*Correspondence author. Andrew Paul Gutierrez, Department of Environmental Science Policy and Management, College of Natural Resources, University of California, Berkeley, CA 94720–3114, USA.
1Vine mealybug Planococcus ficus is an invasive pest of vineyards in many areas of the world. In California, USA, it infests all plant subunits and has a spatial refuge from natural enemies under the bark and on roots. A temporal refuge is created when ants tending the mealybug reduce the efficacy of natural enemies.
2Biological control of vine mealybug is only partially successful and varies among California grape-growing regions. To improve control and help determine appropriate natural enemies for importation, the effects of weather on mealybug regulation by two parasitoids, Anagyrus pseudococci and Leptomastidea abnormis, and a coccinellid predator, Cryptolaemus montrouzieri, were examined across the ecological regions of California.
3Weather-driven, physiologically based age–mass structured demographic models of the mealybug 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, and resource supply/demand ratios were used to scale daily per capita growth, fecundity and survivorship rates from maximal values at optimal conditions.
4The population dynamics of the mealybug and its natural enemies were simulated at 108 locations in California over a 10-year period using observed weather. The simulation data were mapped using a geographical information system (GIS) and analysed using linear multiple regression and marginal analysis.
5The models predictions indicated that: (i) the parasitoid A. pseudococci has a larger impact on vine mealybug than either L. abnormis or C. montrouzieri; (ii) mealybug densities will be lowest in the hot desert 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.
6Synthesis and applications. Models, no matter how detailed, will always be incomplete; despite this, the complexity of tri-trophic systems can be modelled and the effects of biotic factors and of weather separated. The predictions of our model coincided well with field observations on vine mealybug, and clearly showed why the biological control will require additional species of natural enemies and/or why the size of the spatial and temporal refuges must be reduced.
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, the Middle East and Argentina (Cox 1989; Walton, Daane & Pringle 2004), and has recently invaded California and Mexico (Castillo, Hernández & Daane 2005; Daane et al. 2006a). Vine mealybug infests all grape vine subunits but also feeds on a wide range of hosts, including subtropical and tropical crops (Cox 1989) and common weeds (Walton 2003). It has a high fecundity, four to seven generations per year, and excretes far more honeydew than other vineyard mealybugs, such as Pseudococcus maritimus (Ehrhorn) (Geiger & Daane 2001). Natural enemies are thought to play an important role in 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 endoparasitoids, Anagyrus pseudococci (Girault) and Leptomastidea abnormis (Girault) (Hymenoptera: Encyrtidae) (Bartlett 1974; Noyes & Hayat 1994; Daane et al. 2003). The vine mealybug has a spatial refuge under bark and on roots, where it is protected from extreme temperatures and natural enemies (Daane et al. 2003; Castillo, Hernández & Daane 2005) and insecticide applications (Walton 2003). It also has a temporal refuge, created when tending ants reduce the efficacy of natural enemies (Daane et al. 2006b). Much of this biology is summarized in Fig. 1.
The parasitoid A. pseudococci is widely established in California but L. abnormis is much less common. Percentage parasitism may reach > 70% in the San Joaquin Valley of central California, but rarely exceeds 20% in the southern Coachella Valley, where summer temperatures are 5–10 °C higher (Daane et al. 2003; Daane, Malakar-Kuenen & Walton 2004). During hot periods the mealybug is less likely to leave the spatial refuges and migrate to leaves and fruit, where they are readily attacked, and this may in part explain the differences in parasitism at the two locations (Daane et al. 2003). The predator Cryptolaemus is widely distributed and may be abundant in California vineyards. The precise role of natural enemies in the regulation of vine mealybug is poorly understood largely because of difficulties in obtaining accurate field samples (Geiger & Daane 2001; Millar et al. 2002). For this reason, weather-driven, physiologically based demographic models of the species in our system are used to estimate and separate out the relative contribution of each natural enemy and weather to mealybug mortality.
The identification of common processes across trophic levels allows the same functional response and population dynamics models to be used to model the dynamics and interactions of all of the species in the systems (Fig. 2; Gutierrez & Baumgärtner 1984; Gutierrez 1996), including the economic one (Regev et al. 1998). A verbal description of the model is given here, while the mathematical details are reported in Appendix S1 in the supplementary material.
the functional response model
A basic assumption of the model is that all organisms are consumers, and all search for resources (X) and allocate those acquired (S(u)) in priority order to egestion (1 – β), respiration (i.e. Q10) and, with conversion efficiency (λ), to reproductive and growth rates plus reserves (GR) (i.e. the metabolic pool model; Petrusewicz & MacFayden 1970; De Wit & Goudriaan 1978):
The search function (α(N) = 1 − exp(−sN)) is the proportion of X that may be potentially found by N with average per capita search rate s. D is the maximal per capita demand per unit of N under conditions of non-limiting resource and may be estimated by solving for DSmax in equation 1 (Gutierrez & Baumgärtner 1984):
Note that D in our model may vary with age, stage, sex, size, temperature and other factors, and consumer preferences are easily included in equation 2. Dividing both sides of equation 2 by DN yields the supply demand ratio (0 φS/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 search success for each. In plants, leaves search for light and roots search the soil to meet demands for water and nutrients resources. Herbivores and carnivorous predators eat biomass, and parasitoids seek unitary hosts, but they may seek mates and other sources of food, etc. An index for temperature and the various supply/demand ratios (i.e. 0 φ* = φ1φ2 ... φn < 1) is used to scale per capita vital rates from the maximum (e.g. GR = φ*GRmax).
The biology of resource acquisition and allocation is embedded in a distributed maturation time demographic model, used here to simulate the dynamics of structured populations with age, mass and other attributes (Vansickle 1977; DiCola, Gilioli & Baumgärtner 1999). The general model for the ith age class of a population is:
Ni is the density of the cohort, k is the number of age classes, del is the expected mean developmental time, Δa is an increment in age and µi(t) is the proportional net loss rate that includes the rich biology affecting the species’ dynamics (births, deaths, growth, predation, net immigration, etc.).
A model for grapevine growth and development (Wermelinger, Baumgärtner & Gutierrez 1991) based on the above approach was used to capture the bottom-up effects on the mealybug and higher trophic levels and their interactions (Figs 1 and 2; cf. Rochat & Gutierrez 2001). The plant canopy model consists of models of subunit populations (e.g. leaves, stem, root and fruit) and the mealybug attacks all subunits. Grape has a winter dormant period but the mealybug continues to feed on plant reserves.
In addition to age and mass, the insect dynamic models may have attributes such as sex, stage, morph and other factors. Mealybugs in or outside the spatial refuge are modelled as separate populations. Extensive data for the biology of each insect species were found in the literature and 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, maximum age-dependent fecundity, temperature-dependent scalars for growth and reproductive rates, egestion, host-stage preferences and sex ratios were determined. The data were used to parameterize functions used in the model (Table 1, column 1). Only the per capita search rates (s) for each species were estimated by simulation (see equation 2).
Table 1. Biological parameters for the species in the vine mealybug food web
Sex ratio in host stage attacked (females/total) ‡‡
Egg = 0, stage I = 0
Egg = 0, I = 0·0
II = 0·09, III = 0·32
II = 0·25, III = 0·83
Pre-ova = 0·68,
Pre-ova = 0·77
Adult = 0·6
Adult = 0·67
Search parameter (constant or per capita (s))
α = 0·85
s = 0·05
s = 0·004
α = 0·5
Boolean variables in a set-up file are used to determine the combinations of species simulated in the different studies. The same initial population densities (e.g. 50 first instar mealybug per vine) were assumed for all species at all locations. This assumption creates little difficulty, as the goal was to evaluate the effects of site-specific weather on the time evolution of the system at each location and not the time-specific dynamics. Weather from 108 locations in California, USA, were used that included daily maximum and minimum temperatures (°C), solar radiation (kCal cm−2 day−1), rainfall (mm), daily runs of wind (km day−1) and relative humidity for the period January 1995 to December 2005. The temperature in the root zone and canopy were estimated using linear regression on ambient temperatures.
The geo-referenced simulation data were written to files at specified intervals and mapped for altitudes below 750 m using a geographical information system (GIS) based on the open software GRASS. [GRASS is an open-source GIS software package originally developed by the United State Army Corp of Engineers. The version used (2006) is that maintained by the GRASS Development Team, Geographic Resources Analysis 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 used to interpolate the data.
The simulation data were analysed across years and locations using linear multivariate regression. Only independent variables and interaction terms with slopes significantly greater than zero (t-values with P < 0·05) were retained in the model. The goal of the analysis was to estimate the average magnitude and direction of large effects using marginal analysis of the regression models (y/xi).
The mealybug and its natural enemies have been studied intensively in the San Joaquin Valley (Parlier, Fresno Co.) and Coachella Valley (Mecca, Riverside Co.) (Daane et al. 2003, 2006a) and hence simulations for these two locations are presented first to illustrate the time-varying dynamics and suppression of mealybug by natural enemies and weather. A refuge of 60% for the mealybug was assumed.
san joaquin valley
Parlier is located near the centre of the San Joaquin Valley in a region that produces table, raisin and wine grapes. Simulated vine mealybug densities annually reach levels of 30 000–140 000 active stages (crawlers, adults) per vine during mid-summer (Fig. 4a). The dashed line at 105 is a reference level for comparison with simulations for the Coachella Valley (see below). Densities of the coccinellid predator C. montrouzieri remain low despite high mealybug densities (Fig. 4a,b). The two parasitoid species cycle in synchrony with the mealybug, with the proportion of parasitism by A. pseudococci reaching 0·6–0·7 and that by L. abnormis 0·15–0·25 (Fig. 4c,d, respectively). Densities of mealybugs parasitized by A. pseudococci and L. abnormis reach approximately 20 000 and 3000 vine−1, respectively. The lower levels of parasitism by L. abnormis reflect its lower per capita search rate (α = 0·004 vs. 0·05; Table 1), its 20% greater developmental times (after corrections for differences in thermal thresholds) and the effects of interspecific competition.
Warmer temperatures at Mecca produce longer average seasons 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 only occasionally do they exceed 100 000 mealybugs vine−1 (Fig. 4a vs. Fig. 5a). Despite lower mealybug densities, coccinellid larval and adult populations are roughly four to six times higher in the Coachella Valley (Fig. 4b vs. Fig. 5b). The proportion of parasitism is roughly the same at both sites for A. pseudococci but parasitism by L. abnormis is slightly higher in the Coachella Valley (Fig. 5c,d).
evidence of density dependence
Time-series plots of daily number of mealybugs parasitized by each parasitoid species and the numbers of mealybug active stages are shown in Fig. 6. The counter-clockwise rotation of the plots suggests oscillatory regulation by the parasitoids. The data may be viewed as an approximation of each parasitoid's k-values on log mealybug densities. The positive slopes of the linear regressions indicate that the action of both parasitoids is directly density-dependent (Varley & Gradwell 1960). The slopes for A. pseudococci at Parlier and Mecca are 1·136 and 1·15, respectively, suggesting that its action is over-compensating (i.e. the death rate is greater than the mealybug population growth rate). In contrast, the slopes for L. abnormis are 0·64 and 0·83 at Parlier and Mecca, respectively, 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 at Parlier but only 0·40 at Mecca. The reverse trend in r2 is seen for L. abnormis, reflecting its tolerance of higher temperatures (0·09 vs. 0·25).
Plots of number of log C. montrouzieri life stages on log number of mealybugs (active stages + parasitized mealybugs) were also made, but are not illustrated. The interpretation of the results is difficult, as predator increases are not directly translated to mortality rates. The closest relationship occurs with coccinellid eggs, where the slopes of the regressions are 0·19 and 0·015 and the r2 values are 0·056 and 0·003 for Parlier and Mecca, respectively. Regressions for number of C. montrouzieri larvae + adults on number of mealybugs were less informative (slopes of 0·055 and 0·045, and r2 values of 0·007 and 0·002 for Parlier and Mecca, respectively). The results suggest a very weak density-dependent response of the predator to mealybug density.
A measure of season-long pest loads is the cumulative total of daily densities of mealybug active stages (i.e. mealybug days). Similar computations were made for the three natural enemy species. These values vary widely from year to year, and hence we used the average of the yearly simulations for the period 1996–2005 to capture the general patterns (Fig. 7).
Mealybug densities are predicted to be highest in the cooler vineyard regions of California, particularly the north coast regions (Napa and Sonoma Co.) and the Sierra Nevada foothills. Densities are predicted to be lower in the warmer San Joaquin Valley and still lower in the hotter areas such as the Coachella Valley (Fig. 7a). The abundance of the coccinellid beetle C. montrouzieri is predicted to be generally low throughout most of California (Fig. 7b), with the highest densities occurring in the hotter region of southern California (Fig. 4b vs. Fig. 5b). The geographical distribution and relative abundance of A. pseudococci is similar to that of the mealybug (Fig. 7d). The abundance of A. pseudococci is four to five times higher than L. abnormis and its range is wider, except in hotter areas. However, while the maps are informative, further insights into the biology were obtained using multivariate regression of the simulation data. We recognize the statistical problems inherent in using simulation data in our analysis, but the goal is to assess general trends and relationships in the model.
multivariate regression analysis
Multiple linear regression analysis of the yearly simulation data and other runs where refuge size varied were used to assess the impact of weather, natural enemies and refuge size on crop yield and season-long measures of mealybug abundance (V= mealybug days per vine). All regressions used season length in dd, mealybug refuge size (0 ≤ H ≤ 1), and the presence–absence (0,1) of natural enemies (A+, A. pseudococci; C+, C. montrouzieri; L+, L. abnormis) as independent variables. The effects of competition by natural enemies were also examined. The average effect of any independent variable was estimated by the partial regression coefficients given the average effects of all other independent variables. This approach was used successfully in the analysis of the biological control of cassava mealybug in West Africa (Neuenschwander et al. 1989).
The regression model for grape yield (g vine−1) is:
Assuming an average refuge H= 0·5 and an average season length of 2375 dd, H has by far the largest negative effect on yield, followed by season length. In contrast, the average net effect of natural enemy presence and their interactions have a positive effect on yield (A+ >> L+ > C+). Variables for mealybug abundance were not included in the model because the direction of their effect was in H.
Vine mealybug density
Regressing log V (i.e. V= mealybug days) on the same independent variables as in equation 5 yields:
Again assuming H= 0·5, an average season length of 2375dd and no natural enemies, average mealybug days equals 7·37 × 106. Adding the effects of all natural enemies decreases average mealybug days 67·6%, to 2·38 × 106. These are average values across all years and locations, and we note that the order of importance and degree of impact may change in different ecological zones (Fig. 6) and with declines in H. For example, if H= 0, V decreases a further 44·8%, amply illustrating the adverse effect the refuge plays in mealybug control.
Taking the partial derivative of equation 6 for presence–absence of each natural enemy separately yields the following relationships:
This suggests that the general order of impact is A. pseudococci > L. abnormis, with C. montrouzieri serving to increase mealybug density (V).
Interactions among natural enemies
Ignoring the variable for the mealybug refuge, the interactions among the three natural enemy species are significant but exceedingly weak (equation 9, R2 ≤ 0·016, d.f. = 20 516):
The regression coefficients relating the effects of A. pseudococci (A+) and C. montrouzieri (C+) presence on log L. abnormis days (La, cumulative immature stages) are negative, suggesting competition effects from them, while the positive interaction term suggests competition between A+ and C+ that has a positive effect on La. The net effect on L. abnormis abundance is positive (equation 9i).
Similarly, the presence of L. abnormis and C. montrouzieri and their interaction has a net positive effect on log A. pseudococci days (equation 9ii). In the regression for log C. montrouzieri larval days (equation 9iii), the coefficients for the presence of the two parasitoids are positive but the interaction term is negative. The positive terms occur because parasitoid immature stages are food for coccinellid larvae and adults, while the negative interaction coefficient suggests competition from them. The net effect is that the presence of the parasitoids increases log C. montrouzieri larval days.
Climate and abiotic factors limit the distribution and abundance of species, and temperature and other factors affect net growth and reproduction in poikilotherms (Wellington, Johnson & Lactin 1999). Weather sets the limits for trophic interactions among species of poikilotherms and may influence the level of control by natural enemies (Huffaker, Messenger & DeBach 1971). In general, the analysis of natural enemy performance across varying ecological zones is a difficult and recurring problem in biological control (Mills & Getz 1996). A classic example of the effects of temperature on biological control is that of the cottony cushion scale Icerya purchasi Maskell, where in warmer areas it is controlled by the vedalia beetle Rodolia cardinalis Mulsant and in cooler areas by the parasitic fly Crytochaetum iceryae (Will.) (Quezada & DeBach 1973). Other examples are the spotted alfalfa aphid Therioaphis maculata (Buckton) (Force & Messenger 1964), olive scale Parlatoria oleae (Colvée) (Huffaker & Kennett 1966) and red scale Aonidella aurantii (Maskell) (Murdoch, Briggs & Swarbrick 2005).
Biological control of the vine mealybug in California to date has not been successful (Daane et al. 2006a) and with this study we explored the reasons why. To capture and separate weather-related biotic and abiotic effects requires that the biological responses be included in the model (Gilbert & Gutierrez 1973; Gilbert et al. 1976; Murdoch, Briggs & Swarbrick 2005). Models that fail to incorporate this biology have contributed to controversy (Lawton 1977; Gilbert 1984) but adding relevant biology may lead to the well-known trade-off between the benefits of increased realism and the lessened mathematical tractability required to analyse model stability and other properties (Wang & Gutierrez 1980; Godfray & Waage 1991). In this study, graphical methods were used to explore the dynamic properties of the system, and linear multivariate regression and marginal analysis were used to analyse the larger trends in the relationships modelled.
The use of weather-driven physiologically based models simplifies the problem of separating biotic and abiotic effects (Gutierrez & Baumgärtner 1984; Gurney et al. 1996; Gutierrez 1996; 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 olive scale by two parasitoids only after the weather-driven per capita resource acquisition and allocation and forms of competition were included in a physiologically based model. Analysis of biological systems across large landscapes is possible using physiologically based models because the predictions of the model are independent of time and place. This approach was used here to examine the biological control of the exotic vine mealybug across the ecological zones of California.
predictions of the model
Accurate season-long estimates of vine mealybug densities are largely unavailable, and the wide use of insecticides for their control complicates the process of ‘testing’ the model. Populations of mealybug and natural enemies have been sampled at two locations: in the hot Coachella Valley, where lower pest densities were found, and in the cooler San Joaquin Valley (Fig. 8; Daane et al. 2003). Our model makes similar predictions for these sites.
Four predictions of the model were of interest to understand and improve biological control: (i) the average abundance of vine mealybug and its natural enemies across California using observed weather and in the face of predicted climate warming; (ii) the density and efficacy of the predator C. montrouzieri; (iii) the comparable effectiveness of the parasitoids A. pseudococci and L. abnormis to be used as a guide in the importation of new species of parasitoids; and (iv) the importance of the spatial–temporal refuge in mealybug control.
Using daily weather for the period 1995–2005, the model predicts that the distribution and abundance of vine mealybug across years will vary widely because of differing temperature effects on species behaviour, growth rates and interactions (Fig. 7a–d). Pest densities are predicted to be highest in the wine grape regions of northern California and the Sierra Nevada foothills, with lower densities occurring in the hotter southern table grape regions (Fig. 7a). The mealybug has a narrow range of temperature (11–35°C) favourable for its development (Fig. 3) and seeks cooler sites under the bark or in the root zone during periods of high temperatures, where it is also less likely to be attacked by natural enemies (i.e. a spatial refuge). Prior to this work, there was some doubt regarding the level of damage the vine mealybug might pose in the cooler grape regions of California, Oregon and Washington. Here, given the absence of natural enemy activity, we provide evidence that the vine mealybug would not only survive in cooler regions but may also cause significant crop damage.
The model also explains the limitations of C. montrouzieri as a biological control agent. This predator is common in vineyards with very high mealybug densities but it does not readily survive cold winter temperatures (Bartlett 1974; Jalali, Singh & Biswas 1999). By modelling the biological traits and temperature tolerances of the predator and mealybug, the model predicts that C. montrouzieri's abundance would be highest on average in hot climates of southern California (Fig. 7b). The response of the predator C. montrouzieri is weakly density dependent and, in contrast to the observations of Prakasan & Bhat (1985) for Leptomastix dactylopii Howard, its attack on immature stages of the parasitoids does not overly interfere with their activity in grape.
The widely established parasitoid A. pseudococci has the best climatic match to the vine mealybug, and its predicted average geographical distribution and patterns of abundance are similar to that of the mealybug (Fig. 7a vs. Fig. 7c). Simulated densities of L. abnormis are highest in the hotter areas of California, but the densities are greater than those recorded in field studies (Daane et al. 2003).
For regulation to occur, the natural enemies must operate in a density-dependent manner. As with other encrytid parasitoids (Summy, French & Hart 1986), our analysis of the simulation data suggests that A. pseudococci has an over-compensating density-dependent response to vine mealybug that is insufficient for economic control. The parasitoid L. abnormis has a density-dependent action but it is less than compensatory because of a low per capita ‘effective’ search rate (0·004 vs. 0·05). (Note that the search rates were fitted via simulation.) If we assume equal per capita search rates for both parasitoids, say 0·05, the model predicts that L. abnormis would be the more prevalent species, a prediction that coincides with laboratory studies of parasitoid efficiency in the face of interspecific competition. For example, when the mealybug was exposed to both parasitoids in cage studies that reduced parasitoid host-finding effects and eliminated ant interference, L. abnormis out-competed A. pseudococci in some cases (Daane et al. 2003). The dominance of L. abnormis could in these cases be because of the effect of host size structure, as found for the parasitoids on cassava mealybug in Africa, where the parasitoid Epidinocarsis diversicornis (Howard) failed to persist in the field (Neuenschwander et al. 1989). In cassava, Epidinocarsis lopezi (DeSantis) out competes E. diversicornis because it produces more female offspring in smaller hosts, giving it an advantage during periods of drought stress on cassava (Gutierrez, Neuenschwander & van Alphen 1993). In the grape, L. abnormis produces more females on smaller hosts than A. pseudococci and this might explain some of the laboratory results, but host size structure would not appear to be a factor in irrigated fertilized vineyards. More probably, there is a greater impact of ants on L. abnormis that increases the size of the temporal refuge.
The presence of the spatial and temporal refuges is known to interfere with the level of mealybug control (Daane et al. 2006b) but we could not explicitly separate their effects in the model (i.e. as components of H) because there are at least three principal species of ants that tend vine mealybug in California and each has a different geographical distribution and level of aggressiveness. Furthermore, the temporal refuge provided by ants is expected to vary with mealybug density and is expected to be particularly important at low mealybug densities before the copious mealybug honeydew saturates ant demands. However, if we assume the same search rate for both parasitoids, simulation suggests that economic regulation 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 proved useful in assessing the role of the natural enemy impact and interactions on resource species (Neuenschwander et al. 1989). With this approach, the dependent variable might be pest density and the independent variables might be natural enemy presence or absence and other factors. Ideally, field data would be used in the analyses, but unfortunately data for vine mealybug across wide geographical areas are not available because accurate samples in vineyards are difficult to obtain, particularly at low densities (Geiger & Daane 2001). Simulation results across all years and regions indicate that, on average, mealybug density increases with season length and size of the refuge, while the action of the natural enemies decreases pest 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. The analysis suggests that reducing the temporal refuge by controlling ants or limiting the movement of the mealybug to spatial refuges are key elements for economic control of this pest, but this may change with climate warming.
State of the art climate models (http://meteora.ucsd.edu/cap/cccc_model.html, accessed 27 June 2007) have been developed that predict average temperature increases in California of 1·8–4 °C, and an obvious question is how this will affect agricultural crops and their pest complexes. Time-series plots of daily, weekly or monthly temperature, rainfall, vapour-pressure deficit and other variables during periods of pest activity are often used to characterize climate zones favourable for species, and the results are often extrapolated in climate change studies. Davis et al. (1998) called this the ‘climate envelope’ approach (Sutherst, Maywald & Bottomly 1991) and suggested the conclusions concerning the effects of climate change may be misleading if the interactions between species are altered by climate change. The tri-trophic physiologically based GIS demographic modelling approach circumvents most of these limitations (Gutierrez et al. 2005).
If average daily temperatures are increased 2° and 4 °C across all locations, the model predicts mealybug densities would increase generally throughout all regions of California (Fig. 9a vs. Fig. 9e,i). Biological control would decrease with increasing temperatures despite increases in both the density of A. pseudococci (Fig. 9c vs. Fig. 9g,k) and the favourable range and density of the predator C. montrouzieri (Fig. 9b vs. Fig. 9f,j) and the parasitoid L. abnormis (Fig. 9d vs. Fig. 9h,l).
We thank our thoughtful referees for useful suggestions and edits. The University of California Statewide IPM Program and the California Table Grape Commission provided partial funding for this study.