Managing apparent competition between the feral pigs and native foxes of Santa Cruz Island

Ecological Economics 107 (2014) 157–162

Contents lists available at ScienceDirect

Ecological Economics journal homepage: www.elsevier.com/locate/ecolecon

Analysis

Managing apparent competition between the feral pigs and native foxes of Santa Cruz Island Richard T. Melstrom ⁎ Department of Agricultural Economics, Oklahoma State University, United States

a r t i c l e

i n f o

Article history: Received 14 May 2014 Received in revised form 12 July 2014 Accepted 13 July 2014 Available online 31 August 2014 JEL Classification: C61 Q20 Q57

a b s t r a c t This paper presents a model of pest impacts in a multispecies framework. Strong detrimental relationships often form between pest populations and other biota, damaging ecosystem services and reducing social welfare. Under these circumstances, optimal pest management must account for the interactions between pests and other species. The bioeconomic model of competition developed in this manuscript is illustrated using the case of feral pigs (Sus scrofa) on Santa Cruz Island, California. The presence of the pigs, an introduced species, resulted in the near extirpation of the native island fox (Urocyon littoralis) before managers intervened and removed the pigs from the island. The application compares a policy of pig eradication with one of perpetual control, which is found to involve initially over-culling the pigs relative to the equilibrium level. To protect the foxes of Santa Cruz Island, the results suggest that pig eradication rather than pig control is the optimal strategy. © 2014 Elsevier B.V. All rights reserved.

Keywords: Exotic species Invasive species Pests Bioeconomics Multispecies system Feral pigs Island foxes Channel Islands

1. Introduction Pests, both indigenous and exotic, are a form of biological pollution that significantly harms social welfare. Their impacts include billions of dollars in lost marketable goods and control costs, as well as biodiversity loss. It is estimated that more than half of all endangered species are at risk due to competition with or predation by nonindigenous species (Pimentel et al., 2005), although indigenous species, too, have been implicated in endangering native wildlife (DeCesare et al., 2010). A major policy goal in natural resource management is the restoration of habitat conditions and wildlife in high-valued ecosystems impacted by invasives (NISC, 2008). Physical removal or harvesting of pests and harmful invasives is a key method in managing these adverse impacts (Olson, 2006). A large portion of the pest control literature analyzes damage mitigation policies using dynamic bioeconomic models. This approach is

⁎ Department of Agricultural Economics, Oklahoma State University, Stillwater, OK 74074, United States. Tel.:+1 405 744 6171. E-mail address: [email protected].

http://dx.doi.org/10.1016/j.ecolecon.2014.07.004 0921-8009/© 2014 Elsevier B.V. All rights reserved.

useful because pests are biological resources, although it also complicates the analysis (Burnett et al., 2008). Perhaps for this reason, most of the literature limits the bioeconomic model to the pest species itself and explores innovations in control programs. These models have been used to study problems with insects (Ceddia et al., 2009), weeds (Burnett et al., 2006; Eiswerth and van Kooten, 2002; Pannell, 1990) and invasive species (Burnett et al., 2008; Eiswerth and Johnson, 2002; Zivin et al., 2000), as well as generic pest control policies such as eradication (Olson and Roy, 2008). An important consideration in the control of a pest is its interaction with other wildlife (Barbier, 2001; Eppink and van den Bergh, 2007). When these interactions significantly impact ecosystem functions, efficient management strategies must account for the secondary species effects from managing pests and invasives (Zavaleta et al., 2001). Ignoring these interactions means ignoring spillover effects, which can result in inefficient pest control policies. This was recognized early by Feder and Regev (1975), who showed that when pest control applications harm the predator of a pest, myopic decision making can actually increase pest damages. Subsequent work has investigated other situations in which the pest is a predator (Melstrom and Horan, 2014; Settle and Shogren, 2002; Settle et al., 2002), prey (Fenichel et al., 2010; Harper

158

R.T. Melstrom / Ecological Economics 107 (2014) 157–162

and Zilberman, 1989), competitor (Barbier, 2001; Frésard and Boncoeur, 2006) and parasite (Sims et al., 2010).1 However, most of this research has focused on pests that generate market damages rather than those that have significant nonmarket impacts. This paper is concerned with the situation of an exotic pest competing with valuable native wildlife. The theoretical multispecies model is akin to that of Barbier (2001) and Frésard and Boncoeur (2006) who also analyze a pest engaged in interspecific competition, although there are key differences. First, the native wildlife is valued through its existence rather than through some commercial or recreational activity, e.g. harvests. The paper therefore builds on prior work by analyzing ecosystem interactions involving an exotic species and nonmarket impacts. Second, because there is no incentive to harvest the valued wildlife, the system is managed only through predator removal. Optimal control theory is used to solve for the removal policy that maximizes social welfare over time. The optimal removal policy is illustrated for the case of the endangered island fox (Urocyon littoralis) and feral pig (Sus scrofa) on Santa Cruz Island, California. Although exotic species were long recognized for causing damage to the natural resources of the island (NPS, 2002), the pigs' impact on fox survival became a special concern in the late 1990s when the fox population fell to extremely low levels (Coonan, 2003). Rather than directly competing with each other's forage and reproduction activities, the foxes and pigs interact through apparent interspecific competition because they help sustain a common predator. Pig removal was a dominant management issue until an eradication program was successfully carried out in 2006. This paper examines the optimal pig removal policy where pig damages are a function of the fox population, which only has existence value. The model is used to compare several different removal policies designed for fox conservation per se, including perpetual pig control, eradication and doing nothing. The results provide insights into the design of pest control strategies aimed at recovering nonuse valued wildlife and ecosystem services. 2. Multispecies Bioeconomic Model The model should capture the feedbacks between a pest and the flora and fauna within an ecosystem. To keep the analysis tractable, the affected part of the ecosystem is modeled as a single stock f. This stock could be viewed as the biomass for all wildlife in an ecosystem, the biomass of an umbrella species or the population of a charismatic species. The pest stock is notated by p. The biological interaction between the pest and affected wildlife consists of a pair of impacts that determine whether the relationship is one of amensalism, competition or predation. This paper focuses on the competitive case, i.e. that a pest negatively impacts the stock of wildlife and vice-versa. The stock dynamics are therefore modeled as df ¼ gð f Þ−mð f ; pÞ dt

ð1Þ

dp ¼ qðpÞ−nð f ; pÞ−hðt Þ dt

ð2Þ

where g(∙) is the natural growth of f, q(∙) is the natural growth of p, m(∙) is the reduction in growth of f due to competition with the pest and n(∙) is the corresponding reduction in p from competition. The final term in

1 Several other papers do not analyze multispecies pest control specifically but study related problems. In regard to pest management, Skonhoft and Olaussen (2005) study pest harvesting strategies to improve the value of a metapopulation system, Finnoff and Tschirhart (2005) model plant competition to help identify successful invasive plant species, and Gutierrez and Regev (2005) model a multiple trophic level system to show how species maximize their adaptedness over time, which can result in local extinctions for other species. For a review of multispecies bioeconomic modeling in general, see Tschirhart (2009).

Eq. (2) is the reduction in the growth of the pest due to management, which is modeled as a harvest rate. A manager wants to maximize the net benefits of the multispecies system or, equivalently, minimize the damages from the pest plus control costs. The pest creates social damages by reducing f and its ecosystem service value, which is denoted by V(f) with Vf N 0 and Vff b 0, where the f subscript denotes a derivative. The cost of pest control— specifically, pest removal—is defined as c(p)h(t). The term c(p) is the per-unit cost of removing a pest, where cp b 0 and cpp N 0. Removal costs are increasing and convex because it becomes increasingly costly to find and remove pests as the population of pests diminishes (Horan and Melstrom, 2011). The management objective is to Z∞ max SNB ¼

½V ð f Þ−cðpÞhðt Þe

hðt Þ

−ρt

dt

ð3Þ

0

subject to ð1Þ; ð2Þ; 0≤hðt Þ≤hmax ; f ð0Þ ¼ f 0 ; pð0Þ ¼ p0 where ρ is the discount rate. The current value Hamiltonian for problem (3) is H ¼ V ð f Þ−cðpÞhðt Þ þ λðt Þ½g ð f Þ−mð f ; pÞ þ μ ðt Þ½qðpÞ−nð f ; pÞ−hðt Þ ð4Þ where λ(t) and μ(t) are the adjoint or co-state variables (Clark, 1990). The solution to problem (3) involves choosing h to maximize H. The marginal impact of h on H is ∂H ¼ −cðpÞ−μ ðt Þ: ∂h

ð5Þ

The right-hand side (RHS) of Eq. (5) includes the marginal costs of removal, −c(p), and the marginal intertemporal benefit of culling a pest, − μ(t) (the pest co-state will be negative). It is optimal to set h = 0 when Eq. (5) is negative and h = hmax when Eq. (5) is positive. The singular, interior value for h, hSV, is optimal when Eq. (5) is zero. That is, hSV requires μ ðt Þ ¼ −cðpÞ

ð6Þ

which suggests that the pest should only be removed when it has negative value. Assuming the optimal equilibrium strategy does not occur at h = 0 or h = hmax, then Eq. (6) is a necessary condition for a solution. A solution must also satisfy two adjoint equations: h i dλ ¼ ρλðt Þ−V f −λðt Þ g f −m f þ μ ðt Þn f dt

ð7Þ

h i dμ ¼ ρμ ðt Þ þ cp hðt Þ þ λðt Þmp −μ ðt Þ qp −np dt

ð8Þ

Eqs. (7) and (8) show how the co-states should evolve over time. If continuous pest removal proceeds optimally, then Eq. (7) says that λ(t) will vary depending on its own current value, the discount rate, the marginal value of f, the marginal net growth of f, the pest co-state and the marginal effect of f on pest growth. Likewise, Eq. (8) says that μ(t) will vary depending on its own current value, the discount rate, the marginal cost of removal with respect to p, the removal rate, the wildlife co-state, the marginal effect of p on wildlife growth and the marginal net growth of p. Focusing on the interior solution, efficient pest control is determined by using Eqs. (6), (7) and (8). The singular solution for h is found by taking the time derivative of Eq. (6) to get dμ dp ¼ −cp  ¼ −cp ½qðpÞ−nð f ; pÞ−hðt Þ: dt dt

ð9Þ

R.T. Melstrom / Ecological Economics 107 (2014) 157–162

λðt Þ ¼

h i cðpÞ ρ þ np −qp −cp ½qðpÞ−nð f ; pÞ mp

:

ð10Þ

The numerator of Eq. (10) consists of a positive term minus a negative term. The denominator is positive. The complete expression equates the co-state for f with the marginal cost of pest management divided by the marginal effect of the pest on f. In effect, Eq. (10) says that the manager should only invest more resources into pest control if society places greater value on f. An explicit equation for hSV is found using Eqs. (7) and (10). Taking the time derivative of Eq. (10) yields dλ ∂λðt Þ df ∂λðt Þ dp ¼  þ  dt dt ∂f ∂p dt ∂λðt Þ ∂λðt Þ ¼  ½g ð f Þ−mð f ; pÞ þ  ½qðpÞ−nð f ; pÞ−hðt Þ: ∂f ∂p

ð11Þ

Inserting this expression into Eq. (7) yields the following: hSV ð f ; pÞ ¼ qðpÞ−nð f ; pÞ h i V f þ λ g f −m f −ρ −μn f þ ∂λ=∂f  ½g ð f Þ−mð f ; pÞ þ ð12Þ ∂λ=∂p where the time notation is dropped for conciseness. From Eq. (12), the singular value of h is a feedback rule that depends on the state values of f and p. Eq. (12) yields an infinite number of possible trajectories that could be used in an interior solution. However, in the case study the only trajectory that satisfies the necessary conditions in the long run is the path that moves to an interior equilibrium. Except by chance the system will not start on this path so it will be necessary to move to the path using a bang–bang control (h = 0 or h = hmax). Thus, a complete pest control strategy may combine the feedback control hSV(f,p) with a bang–bang control. Why would bang–bang controls alone not be the best way to approach equilibrium? The answer lies in the characteristics of the management problem, which involves managing a multispecies system with only a single control. The objective of pest removal is to recover one or more impaired species. Intuitively, a bang–bang control is too crude a method to optimally guide several populations. Note that this means the interior equilibrium strategy is not reached via a quick adjustment (i.e. a most-rapid-approach-path). Instead, the ideal pest control strategy uses a bang–bang control to reach the path in f − p space defined by hSV(f,p) that moves to equilibrium. This path, which implies sluggish adjustment, is the preferred route to equilibrium because h directly affects only one state so efficiently managing the entire system requires gradual adjustments in the control. Of course, an interior solution is not necessarily first-best if eradication (or doing nothing) is also feasible. These strategies must be analyzed numerically and compared to determine the optimal management strategy. This matter is taken up in the following section.

(Urocyon cinereoargenteus) (Roemer, 2004). The island fox has been subject to several mortality pressures brought about by humaninduced landscape changes, including the introduction of feral pigs (S. scrofa) in the nineteenth century. This paper focuses, in particular, on the fox–pig dynamic observed on Santa Cruz Island. A form of apparent competition developed between the foxes and feral pigs of Santa Cruz Island (Roemer et al., 2001). Feral pigs do not compete with foxes over habitat resources, but they can act as an abundant food source for predators that, in turn, overexploit native species, such as the island fox. Numerous endangered species problems are linked to this form of competition (DeCesare et al., 2010). In the 1990s, the large pig population allowed golden eagles to colonize Santa Cruz Island from the mainland. Eagle predation of the foxes and pigs facilitated apparent competition and drove the fox onto the U.S. endangered species list. This effect is illustrated in Fig. 1, which is parameterized for the numerical model in the following section. In the figure, there are two pairs of df / dt = 0 and dp / dt = 0 isoclines (nullclines) representing the thresholds for changes in f and p, respectively, before and after the onset of apparent competition. When there is no competitive interaction (m = n = 0) the fox and pig populations are near their carrying capacities at point A. With apparent competition the two populations fall to point B. Note that the ex post nullclines do not intersect, which suggests that the pigs would eventually drive foxes to extinction. Recovering the fox population required an intensive ecosystem management program. Apparent competition with the pigs caused the fox population on Santa Cruz Island to fall from approximately 1500 to 100. The recovery program included eagle translocation early on, but eagles from the mainland and other islands could replace the removed birds (Roemer et al., 2001). It was therefore determined that conserving the fox required feral pig control (Coonan, 2003; Roemer et al., 2002). In 2005, the U.S. National Park Service and the Nature Conservancy, which owns most of Santa Cruz Island, implemented a pig removal program. Within a year over 5000 pigs were removed and the species was successfully eliminated from the island (Griggs, 2007). The fox population has subsequently rebounded to a healthy level (estimated 734 ± 254 in 2008; Morrison, 2011).

df0/dt=0

A

dp1/dt=0

Foxes, f

The expressions for μ(t) and dμ/dt from Eqs. (6) and (9), respectively, should be inserted into Eq. (8). This yields the following:

159

dp0/dt=0 df1/dt=0

3. Empirical Study 3.1. California Channel Islands Foxes and Feral Pigs An interesting case of an ecosystem pest problem is found on the California Channel Islands. This group of islands, located off the coast of the southwestern United States, is home to a number of unique, endemic species. One of these species is the island fox (U. littoralis), the smallest canid of North America and a descendent of the gray fox

B

Pigs, p Fig. 1. The decline in the fox and pig populations at the onset of apparent competition. Before competitive interaction the system lies near point A, at the intersection of the dashed nullclines di0 / dt for i = f,p. Once the species begin to compete the nullclines shift to the solid lines di1 / dt for i = f,p and the system proceeds along the bolded trajectory to point B.

R.T. Melstrom / Ecological Economics 107 (2014) 157–162

3.2. Equations and Parameters Explicit functional forms are necessary to numerically determine a solution. The biological functions adopted here are consistent with those used in prior work (e.g. Burnett et al., 2006; Kar and Chauduri, 2003). Fox growth is modeled as g(f) = rf∙(1 − f / kf)∙f with the competitive effect m(f,p) = γ · f · p, where rf is the intrinsic growth rate of foxes, kf is the carrying capacity for foxes and γ is a parameter accounting for apparent competition. Pig growth is modeled as q(p) = rp∙(1 − p / kp)∙p with the competitive effect n(f,p) = η∙(f + δ)∙p, where rp is the intrinsic growth rate of pigs, kp is the carrying capacity for pigs, η is a parameter accounting for apparent competition and δ accounts for the mortality from eagles when f → 0. The biological parameter values are based upon work from published sources. The fox intrinsic growth rate, rf, is 0.32 and carrying capacity, kf, is 1544 (Roemer et al., 2002). The pig intrinsic growth rate, rp, is 0.78 and carrying capacity, kp, is 15,189 (Roemer et al., 2002). The competitive effect on foxes, γ, is 0.000066 so that the system (1)–(2) when left unmanaged simulates a population of 133 foxes 15 years after the onset of apparent competition (Roemer et al., 2002). The parameter δ is selected such that 5000 pigs would be left if foxes went extinct (Roemer et al., 2001), i.e. 0 = 0.78∙(1–5000 / 15,189) − η · δ · 5000, which implies that δ = 0.523/η. The parameter η is 0.000013 so that the model forecasts 5036 pigs 15 years after eagles arrive and enable apparent competition, which is the number observed during the eradication effort (Griggs, 2007). The nature of the economic benefits of the foxes is unknown, but given Vf N 0 and Vff b 0 it seems reasonable to use V(f) = v∙ln(1 + f), where v is a parameter. The island fox appears to be a charismatic species with substantial existence value, as evidenced by private conservation efforts (Friends of the Island Fox, 2014). There are no published studies of the economic benefits of these foxes, so it is not possible to determine their nonmarket value or parameterize the benefits function with certainty. Therefore, benefits transfer is used to establish a value for v. The closest related endangered species with obtainable value estimates appears to be the gray wolf (Canis lupus) (gray wolves and island foxes are two of only a handful of North American canids on the U.S. endangered species list), so the benefit function is parameterized as v = (aggregate WTPwolf) / ln(1 + kf). Chambers and Whitehead (2003) calculate the willingness to pay (WTP) of Minnesota households to pay for gray wolf preservation in Minnesota at $21.49 per household with a 95% confidence interval of (10.66, 32.32). After multiplying by 1.14 to get $24.50 (12.15, 36.84) in 2006 dollars (the year of pig eradication), this WTP is adopted as the benchmark monetized value of the foxes to California households. There were about 12.29 million households in California in 2006, which suggests a lump-sum WTP for fox preservation of $264.11 million. Using a discount rate of 5% to annualize benefits, aggregate WTP is $13,205,605, which suggests that v is 1,798,448. Due to uncertainty over the true value of the foxes, the robustness of the optimal management strategy to a variety of WTP amounts is tested in a sensitivity analysis. The form of the removal cost function is based on a style used in the literature because the true function is unknown. The marginal cost of removal is c(p) = c / p where c is a parameter. It is known that the pig eradication required the removal of 5036 pigs and cost $5 million (Griggs, 2007). Assuming that eradication occurs when p ≤ 1, the pa-

the foxes. There are three candidate optimal strategies: no pig control, perpetual control of a pig population through removal, and pig eradication. The first, no control strategy yields SNB of $157.2 million (with the foxes going extinct). The second candidate strategy, which involves perpetual pig removal, is referred to as the pig control strategy. Fig. 2 shows that this solution uses a combination of bang–bang and singular controls to reach equilibrium. The local dynamics of the system, determined by hSV (f,p), are indicated by phase arrows. The dp / dt| hSV(f,p) = 0 isocline intersects the df / dt = 0 isocline at point B, which forms an interior saddle point equilibrium. To reach equilibrium there is a saddle path, labeled SP in the figure. This path also functions as a switching curve that indicates that maximum removal is best when the system lies to the right of the curve and no removal is best when the system lies to the left of the curve. The first phase of this strategy therefore involves culling a large number of pigs to move the system to SP because the system begins to the right of point A. The second phase begins once the system reaches SP and engages h = hSV(f,p) to proceed along the saddle path toward equilibrium. The third and final phase is reached at equilibrium, which requires perpetual removal to maintain a population of 98 pigs and 1513 foxes. Note that this candidate strategy involves over-culling the pig population relative to the equilibrium level to jumpstart fox recovery. In the first years following the initial cull, the pig population is small (b20) and few pigs should be removed. This allows for the foxes to recover rapidly. In contrast, the pigs recover only modestly, with the rate of removal intensifying as the population grows until equilibrium. The time path of this solution is presented in Fig. 3(a). This pig control strategy yields SNB of $238.4 million. Now suppose that rather than initially overshooting the equilibrium, a manager might instead cull just enough pigs to reach the desired long run level. In fact, this is akin to a most-rapid-approach-path to equilibrium, which would appear optimal if the role of the foxes on the pigs was omitted from the bioeconomic model. However, eventually achieving equilibrium still requires varying h over time because changes in the fox population inevitably impact the net growth of the pigs. To stabilize the pig population after the initial cull, h must be slightly higher than the equilibrium level but can be gradually reduced as the foxes recover. The time path of this solution is presented in Fig. 3(b). This alternative

B

dp/dt|h

df/dt=0

=0

SV(f,p)

Foxes, f

160

SP h= hSV(f,p)

5036

rameter c can be determined by the formula ∫ ½c=pdp ¼ 5; 000; 000⇒ 1

h= hmax

c ln ð5036Þ ¼ 5; 000; 000, which indicates that c is 586,554.

A

3.3. Pig Removal Now consider optimal ecosystem management. This is the program that maximizes the value from the fox–pig ecosystem by recognizing that the economic damages from the pigs arise from their impact on

Pigs, p Fig. 2. Feedback control diagram of the singular solution, i.e. the pig control strategy. Note the change in scale from Fig. 1.

R.T. Melstrom / Ecological Economics 107 (2014) 157–162

p

Population

Population

Population

f/10

f/10

f/10

p

h

h

(a)

161

Time

Time

(b)

Time

(c)

Fig. 3. Time paths of f, p and h for the optimal pig control strategy (a), an alternative control strategy that adjusts p to the interior equilibrium level immediately (b) and the eradication strategy (c).

control strategy yields SNB of $238.3 million, which is only slightly less than the value of the pig control strategy. The final candidate strategy is pig eradication. Employed efficiently, this strategy will remove all pigs as quickly as possible, as any delay can only increase damages and future control costs. After pigs are eradicated (which is modeled as culling p ≤ 1), the foxes recover to their carrying capacity. The time path of this solution is presented in Fig. 3(c). This strategy yields SNB of $239.3 million, which makes pig eradication first-best, under the benchmark parameter values. The near-equivalence between the SNB of the eradication and two pig control strategies arises because the tradeoffs between the three are rather minor. All of the strategies involve a large initial cull, which allows the fox population to steadily recover over roughly the same period of time. The advantage of a larger cull is that it allows the foxes to recovery more quickly. Recovery is therefore fastest when pigs are eradicated. This, combined with the fact that a pig control program is persistently costly, makes eradication the ideal policy although it is the most expensive in the short run. Likewise, comparing the two pig control strategies, the preferred strategy is the one that uses a larger initial cull.

in Chambers and Whitehead (2003) were used to initially develop alternative benefit estimates for the foxes. For the interior solution, simulations show that a smaller WTP amount makes pig control less worthwhile, which yields fewer foxes and more pigs in equilibrium. On the other hand, a larger WTP amount means more foxes and fewer pigs in equilibrium. Furthermore, when the removal costs are less there should be more stringent pig control, benefiting the foxes, and when the removal costs are more there should be fewer investments in pig control, to the detriment of the foxes. However, in all of these scenarios, pig eradication remains the first-best strategy. WTP must be substantially smaller than the benchmark value to make pig control the preferred strategy. Specifically, Table 1 shows that pig control generates higher net benefits compared with pig eradication only once annual WTP per household is a few dollars. Now, compared with the benchmark scenario, the complete recovery of the fox population is worth much less, making large investments in pig removal (as required by the eradication strategy) suboptimal. Next, consider changes to the discount rate. This portion of the sensitivity analysis will reveal whether the optimal management strategy is sensitive to the treatment of economic values over time. Relative to the benchmark pig control strategy, a smaller discount rate leaves more foxes and fewer pigs in equilibrium, while a larger discount rate has the opposite effect. Pig eradication remains the optimal strategy in the former scenario but becomes suboptimal in the latter. This is because a higher discount rate places more weight on current values and in the short run pig eradication is more costly than pig control. Further simulations reveal that the break-even point for the discount rate with regard to eradication versus control is about 0.067.

3.4. Sensitivity Analysis of Economic Parameters There was some uncertainty in the choice of economic parameters. In particular, the economic value of the foxes is unknown and so a proxy value was established using benefit transfer, and the discount rate was assumed. So consider a sensitivity analysis to study how changing these parameters affects the results (Table 1). First, the 95% confidence interval bounds on the WTP estimate reported

Table 1 Simulation results of candidate management strategies. Model scenario

Parameter change

No control SNB

Benchmark Fox WTP/household reduced to $12.15 Fox WTP/household increased to $36.84 Fox WTP/household reduced to $5.00 Removal cost halved Removal cost doubled Discount rate halved Discount rate doubled a b

Benefits are in millions of dollars. Steady state populations.

N/A v = 1,016,805 v = 3,082,053 v = 502,126 c = 293,277 c = 1,173,108 ρ = 0.025 ρ = 0.10

a

157.2 88.9 269.4 36.6 157.2 157.2 288.3 82.7

Pig control f

b

1513 1485 1526 1373 1529 1477 1529 1473

Pig eradication b

a

p

SNB

98 184 56 538 47 212 46 222

238.4 132.6 412.4 52.0 241.1 233.4 497.3 111.4

SNBa 239.3 133.1 413.6 51.9 241.8 234.3 501.3 110.4

162

R.T. Melstrom / Ecological Economics 107 (2014) 157–162

4. Discussion and Conclusion This paper examined the tradeoffs involved in controlling a pest that negatively impacts ecosystem services. The objective of pest control is to reduce lost ecosystem service values, but the source of these values cannot be taken for granted. Removing a pest will not immediately replace lost values because ecosystems are dynamic and it takes time for wildlife to recover. Furthermore, it is important to account for the secondary effects of pest management, which arise due to the feedback responses between pests and other species. For example, as a pest control program proceeds over time, interspecific competition from recovering native species may exert negative pressures on the pest, which may help to reduce the magnitude and costs of a control program. The application of the model to the feral pig problem on Santa Cruz Island provides insights into managing an ecosystem pest problem. The ideal perpetual control program initially over-culled the pig population relative to the equilibrium level, which itself had relatively few pigs compared with the no-control outcome. Over the long run, this containment policy allowed the fox population to nearly reach carrying capacity. Nevertheless, this strategy was suboptimal to pig eradication at benchmark parameter values. Additional modeling simulations suggested that this result is sensitive to changes in the discount rate and, therefore, that the temporal distribution of the costs and benefits of pig management matters. In evidence, the pig control strategy, which had relatively fewer costs in the early years of management, became optimal once the discount rate equaled or was greater than 7%. This threshold lies within the range of values commonly used for calculating net present values in cost-benefit analysis. Consequently, these results cannot be used to determine with certainty whether the 2006 Santa Cruz Island pig eradication plan was optimal, although they do suggest that from an economic standpoint it was not an unreasonable policy. In conclusion, removal strategies can be used to efficiently recover wildlife populations damaged by a pest or invasive species. Of course, the optimal removal strategy is significantly determined by the value of the impaired resource, which is not well known for many ecosystem management problems that involve nonuse valued species. Nonmarket valuation of wildlife, especially endangered species, therefore remains an important issue in bioeconomic research. References Barbier, E.B., 2001. A note on the economics of biological invasions. Ecol. Econ. 39 (2), 197–202. Burnett, K., Kaiser, B., Pitafi, D.A., Roumasset, J., 2006. Prevention, eradication, a containment of invasive species: illustrations from Hawaii. Agric. Resour. Econ. Rev. 35 (1), 63–77. Burnett, K.M., D'Evelyn, S., Kaiser, B.A., Nantamanasikarn, P., Roumasset, J.A., 2008. Beyond the lamppost: optimal prevention and control of the Brown Tree Snaker in Hawaii. Ecol. Econ. 67 (1), 66–74. Ceddia, M.G., Heikkilä, J., Peltola, J., 2009. Managing invasive alien species with professional and hobby farmers: insights from ecological-economic modelling. Ecol. Econ. 68 (5), 1366–1374. Chambers, C.M., Whitehead, J.C., 2003. A contingent valuation estimate of the benefits of wolves in Minnesota. Environ. Resour. Econ. 26 (2), 249–267. Clark, C.W., 1990. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. John Wiley & Sons, New York. Coonan, T.J., 2003. Recovery strategy for island foxes (Urocyon littoralis) on the northern Channel Islands. National Park Service, Channel Islands National Park, Ventura, California. DeCesare, N.J., Hebblewhite, M., Robinson, H.S., Musiani, M., 2010. Endangered, apparently: the role of apparent competition in endangered species conservation. Anim. Conserv. 13 (4), 353–362.

Eiswerth, M.E., Johnson, W.S., 2002. Managing nonindigenous invasive species: insights from dynamic analysis. Environ. Resour. Econ. 23 (3), 319–342. Eiswerth, M.E., van Kooten, C.G., 2002. Uncertainty, economics, and the spread of an invasive plant species. Am. J. Agric. Econ. 84 (5), 1317–1322. Eppink, F.V., van den Bergh, J.C.J.M., 2007. Ecological theories and indicators in economic models of biodiversity loss and conservation: a critical review. Ecol. Econ. 61 (2–3), 284–293. Feder, G., Regev, U., 1975. Biological interactions and environmental effects in the economics of pest control. J. Environ. Econ. Manag. 2 (2), 75–91. Fenichel, E.P., Horan, R.D., Bence, J.R., 2010. Indirect management of invasive species through bio-controls: a bioeconomic model of salmon and alewife in Lake Michigan. Resour. Energy Econ. 32 (4), 500–518. Finnoff, D., Tschirhart, J., 2005. Identifying, preventing and controlling invasive plant species using their physiological traits. Ecol. Econ. 52 (3), 397–416. Frésard, M., Boncoeur, J., 2006. Controlling the biological invasion of a commercial fishery by a space competitor: a bioeconomic model with reference to the Bay of St-Brieuc Scallop Fishery. Agric. Resour. Econ. Rev. 35 (1), 78–97. Friends of the Island Fox, 2014. Friends of the Island Fox. Web. (12 May, bhttp://www1. islandfox.orgN). Griggs, G.W., 2007. Island pig eradication completed. Los Angeles Times, (30 August). Gutierrez, A.P., Regev, U., 2005. The bioeconomics of tritrophic systems: applications to invasive species. Ecol. Econ. 52 (3), 383–396. Harper, C.R., Zilberman, D., 1989. Pest externalities from agricultural inputs. Am. J. Agric. Econ. 71 (3), 692–702. Horan, R.D., Melstrom, R.T., 2011. No sympathy for the devil. J. Environ. Econ. Manag. 62 (3), 367–385. Kar, T.K., Chauduri, K.S., 2003. On non-selective harvesting of two competing fish species in the presence of toxicity. Ecol. Model. 161 (1–2), 125–137. Melstrom, R.T., Horan, R.D., 2014. Interspecies management and land use strategies to protect endangered species. Environ. Resour. Econ. 58 (2), 199–218. Morrison, S.A., 2011. Trophic considerations in eradicating multiple pests. In: Veitch, C.R., Clout, M.N., Towns, D.R. (Eds.), Island Invasives: Eradication and Management. IUCN, Gland, Switzerland, pp. 208–212. National Invasive Species Council (NISC), 2008. 2008–2012 National Invasive Species Management Plan. National Invasive Species Council, Washington, D.C. National Park Service (NPS), 2002. Santa Cruz Island Primary Restoration Plan. Final Environmental Impact Statement. Channel Islands National Park, Santa Cruz Island — Santa Barbara, California. Olson, L.J., 2006. The economics of terrestrial invasive species: a review of the literature. Agric. Resour. Econ. Rev. 35 (1), 178–194. Olson, L.J., Roy, S., 2008. Controlling a biological invasion: a non-classical dynamic economic model. Economic Theory 26 (3), 453–469. Pannell, D.J., 1990. An economic response model of herbicide application for weed control. Am. J. Agric. Econ. 34 (3), 223–241. 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. Roemer, G.W., 2004. Island foxes. In: Macdonald, D.W., Sillero-Zubir, C. (Eds.), The Biology and Conservation of Wild Canids. Oxford University Press, New York, pp. 173–183. Roemer, G.W., Coonan, T.J., Garcelon, D.K., Bascompte, J., Laughrin, L., 2001. Feral pigs facilitate hyperpredation by golden eagles and indirectly cause the decline of the island fox. Anim. Conserv. 4 (4), 307–318. Roemer, G.W., Donlan, C.J., Courchamp, F., 2002. Golden eagles, feral pigs, and insular carnivores: how exotic species turn native predators into prey. Proc. Natl. Acad. Sci. 99 (2), 791–796. Settle, C., Shogren, J.F., 2002. Modeling native–exotic species within Yellowstone Lake. Am. J. Agric. Econ. 84 (5), 1323–1328. Settle, D., Crocker, T.D., Shogren, J.F., 2002. On the joint determination of biological and economic systems. Ecol. Econ. 42 (1–2), 301–311. Sims, C., Aadland, D., Finnoff, D., 2010. A dynamic bioeconomic analysis of mountain pine beetle epidemics. J. Econ. Dyn. Control. 34 (12), 2407–2419. Skonhoft, A., Olaussen, J.O., 2005. Managing a migratory species that is both a value and a pest. Land Econ. 81 (1), 34–50. Tschirhart, J., 2009. Integrated ecological-economic models. Ann. Rev. Resour. Econ. 28, 1–27. Zavaleta, E.S., Hobbs, R.J., Mooney, H.A., 2001. Viewing invasive species removal in a whole-ecosystem context. Trends Ecol. Evol. 16 (8), 454–459. Zivin, J., Hueth, B.M., Zilberman, D., 2000. Managing a multiple-use resource: the case of feral pig management in California rangeland. J. Environ. Econ. Manag. 39 (2), 189–204.