FORUM Eradication of Invasive Species: Why the Biology Matters

1,2,3 2,4 ANDREW PAUL GUTIERREZ AND LUIGI PONTI

Environ. Entomol. 42(3): 395Ð411 (2013); DOI: http://dx.doi.org/10.1603/EN12018 ABSTRACT Published bi- and tri-trophic physiologically based demographic system models having similar sub components are used to assess prospectively the geographic distributions and relative abundance (a measure of invasiveness) of six invasive herbivorous insect species across the United States and Mexico. The plant hosts and insect species included in the study are: 1) cotton/pink bollworm, 2) a fruit tree host/Mediterranean fruit ßy, 3) olive/olive ßy, 4) a perennial host/light brown apple moth, 5) grapevine/glassy-winged sharpshooter and its two egg parasitoids, and 6) grapevine/European grapevine moth. All of these species are currently or have been targets for eradication. The goal of the analyses is to predict and explain prospectively the disparate distributions of the six species as a basis for examining eradication or containment efforts against them. The eradication of the new world screwworm is also reviewed in the discussion section because of its pivotal role in the development of the eradication paradigm. The models used are mechanistic descriptions of the weather driven biology of the species. Observed daily weather data (i.e., maxÐmin temperatures, solar radiation) from 1,221 locations across the United States and Mexico for the period 1983Ð2003 were used to drive the models. Soil moisture and nutrition were assumed nonlimiting. The simulation results were mapped using GRASS GIS. The mathematical underpinnings of the modeling approach are reviewed in the appendix and in the supplemental materials.

KEY WORDS light brown apple moth, fruit ßies, pink bollworm, glassy winged sharpshooter, European grapevine moth

We’re in the middle of an eradication program pesticides, pheromones, cultural practices, quarantine, and can’t afford the luxury of research. and combinations including applications of biotechnol- ÑA “high USDA ofÞcial” quoted by Paul ogy (Robinson 2002) have been used in eradication or Ehrlich (see Burk and Calkins 1983). containment efforts. However, despite years of effort and expenditures of hundreds of millions of dollars, many How would you make recommendations for con- invasive species problems remain unresolved. trol of an invasive species in the absence of infor- In this article we examine prospectively the effects mation? of weather on the distribution and relative abundance ÑQuestion to A.P. Gutierrez from an invasive (invasiveness) of six invasive herbivorous insect spe- species scientist, USDA/APHIS/PPQ, Raleigh, cies across the United States and Mexico, and use the NC. results to examine the eradication or containment efforts against them. We use published weather- Invasive species may be of any taxa, and collectively driven, physiologically based demographic models are estimated to cause in excess of $140 billion in losses (PBDMs) developed by us and our colleagues in this annually in the United States (Pimentel et al. 2005) effort. and a trillion worldwide (Oerke and Dehne 2004). The host/insect systems in our study are: 1) cot- Eradication of an invasive species may be desirable but ton (Gossypium hirsutum L.)/pink bollworm (Pecti- elusive, and need not be attempted in some cases (see nophora gossypiella (Saunders)) (Gutierrez et al. Myers et al. 1998, 2000). The sterile insect technique 2006b); 2) a fruit tree host/Mediterranean fruit ßy (SIT) (Knipling 1955), and other methods including (medßy, Ceratitis capitata (Wiedemann)) (Gutierrez and Ponti 2011); 3) olive (Olea europaea L.)/olive ßy (Bactrocera oleae (Rossi)) (Gutierrez et al. 2006c, 1 Division of Ecosystem Science, College of Natural Resources, 2009; Ponti et al. 2009a, b); 4) grapevine (Vitis vinifera University of California, Berkeley, CA 94720-3114. 2 Center for the Analysis of Sustainable Agricultural Systems (CA- L.)/glassy-winged sharpshooter (Homalodisca vitripen- SAS Global), 37 Arlington Ave., Kensington, CA 94707. nis (Germar))/two egg parasitoids (Wermelinger et al. 3 Corresponding author, e-mail: [email protected]. 1991, Gutierrez et al. 2011); 5) a perennial host plant/ 4 Laboratorio Gestione Sostenibile degli Agro-Ecosistemi (UTAGRI- light brown apple moth (Epiphyas postvittana (Walker)) ECO), Agenzia nazionale per le nuove tecnologie, lÕenergia e lo sviluppo economico sostenibile (ENEA), Centro Ricerche Casaccia, Via Anguil- (Gutierrez et al. 2010a); 6) grapevine/European grape- larese 301, 00123 Roma, Italy. vine moth (Lobesia botrana (Denis and Schiffermu¨ller))

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(Gutierrez et al. 2012). Because of the pivotal role the Appendix). PBDMs capture mechanistically the biol- native new world screwworm (Cochliomyia hominivorax ogy of species in response to weather and trophic (Coquerel)) played in the development of the eradica- interactions independent of species distribution data. tion paradigm, its eradication in the United States, Mex- Tri-trophic PBDM systems may include bottom-up ico, and Libya is reviewed in the discussion section effects on phenology, growth and development of (Gutierrez and Ponti in press). The extensive literature whole plants and plant subunits (e.g., fruits, leaves, and the basic mathematical structure underpinning the etc.); the relevant biology and dynamics of herbivo- models are outlined in the cited articles, while the gen- rous species feeding on them; and as required the eral form of the physiologically based demographic mod- top-down action of natural enemies (e.g., Gutierrez els (PBDMs) common to all of the species is reviewed in and Baumga¨rtner 1984, Gutierrez et al. 1994). Con- the Appendix and the Supplemental Materials. sumer species affect the dynamics of the resource Central to the analysis of the distribution and abun- species and vice versa. The tri-trophic grapevine/ dance of heterotherm species is the inßuences of glassy-winged sharpshooter/parasitoid system model weather and climate (e.g., Andrewartha and Birch provides a good overview of the PBDM approach 1954). Climate is the long-run pattern of meteorolog- (Gutierrez et al. 2011). ical factors (e.g., temperatures, rainfall, etc.) in a given With variations, the PBDM approach to modeling location or larger region, while the term weather re- plant growth and development is well established in fers to short-run measures of these factors. The biol- the literature (see Marcelis and Heuvelink 2007, ogy of heterotherm species evolves in response to Rodrõ´guez et al. 2011). PBDMs for plants consist of age climate, interacting species, and other factors in the and mass structured subunit population dynamics native range that in total deÞne its ecological niche models linked via photosynthate availability that gov- (see van der Putten et al. 2010). This biology deter- erns growth and development of extant subunits and mines a speciesÕ temporal and spatial dynamics and geo- the production of new ones. Photosynthesis is esti- graphic range, and the potential areas it may invade. mated using a functional response model (predator Weather (e.g., daily) affects heterotherm physiology, form) driven by current age structured assimilation behavior, interactions with other species, and hence the demands, leaf area index, light, temperature, and other dynamics of the species in current time and place. factors (see Gutierrez et al. 2005, 2006b). We assumed nonlimiting water and nutrients in our analyses be- cause data on plant species root depth, soil moisture Modeling the Distribution and Abundance of holding capacity, and soil fertility on a continental Invasive Species scale were unavailable. This may lead to over predic- Several methods have been used to assess the geo- tion of plant distribution in arid areas (see Hickler et graphic distribution of heterotherm species. For per- al. 2009). A tri-trophic study of the noxious yellow spective, we contrast the commonly used ecological starthistle (Centaurea solstitialis L.) in California in- niche modeling (ENM) approach(s) and the PBDM cluded soil moisture and explained the failed biolog- approach used here. Each approach has strengths and ical control of the weed (Gutierrez et al. 2005). weaknesses. PBDMs for the insect species are also age-struc- ENM Approach. The ENM may be statistical, phys- tured but may have attributes of stage, mass, sex, dor- iological indices, or based on information theory (see mancy, behavior, and other factors as necessary. The Elith and Leathwick 2009). ENMs are relatively easy data required to formulate the models for each insect to implement and seek to characterize climatically the species are outlined in the Appendix (Figs. A1 and geographic range of a species based on aggregate A2). The herbivore models are driven primarily by weather data (and other factors) from areas of the temperature and the demand for and supply of pre- recorded distribution (Beaumont et al. 2009). ENMs ferred plant subunits. The acquisition biology of this are used to predict the potential native range of the and higher trophic levels is captured by the same species and prospectively its range in new areas. How- functional response model used for plant photosyn- ever, ENMs have implicit ecological and mathematical thesis, albeit with different units, and using either the assumptions that lack mechanistic biological under- predator or parasitoid forms as appropriate (see Ap- pinnings (Sobero´n and Nakamura 2009), and as the pendix equations A3i and ii). Similarly, natural enemy Fourth Assessment Report of the Intergovernmental models are driven by temperature and their demand Panel on Climate Change Working group 2 (Fischlin for and supply of preferred host or prey stages. et al. 2007) concluded, ENMs are unable to account for species interactions and population processes. Weather, Simulation, and GIS Analyses These deÞciencies make them problematic when ex- tended to climate change scenarios. We note that the Weather. Daily weather data (i.e., maximum and physiological index ENM (e.g., CLIMEX) has ele- minimum temperatures, solar radiation (cal/cm2/d)) ments in common with the PBDM approach outlined from 1,221 locations across the continental United below (see Gutierrez et al. 1974, Sutherst and May- States and Mexico for the period 1 January1983 wald 1985, Sutherst et al. 2007). through 31 December 2003 were used to run the mod- PBDM Approach. Applications of the PBDM and els continuously across years. Weather data for Hawaii other demographic approaches were reviewed by Bar- were available from very few locations. The weather low (1999) and Hawkins and Cornell (1999) (see data were obtained from the Research Data Archive June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 397

(RDA), Computational and Information Systems Lab- northward into the Central Valley and elsewhere oratory (CISL), National Center for Atmospheric Re- (Stern and Sevacherian 1978). search (NCAR), Boulder, CO. In 1968, the U.S. Department of Agriculture Simulation. The species are assumed present at all (USDA) and the California Department of Agricul- locations with weather driving the dynamics models ture (CDFA) began an eradication program in Ari- and determining the relative favorability of each lo- zona and California using the sterile insect technique cation for them. Initial conditions differed among the (SIT) (Staten et al. 1992), but when eradication systems, but were the same for all locations within a proved elusive (Chu et al. 1996), the program was system study (e.g., olive/olive ßy). We do not attempt redirected with the goal of preventing the establish- to model the geographic invasion of the species as this ment of pink bollworm in Central Valley cotton. In is an impossible task. Numerous life-history variables 1997, genetically modiÞed cotton expressing the pro- are computed daily for each species in each system, toxin of the bacterium Bacillus thuringiensis (Bt) was but total pupae per year was used as a measure of introduced across much of the U.S. cotton belt, but not favorability for the holometabolus medßy, olive ßy, in the Central Valley of California (Godfrey 2004; apple moth, and grapevine moth; total diapause larvae Gutierrez et al. 2006a, b). Bt cotton is highly effective plant per year was used for pink bollworm, and total against pink bollworm reducing its populations to very new adults per year was used for the hemimetabolous low levels (e.g., Tabashnik et al. 2010), and this created glassy-winged sharpshooter. These summary variables conditions thought favorable for the renewal of erad- should be viewed as indices of favorability. ication efforts. The output variables were geo-referenced and writ- In 2001 to 2002, a three-phase SIT eradication pro- ten by year to batch Þles. Means, SDs and coefÞcients gram piggybacked on the Bt cotton technology was of variation were computed for each variable across initiated in the United States and Mexico (Grefen- years at each location. The system models were as- stette et al. 2009; see Fig. 1a). Phase 1 targeted the El sumed equilibrating to local weather during the Þrst Paso/Trans Pecos region of west Texas, southÐcentral year (1983), and hence these data were not used in New Mexico, and northern Chihuahua, Mexico. Phase calculating the summary statistics. 2 was begun in Arizona and New Mexico in 2006, and GIS. Except in Hawaii, wherea1kmgrid was used, sub phase 3aÐb was begun in 2007Ð2008 along the the simulation data were mapped using inverse dis- Colorado River and in the desert valleys of Arizona, tance weighting ona3kmraster grid using the GIS California, and Mexico (http://www.aphis.usda.gov/ software GRASS (Geographic Resources Analysis plant_health/plant_pest_info/cotton_pests). The Cen- Support System, GRASS Development Team 2011, tral Valley is considered an area of pink bollworm sup- http://grass.osgeo.org). The distribution patterns in pression and control because the USDA claimed its SIT the maps reßect average local site favorability and the program has prevented the mothÕs establishment there geographic distribution and distance between loca- (Staten et al. 1992). tions. Red on the color bar indicates high favorability Based on abundant data, PBDMs for cotton and pink and clear indicate very low favorability. The dots in bollworm used in this study were developed by Guti- the maps are the locations of the weather station used. errez et al. (1977), reÞned by Stone and Gutierrez (1986) with the effects of Bt cotton on the major cotton pests in California added by Gutierrez and Ponsard (2006) and Gutierrez et al. (2006a). Critical Integration of the Biology and Model Results elements of pink bollworm biology include tight links The scope of the study is large, and hence a brief to the phenology and dynamics of cotton fruiting, dia- review of the biology, invasion history, and eradica- pause initiation in late summer in response to decreasing tion or containment efforts for each of the six invasive photoperiod, and temperature (Gutierrez et al. 1981), species is given as background for evaluating their and cold-intolerance of diapause larvae (Gutierrez et al. prospective geographic distribution and abundance. 1977, 2006b; see data in Venette et al. 2000). The species are discussed in chronological order of Pink Bollworm Distribution and Relative Abundance. their invasion of California. Three measures of favorability for pink bollworm Pink Bollworm. The stenophagous pink bollworm is were estimated: normalized average winter survival of a tropical species of Indian or more likely Papua-New diapause larvae (Fig. 1b), average number of diapause GuineaÐNorth Australian origins (van den Bosch and larvae/plant/year (Fig. 1c), and average cumulative Messenger 1973, see Grefenstette et al. 2009). It is larvae/plant/year (i.e., larval days, Fig. 1d). Not all widely distributed in cotton growing areas worldwide areas with temperatures favorable for pink bollworm where it also attacks other species of Malvaceae (e.g., have sufÞcient rainfall and/or irrigation for cotton okra and hollyhock). Pink bollworm was Þrst discov- production (i.e., roughly the desert areas outside the ered in Florida in 1932 on tree cotton, and spread to shaded zones in Fig. 1a). commercial cotton in the United States and Mexico. Winter survival is predicted to be highest in the The moth invaded the desert cotton areas of Arizona southern desert regions of Arizona, California, and and southern California in the late 1960s where it northwestern Mexico (Fig. 1b) where before the in- became the key pest. Dispersal of the pest in California troduction of Bt cotton, high densities of diapause is aided by southwesterly monsoon winds that annu- larvae and summer larval populations were common ally carry adult moths from the southern desert valleys (Fig. 1c and d, respectively). In sharp contrast, very 398 ENVIRONMENTAL ENTOMOLOGY Vol. 42, no. 3

Fig. 1. Prospective distribution and abundance of the pink bollworm in the United States and Mexico below 2,000 m during 1984Ð2003 using the model of Gutierrez et al. (2006b): (a) phases of the USDA eradication program (phases 1Ð3b, see text) and the Central Valley (CV) exclusion zone; (b) the normalized average winter survival of diapause larvae; (c) average diapause larvae/plant/year; and (d) cummulative daily counts of larvae/plant/year. Note that shaded areas in Fig. 1a are roughly the distribution of commercial cotton in the southÐwest United States and northern Mexico. (Image reference: http://www.oxitec.com/moth-gallery/k10075Ð6-ars-pink-bollworms/). low winter survival is predicted in the Central Valley in southern California until 1980 (Myers et al. 2000) (CV) of California (see Gutierrez et al. 2006aÐc), and when a detection/eradication program based on pro- over much of the cotton belt in the southÐeast United tein-bait and insecticides was begun. An ongoing SIT States and the northern half of Texas, southern New program against medßy was begun in 1994 that cur- Mexico, and northÐcentral Mexico (Fig. 1b). High rently extends through Mexico and Guatemala. winter survival is predicted in the Yucatan Peninsula Low numbers of adult medßy have been detected (Fig. 1b), but a combination of high temperatures and periodically in the Los Angeles Basin that Meixner et photoperiod in the region adversely affect diapause al. (2002), using microsatellite and mitochondrial induction (see Gutierrez et al. 1981), and hence pop- DNA analyses, determined were new invasions. The ulation development (Fig. 1c and d). ßy was also discovered during 1975, 1980, and 1981 in The predictions of our model contrast sharply with Santa Clara County south of San Francisco Bay, and the Þndings of Venette et al. (2000) that abiotic factors has occasionally been found in inland locations in the do not preclude pink bollwormÕs establishment over state (J.R. Carey http://entomology.ucdavis.edu/ much of the cotton belt, and that its absence is the news/califmedßiescities. html, see Gutierrez and result of federal monitoring, quarantine, and local Ponti 2011). We note that no ongoing measureable eradication programs. The predictions of the model populations of the ßy have been found in California. also conßict with the claim that the ongoing SIT erad- Key features of medßyÕs biology are its narrow ther- ication or suppression program has kept pink boll- mal limits and reproductive quiescence in females worm from establishing in the Central Valley of Cal- when fruit are unavailable. To analyze prospectively ifornia (Staten et al. 1992) under current climate, but the potential distribution of the ßy in tropical areas this is expected to change with climate warming such as Florida, Hawaii, and Mexico, the model de- (Gutierrez et al. 2006aÐc). We note that piggybacking veloped by Gutierrez and Ponti (2011) for ArizonaÐ the SIT program on the Bt cotton technology in areas California and Italy was modiÞed so that fruit hosts where PBW is able to persist increases the likelihood would be available nearly all year-around. This change of success for the ongoing eradication program. enabled separation of the limiting effects of temper- Mediterranean Fruit Fly. The polyphagous Medi- ature on ßy dynamics from host availability. terranean fruit ßy (medßy) is a tropical species of East Medfly Distribution and Abundance. The model African origins (Balachowski 1950) that is established predicts that only the coastal plain of southern Cali- in sub Saharan Africa, the Mediterranean Basin (e.g., fornia and Hawaii are potentially favorable for medßy Italy), Argentina, Western Australia, Hawaii, Mexico, (Fig. 2a and c), with Florida being less favorable, and and Central America. The ßy was Þrst detected in other areas of the United States being unfavorable southern California in 1975 (Carey 1991) and an in- (Fig. 2b). As observed, tropical southern Mexico and tensive area-wide eradication program based on in- areas bordering Guatemala are highly favorable for secticides was initiated. The ßy was not detected again the ßy, while the vast desert-highlands areas of north- June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 399

The limited distribution of medßy in California (and the United States), and more important, its fail- ure to establish and spread after multiple introduc- tions (Meixner et al. 2002) suggest that medßy is not a serious threat to California (or United States) under current climate. Our results questions claims of estab- lishment (Carey 1991, 1996) and hence of eradication. Olive Fly. Drought tolerant olive is of African ori- gin, and has been planted worldwide in Mediterra- nean climates. Earliest plantings in California were introduced from Mexico during the Spanish colonial period. Olive is widely grown in the Central Valley and in southern desert areas of California with some cul- tivation in central Arizona and other areas of the United States (e.g., Texas and Florida). The host spe- ciÞc olive ßy was Þrst detected in the Los Angeles Basin in 1998, and quickly spread to the major olive growing areas of the state. The extensive European literature was used to de- Fig. 2. Prospective distribution and abundance of medßy velop the PBDMs for olive and olive ßy (see Gutierrez (pupae/plant/year) below 2,000 m during 1984Ð2003 using the modiÞed Gutierrez and Ponti (2011) model: (a) Cali- et al. 2009). Olive requires moderate chilling to pro- fornia, (b) continental United States and Mexico, and (c) duce fruit, but this may not occur in some tropical Hawaii. Note that the scales used for Fig. 2aÐb and c differ. areas limiting olive production and the distribution of (Image reference: http://www.freshfromßorida.com/pi/ the ßy. In addition, the thermal limits of olive are medßy/index.html). considerably broader than those of the ßy. Moderate cold and hot temperatures reduce adult ßy survival ern Mexico are unfavorable and may serve as a barrier and reproduction, and females become reproduc- to overland infestation of the United States. Predicted tively quiescent when fruit are unavailable and/or population levels in southern California and Hawaii temperatures are high. are about a third those in southern Mexico, while Olive Fly Distribution and Abundance. The model levels in Florida are about a fourth. We note that the predicts a wide geographic distribution for olive in the same model predicted the observed wide distribution United States and Mexico (Fig. 3a), while the distri- of the ßy in Italy (Gutierrez and Ponti 2011). bution of olive ßy is considerably smaller (Fig. 3b).

Fig. 3. Prospective distribution and abundance of olive yield and olive ßy pupae below 2,000 m during 1984Ð2003 using the Gutierrez et al. (2009) model: (a) prospective distribution of olive yield (grams/tree/year), and (b) cumulative olive ßy pupae/tree/year in the United States and Mexico, and using enlarged maps and different scales for (c) Arizona and California and (d) the southÐeast United States. (Image reference: Marshall W. Johnson, nature.berkeley.edu). 400 ENVIRONMENTAL ENTOMOLOGY Vol. 42, no. 3

Fig. 4. Prospective distribution and abundance of glassy winged sharpshooter below 2,000 m during 1984Ð2003 using the

Gutierrez et al. (2011) model: (a) average log10 cumulative new adults/vine/year in the absence of natural enemies, and (b) average cumulative new adult glassy-winged sharpshooter/grapevine/year (arithmetic scale) after the action of the para- sitoids G. ashmeadi and G. triguttatus. (Image references: http://www.acgov.org/ cda/awm/agprograms/pestexclusion/ sharpshooter.htm and http://biocontrol.ucr.edu/irvin/ California_agriculture.pdf).

The ßy is reported only from California where highest other plants (e.g., oleanders and almonds) (Purcell densities are predicted in coastal south and central 1997). The sharpshooter lacks a dormant stage and California with penetration into the northern half of over-winters as reproductively dormant adults the Central Valley (Fig. 3c). The ßy is limited in the (Turner and Pollard 1959) with citrus being a major southern reaches of the Central Valley and desert over-wintering host (Hummel et al. 2006). valleys of California and Arizona by high summer High populations were initially found in southern temperatures (Gutierrez et al. 2009, see also Wang et California where two or more generations occur per al. 2009, Johnson et al. 2011). Olive ßy densities in year (Blua et al. 2001). An area-wide control program central Florida are predicted to be half those of south- based on insecticides and quarantine measures was ern California, while areas of coastal Texas and Lou- used with modest success to limit its spread (Califor- isiana are predicted marginal (Fig. 3c vs. 3d). The nia Department of Food and Agriculture [CDFA] areas of highest favorability for the ßy are predicted to 2003). Biological control by egg parasitoids (Gonato- be south and central Mexico, but no infestations are cerus ashmeadi Girault (GA) and G. triguttatus Girault reported there. (GT)) (Hymenoptera: Mymaridae) greatly reduced The model predicted the distribution of olive and sharpshooter densities in California (Pilkington et al. olive ßy in California (see Wang et al. 2009) and Italy 2005, Gutierrez et al. 2011). including the microclimates along the northern Italian Glassy-Winged Sharpshooter Distribution and Abun- lakes (Gutierrez et al. 2009). The model was tested dance. PBDMs for glassy-winged sharpshooter and its against Þeld data from Sardinia (Ponti et al. 2009a), parasitoids (Gutierrez et al. 2011) were linked to a and was used to map the prospective distribution of model for grapevine (Vitis vinifera L) (Wermelinger the ßy in the Mediterranean Basin (Ponti et al. 2009b). et al. 1991). In the absence of parasitism, the model SIT eradication of the ßy was attempted in the predicts prospectively a wide geographic distribution Mediterranean Basin but failed (Estes et al. 2011). and high abundance of the sharpshooter in the United Eradication was not attempted in California where the States and Mexico (Fig. 4a). Cold limits the sharp- ßy has reached the limits of its climatic/geographic shooter northwardly in the United States and in the distribution. central highlands of Mexico. Highest favorability is Glassy-Winged Sharpshooter. Glassy-winged sharp- predicted in subtropical areas of the United States, and shooter is a polyphagous subtropical species native to especially in tropical areas of Mexico. Texas, the southÐeast United States and Mexico (Tria- Including the action of the egg parasitoids in the pitsyn and Phillips 2000) that in 1989 extended its model changes the distribution and abundance of the range into California (Sorensen and Gill 1996). The sharpshooter dramatically to roughly its recorded na- sharpshooter feeds on nutrient-poor xylem (Mizell et tive range (see Triapitsyn and Phillips 2000; Fig. 4a vs. al. 2008) of numerous host plants (Lauzie`re and Se´- 4b). The predicted distribution and reduced abun- tamou 2009). It vectors the pathogenic bacterium, dance in California accord with current Þeld obser- Xylella fastidiosa (Wells et al. 1987) that causes vations (see Gutierrez et al. 2011). With parasitism, PierceÕs disease in grape and scorch-like diseases in very low densities are predicted in cold areas of Ar- June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 401

Fig. 5. Prospective distribution and abundance of the light brown apple moth (larval-days) below 2,000 m during 1984Ð2003 using the Gutierrez et al. (2010a) model: (a) observed (USDAÐAPHIS-PPQ) and predicted distributions in California, and (b) the prospective distribution and abundance (i.e., larval-days) across the United States and Mexico. (Image reference: http://ucanr.edu/blogs/bugsquad/blogÞles/964.jpg). izona and New Mexico, and at higher elevations in completion of three generations, and where winter central and southern Mexico. Mid-range populations temperatures did not fall below Ϫ16ЊC. In response to are predicted in south Florida, the Yucatan, and the this perceived threat, the USDA quarantined the af- tropical areas of western and eastern Mexico. Highest fected counties in California, and Hawaii (Federal densities are predicted in south Texas and areas of Quarantine Order of 2 May 2007). In late 2007, an western Mexico and Baja California. The change in eradication program was initiated in California using apparent distribution with parasitism supports con- pheromones and insecticides that engendered con- jecture by Davis et al. (1998) and van der Putten et al. siderable public protest concerning claimed public (2010) that higher trophic levels may need to be in- health and ecological risks. This led to numerous pub- cluded in analyses to estimate the geographic distri- lic meetings including California State Senate hear- bution of invasive species. ings, and to an NAS Panel review in 2009 that con- Light Brown Apple Moth. The polyphagous, tem- cluded the USDAÕs projections of the mothÕs “... perate-climate light brown apple moth is indigenous potential geographic distribution in the United States are to Australia where it is recorded from a wide range of problematic and in some cases not based on sound, rig- crops, ornamentals, herbaceous weeds, and pome fruit orous science” (http://www.nap.edu/catalog/12762. and grape (see Geier and Briese 1981). The moth was html). The eradication program was switched to a SIT detected in California in 2007, and has since been program, and later to a containment effort with strong found in 15 coastal and near coastal counties (Fig. 5a; enforcement. Gutierrez et al. 2010a). Its wide distribution in Cali- Our model predicts the apple mothÕs distribution in fornia when found suggests that it had been present California is restricted to near-coastal and inland areas for several years before detection. moderated by ocean breezes (i.e., the DavisÐSacra- The PBDM for apple moth was developed using mento area), with the Central Valley of California mostly Australian data (e.g., Danthanarayana 1975, being considerably less favorable (Gutierrez et al. 1976aÐc), and was linked to a model for a generic 2010a; Fig. 5). The Þne scale predictions of our model perennial host plant (Gutierrez et al. 2010a). The for California are in accord with the 2010 county PBDM system was used to analyze prospectively the level distribution records (http://www.nappfast.org/ mothÕs distribution in Arizona and California, and here powerpointpres/08_Fowler_Pathway_Analysis. to assess the distribution across the United States and pdf); see Fig. 5a). Mexico. Salient features of the apple mothÕs biology Prospectively on a continental scale, coastal and include narrow thermal limits for development, lack of near-coastal areas of the Gulf States, eastern Florida, a dormant stage, and low host plant availability during southern and eastern Georgia, and the coastal parts of hot-dry summers in nonirrigated areas. the Carolinas are predicted moderately favorable. Light Brown Apple Moth Distribution and Abun- Large areas of Mexico are predicted to be highly fa- dance. Fowler et al. (2009) predicted a wide distri- vorable. Lozier and Mills (2011) used the ENM Max- bution for the apple moth that included all areas of the Ent algorithm (Phillips and Dudõ´k 2008) and predicted United States having sufÞcient thermal units for the a similar distribution for the apple moth in the United 402 ENVIRONMENTAL ENTOMOLOGY Vol. 42, no. 3

Fig. 6. Prospective distribution and abundance of the European grapevine moth (pupae/vine/year) below 2,000 m during 1984Ð2003 using the Gutierrez et al. (2012) model: (a) California and (b) the United States and Mexico (note the different scales for a and b). (Image reference: http://www.co.lake.ca.us/Government/Directory/Ag/Agprograms/EGVM.htm).

States and Mexico. He et al. (2012) used the CLIMEX 2012). Larvae are stimulated to enter diapause in late algorithm to map the potential global distribution of summer in response to decreasing daylength, but con- the moth, but the coarse grain of the maps makes tinue development until maturity when they pupate in comparison difÞcult. sheltered places on the vine bark. European Grapevine Moth. The polyphagous, tem- European Grapevine Moth Distribution and Abun- perate-climate European grapevine moth is the most dance. The model predicts prospectively that the important pest of grape in the Mediterranean Basin moth could infest all of the major agricultural areas of (SavopoulouÐSoultani et al. 1990). The moth larvae the state (Fig. 6a) and wide areas of the United States feed on the inßorescence and fruit of plants in Ͼ27 and Mexico (Fig. 6b). This prediction is in accord with plant families over a geographic area that spans central the range in the United States posited by Fowler and Europe, the Mediterranean Basin, southern Russia, Lakin (2002). Highest favorability is predicted for Japan, the Middle East, Near East, and northern and subtropical and tropical areas of the United States and western Africa (Venette et al. 2003). Based on vege- parts of Mexico. The Yucatan Peninsula and the State tation type and area, Venette et al. (2003) estimated of Chiapas are only moderately favorable. that Ϸ29% of the continental United States would be favorable for the moth. Discussion The grapevine moth was discovered in northern California in 2009, and by the end of the 2010 season Liebhold and Tobin (2008) reviewed the ecology of had been detected in nine north central counties (Va- insect invasions and management, and proposed that rela et al. 2010). An ongoing eradication program using strategies to eradicate newly established populations quarantine, insecticide, and pheromone for detection should in theory focus on suppressing populations and mating disruption was initiated in 2010. High num- below Allee thresholds where extinction proceeds bers of adult moths were trapped in Napa County in without further intervention (see Stephens et al. 2010, but very low numbers were trapped during the 1999). On a more practical level, the factors deter- unseasonably cold-rainy springÐsummer of 2011 when mining the potential geographic range and invasive- the eradication program was also fully active (USDA ness of exotic species must be known to assess their APHIS-PPQ data reported in Varela et al. 2011). Very invasive potential, and to help guide development of few adults were captured during 2011and 2012 in other strategies for eradication, or management should erad- infested areas. ication fail (e.g., Gutierrez et al. 2012). Nonetheless, Extensive European data were used to develop the how to make these assessments is an open question. model for grapevine moth (Gutierrez et al. 2012) that ENM approaches based on species distribution data was linked to a model for grapevine growth and de- have been widely used for unbiased screening of the velopment (Wermelinger et al. 1991). The moth has a potential range of invasive species (e.g., Thuiller et al. wide tolerance to temperature, and depending on 2005, Lozier et al. 2009). Important limitations of temperature produces 2Ð5 generations per year across ENMs were outlined in the text, and their bases con- its Palearctic range and in California (Gutierrez et al. trasted to the mechanistic, weather-driven, PBDMs used June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 403

Table 1. Type and adequacy of data used to develop PBDMs for seven invasive species in North America

Pink Apple Grapevine Glassy-winged Medßy Olive ßy Screwworm bollworm moth moth sharpshooter Climate type Tropical Tropical Subtropical Temperate Temperate Subtropical Tropical Origins Exotic Exotic Exotic Exotic Exotic Native Native Host speciÞcity Stenoa Poly SpecÞc Poly Poly Poly Poly Host modelb ؉ — ؉ — ؉؉ O Functional response ؉؉ ؉ ؉ ؉ ؉ O — Developmental rate ؉؉ ؉ ؉ ؉ ؉ — Fecundity ؉؉ ؉ ؉ ؉ ؉ — Mortality(T) ؉؉ ؉ ؉ ؉ ؉ Mortality (biotic) — OO —— ؉ O Dormancy Strong Transient Transient None Strong None None c $ cost ϫ 106 Ͼ300d Ͼ450e Unknownf 25Ð50 Ͼ25 Ͻ5 Ͼ750 Eradication successg UU A A U B P

a Poly, polyphagous; steno, stenophagous; speciÞc, host speciÞc. b Symbol ϩ, sufÞcient data; Ñ, marginal data; O, insufÞcient data. c Conservative estimates made from the literature. d 156 million for the current ongoing eradication efforts ϩ prior costs. e 14 million per year since 1980 ϩ emergency spray program costs. f Eradication costs in the Mediterranean Basin unknown. g U, unknown; A, abandoned; B, effective biological control; P, probable. here to predict the distribution, dynamics, and invasive- tion in Texas during the 1960Ð1970s (see Krafsur et al. ness of six invasive species. To develop PBDMs requires 1986) and in Libya during the early 1990s (see VargasÐ sound biological and ecological data that may not be Tera´n et al. 2005) was greatly aided by periods of dry cold available or be of marginal quality (Fig. A2). The ade- weather that greatly reduced ßy populations. quacy of the data in the literature used to formulate Pink Bollworm. The ongoing $300 million SIT erad- our models is summarized in Table 1 as sufÞcient ication program against pink bollworm (see Grefen- (symbol ϩ), marginal (—), and insufÞcient (O) with stette et al. 2009) appears to have a good chance of nominal values of 1, 0.5, and 0, respectively. A plot of success, but claims that the program prevented the estimated costs of the eradication or containment efforts establishment of the moth in the Central Valley of ($ ϫ 106) gleaned from the literature on the sum of the California (Staten et al. 1992) conßicts with biological nominal values (V) yields an inverse relationship data and modeling that predict that low winter tem- (costs ϭϪ85.7V ϩ 1045.3; R2 ϭ 0.83; df ϭ 6); see Supp. peratures are the limiting factor (see text; Gutierrez et Fig. 1 [available online only]). al. 2006b). Eradication Programs. Controversy, for various rea- Medfly. An eradication/detection program against sons, has been associated with eradication programs. the medßy is ongoing in California, and in Mexico and Two major reasons have been the lack of adequate sci- Guatemala where medßy is a serious pest. The total entiÞc documentation and analysis, and the high costs. costs of the eradication program have been more than Screwworm. The eradication of the native tropical $450 million. Despite multiple introductions in Cali- new world screwworm in North America during the fornia (Meixner et al. 2002), and claims that the ßy is 1960s and 1970s is the hallmark of the eradication established at densities below detection levels (Carey paradigm (USDA 2012). That eradication occurred is 1991, 1996), no permanent populations have been beyond doubt, but what role did weather play? De- found. The model predicts that persistence of the ßy spite costs of more than $750 million since the incep- is likely only in the coastal plain of southern California tion of the program (Myers et al. 1998), data to (Gutierrez and Ponti 2011), and suggests the threat to develop a sound PBDM to assess the relative contri- California agriculture (and the United States) was bution of weather, chemical control, and SIT in the greatly over-estimated. eradication effort remain sparse (see Table 1; Supp. Olive Fly. In contrast to medßy, the olive ßy estab- Fig. 1 [available online only]). Novy (1991) reported lished and quickly spread to its climatic limits within that periods of rain and warm temperatures in arid California (Gutierrez et al. 2009). SIT eradication of areas of the United States and Mexico enabled the ßy the olive ßy was attempted in the Mediterranean Basin to build rapidly and to disrupt eradication efforts until where it failed (Estes et al. 2011). Eradication was not normal weather patterns returned. Readshaw (1986, attempted in California. 1989) argued that cold weather rather than the SIT Glassy-Winged Sharpshooter. Invasion of California program was responsible for the decline of screw- by glassy-winged sharpshooter was an extension of its worm. A PBDM based on the limited available data native range from Texas, the southÐeast United States (Gutierrez and Ponti in press) supports observations and northern Mexico. Eradication of this pest in Cal- by Bushland (1985) that low nonfreezing tempera- ifornia proved infeasible as it quickly spread aided by tures and/or low rainfall limit screwworm winter per- the movement of nursery stocks. Effective biological sistence in the United States to south Texas and south control by egg parasitoids helped resolve the problem Florida. The PBDM analysis also suggests that eradica- in California (Pilkington et al. 2005) and in French 404 ENVIRONMENTAL ENTOMOLOGY Vol. 42, no. 3

Polynesia (see Gutierrez et al. 2011). In contrast to medßy eradication program in California, concluding other eradication efforts, the costs of the program that decision makers were unable to determine im- were relatively low. portant areas of uncertainty, identify and interpret Light Brown Apple Moth. A $100 million eradication feedback (expert opinion), and respond adaptively to effort was proposed for light brown apple moth in the evolving problem. Discussions with scientists in California based on a predicted wide distribution and government agencies responsible for eradication pro- high economic damage (Fowler et al. 2009, see text). grams suggests the agencies often lack the ßexible The eradication program was abandoned, and yet no administrative structure to allow their scientists the outbreaks of the moth have been reported in Califor- freedom to inform agency decision making. Our ex- nia (Wang et al. 2012, N.J. Mills personal communi- tensive experience with government agencies respon- cation). The observed and predicted geographic range sible for the eradication or containment programs of the moth remains primarily near the coast (Guti- strongly suggests a distrust of non-inhouse analyses. errez et al. 2010a). Furthermore, eradication or containment programs European Grapevine Moth. The ongoing eradication are often implemented using militaristic metaphors to program against European grapevine moth in Califor- describe the problem and control tactics; metaphors nia seeks to eradicate the moth while its distribution that often hinder the development of realistic man- is relatively limited. If eradication fails, the range of agement and conservation goals (Larson 2005). the moth will be very large (Fig. 6). However, the In the absence of sound analyses of the dominant European experience has shown that the pest is easily factors determining the distribution and abundance of managed, albeit with associated increases in produc- invasive species, claims of eradication need (e.g., light tion costs and environmental damage (see Gutierrez brown apple moth in California; Gutierrez et al. et al. 2012). 2010a) or of success (e.g., medßy in California, Guti- The Biology Matters. While the PBDMs were able errez and Ponti 2011) may not hold up to scientiÞc to predict prospectively the geographic range of the scrutiny, and at times may be exercises that appear to six invasive species in our study, no set of biological succeed (e.g., pink bollworm in the Central Valley of traits emerged that a priori would enable forecasting California; Gutierrez et al. 2006b, Grefenstette et al. their invasiveness, much less their geographic 2009), or may succeed after sufÞcient investment of ranges. The geographic patterns of prospective fa- resources (e.g., screwworm; Krafsur et al. 1986, USDA vorability of the species across North America are 2012, Gutierrez and Ponti in press). We propose that checkered. Focusing on California, subtropical and the Þeld of invasion biology has matured sufÞciently temperate species such as olive ßy, glassy-winged so that realistic prospective analyses of exotic species, sharpshooter, apple moth, and grapevine moth readily be they ENM or PBDM based, can be made in a timely established but in different areas of the state, while the manner and used to help develop science based erad- tropical pink bollworm established only in frost-free ication or containment policies and strategies. We desert areas. Establishment of the tropical medßy ap- favor the PBDM approach because the models serve pears tenuous in coastal southern California, and yet as a dynamic library of the biology as it becomes its observed establishment is predicted in Italy (see available, and can be used to develop testable man- Gutierrez and Ponti 2011) and southern Mexico/Gua- agement scenarios (e.g., Gutierrez et al. 2012). As a temala (this study). Þnal plea in a time of diminishing budgets, we are Dormancy may enable species to survive adverse reminded of Sir Ernest RutherfordÕs (Nobel Laureate periods (see Nechols et al. 1999), but it occurs in only in Chemistry) admonition: “Gentlemen, we have run two of our six species: the pink bollworm and Euro- out of money. It is time to start thinking.” pean grapevine moth. Dormant pink bollworm larvae are cold susceptible limiting the pestÕs northward range, while a combination of unfavorable high tem- Acknowledgments peratures and daylength may affect diapause devel- opment (see Gutierrez et al. 1981) limiting its geo- We are grateful to the Þve reviewers whose criticisms and graphic range in tropical areas (e.g., the Yucatan). In suggestions helped guide the development of the article. The forbearance of Editor E. Alan Cameron during the arduous contrast, dormant grapevine moth pupae are cold tol- Augean Þfth task effort to pare the article requires special erant and have wide thermal limits that enable the pest mention. Continued thanks are due M. Neteler (Fondazione to invade a wide variety of climatic regions. The trop- Edmund MachÐCentro Ricerca e Innovazione, Trento, Italy, ical medßy and subtropical olive ßy lack a true dor- http://gis.fem-environment.eu) and the international net- mant stage but may enter reproductive quiescence work of co-developers for maintaining the GRASS software, when hosts densities are low, but only olive ßy was and making it available to the scientiÞc community. The able to establish widely in California because of its research was supported by the Center for the Analysis of wider thermal limits. Sustainable Agricultural Systems (CASAS Global), Kensing- A common thread across the invasive species stud- ton, CA (http://cnr.berkeley.edu/ casas/); and a Marie Cu- rie International Reintegration Grant within the seventh ied is that decisions to initiate eradication or contain- European Community Framework Program (project num- ment efforts were often not based on sound prospec- ber: 224091; acronym: GlobalChangeBiology). No extramural tive analyses of the factors determining the potential funding for the work came from United States sources. Im- distribution and invasiveness. Lorraine (1991) cap- ages of the various species were copied from open sources on tured the essence of the problem in a study of the the Internet, and are acknowledged in the Þgure legends. June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 405

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Appendix: A Review of PBDM 1977) were used to model the dynamics of all popu- lations in case studies be they plant or insect (see Di Cola et al. 1999, pp. 523Ð524). The forcing variable is Overview temperature (T), and time (t) is a day that from the Tritrophic population dynamics models, including perspective of the poikilotherm organisms is of vari- the physiologically based demographic modeling ap- able length in physiological time units above its lower proach (PBDM), were reviewed in Hawkins and Cor- thermal threshold. The numerical solution for the nell (1999). Barlow (1999) proposed that PBDMs have time-varying model for the ith age class of a life stage large numbers of parameters and hence are difÞcult to with i ϭ 1, 2,...,kage classes (see Fig. A1) is equation develop, but this is not the case. All of the models in A1 (see Severini et al. 2005). this study, except pink bollworm, were developed using data in the literature. However, in the absence ⌬x͑t͒ ⅐ k ͑ ϩ ͒ ϭ ͑ ͒ ϩ ͭ ͑ ͒ Ϫ ͑ ͒ ⅐ of sufÞcient available data on a species, the model r t 1 r t r Ϫ t r t i i X͑t͒ i 1 i structure provides guidance as to the data to be col- lected, and this greatly shortens the process of model X͑t͒ ϩ ͓␮i͑t͒ Ϫ 1͔ ⅐ X͑t Ϫ 1͒ development (see below). Data to parameterize the ͩ1 ϩ ͪͮ [A1] ⌬x͑t͒ ⅐ k submodels may be obtained in a variety of ways with the most direct one being laboratory age-speciÞc life table studies at different temperatures and gradients The state variable ri(t) is density as a rate that may of limiting factors as required. Such data enable cap- be in units of number or mass. Mean developmental time (X) in degree-days (dd) may vary on two con- turing the effects of these factors on time varying vital Ϫ rates in the Þeld (e.g., daily) as driven by temperature, secutive days (X(t), X(t 1)) because of nutrition and resource availability, and other factors. Observations other factors (e.g., fertilizer for a plant or fruit age in ϭ Ϫ on behavior may be critical and must be made. pink bollworm). If X is constant (i.e., X(t) X(t 1)), Modeling is facilitated by the fact that the same dy- the model becomes the time-invariant form of the ⌬ ͑ ͑ ͒͒ namics model and submodels for analogous processes in model. x t T is an increment of physiological age ␮ ͑ ͒ the life histories are used across trophic levels (see be- (x) (see below), and i t is the proportional age low). The linkages between trophic levels encourages a speciÞc net loss rate that includes the rich biology modular structure permitting different combinations of affecting age class deaths, growth, predation, net im- interacting species to be implemented in a model run migration, and other factors as required by the biology using Boolean variables (e.g., Gutierrez et al. 2006aÐc, of each species or stage. Immigration was not included 2008a, b, 2010b; Gutierrez and Ponti 2011). The analyses in our models. Births ßow into the Þrst age class (k ϭ may be viewed from the perspective of any species in the 1, see below), and some individuals exit as deaths at system. Population dynamics models developed in this maximum age (from cohort k). The density of cohort ͑ ͒ ϭ ͑ ͒ ⅐ ͑ ͑ ͒͒ manner may be viewed as time-varying life tables (sensu; i is Ni t ri t X T t /k, and the total density in ͑ ͒ ϭ ͸k ͑ ͒ Gilbert et al. 1976). The models were implemented in a life stage (or population) is N t i ϭ 1Ni t , Borland Delphi Pascal. where k ϭ X2/var, and var is the variance of observed developmental times. One scheme for modeling the ßow between ages and stages in the dynamics model The Dynamics Model is illustrated in Fig. A1a, but other schemes may also The time invariant and time-varying distributed- be developed. Fig. A1b shows the distribution of de- maturation time demographic models (see Vansickle velopmental times with different values of k. June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 409

Submodels equations A3i and ii are type II models if ␣ is constant, but type III if ␣ is increasing on N (i.e., ␣(N)). Here SubÞgures in Fig. A2 lack numerical scales indicat- we focus on the parasitoid form, though similar argu- ing that the shapes of the functions are similar across ments apply for the predator form. species, albeit with different units. To parameterize equation A3i, we assume for ex- Developmental Rates and Time. The developmen- position purposes that an herbivore female lays one or tal rate is nonlinear with temperature (R(t(T)) (equa- more eggs per host (e.g., a parasitoid). If only one tion A2 ; Fig. A2a; Briere et al. 1999), but can also be ` progeny survives per host, the supernumeraries are inßuenced by other factors. assumed to die. Further, assume that from life table studies females have a maximum average age-speciÞc a͑T͑t͒ Ϫ TL͒ R͑t͑T͒͒ ϭ 1/days͑T͒ ϭ Ϫ oviposition proÞle at optimum temperature topt (i.e., 1 ϩ bT TU ϭ f(x, Topt) eggs/female; at Topt and age x) (Fig. A2c; [A2] equation A4; Bieri et al.1983). ax ͑ ͒ ϭ Variables aand bare Þtted constants and TL and TU are f x,Topt x [A4] the lower and upper temperature thresholds. A cohort b initiated at some time t0 completes development on The total eggs load (i.e., D(t,T)) of the adult female t average when ͵ R͑t͑T͒͒dt ϭ 1. Average developmen- population (C(x,t)) with age structure (x0 to xmax)is t0 tal time in dd is computed in the linear range of favor- xmax ϭ ͑ ͒ ⅐ ͑ ͑ ͒ Ϫ ͒ D͑t,T͒C͑t͒ ϭ sr ⅐ ␾ ͑t͑T͒͒͵ f͑ x,T ͒ ⅐ C͑ x,t͒dx able temperatures as X day T T t TL ). Daily T opt increments of physiological time are computed as x0 ⌬ ͑ ͑ ͒͒ ϭ ͑ ͑ ͒͒ x t T R t T X. [A5] Developmental times vary with temperature (equa- tion A2) but it may also vary with nutrition (e.g., fruit The variable sr is the sex ratio that may vary over ␾ ͑ ͑ ͒͒ age for pink bollworm) that increases developmental time, and T t T scales for the effects of temperature time compared with the minimum time from the base (Fig. A2d). scalar value of 1. A scalar function such as that illus- Substituting D(t,T)C(t) and host densities in equa- trated in Fig. A2b could be used to correct X(t(T))in tion A3i enables computation of the number of egg laid equation A1 for the effects of say nutrition or some (S) in hosts, with the ratio 0ϽS/DCϽ1 being the pro- other factor. In the time-varying form of the model, portion of the demand satisÞed. Other factors may X(t(T)) may vary on daily or shorter time scales. affect the time-varying demand rate (Gutierrez 1992, 1996), and S/D may affect demographic variables such as developmental times, and emigration and survival Growth and Reproduction rates. Adult and immature stages often have different The Functional Response. All organisms are con- resource requirements, and the model formulation sumers, and the process of resource acquisition in the must accommodate this as well. Similar logic could be models is demand driven (Gutierrez 1992, 1996, Guti- developed for plants seeking light, water, or nutrients errez and Baumga¨rtner 1984). The per capita resource or predators seeking prey (e.g., Rodrõ´guez et al. 2011). acquisition rate S is computed using the ratio-depen- dent functional response model (equation A3) at re- Mortality source (N) and consumer (C) densities, where D is the per capita consumer demand, and ␣ is the pro- Temperature and other factors affect the daily mor- portion of the resource that may be discovered during tality rate and enter equation A1 as components of ⌬t. The demand may be for photosynthate, water and ␮͑t͑T͒͒. These effects vary widely across species but nitrogen in plants, or prey biomass or hosts by higher may be captured by similar functions (e.g., Fig. A2e). trophic levels including the economic level (Regev et al. 1998). As appropriate for the biology, the per capita Dormancy functional response model may be the parasitoid (equation A3i; Frazer and Gilbert, 1976) or predator A review of dormancy in insects is found in Nechols (equation A3ii) forms of the model (see discussion in et al. (1999). In our study, dormancy (say winter dia- Gutierrez 1996, p. 81). The predator form of the model pause) occurs in the European grapevine moth in re- is related to WattÕs model (Watt 1959). sponse to daylength (Fig. A2f; Gutierrez et al. 2012), or in pink bollworm in response to temperature and day- Ϫ␣N ϪDC length (Fig. A2g; Gutierrez et al. 1981). Dormancy may ͩ1 Ϫ e DC ͪ S ϭ Nͫ 1 Ϫ e N ͬ (parasitoid form) be transient and induced by low host density and/or high temperatures (e.g., olive ßy, medßy; see Gutierrez et al. [A3i] 2009, 2011). In some species, dormancy may also be inßuenced by nutrition (e.g., pink bollworm, olive ßy), ␣N Ϫ and other factors that may be included in the model as S ϭ DC͑1 Ϫ e DC͒ (predator form) identiÞed. As a practical consideration, individuals en- [A3ii] tering dormancy may be transferred to a separate dy- 410 ENVIRONMENTAL ENTOMOLOGY Vol. 42, no. 3 namics model formulated using equation A1, where de- mapping of the data. The simulation data might also be velopment proceeds on a different time scale. summarized using multiple regression, and the mar- ginal effects of each (or combinations of) indepen- dent variables on a dependent variable of interest GIS Analysis ␦ ␦ assessed (e.g., total pupae/year; y/ xi). An extensive Figure A3 shows the ßow of the analysis, including example of the use of marginal analysis is provided by weather data acquisition, simulation runs, and GIS Gutierrez et al. (2005).

Fig. A1. Population dynamics: (a) an age structured model for the dynamics for the egg (symbol e), larval (l), pupal (p), and adult (a) stages with ßows (aging) between age classes and stages, with the double arrows indicating net age speciÞc mortality, and (b) the distribution of developmental times based on the number of age cohorts (k) in sub Þgure A1a (see Severini et al. 2005).

Fig. A2. Submodels of biological processes: (a) the rate of development on temperature (Brie`re et al. 1999), (b) a scalar for the effects of say nutrition on developmental time, (c) the per capita fecundity proÞle on female age (x) (Bieri et al. 1983) at the optimum temperature (see the vertical dashed line in 2d, e), (d) the effects of temperature on normalized fecundity, (e) the mortality rate per day on temperature, (f) the proportion diapause induction as a function of daylength (e.g., grapevine moth; Gutierrez et al. 2012), and (g) diapause as a function of daylength and temperature (e.g., pink bollworm; see Gutierrez et al. 1981). SubÞgures without references apply to all species. June 2013 GUTIERREZ AND PONTI:ERADICATION OF INVASIVE SPECIES 411

Fig. A3. Flow of the analysis in the PBDM/GIS system (see Appendix text).