Control of Invasive Species: Lessons from Miconia in Hawaii

Transcription

1 Cotrol of Ivasive Species: Lessos from Micoia i Hawaii by Brooks Kaiser, Gettysburg College ad Uiversity of Hawaii at Maoa, Kimberly Burett, Departmet of Ecoomics, Uiversity of Hawaii at Maoa, ad James Roumasset, Departmet of Ecoomics, Uiversity of Hawaii at Maoa Workig Paper No April 11, 2006 Abstract Oce established, ivasive species ca rapidly ad irreversibly alter ecosystems ad degrade the value of ecosystem services. Optimal cotrol of a exotic pest solves for a trajectory of removals that miimizes the preset value of removal costs ad residual damages from the remaiig pest populatio. The shrubby tree, Micoia calvesces, is used to illustrate dyamic policy optios for a forest ivader. Potetial damages to Hawaii's forest ecosystems are related to decreased aquifer recharge, biodiversity, ad other ecosystem values. We fid that populatio reductio is the optimal maagemet policy for the islads of Oahu, Maui, ad Hawaii. O the islad of Kauai, where tree desity is lower ad search costs higher, optimal policy calls for deferrig removal expeditures util the steady state populatio is reached. JEL Classificatio: Q23, Q51, Q57 Address: James Roumasset, Professor, Departmet of Ecoomics, Uiversity of Hawaii at Maoa, 2424 Maile Way, Hoolulu, HI Phoe: (808) Fax: (808) <jimr@hawaii.edu>

2 1. Itroductio Ivasive species chage ecosystems ad the ecoomic services that ecosystems provide. Policy decisios regardig existig ivasive species must compare the aticipated ad actual costs ad beefits of ay mitigatig actios oce a species has become established to the aticipated costs ad beefits of accommodatig the chage. Optimal policy regardig ivasive species will miimize the expected damages ad costs of cotrol withi a ecosystem. Theoretical treatmet of ivasios itroduces coditios for eradicatio (Olso ad Roy, 2002), policy optios uder ucertaity (Hora et al, 2002; Eiswerth ad va Koote, 2002; Olso ad Roy, 2002), ad itegrated prevetio ad cotrol (Pitafi ad Roumasset, 2005). Here, we seek to apply the theory to the case of a ivasive shrubby tree, Micoia calvesces, ow preset i Hawaii. By testig the theory with a real-world case, we ited to highlight both the usefuless of the theory ad its limitatios. The case of Micoia is used to illustrate dyamic policy optios for forest ivasive species that are already preset i a ecosystem. Hawaii s forest ecosystems provide direct ad idirect ecosystem services, with high expected value geerated from the preservatio of existig ecosystem coditios stemmig from uique biodiversity assets. Micoia geerates cocers that exted from biodiversity to ifrastructure for water supply as it threates moist tropical islad watersheds ad forest ecosystems. I most if ot all cases, the most costly aticipated chages are irreversible. Due to the eed to aticipate irreversible chage, policy decisios may vary with the status of ecosystem health, i.e. the levels of ivasio ad the immiece of the threat. I this work, we seek to explai how biology ad ecoomics work together to determie policy. To improve outcomes ad avoid costly mistakes ragig from deyig beeficial itroductios to spedig good moey o ecologically impossible cotrol or eradicatio efforts, these policies must be see as a cotiuous effort to maage ecosystems rather tha separate decisios hadled as emergecies as they arrive. A case study approach allows us to ivestigate how useful the existig ecoomic theory of ivasios will be at facilitatig these efforts. 2. Case Overview: Micoia Calvesces Oe sigificat threat to Hawaii s forest ecosystems comes i the form of the woody shrub, Micoia calvesces. A member of the Melastomataceae family from Cetral America, the plat was purposefully itroduced to Hawaii. Startig i a hadful of back yards ad arboretums four decades ago, it has bee spreadig with icreasig rapidity o the islads of Maui ad Hawaii. It is also preset o Kauai ad Oahu, though it has ot yet claimed sigificat acreage i either locatio. Micoia is ot thought to be preset o the islad of Molokai. A model of its potetial expasio ad damages is available through compariso with Tahiti, where dese, mootypic stads of the tree ow cover 65% or more of the mai islad after a sigle specime was itroduced to the Papeari Botaical Garde i 1937 (Medeiros, Loope et al. 1997). Micoia has eared itself descriptors like the gree cacer of Tahiti ad the purple plague of Hawaii. Vast tracts of Micoia have wiped out ative forest ad reduced 2

3 forest cover, icreasig the potetial for soil erosio, ladslides, ad damages to ear-shore resources. The explosive growth ad potetial damages were ot appreciated i Tahiti util the 1980s, however. By that time, Micoia was already established i Hawaii. The damages i Tahiti ad the potetial threats to Hawaiia biodiversity ad forested watersheds have redered Micoia a priority weed i Hawaii. Sice the early 1990s, millios of dollars have bee spet i the battle agaist its spread, though success at spatial cotaimet o Hawaii ad Maui ad eradicatio o Oahu ad Kauai remais at bay. We explore quatitatively the policy optios ad their ecoomic cosequeces for the cotiued treatmet of the ivasio i the modelig ad discussio sectios below. 3. Methodology: Optimal cotrol of a Existig Ivader As the theoretical literature metioed above demostrates, optimal cotrol theory provides a excellet methodology for cosiderig ecoomic policy toward ivasive species. Usig optimal cotrol, we defie our problem so that we miimize the expected costs ad damages from the presece of ad cotrol activities udertake agaist the ivadig species. Thus the objective fuctio is: rt MAX e c( γ ) dγ + D( ) dt 0 -x subject to: = g( ) x (1) 0 x (2) 0 give, (3) where ad are the populatio of the ivasive species ad its associated time derivative, g() the growth fuctio of the ivasive, x represets the umber of removals, c() the margial cost fuctio for removals, which varies with populatio level, ad D() the damages icurred at populatio. 3.1 Mitigatio without Eradicatio: Iteral Solutios We first seek a iteral solutio for the choice of cotrol level x i the stadard maer (e.g. Clark, 1990), defiig the curret value Hamiltoia as: H = c( γ ) dγ D( ) + λ[ g( ) x]. -x Applicatio of the Maximum Priciple (assumig a iterior solutio for x) geerates first order coditios: H x = c( x) λ = 0 (4) 3

4 H = [ c( ) c( x)] D '( ) + λg '( ) = rλ λ (5) H = g ( ) x = λ (6) Takig time derivatives of (4) yields λ = c '( x)( x ) (7) Substitutig (4), (6), ad (7) ito (5) yields c( ) + D '( ) + [ g '( ) r 1] c( x) x = g( ) x +. c '( x) (8) Optimal harvest of the ivasive species will result i a steady state populatio whe x = = g( ) x ad thus c( ) + D '( ) + [ g '( ) r 1] c( x) = 0, (9) c '( x) or c( ) D '( ) = [ g '( ) r 1] c( x). (10) I other words, the margial costs ad damages of the steady state populatio (LHS) must be just equal to the margial opportuity costs of maitaiig that populatio (RHS). If the LHS is greater tha the RHS, we should be icreasig the harvest rate, while if the LHS is less tha the RHS, we should be decreasig the harvest rate. 3.2 Eradicatio or Accommodatio: Corer Solutios The iteral solutio must be compared to alterative policy optios of eradicatio (x*=) or accommodatio (x*=0). Thus, we compare the preset value of eradicatio ad accommodatio policies to the preset value of the iteral solutio to determie if the iteral solutio is domiated by either alterative. The optimal policy for a existig ivader ca the be summarized by cosiderig first where the populatio is i relatio to a optimal steady state populatio, as determied by miimizig the preset value of damages ad cotrol costs across a ifiite time horizo. If the populatio is curretly at this steady state populatio, ew growth should be cotiually harvested at the steady state, geeratig a stream of miimized ecoomic costs ad damages idefiitely, uless eradicatio or accommodatio has a lower expected preset value of costs ad damages. If the populatio is curretly above the steady state populatio, cotrol costs should be expeded to reduce the populatio to its steady state ad the maitai that populatio, 4

5 uless, agai, a corer solutio is preferable. If the populatio lies below the steady state populatio, damages should be accumulated as the populatio grows which are lower tha the costs of maitaiig these lower populatios, util at the steady state populatio maiteace is iitiated as described above. 4. Empirical Ivestigatio We ivestigate empirically the case of Micoia calvesces, discussed above. We determie cost, damage, ad growth fuctio parameters with the help of scietists researchig the species ad resource maagers actively pursuig Micoia cotrol. As potetial habitat size, costs of cotrol, ad damages vary widely across space, we specify each by islad. The parameters are discussed below, followed by results. 4.1 Growth Fuctio We utilize a stadard logistic growth fuctio to represet the spread of the ivasive tree. Thus: g( ) = b1, N max (11) where b is the itrisic growth rate, assumed here to be 0.3, ad N max is the carryig capacity, estimated to be 100 trees per acre over 1.2 millio acres, or 120,000,000. The carryig capacity is determied by the chief limitig factor for Micoia i Hawaii, precipitatio, so the potetial rage idicates areas above the 1800 mm/yr raifall lie as delieated i state GIS data (DBEDT, 2005). The growth rate was determied by aalyzig the spread of the tree o Hawaii, where we kow the origis of the first populatio ad its spread util harvestig bega i the mid 1990s. The stadard logistic fuctio is chose because a sigle tree is capable of startig a populatio. The seed bak is ot addressed directly by the growth fuctio; istead, we rely o the eed to retur to a tree to treat its seed bak over time to build i the effects of the seed bak o reducig the effectiveess of cotrol cost expeditures (see cost fuctio discussio). Carryig capacities for each islad are listed i Table 1. Table 1. Carryig Capacity by islad Islad N max Kauai 15,849,057 Oahu 8,713,551 Maui 14,133,791 Hawaii 78,216,124 Molokai 3,087,479 5

6 4.2 Damage (Net Beefit) Fuctio We estimate damages from Micoia as evolvig from idirect ecosystem services as well as o-market goods like biodiversity. Particularly sigificat threats are a reductio i habitat for edagered species ad a shift i the hydrological cycle that may reduce freshwater recharge ad icrease ruoff ad sedimetatio. Figure 1 illustrates the potetial rage for Micoia ad the primary biological resources threateed by ivasio. Figure 1. Micoia s Rage ad Damage Potetial The characteristics of the species that have braded it a uisace species have three major dimesios for potetial damages. First, it is a aggressive ivader that appears to ivade healthy ative forest with success (Meyer 1998). Native forest ad its biodiversity are replaced with dese, mootypic stads of Micoia that shade out all udergrowth ad may chage soil chemistry. Secod, the seed bak develops quickly oce the tree reaches flowerig ad fruitig size of 4-5 meters (4 cm dbh; at least 4-5 years of age) as a sigle tree ca flower ad fruit 2-3 times a year, with a typical fruitig evet producig 3 millio seeds (Loope 1997). Third, the seed bak has some logevity. It is kow to last over 2 years, ad may be as log as 10 years (Loope 1997; D. Duffy persoal commuicatio 2005). Caopy opeigs are quickly take advatage of by ew seedligs. Wid dispersal appears most prevalet, though birds are also 6

7 dispersal agets. With sufficiet raifall (greater tha 1800 mm / yr) ad caopy opeigs, a sigle specime may, i 5-15 years, start a stad that covers several hudred acres. Hawaii is home to a great percetage of the Uited States ad the world s idetified edagered species. Chages i forest compositio as described may threate edagered plat species, bird species, ad ivertebrate species i particular. Hawaii s evolutioary isolatio has led to much adaptive radiatio of species, where a sigle acestor has geerated a set of species that each deped o ew ad differet types of habitat; the state is cosidered to house the most uique ad diverse sail populatio i the world despite the limitatio that oly 15% of sail families are represeted (Asquith 1995). The wet, higher elevatios of Maui ad Hawaii cotai most of the oly healthy remaiig ative forest supportig such diversity i the state, ad are ow threateed by Micoia. For example, the upper Kipahulu Valley o Maui is a coservatio district reserve cotaiig stads of Ohia (Metrosideros polymorphata) ad Koa (Acacia koa) that are the primary habitat for rare ative Hawaiia birds ad isects, ad Micoia has bee discovered i the lower valley (Staff 2001). I the federal register listig materials for the edagered Elepaio (Chasiempis sadwichesis) bird o Oahu, the mai justificatio for protectio is based o the bird s reliace o the curret forest structure (see Service 2001 for example). Sice Micoia poses a sigificat threat to that structure, the plat is listed directly as oe of the cocers for the bird s survival. A set of studies idicates that, o average, each household would be willig to pay $31 (95% cofidece iterval of $16.66-$48.92) per bird species per year to keep a species from extictio (Loomis ad White 1996). This amouts to a aual value for Hawaii state residets of $12.4 millio per avia species preserved. From the cofidece iterval, we assume the damages would lie betwee $6.7m ad $19.6m. Ecoomic theory ad research predicts that households will value ivertebrates ad plats at lower levels (Loomis ad White 1996), ad that o-residets will also have lower aggregate values. For these reasos, we focus o bird losses to provide a lower boud estimate of expected damages. Additioally, damages to watershed fuctios are expected from dese stads of Micoia. The hydrological properties of Micoia suggest that there may be a sigificat chage i the water balace, with a icrease i ruoff ad a potetial reductio i groudwater recharge 1. Estimates of potetial expected losses from a ivasio of Micoia o Oahu to groudwater recharge suggest that a loss of 41 millio gallos per day (mgd) would geerate ecoomic losses of $137 millio per year (Kaiser ad Roumasset 2002), or $3.3 millio per mgd. Additioally, icreased surface water ruoff is expected to icrease damages by $1.2 millio per mgd reductio i groudwater due to icreased sedimetatio costs (Kaiser ad Roumasset 2000). Figure 2 illustrates the groudwater assets at risk. 1 The particular role of Micoia i groudwater recharge is ucertai; o the oe had, icreased ruoff suggests there is less water available for recharge, but chages i evapotraspiratio rates may couteract this loss. Surveys of forested watershed experts list Micoia as a very serious threat, however (see for survey results o threats to watershed quality o Oahu). 7

8 Figure 2. Groudwater Resources ad Micoia Table 2 shows the expected maximum damages (from a complete accommodatio of the ivasio) by islad, givig a low, medium, ad high estimate. We calculate damages by first compilig the assets at risk for each islad i terms of threateed or edagered bird species ad groudwater recharge to aquifers (mgd). The the dollar figures described above are icluded accordigly. The umber of threateed or edagered bird species o the islad is show i colum 2 of Table 2. We coservatively assume that ½ of these birds is at risk from habitat loss to Micoia, (Figure 1 illustrates), ad that residets of Hawaii value birds equally regardless of whether they are o the same islad as the household or ot, while o-hawaiia household values are ot cosidered though they certaily would icrease expected damages. We ca the calculate a lower boud rage of damages by usig half the umber of birds per islad multiplied by the umber of households i Hawaii (400,000) ad the estimated loss to a household from a bird s extictio. Note agai this is expected to be a coservative estimate i that it oly icludes beefits to the state residets, ad that eve though virtually all of the species live i the same pristie habitat that the tree is likely to ivade, we cout at most half of the birds as threateed by the potetial ivasio. The ucertaity associated with this estimate is particularly high; we create a rage of estimates usig the 95% cofidece iterval to uderscore a portio of this ucertaity. The potetial loss to aquifers is calculated by first summig the sustaiable yield estimates from the HI Departmet of Lad ad Natural Resources (show i Figure 2) for aquifers that lie beeath potetial Micoia habitat. The, usig estimates take from survey data of forested watershed experts i Oahu regardig the expected icrease i ruoff that would occur with a shift i forest structure to oe domiated by Micoia (Kaiser ad Roumasset, 2005), we 8

9 calculate the expected aual reductio i recharge for these areas. The surveys of experts idicate that a 0.85% to 1.04% aual decrease i ruoff might occur. We determie a lower boud ad a upper boud estimate for lost recharge damages by multiplyig these decreases by the sustaiable yield. A dollar value is attached by multiplyig this groudwater loss by $4.5 millio ($3.3 millio i groudwater + $1.2 millio i surface water geerated losses). Table 2: Damage Estimate Characteristics by Islad mgd lost recharge (aual) Total aual damages by islad (millios) Islad # birds low high Low Medium High Kauai Oahu Maui Big Islad Molokai 11 N/A N/A Total expected damages for ay give populatio are described by the fuctio 2 : D( ) = di, (12) Where d i is the liearized per-uit medium damage estimate as show i Table 4 below. 4.3 Cotrol Cost Fuctio Cotrol efforts bega o Maui i 1991 ad cotiue to expad o the four ivaded islads. Cotrol i these areas begis with recoaissace i helicopters to idetify ifestatios ad is followed by either herbicide treatmet from the helicopters themselves or by operatios o the groud to treat or maually pull the trees. I ay case, there are two separate activities that must occur the trees must first be foud, the treated. We therefore defie a cost fuctio cosistig of two parts, the search compoet ad the treatmet compoet. While the uit cost of treatig a tree with herbicide ad/or cuttig a tree may be costat across populatio levels, the cost of fidig a tree is rapidly decreasig i populatio size. That is, it is extremely expesive to fid the last tree, but much less so to fid oe tree out of 120 millio trees. Because each islad is uique i aspects such as topography, area, ad vegetatio, it is helpful to estimate separate cost of cotrol fuctios for all five major islads. We determie the two compoets for each islad i the followig maer. The search compoet ivolves a fixed 2 For simplicity, we assume a uiform distributio fuctio where ay tree cotributes to the loss equally, give the existig populatio level, ad the cumulative distributio as the probability of total losses for ay give populatio,, is just /N max. We assume N max is 120,000,000 plats, based o a desity of 100 plats per acre ad 1,200,000 potetial acres of habitat. To model a potetially more realistic situatio where the damages are icreasig at a icreasig rate with populatio, the beta distributio might be preferred. 9

10 cost which depeds o the islad s potetial habitat acreage ad which decreases with icreased access to that habitat. Based o discussios with resource maagers, searchig oe average acre for Micoia costs approximately $1,000. Therefore, the umerator of the search compoet is obtaied by multiplyig the umber of potetial acres by $1,000. However, the ability to search a islad s habitat will deped o several characteristics of the surroudig area, such as desity of vegetatio, the steepess of the terrai, etc. Oe major determiat is ease of access ito the potetial habitat. We use the combied legth of roads ad trails as a proxy for this variable. The legth of roads ad trails as compared to Molokai, the most expesive islad to search because it has the fewest roads ad trails per acre of habitat, is used to determie the coefficiet i the deomiator of the search compoet. Higher values for imply greater ease of access, which traslate ito lower search costs. $1, 000* potetial acres σ ( x) =, τ ( x) = 13.39, γ where σ ( x) represets the search cost compoet ad τ ( x) represets the cost of treatmet, costat across all populatio levels. Total margial cost is thus defied as: $1, 000* potetial acres c(, x) = σ ( x) + τ ( x) = , so that the total cost of searchig ad treatig x trees is: γ $1, 000* potetial acres c(, x) = * x γ (13) While search costs will differ across islads, we assume that treatmet costs remai costat across islads. We begi by fittig these fuctios for the islads of Oahu ad Maui. While the exact budget for all islads is ucertai, we do have a good uderstadig of cotrol budgets o Oahu ad Maui. Oahu Ivasive Species Committee allocated $321,000 to Micoia cotrol i 2005 (Rya Smith, persoal commuicatio) while Maui expeds approximately $1 millio per year o Micoia related activities (Teya Peima, persoal commuicatio). These status quo levels of expeditures, alog with estimates of curret populatios, allow us to parameterize the cotrol fuctio appropriately. Specificatios for each islad s cotrol costs are give i Table 3. Table 3: Cost of Cotrol Fuctio Parameters Islad Search Costat (acres*1000) Search Coefficiet () Kauai 158,490, Oahu 87,135, Maui 141,337, Treatmet Coefficiet

11 Big Islad 782,161, Molokai 30,874, Optimal Cotrol Results Usig the parameters calculated above ad the assumptio that the curret stock of Micoia i Hawaii is give by the iitial populatios listed with the summary of parameters i Table 4, we fid the followig. Optimal policy calls for populatio reductio o the islads of Oahu, Maui, ad Hawaii, populatio expasio o Kauai, ad cotiued prevetio o Molokai. Table 4: Summary of Bio-ecoomic Parameters Islad 0 K Coefficiet o Damage fuctio Cost of cotrol fuctio 158, 490,570 Kauai 1,540 15,849, * x 87,135,510 Oahu 6,890 8,713, * x 141,337,910 Maui 111,050 14,133, * x 782,161, 240 Hawaii 315,000 78,216, * x 30,874,790 Molokai 0 3,087, * x Differeces i steady state populatios are maily the result of variatios i search costs ad potetial habitats. For example, the populatio o Kauai is curretly too small, that is, the high search cost calls for waitig util the populatio is larger to ivest i harvestig. Although the damage per tree is sigificat, it does ot outweigh the magitude of the search compoet of cotrol. O the islad of Oahu, however, ease of access to Micoia habitat is facilitated by the comparatively large amout of roads ad trails o the islad. Furthermore, the search cost o Oahu is almost half that of Kauai (due to fewer potetial acres of habitat). Therefore, we fid reductio of approximately 1,400 trees to be optimal. Maui ad Hawaii have lower per uit expected damages tha Oahu, ad higher search costs due to both greater amouts of habitat ad more difficult access. While optimal populatios are higher tha Oahu ad Kauai, sigificat reductios of the Maui ad Hawaii populatios are preferred to the curret state. Because there are curretly o trees kow to exist o the islad of Molokai, the complete solutio requires a itegrated model of prevetio ad cotrol (see e.g., Burett et al. 11

12 2006). For illustrative purposes, we fid that if prevetio fails ad a populatio establishes o the islad, we fid the steady state populatio occurs at 2,300 trees. At this level, aual costs of the ivasio are miimized at $149,000, sigificatly higher tha curret moitorig expeditures of $13,500. Table 5. Iitial versus Optimal Populatios for the Five Major Hawaiia Islads Islad * 0 Kauai 1,540 9,171 Oahu 6,890 5,495 Maui 111,050 8,901 Hawaii 315,000 39,937 Molokai 0 0 While the results for Micoia suggest a iteral optimum, a species with differet bio-ecoomic parameters may require a corer solutio of accommodatio or eradicatio. We explore this possibility ad illustrate how our model ca facilitate these results i the Appedix. 4.5 Status Quo vs. Optimal Policy Curret Micoia policy i Hawaii etails spedig differet amouts o cotrol efforts o each islad. As a fial exercise for this species, we compare the cosequeces of status quo spedig to those associated with the optimal policy program for Oahu ad Maui i order to ivestigate the extet to which status quo expeditures may be misaliged with optimal expeditures. We also highlight cosequeces of two other potetial policies: doig othig, or spedig o cotrol i order to remai at the same iitial populatio forever. Comparisos are draw i Table 6 below. Table 6. Preset Value Policy Comparisos for Oahu ad Maui Islad Policy Do othig Remai at curret populatio forever Status quo spedig Optimal policy of populatio reductio Oahu $3.08 billio $10.5 millio $16.9 millio $10.4 millio Maui $4.6 billio $73.5 millio $51.7 millio $17.2 millio From Table 6, we see that if Oahu switches to the optimal policy of populatio reductio istead of spedig $321,000 per year from today ito the future, a preset value beefit of $6.5 millio ca be realized. Likewise, if Maui switches to their optimal policy of populatio reductio, a et preset value beefit of $34.5 millio is possible. The differece is more sigificat for Maui due to their larger curret populatio ad higher cost of cotrol. 12

13 5. Cocludig remarks Usig optimal cotrol theory, we geerate appropriate comparisos for policy optios cocerig a existig ivasive species. For the islads aalyzed, we show that the status quo policy for Micoia is iefficiet. The removal expeditures o Oahu, Maui, ad Hawaii are iadequate to remove aual growth ad therefore simply postpoe the growth of the pest populatio towards carryig capacity ad high, sustaied damages. The optimal policy ivolves spedig more ow to reduce the populatio thus allowig lower removal expeditures i the future. Potetial gais from switchig to the optimal policy are large. O Maui, for example, cotiuig to sped oe millio dollars o removal each year results i a preset value of $51.7 millio i removal ad damage costs. Switchig to the status quo reduces those costs to $17.2 millio. A stitch i time saves ie. I cotrast, optimal expeditures o Kauai are less tha what is curretly beig spet. This is largely because of high search costs ecessitated by the vast dese ad rugged habitat. Optimal policy calls for spedig othig o removal util the populatio size makes growth more affordable. I computig the optimal outcomes for Micoia, we ecoutered quatitative challeges regardig the specificatio of fuctioal forms for all three essetial compoets: costs, damages, ad growth. I particular, choosig fuctioal forms that both accurately reflected our uderstadig of the biological ad ecoomic processes ad resulted i computatioally feasible equatios required several simplificatios upo which further research might improve. For example, we chose to model the seed bak by assumig that the removal of a sigle tree would require re-treatmet over time. This subsumes the removal of future growth from seeds ito the cost of removig the paret tree ad avoids the eed for delay-differetial equatios, which would greatly complicate computatios. We also abstracted away from importat spatial cosideratios of the problem. It may be desirable to cosider strategies such as cotaimet of the core (dese, origial ifestatios) or satellite (more sparse, spread out offsprig) populatios of Micoia. While spatial elemets are implicitly represeted with search cost fuctios that differ across islads ad iclude cosideratios of access, it would be useful to model these cosideratios more explicitly. 13

14 Bibliography Asquith, A Alie Species ad the Extictio Crisis of Hawaii s Ivertebrates. Edagered Species Update 12(6): Burett, K., B. Kaiser, B. Pitafi, ad J. Roumasset Prevetio, Eradicatio, ad Cotaimet of Ivasive Species: Illustratios from Hawaii. Agricultural ad Resource Ecoomics Review 35(1). Clark, C Mathematcal Bioecoomics: The Optimal Maagemet of Reewable Resources, 2 d Ed. Hoboke, NJ: Wiley-Itersciece. Departmet of Busiess, Ecoomic Developmet, ad Tourism (DBEDT) Dowloadable layers. (accessed Jauary 2005). Eiswerth, M.E. ad G.C. va Koote Ucertaity, Ecoomics, ad the Spread of Ivasive Plat Species. America Joural of Agricultural Ecoomics 84(5): Hora, R.D., C. Perrigs, F.Lupi, ad E.H. Bulte The Ecoomics of Ivasive Species Maagemet: Biological Pollutio Prevetio Strategies uder Igorace. America Joural of Agricultural Ecoomics 84(5): Kaiser, B. ad J. Roumasset Valuig Watershed Coservatio for Groudwater ad Nearshore Ecology. Proceedigs of AWRA Summer Specialty Coferece, Hoolulu, HI, Jue 27-29, Kaiser, B. ad J. Roumasset Valuig Idirect Ecosystem Services: The Case of Tropical Watersheds. Eviromet ad Developmet Ecoomics 7(4): Kaiser, B. ad J. Roumasset Water Maagemet ad the Valuatio of Idirect Evirometal Services. Iterdiscipliary Evirometal Review 2(2): Loomis, J.B. ad D.S. White Ecoomic Beefits of Rare ad Edagered Species: Summary ad Meta-aalysis. Ecological Ecoomics 18(3): Loope, L.L HNIS Report for Micoia Calvesces. Hoolulu, USGS/BRD. Medeiros, A.C., L.L. Loope, P. Coat, ad S. McElvaey Status, Ecology ad the Maagemet of the Ivasive Plat, Micoia calvesces DC (Melastomataceae) i the Hawaiia Islads. Records of the Hawaii Biological Survey for 1996, Bishop Museum Occasioal Papers 48: Meyer, J.-Y Epidemiology of the Ivasio by Micoia Calvesces ad Reasos for a Spectacular Success. Proceedigs of the First Regioal Coferece o Micoia Cotrol, August 26-29, 1997, Papeete, Tahiti. Gouveremet de Polyésie fraçaise/uiversity of Hawaii at Maoa/Cetre ORSTROM de Tahiti. Olso, L.J, S. Roy The Ecoomics of Cotrollig a Stochastic Biological Ivasio. America Joural of Agricultural Ecoomics 84(5): Pitafi, B. ad J. Roumasset The Resource Ecoomics of Ivasive Species. Mauscript preseted at the NAREA Ivasive Species Workshop, held i Aapolis, MA Jue 14-15, Service, U.S.F.a.W Edagered ad Threateed Wildlife ad Plats; Reopeig of Commet Period ad Notice of Availability of the Draft Ecoomic Aalysis for Proposed Critical Habitat for the Oahu Elepaio. Departmet of the Iterior: Staff Oheo Gulch Etrace Fee to Help Micoia Eradicatio Program. Maui News, Maui, HI. 14

15 Appedix While we cojecture that our parameterizatio best describes the Micoia story i Hawaii, we repeat our aalysis usig differet fuctioal forms ad parameters for the damages ad costs to give a idicatio of the sesitivity of the results ad to explicate potetial chages i optimal policy as bio-ecoomic coditios chage. I particular, we examie chages i the cost fuctio that allow for the possibility of eradicatio ad chages i the damage fuctio that are o-liear ad/or allow for the possibility of accommodatio. 1. Alterative Fuctioal Forms for Damages: Cotrol versus Accommodatio The parameters above assume costat margial damages across populatio levels. If we istead use the icreasig margial damage fuctios 3 show i colum 2 of Table A1, we fid higher steady state equilibrium populatios, sice margial damages at lower populatios will be lower as the damages are delayed util the populatio is greater. Optimal policy still calls for populatio reductio o both Maui ad the islad of Hawaii due to their high iitial umber of trees ad thus high damages, but ow requires Oahu to egage i populatio expasio. This is a reflectio of the much lower damages 4 icurred at low populatio levels uder this damage fuctio. Table A1. Icreasig Margial Damages Islad Damage fuctio Kauai Oahu Maui Hawaii Molokai * 0 = ,540 20,009 = ,890 12,833 = ,050 18,787 = ,000 56,895 = D( ) 8*10 6*10 D( ) 2*10 1.3*10 D( ) 5* *10 D( ) 1* *10 D( ) 5*10 7.1*10 If damages are sufficietly small or sufficietly delayed, accommodatio may become more attractive tha cotrol. However, for this case, maximum damages would have to be over two orders of magitude smaller tha our miimum estimates to meet this coditio. For expositioal purposes, the liear coefficiets o demad for each islad for which the optimal iteral solutio ad accommodatio geerate equivalet preset value societal losses are provided i Table A2 below. Islad Table A2: Damage Specificatios: Cotrol versus Accommodatio Cotrol domiates accommodatio Cotrol ad accommodatio equivalet Maximum total damages below which accommodatio becomes optimal (d i K i ) 3 This damage fuctio was fitted such that total damages at the islad capacities match estimated damages, ad are equal to the liear damage values at =10% of capacity. 4 Smaller damages at lower populatio levels is a reasoable assumptio, i that most watershed ad biodiversity damage is expected to be bore uder dese stads of the trees, rather tha with a sparse umber of trees spread out aroud the islad. 15

16 d i * d i * Kauai , , x10 6 Oahu , , x10 6 Maui , , x10 7 Hawaii , , x10 7 Molokai x10 6 Islad 2. Lower Search Costs at Low Populatio Levels: A Case for Eradicatio As a third case, we cosider the possibility that the search costs for the last trees are ot so extravagat, ad that eradicatio costs are ot ifiite. This might correspod to a case where spatial cotaimet is possible, so that search could be limited i area. With both wid ad bird dispersal of Micoia seeds, this seems ulikely to be the case, but we cosider it for expository purposes. We make the followig adjustmets i cost fuctios, show i reducig both the fixed compoet of the search cost ad the rate at which costs declie. potetial acres c(, x) = * x ( ) γ, where we assume that search costs average to $1 per acre for the fial tree o each islad, or, alteratively, that the problem is spatially cofied ad we eed oly seek across about 1/1000 of the habitat. The coefficiets o search are reduced as show i Table A3, ad treatmet costs remai the same. The margial costs at 0 ad K are show for compariso to the existig data, which they match well. We use the liear demad fuctios whose coefficiets are listed i colum 2 of Table A2. Table A3: Reduced Cost Fuctios ad Optimal Populatios of Zero Search Search Costat Implied margial Coefficiet (potetial acres) cost at ( ) 0 Implied margial cost at K 0 * Kauai 158, $ $ ,540 0 Oahu 87, $ $ ,890 0 Maui 141, $ $ ,050 0 Hawaii 782, $ $ ,000 0 Molokai 30, $77, $ I this case, eradicatio is optimal o each islad for each iitial populatio. At the damage levels where there was before idifferece betwee accommodatio ad a iteral solutio, however, accommodatio is ow the cost effective strategy. I other words, these flatter margial costs, which impose slightly greater costs of removal at capacity (e.g. $19.8 vs. $13.4 for Kauai) geerate sufficietly large preset value costs so that accommodatio is preferable. 16