restoration rate is assumed here to be a constant parameter, but it might easily be analyzed as a choice variable. The equations of motion for the state variables are as follows: ẋ x t y t x t y t = ( ) ( ) + ( ) ( ) ( ) a g 1 Eq. 1 ẏ x t y t x t y t y t = ( ) ( ) ( ) ( ) ( ) ( ) a b 1 Eq. 2 in which a (= the invasion rate, -1 £ a £ 1) and g (= the restoration rate, 0 £ g £ 1) are fixed parameters, and b(t) (= the control rate, 0 £ b(t) £ 1) is a choice variable. 1 x(t) y(t) is the proportion of the total space cleared of invasive species. For most biological invasion problems, a will be strictly positive, implying that invasives spread at a positive rate, but a may also be negative. This is the case where introduced species are unable to establish themselves, naturalize, or spread. With these we can identify some of the dynamics of the native and invasive species. Once a potentially invasive species has been introduced, y(t) > 0, the condition for it to spread is that it become established. A potentially invasive species may be said to be established when it has passed the threshold for growth. This threshold is defined by the values of x(t) and y(t) at which ẏ > 0. From Eq. 2 it follows that the invasive species will spread only if 544 BULLETIN OF MARINE SCIENCE, VOL. 70, NO. 2, 2002 y t x t t ( ) > ( ) + ( ) Ê