Prospective evaluation of the biological control of vine
mealybug: refuge effects and climate
Andrew Paul Gutierrez
1,2
*, Kent M. Daane
1
, Luigi Ponti
1
, Vaughn M. Walton
3
and C. Ken Ellis
1
1
Department of Environmental Science Policy and Management, College of Natural Resources, University of California, Berkeley, CA 94720–3114, USA;
2
Center for the Analysis of Sustainable Agricultural Systems (CASAS), Kensington, CA
94707, USA; and
3
Department of Horticultural Sciences, Oregon State University, Corvallis, OR 97331-7304, USA
Summary
1.
Vine mealybug
Planococcus ficus
is an invasive pest of vineyards in many areas of the world. InCalifornia, USA, it infests all plant subunits and has a spatial refuge from natural enemies under thebark and on roots. A temporal refuge is created when ants tending the mealybug reduce the efficacyof natural enemies.
2.
Biological control of vine mealybug is only partially successful and varies among Californiagrape-growing regions. To improve control and help determine appropriate natural enemies forimportation, the effects of weather on mealybug regulation by two parasitoids,
Anagyrus pseudococci
and
Leptomastidea abnormis
, and a coccinellid predator,
Cryptolaemus montrouzieri
, were examinedacross the ecological regions of California.
3.
Weather-driven, physiologically based age–mass structured demographic models of themealybug and its natural enemies were parameterized using laboratory data and field observations.Temperature was used to define the thermal limits and development rates of each species, andresource supply/demand ratios were used to scale daily per capita growth, fecundity and survivor-ship rates from maximal values at optimal conditions.
4.
The population dynamics of the mealybug and its natural enemies were simulated at 108 loca-tions in California over a 10-year period using observed weather. The simulation data were mappedusing a geographical information system (GIS) and analysed using linear multiple regression andmarginal analysis.
5.
The models predictions indicated that: (i) the parasitoid
A. pseudococci
has a larger impact on vinemealybug than either
L. abnormis
or
C. montrouzieri
; (ii) mealybug densities will be lowest in the hotdesert regions of southern California and highest in the cooler areas of northern California; (iii)mealybug density increases with season length and the size of the combined spatial–temporal refuge;(iv) biological control of mealybug could be achieved by reducing the size of the spatial–temporal refuge.
6.
Synthesis and applications.
Models, no matter how detailed, will always be incomplete; despitethis, the complexity of tri-trophic systems can be modelled and the effects of biotic factors and ofweather separated. The predictions of our model coincided well with field observations on vinemealybug, and clearly showed why the biological control will require additional species of naturalenemies and/or why the size of the spatial and temporal refuges must be reduced.
Key-words
: climate change, cultivated grape, GIS, physiologically based models,
Planococcusficus
, population regulation, refuges
Introduction
The vine mealybug
Planococcus ficus
(Signoret) (Hemiptera:Pseudococcidae) is a pest of the cultivated grape
Vitis vinifera
L. in the Mediterranean regions of Europe, Africa, theMiddle East and Argentina (Cox 1989; Walton, Daane &Pringle 2004), and has recently invaded California andMexico (Castillo, Hernández & Daane 2005; Daane
et al
.2006a). Vine mealybug infests all grape vine subunits but alsofeeds on a wide range of hosts, including subtropical andtropical crops (Cox 1989) and common weeds (Walton 2003).It has a high fecundity, four to seven generations per year, and
*Correspondence author. Andrew Paul Gutierrez, Department ofEnvironmental Science Policy and Management, College of NaturalResources, University of California, Berkeley, CA 94720–3114, USA.
excretes far more honeydew than other vineyard mealybugs,such as
Pseudococcus maritimus
(Ehrhorn) (Geiger & Daane2001). Natural enemies are thought to play an important rolein regulating vine mealybug (Berlinger 1977; Duso 1989;Walton 2003) and three have been introduced to California:the predator
Cryptolaemus montrouzieri
Mulsant (Coleoptera:Coccinellidae) and two arrhenotokous, kionobiont endopar-asitoids,
Anagyrus pseudococci
(Girault) and
Leptomastideaabnormis
(Girault) (Hymenoptera: Encyrtidae) (Bartlett1974; Noyes & Hayat 1994; Daane
et al
. 2003). The vinemealybug has a spatial refuge under bark and on roots, whereit is protected from extreme temperatures and natural enemies(Daane
et al
. 2003; Castillo, Hernández & Daane 2005) andinsecticide applications (Walton 2003). It also has a tempo-ral refuge, created when tending ants reduce the efficacy ofnatural enemies (Daane
et al
. 2006b). Much of this biology issummarized in Fig. 1.
The parasitoid
A. pseudococci
is widely established in Cal-ifornia but
L. abnormis
is much less common. Percentageparasitism may reach > 70% in the San Joaquin Valley of cen-tral California, but rarely exceeds 20% in the southernCoachella Valley, where summer temperatures are 5–10
°
Chigher (Daane
et al
. 2003; Daane, Malakar-Kuenen & Wal-ton 2004). During hot periods the mealybug is less likely toleave the spatial refuges and migrate to leaves and fruit, wherethey are readily attacked, and this may in part explain the dif-ferences in parasitism at the two locations (Daane
et al
. 2003).The predator
Cryptolaemus
is widely distributed and may beabundant in California vineyards. The precise role of naturalenemies in the regulation of vine mealybug is poorly under-stood largely because of difficulties in obtaining accurate fieldsamples (Geiger & Daane 2001; Millar
et al
. 2002). For thisreason, weather-driven, physiologically based demographicmodels of the species in our system are used to estimate andseparate out the relative contribution of each natural enemyand weather to mealybug mortality.
Model overview
The identification of common processes across trophic levelsallows the same functional response and population dynam-ics models to be used to model the dynamics and interactionsof all of the species in the systems (Fig. 2; Gutierrez &Baumgärtner 1984; Gutierrez 1996), including the economicone (Regev
et al
. 1998). A verbal description of the model isgiven here, while the mathematical details are reported inAppendix S1 in the supplementary material.
THE
FUNCTIONAL
RESPONSE
MODEL
A basic assumption of the model is that all organisms are con-sumers, and all search for resources (
X
) and allocate thoseacquired (
S
(
u
)) in priority order to egestion (1 –
β
), respira-tion (i.e.
Q
10
) and, with conversion efficiency (
λ
), to reproduc-tive and growth rates plus reserves (
GR
) (i.e. the metabolicpool model; Petrusewicz & MacFayden 1970; De Wit &Goudriaan 1978):
GR
=
(
S
(
u
)
β
−
Q
10
)
λ
eqn 1
Per capita acquisition of
S
=
S
(
u
) in a time-varying environ-ment is a search process, and to estimate this we use thedemand-driven ratio-dependent Gutierrez & Baumgärtner(1984) functional response model (equation 2). This model isa modification of Watt’s model (1959) (Gutierrez 1996). Atthe population level (
in our model may vary with age, stage, sex, size,temperature and other factors, and consumer preferences areeasily included in equation 2. Dividing both sides of equation2 by
DN
yields the supply demand ratio (0
≤
φ
S/D
=
S/D
< 1)(Gutierrez
et al
. 1994).However, organisms may search for multiple resources, and
the same functional response model is used to estimate searchsuccess for each. In plants, leaves search for light and rootssearch the soil to meet demands for water and nutrientsresources. Herbivores and carnivorous predators eat biomass,and parasitoids seek unitary hosts, but they may seek matesand other sources of food, etc. An index for temperature andthe various supply/demand ratios (i.e. 0
≤
φ
*
=
φ
1
φ
2
...
φ
n
< 1)is used to scale per capita vital rates from the maximum (e.g.
GR
=
φ
*GR
max
).
POPULATION
DYNAMICS
The biology of resource acquisition and allocation is embeddedin a distributed maturation time demographic model, usedhere to simulate the dynamics of structured populationswith age, mass and other attributes (Vansickle 1977; DiCola,Gilioli & Baumgärtner 1999). The general model for the
i
thage class of a population is:
eqn 4
N
i
is the density of the cohort,
k
is the number of age classes,
del
is the expected mean developmental time,
Δ
a
is an incre-ment in age and
μ
i
(
t
) is the proportional net loss rate that
includes the rich biology affecting the species’ dynamics(births, deaths, growth, predation, net immigration, etc.).
MODELS
A model for grapevine growth and development (Wermelinger,Baumgärtner & Gutierrez 1991) based on the above approachwas used to capture the bottom-up effects on the mealybug andhigher trophic levels and their interactions (Figs 1 and 2; cf.Rochat & Gutierrez 2001). The plant canopy model consistsof models of subunit populations (e.g. leaves, stem, root and fruit)and the mealybug attacks all subunits. Grape has a winter dormantperiod but the mealybug continues to feed on plant reserves.
In addition to age and mass, the insect dynamic modelsmay have attributes such as sex, stage, morph and otherfactors. Mealybugs in or outside the spatial refuge aremodelled as separate populations. Extensive data for thebiology of each insect species were found in the literatureand are summarized in Table 1 and Fig. 3. From the data,estimates of temperature thresholds, duration of life stages,non-linear temperature-dependent developmental rates, maxi-mum age-dependent fecundity, temperature-dependent scalarsfor growth and reproductive rates, egestion, host-stagepreferences and sex ratios were determined. The data wereused to parameterize functions used in the model (Table 1,column 1). Only the per capita search rates (
s
) for each specieswere estimated by simulation (see equation 2).
Boolean variables in a set-up file are used to determine thecombinations of species simulated in the different studies.The same initial population densities (e.g. 50 first instarmealybug per vine) were assumed for all species at all loca-tions. This assumption creates little difficulty, as the goal wasto evaluate the effects of site-specific weather on the time evo-lution of the system at each location and not the time-specificdynamics. Weather from 108 locations in California, USA,
D S GR Q ( / )/max max( )≈ = +t λ β10
Fig. 2. Biology of the vine mealybug (Vmb)system with natural enemies: encyrtidparasitoids Anagyrus pseudococci (Ap),Leptomastidea abnormis (La) and coccinellidpredator Cryptolaemus montrouzieri (Cm).
Egg to oviposition Egg to adult Egg to adult Pre-ovipositionDevelopment stages used a 0·0018 0·0025** 0·0019 Polynomial fit = [0·2813 – 0·00005T 2 + 0·0034T 1 − 0·0576T]
b 1·45 1·5 1·8Rate of development ¶ c 1·12 1·065 1·055
T1 30·5 °C 38 °C 41 °CT2 24 °C 27 °C 28 °C
Egestion rate 1 – β 0·5 NA NA 0·26Temperature scalars †† Tmin 12·5 °C 12·8 °C 10·28 °C 14·5 °C
Tmax 34·0 °C 36·0 °C 37·0 °C 38·5 °CMaximum age (x) specific fecundity/day at 27 °C a 90·0 15·5 15·5 36( f(x) = ax/bx) b 1·7 1·38 1·385 1·4
Host stage preference ξ Plant sap VMB VMB VMB: all stages attackedEgg = 0·0, I = 0·0 Egg = 0, I = 0 Parasitoid: egg-larval stages;II = 0·114, III = 0·34 II = 0·383, III = 0·206 Coccinellid: stages younger than consumerPre-ova = 0·54 Pre-ova = 0·206Adult = 0·54 Adult = 0206Parasitized host = 0·05 Parasitized host = 0·05
Sex ratio in host stage attacked (females/total)‡‡ 0·5 VMB VMB 0·55Egg = 0, stage I = 0 Egg = 0, I = 0·0II = 0·09, III = 0·32 II = 0·25, III = 0·83Pre-ova = 0·68, Pre-ova = 0·77Adult = 0·6 Adult = 0·67
Search parameter (constant or per capita (s)) α(s, N) α = 0·85 s = 0·05 s = 0·004 α = 0·5
Delay parameter k 45 25 25 25
*K. M. Daane, unpublished data; Islam, Perera & Copland (1997); Walton (2003); Daane et al. (2003).†Islam & Copland (1997, 2000); Tingle & Copland (1988a,b, 1989); De Jong & Van Alphen (1989); Daane, Malakar-Kuenen & Walton (2004).‡Cadée & Van Alphen (1997).§Ramesh & Azam (1988); Reddy, Sreedharan & Bhat (1991); Heidari & Copland (1992); Jalali, Singh & Biswas (1999); Mani & Krishnamoorthy (1999); Venkatesan, Singh & Jalali (2001); Heidari (2001); Persad & Khan (2002).¶Janisch (1925) model: the rates of development were calculated based on data for some life stages and adjusted in the model for the entire life cycle.**All available data used.††Tmid = (Tmax − Tmin)/2. ‡‡Sagarra, Vincent & Stewart (2001): oviposition data on A. kamali used for both A. pseudococci and L. abnormis.
were used that included daily maximum and minimumtemperatures (°C), solar radiation (kCal cm–2 day–1), rainfall(mm), daily runs of wind (km day–1) and relative humidity forthe period January 1995 to December 2005. The temperaturein the root zone and canopy were estimated using linearregression on ambient temperatures.
The geo-referenced simulation data were written to files atspecified intervals and mapped for altitudes below 750 musing a geographical information system (GIS) based on theopen software GRASS. [GRASS is an open-source GIS soft-ware package originally developed by the United State ArmyCorp of Engineers. The version used (2006) is that maintainedby the GRASS Development Team, Geographic ResourcesAnalysis Support System (GRASS) Software, ITC-irst,Trento, Italy (http://grass.itc.it, accessed 27 July 2007).]Raster-based triangulation kriging on a 1-km grid was usedto interpolate the data.
The simulation data were analysed across years and loca-tions using linear multivariate regression. Only independentvariables and interaction terms with slopes significantlygreater than zero (t-values with P < 0·05) were retained in themodel. The goal of the analysis was to estimate the averagemagnitude and direction of large effects using marginal ana-lysis of the regression models (∂y/∂xi).
Results
The mealybug and its natural enemies have been studiedintensively in the San Joaquin Valley (Parlier, Fresno Co.) andCoachella Valley (Mecca, Riverside Co.) (Daane et al. 2003,2006a) and hence simulations for these two locations arepresented first to illustrate the time-varying dynamics andsuppression of mealybug by natural enemies and weather. Arefuge of 60% for the mealybug was assumed.
SAN JOAQUIN VALLEY
Parlier is located near the centre of the San Joaquin Valleyin a region that produces table, raisin and wine grapes.Simulated vine mealybug densities annually reach levels of30 000–140 000 active stages (crawlers, adults) per vine duringmid-summer (Fig. 4a). The dashed line at 105 is a referencelevel for comparison with simulations for the Coachella Valley(see below). Densities of the coccinellid predator C. montrouzieriremain low despite high mealybug densities (Fig. 4a,b). Thetwo parasitoid species cycle in synchrony with the mealybug,with the proportion of parasitism by A. pseudococci reaching0·6–0·7 and that by L. abnormis 0·15–0·25 (Fig. 4c,d, respec-tively). Densities of mealybugs parasitized by A. pseudococciand L. abnormis reach approximately 20 000 and 3000 vine–1,respectively. The lower levels of parasitism by L. abnormisreflect its lower per capita search rate (α = 0·004 vs. 0·05;Table 1), its 20% greater developmental times (after correc-tions for differences in thermal thresholds) and the effects ofinterspecific competition.
COACHELLA VALLEY
Warmer temperatures at Mecca produce longer averageseasons for grape growth than in the San Joaquin Valley [i.e.4007 vs. 2644 degree-days (dd) > 7 °C, respectively]. However,densities of mealybug are predicted to be lower and onlyoccasionally do they exceed 100 000 mealybugs vine–1 (Fig. 4avs. Fig. 5a). Despite lower mealybug densities, coccinellidlarval and adult populations are roughly four to six timeshigher in the Coachella Valley (Fig. 4b vs. Fig. 5b). The pro-portion of parasitism is roughly the same at both sites forA. pseudococci but parasitism by L. abnormis is slightly higherin the Coachella Valley (Fig. 5c,d).
Fig. 3. Developmental rates as a function oftemperature, the daily oviposition pattern at27 °C and the estimated thermal limits onaverage temperature (see Table 1 for details):(a–c) vine mealybug, (d–f), A. pseudococci,(g–i) L. abnormis and (j–l) C. montrouzieri.References for data sources are summarizedin Table 1.
Time-series plots of daily number of mealybugs parasitizedby each parasitoid species and the numbers of mealybugactive stages are shown in Fig. 6. The counter-clockwise rota-tion of the plots suggests oscillatory regulation by the para-sitoids. The data may be viewed as an approximation of eachparasitoid’s k-values on log mealybug densities. The positiveslopes of the linear regressions indicate that the action of bothparasitoids is directly density-dependent (Varley & Gradwell1960). The slopes for A. pseudococci at Parlier and Meccaare 1·136 and 1·15, respectively, suggesting that its action isover-compensating (i.e. the death rate is greater than themealybug population growth rate). In contrast, the slopes forL. abnormis are 0·64 and 0·83 at Parlier and Mecca, respec-tively, and suggest that its action is under-compensating (i.e.the death rate is less than the mealybug population growth
rate). The r2 of the regression for A. pseudococci is 0·88 atParlier but only 0·40 at Mecca. The reverse trend in r2 is seenfor L. abnormis, reflecting its tolerance of higher temperatures(0·09 vs. 0·25).
Plots of number of log C. montrouzieri life stages on lognumber of mealybugs (active stages + parasitized mealybugs)were also made, but are not illustrated. The interpretation ofthe results is difficult, as predator increases are not directlytranslated to mortality rates. The closest relationship occurswith coccinellid eggs, where the slopes of the regressions are0·19 and 0·015 and the r2 values are 0·056 and 0·003 for Parlierand Mecca, respectively. Regressions for number of C. mon-trouzieri larvae + adults on number of mealybugs were lessinformative (slopes of 0·055 and 0·045, and r2 values of 0·007and 0·002 for Parlier and Mecca, respectively). The resultssuggest a very weak density-dependent response of thepredator to mealybug density.
Fig. 4. Vine mealybug–predator system,(a) mealybug, (b) C. montrouzieri, (c) A.pseudococci and (d) L. abnormis, simulatedusing weather data from Parlier in the SanJoaquin Valley of central California duringthe period 1 January 1995 to 31 December2005.
Fig. 5. Vine mealybug–predator system,(a) mealybug, (b) C. montrouzieri, (c) A.pseudococci and (d) L. abnormis, simulatedusing weather data from Mecca in the desertarea of southern California during the periodfrom 1 January 1995 to 31 December 2005.
A measure of season-long pest loads is the cumulative total ofdaily densities of mealybug active stages (i.e. mealybug days).Similar computations were made for the three natural enemyspecies. These values vary widely from year to year, and hencewe used the average of the yearly simulations for the period1996–2005 to capture the general patterns (Fig. 7).
Mealybug densities are predicted to be highest in the coolervineyard regions of California, particularly the north coastregions (Napa and Sonoma Co.) and the Sierra Nevada foot-hills. Densities are predicted to be lower in the warmer SanJoaquin Valley and still lower in the hotter areas such as theCoachella Valley (Fig. 7a). The abundance of the coccinellidbeetle C. montrouzieri is predicted to be generally lowthroughout most of California (Fig. 7b), with the highestdensities occurring in the hotter region of southern California(Fig. 4b vs. Fig. 5b). The geographical distribution andrelative abundance of A. pseudococci is similar to that of themealybug (Fig. 7d). The abundance of A. pseudococci is fourto five times higher than L. abnormis and its range is wider,except in hotter areas. However, while the maps are informa-tive, further insights into the biology were obtained usingmultivariate regression of the simulation data. We recognizethe statistical problems inherent in using simulation data inour analysis, but the goal is to assess general trends and rela-tionships in the model.
MULTIVARIATE REGRESSION ANALYSIS
Multiple linear regression analysis of the yearly simulationdata and other runs where refuge size varied were used toassess the impact of weather, natural enemies and refugesize on crop yield and season-long measures of mealybug
abundance (V = mealybug days per vine). All regressions usedseason length in dd, mealybug refuge size (0 ≤ H ≤ 1), and thepresence–absence (0,1) of natural enemies (A+, A. pseudo-cocci; C+, C. montrouzieri; L+, L. abnormis) as independentvariables. The effects of competition by natural enemies werealso examined. The average effect of any independent variablewas estimated by the partial regression coefficients giventhe average effects of all other independent variables. Thisapproach was used successfully in the analysis of the biologicalcontrol of cassava mealybug in West Africa (Neuenschwanderet al. 1989).
Crop yield
The regression model for grape yield (g vine–1) is:
Assuming an average refuge H = 0·5 and an average seasonlength of 2375 dd, H has by far the largest negative effect onyield, followed by season length. In contrast, the average neteffect of natural enemy presence and their interactions have apositive effect on yield (A+ >> L+ > C+). Variables for mealy-bug abundance were not included in the model because thedirection of their effect was in H.
Vine mealybug density
Regressing log V (i.e. V = mealybug days) on the same inde-pendent variables as in equation 5 yields:
Fig. 6. Time–series plots of log naturalenemy numbers on log vine mealybug mobilestages: vine mealybug parasitized by (a, c) A.pseudococci and (b, d) L. abnormis at Parlierin the great central Valley and Mecca in theCoachella Valley of southern California. Thecircle symbol is the initial starting point.
Again assuming H = 0·5, an average season length of 2375ddand no natural enemies, average mealybug days equals7·37 × 106. Adding the effects of all natural enemies decreasesaverage mealybug days 67·6%, to 2·38 × 106. These are aver-age values across all years and locations, and we note thatthe order of importance and degree of impact may changein different ecological zones (Fig. 6) and with declines inH. For example, if H = 0, V decreases a further 44·8%,amply illustrating the adverse effect the refuge plays inmealybug control.
Taking the partial derivative of equation 6 for presence–absence of each natural enemy separately yields the followingrelationships:
eqn 8
This suggests that the general order of impact is A.pseudococci > L. abnormis, with C. montrouzieri serving toincrease mealybug density (V ).
Interactions among natural enemies
Ignoring the variable for the mealybug refuge, theinteractions among the three natural enemy species are
Fig. 7. Mapping of simulated average yearly per plant cumulative daily densities of (a) vine mealybug active stages (i.e. VMB days),(b) C. montrouzieri larvae, (c) A. pseudococci and (d) L. abnormis egg–larval stages for the period 1 January 1995–31 December 2005.The circle and triangle symbols are Fresno and Mecca, California, USA, respectively, and the smaller dots are the meteorological stations. Thecolour scale on the left-hand side of each figure indicates relative densities in each map.
The regression coefficients relating the effects of A. pseudococci(A+) and C. montrouzieri (C+) presence on log L. abnormisdays (La, cumulative immature stages) are negative, suggestingcompetition effects from them, while the positive interactionterm suggests competition between A+ and C+ that has a positiveeffect on La. The net effect on L. abnormis abundance ispositive (equation 9i).
Similarly, the presence of L. abnormis and C. montrouzieriand their interaction has a net positive effect on log A.pseudococci days (equation 9ii). In the regression for logC. montrouzieri larval days (equation 9iii), the coefficientsfor the presence of the two parasitoids are positive but theinteraction term is negative. The positive terms occur becauseparasitoid immature stages are food for coccinellid larvaeand adults, while the negative interaction coefficient suggestscompetition from them. The net effect is that the presence ofthe parasitoids increases log C. montrouzieri larval days.
Discussion
Climate and abiotic factors limit the distribution and abun-dance of species, and temperature and other factors affect netgrowth and reproduction in poikilotherms (Wellington,Johnson & Lactin 1999). Weather sets the limits for trophicinteractions among species of poikilotherms and mayinfluence the level of control by natural enemies (Huffaker,Messenger & DeBach 1971). In general, the analysis of naturalenemy performance across varying ecological zones is adifficult and recurring problem in biological control (Mills &Getz 1996). A classic example of the effects of temperature onbiological control is that of the cottony cushion scale Iceryapurchasi Maskell, where in warmer areas it is controlled by thevedalia beetle Rodolia cardinalis Mulsant and in cooler areasby the parasitic fly Crytochaetum iceryae (Will.) (Quezada &DeBach 1973). Other examples are the spotted alfalfa aphidTherioaphis maculata (Buckton) (Force & Messenger 1964),olive scale Parlatoria oleae (Colvée) (Huffaker & Kennett1966) and red scale Aonidella aurantii (Maskell) (Murdoch,Briggs & Swarbrick 2005).
Biological control of the vine mealybug in California todate has not been successful (Daane et al. 2006a) and withthis study we explored the reasons why. To capture and sep-arate weather-related biotic and abiotic effects requires thatthe biological responses be included in the model (Gilbert
& Gutierrez 1973; Gilbert et al. 1976; Murdoch, Briggs &Swarbrick 2005). Models that fail to incorporate this biologyhave contributed to controversy (Lawton 1977; Gilbert 1984) butadding relevant biology may lead to the well-known trade-offbetween the benefits of increased realism and the lessenedmathematical tractability required to analyse model stabilityand other properties (Wang & Gutierrez 1980; Godfray &Waage 1991). In this study, graphical methods were used toexplore the dynamic properties of the system, and linearmultivariate regression and marginal analysis were used toanalyse the larger trends in the relationships modelled.
The use of weather-driven physiologically based modelssimplifies the problem of separating biotic and abiotic effects(Gutierrez & Baumgärtner 1984; Gurney et al. 1996; Gutierrez1996; Holst et al. 1997). For example, Rochat & Gutierrez(2001) were able to confirm the field observations of Huffaker& Kennett (1966) concerning the biological control of olivescale by two parasitoids only after the weather-driven percapita resource acquisition and allocation and forms ofcompetition were included in a physiologically based model.Analysis of biological systems across large landscapes ispossible using physiologically based models because thepredictions of the model are independent of time and place.This approach was used here to examine the biologicalcontrol of the exotic vine mealybug across the ecologicalzones of California.
PREDICTIONS OF THE MODEL
Accurate season-long estimates of vine mealybug densitiesare largely unavailable, and the wide use of insecticides fortheir control complicates the process of ‘testing’ the model.Populations of mealybug and natural enemies have beensampled at two locations: in the hot Coachella Valley, wherelower pest densities were found, and in the cooler San JoaquinValley (Fig. 8; Daane et al. 2003). Our model makes similarpredictions for these sites.
Four predictions of the model were of interest to under-stand and improve biological control: (i) the average abun-dance of vine mealybug and its natural enemies acrossCalifornia using observed weather and in the face of predictedclimate warming; (ii) the density and efficacy of the predatorC. montrouzieri; (iii) the comparable effectiveness of theparasitoids A. pseudococci and L. abnormis to be used as aguide in the importation of new species of parasitoids;and (iv) the importance of the spatial–temporal refuge inmealybug control.
Using daily weather for the period 1995–2005, the modelpredicts that the distribution and abundance of vine mealybugacross years will vary widely because of differing temperatureeffects on species behaviour, growth rates and interactions(Fig. 7a–d). Pest densities are predicted to be highest in thewine grape regions of northern California and the SierraNevada foothills, with lower densities occurring in the hottersouthern table grape regions (Fig. 7a). The mealybug has anarrow range of temperature (11–35 °C) favourable for itsdevelopment (Fig. 3) and seeks cooler sites under the bark or
in the root zone during periods of high temperatures, where itis also less likely to be attacked by natural enemies (i.e. a spa-tial refuge). Prior to this work, there was some doubt regard-ing the level of damage the vine mealybug might pose in thecooler grape regions of California, Oregon and Washington.Here, given the absence of natural enemy activity, we provideevidence that the vine mealybug would not only survive incooler regions but may also cause significant crop damage.
The model also explains the limitations of C. montrouzierias a biological control agent. This predator is common invineyards with very high mealybug densities but it does notreadily survive cold winter temperatures (Bartlett 1974; Jalali,Singh & Biswas 1999). By modelling the biological traits andtemperature tolerances of the predator and mealybug, themodel predicts that C. montrouzieri’s abundance would behighest on average in hot climates of southern California(Fig. 7b). The response of the predator C. montrouzieri isweakly density dependent and, in contrast to the observa-tions of Prakasan & Bhat (1985) for Leptomastix dactylopiiHoward, its attack on immature stages of the parasitoids doesnot overly interfere with their activity in grape.
The widely established parasitoid A. pseudococci has thebest climatic match to the vine mealybug, and its predictedaverage geographical distribution and patterns of abundanceare similar to that of the mealybug (Fig. 7a vs. Fig. 7c).Simulated densities of L. abnormis are highest in the hotterareas of California, but the densities are greater than thoserecorded in field studies (Daane et al. 2003).
For regulation to occur, the natural enemies must operatein a density-dependent manner. As with other encrytidparasitoids (Summy, French & Hart 1986), our analysis of thesimulation data suggests that A. pseudococci has an over-compensating density-dependent response to vine mealybugthat is insufficient for economic control. The parasitoid L.abnormis has a density-dependent action but it is less thancompensatory because of a low per capita ‘effective’ searchrate (0·004 vs. 0·05). (Note that the search rates were fitted viasimulation.) If we assume equal per capita search rates forboth parasitoids, say 0·05, the model predicts that L. abnormis
would be the more prevalent species, a prediction thatcoincides with laboratory studies of parasitoid efficiency inthe face of interspecific competition. For example, when themealybug was exposed to both parasitoids in cage studiesthat reduced parasitoid host-finding effects and eliminatedant interference, L. abnormis out-competed A. pseudococci insome cases (Daane et al. 2003). The dominance of L. abnormiscould in these cases be because of the effect of host sizestructure, as found for the parasitoids on cassava mealybugin Africa, where the parasitoid Epidinocarsis diversicornis(Howard) failed to persist in the field (Neuenschwander et al.1989). In cassava, Epidinocarsis lopezi (DeSantis) out com-petes E. diversicornis because it produces more female off-spring in smaller hosts, giving it an advantage during periodsof drought stress on cassava (Gutierrez, Neuenschwander &van Alphen 1993). In the grape, L. abnormis produces morefemales on smaller hosts than A. pseudococci and this mightexplain some of the laboratory results, but host size structurewould not appear to be a factor in irrigated fertilized vine-yards. More probably, there is a greater impact of ants onL. abnormis that increases the size of the temporal refuge.
The presence of the spatial and temporal refuges is knownto interfere with the level of mealybug control (Daane et al.2006b) but we could not explicitly separate their effects in themodel (i.e. as components of H) because there are at leastthree principal species of ants that tend vine mealybug in Cal-ifornia and each has a different geographical distribution andlevel of aggressiveness. Furthermore, the temporal refugeprovided by ants is expected to vary with mealybug densityand is expected to be particularly important at low mealybugdensities before the copious mealybug honeydew saturatesant demands. However, if we assume the same search ratefor both parasitoids, simulation suggests that economicregulation of mealybug would still not occur if more than 50%of the mealybugs are in refuges (e.g. log mealybug days =6·51H + 1·06).
Marginal analysis of multivariate regression models proveduseful in assessing the role of the natural enemy impact andinteractions on resource species (Neuenschwander et al.
Fig. 8. Seasonal vine mealybug abundancepatterns in the Coachella Valley and SanJoaquin Valley, as measured by 3-min counts ineach of seven vine sections (21 min vine–1)(from Daane et al. 2003).
1989). With this approach, the dependent variable might bepest density and the independent variables might be naturalenemy presence or absence and other factors. Ideally, fielddata would be used in the analyses, but unfortunately data forvine mealybug across wide geographical areas are not availablebecause accurate samples in vineyards are difficult to obtain,particularly at low densities (Geiger & Daane 2001). Simula-tion results across all years and regions indicate that, on aver-age, mealybug density increases with season length and size ofthe refuge, while the action of the natural enemies decreasespest density only 68% (equation 7). The net action of L.abnormis was under-compensating and density dependent,and that of A. pseudococci was slightly over-compensatory,but overshadowing this was the large mealybug refuge. Theanalysis suggests that reducing the temporal refuge bycontrolling ants or limiting the movement of the mealybug tospatial refuges are key elements for economic control of thispest, but this may change with climate warming.
CLIMATE WARMING
State of the art climate models (http://meteora.ucsd.edu/cap/cccc_model.html, accessed 27 June 2007) have been devel-oped that predict average temperature increases in Californiaof 1·8–4 °C, and an obvious question is how this will affect
agricultural crops and their pest complexes. Time-series plotsof daily, weekly or monthly temperature, rainfall, vapour-pressure deficit and other variables during periods of pestactivity are often used to characterize climate zones favoura-ble for species, and the results are often extrapolated in cli-mate change studies. Davis et al. (1998) called this the ‘climateenvelope’ approach (Sutherst, Maywald & Bottomly 1991)and suggested the conclusions concerning the effects of cli-mate change may be misleading if the interactions betweenspecies are altered by climate change. The tri-trophic physio-logically based GIS demographic modelling approach cir-cumvents most of these limitations (Gutierrez et al. 2005).
If average daily temperatures are increased 2° and 4 °Cacross all locations, the model predicts mealybug densitieswould increase generally throughout all regions of California(Fig. 9a vs. Fig. 9e,i). Biological control would decrease withincreasing temperatures despite increases in both the densityof A. pseudococci (Fig. 9c vs. Fig. 9g,k) and the favourablerange and density of the predator C. montrouzieri (Fig. 9b vs.Fig. 9f,j) and the parasitoid L. abnormis (Fig. 9d vs. Fig. 9h,l).
Acknowledgements
We thank our thoughtful referees for useful suggestions and edits. The Univer-sity of California Statewide IPM Program and the California Table GrapeCommission provided partial funding for this study.
Fig. 9. Mapping of simulated average yearly per vine cumulative daily species densities (columns) using three weather scenarios, i.e. observeddaily temperatures (+0 °C) and increases of +2 °C and +4 °C for the period 1 January 1995 to 31 December 2005 (rows): vine mealybug activestages (i.e. VMB days; a, e, i), C. montrouzieri larvae (b, f, j), A. pseudococci (c, g, k) and L. abnormis (d, h, l) egg–larval stages. The colour scaleon the left-hand side of each figure indicates relative densities in each map.
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Received 8 December 2006; final copy received 5 March 2007Handling Editor: Joan Cossentine
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