INTRODUCTION
The red palm mite, Raoiella indica Hirst (Acari: Tenuipalpidae), is an invasive pest in the New World with high potential for dispersal and establishment in new areas (1). This mite can reach high population densities and inflict severe economic losses to ornamental plants, banana, and several palm trees, especially coconut (Cocos nucifera L.) (25). In Brazil, the red palm mite was first reported in the northern state of Roraima in 2009 (6), and since then it has spread to other regions, including to the Northeast, the main coconut producing region in the country (7).
Recent research has focused on biological (2, 8) and chemical control (9) strategies aiming at reducing the problems associated with infestation of R. indica. Although pesticides have shown to efficiently control R. indica (9), to date none of them is registered in Brazil to control this pest in coconut fields (10). Therefore, a growing concern is the use of broadspectrum pesticides to control this pest.
Regarding biological control, several studies have been conducted to identify and evaluate the potential of native predators in the control of R. indica (2, 7, 8, 11,12,13,14). Among predatory mites, phytoseiids are the most important natural enemies associated with R. indica (2, 11,12,13). Amblyseius largoensis Muma has been found in association with R. indica in coconut plantations in several countries, including in Brazil and Cuba (11,12,13). This predator feeds on all stages of R. indica and can be efficient in controlling the red palm mite, mainly at low pest densities (7, 14). Furthermore, A. largoensis can reduce R. indica densities under greenhouse conditions (14). In Brazil, Iphiseiodes zuluagai Denmark and Muma is also associated with R. indica (11), whereas Typhlodromus (Anthoseius) ornatus Denmark and Muma is often found foraging on coconut trees (15, 16). Therefore, it is reasonable to conjecture that such predatory mites could act as biological control agent of this pest in the field.
One of the most important approaches to evaluate the potential of predators as biological control agents is the study of their functional and numerical responses (17, 18). The functional response assesses the predation rate in relation to prey density (19), whereas the numerical response evaluates the variation at the predator population density in response to changes in prey densities. Accordingly, the efficacy of T. ornatus, A. largoensis, and I. zuluagai was assessed by comparing their functional and numerical responses to increasing densities of R. indica eggs. We aimed to evaluate the potential of these three predatory mite species as biological control agents of R. indica.
MATERIAL AND METHODS
Rearing of predatory mites
Stock colonies of A. largoensis and I. zuluagai were established with individuals collected from unsprayed coconut leaf of the dwarf green variety in Aracaju (10° 54' 36'' S, 37° 04' 12'' W) and Neopolis (10º19' 12'' S, 36º34' 46'' W) cities, respectively, Sergipe State, Brazil. Colonies of T. ornatus were initiated with individuals collected from unsprayed coconut fruits of the dwarf green variety in São Luís city (02° 35' 03'' S, 44° 12' 32'' W), Maranhão State, Brazil. Mite species identification was performed using taxonomic keys, and voucher specimens were deposited in the collection of Maranhão State University (UEMA), São Luís, Brazil.
Colonies of T. ornatus were maintained under controlled laboratory conditions (27 ± 3°C temperature, 70 ± 10 % relative humidity and a 12 h photoperiod) on rectangular PVC sheets (23 cm length x 4 cm width) sitting on watersoaked polyurethane foam (24 cm length x 5 cm width x 0.33cm depth) placed in a plastic tray. A barrier of watersoaked cotton wool (1 cm high) was placed around the edge of the PVC sheet to prevent the mites from escaping. Cotton threads under cover slips (18 x 18 mm) were placed on PVC sheets as shelter and oviposition sites. Pollen of castor bean, Ricinus communis L., all developmental stages of R. indica, and honey were provided every other day as a food source.
Functional and numerical responses
Bioassays were performed under the same environmental conditions used for rearing. Experimental units consisted of PVC discs (6 cm diameter) sitting on watersoaked polyurethane foam (6 cm diameter x 0.33 cm depth) inside a plastic container (6.2 cm diameter x 5 cm depth) without lid. A watersoaked cotton wool barrier (1 cm high) was placed around the edge of the PVC disc to confine mites.
Bioassays were conducted separately for each predatory mite species (i.e. T. ornatus, A. largoensis, I. zuluagai). In short, coconut leaflet sections (1cm^{2}) containing 5, 10, 20, 30, 40, 50 and 80 eggs of R. indica were transferred to each PVC disc. Eggs of R. indica (13 day old) were taken from unsprayed coconut leaves. Subsequently, one mated female of each predator, at the beginning of its reproductive period (710 day old), was transferred to each disc containing increasing densities of R. indica eggs. Fourteen replicates were included for each egg density. To determine the functional response, the numbers of prey killed were recorded after 24 hours without prey replacement. To assess the numerical response, the eggs laid by each predatory mite species in relation to prey density were evaluated during 2 days, with prey replacement at the end of the first day. Data of oviposition on the first day were discarded to minimize the effect of previous diets (7).
Statistical analyses
For each predatory mite species, the type of the functional response curve was estimated using a logistic regression analysis of the proportion of the prey killed in relation to prey density following the protocol of Juliano (20) using Proc CATMOD of SAS software (21). The linear coefficient sign of the equation generated from the proportion of prey killed in relation to the original density of prey was used to determine the type of functional response (19). The linear coefficient, if not significant, indicates a type I functional response (linear rise in prey consumption as a function of prey density); when significant and with a negative sign, it indicates a type II functional response (increase in prey consumption with prey density to a plateau  predator saturation); and when significant and with a positive sign, it denotes a type III functional response (accelerated rise in prey consumption with prey density rendering a sigmoidal curve). The functional response is based on the parameters handling time (Th), which involves the killing and ingestion of prey, and the attack rate (a'), which is the efficiency in prey searching (19, 22). These parameters were subsequently estimated using nonlinear regression with the method of least squares (PROC NLIN SAS) (21). As the experiments were conducted without prey replacement during the functional response experiment, the random predator equation (23) was used as a description of the type II functional response.
where N_{e} is the number of prey consumed, N_{0} is the initial density of prey, T is the time interval (24 hours), α is the attack rate, T_{h} is the handling time. The consumption peak was calculated for each predatory mite based on the reciprocal of Th $\left(\frac{1}{Th}\right)\left(\frac{1}{Th}\right)$ and compared using confidence intervals. The variation in prey consumption for each predator at each density was calculated according to the following equation: $\u2206{N}_{a}=\frac{{N}_{a}{N}_{max}{N}_{a}{N}_{min}}{{N}_{max}{N}_{min}}$ , where NaN_{min} and NaN_{max} stand for the minimum and maximum numbers of prey consumed, respectively. N_{min} and N_{max} are the minimum and maximum prey densities (24). The variation in prey consumption was subjected to oneway ANOVA followed by Tukey test using the software SAS (21). Oviposition rates of the three predatory mites as a function of R. indica egg density were submitted to a regression analyses using PROC REG of SAS Software (21).
RESULTS
The regression analyses generated significant linear coefficients with negative signs, indicating that T. ornatus, A. largoensis, and I. zuluagai presented type II functional responses to eggs of R. indica (Table 1). For all predator species, the number of prey consumed increased with egg density, (Fig 1). The predator A. largoensis consumed close to 100 % prey up to the density of 40 R. indica eggs. In contrast, T. ornatus and I. zuluagai consumed the same amount of prey up to the densities of 10 and 5 R. indica eggs, respectively (Fig 2). At highest prey density (80), A. largoensis consumed roughly 60 % of R. indica eggs, whereas I. zuluagai and T. ornatus killed 26 % and 32 %, respectively.
Table 1.
Estimated parameters of the logistic regression of the proportion of Raoiella indica eggs consumed by females of three species of predatory mites/ Parámetros estimados de la regresión logística de la proporción de huevos de Raoiella indica consumidos por hembras de tres especies de ácaros depredadores.
Fig. 1.
Mean number (± SE) of Raoiella indica eggs consumed by females of three species of predatory mites in relation to prey density. /Número medio (±EE) de huevos de Raoiella indica consumidos por hembras de tres especies de ácaros depredadores con relación a la densidad de presas.
Fig. 2.
Mean (± SE) proportion of Raoiella indica eggs consumed by females of three species of predatory mites in relation to prey density. /Proporción media (±EE) de huevos de Raoiella indica consumidos por hembras de tres especies de ácaros depredadores con relación a la densidad de presas.
The attack rate (a’) did not vary among predator species. Handling time (Th) was shorter for A. largoensis in comparison with T. ornatus and I. zuluagai (Table 2). The prey consumption peak estimated for A. largoensis was higher than those estimated for T. ornatus and I. zuluagai (Table 2). The predator A. largoensis also had a higher variation in the consumption of R. indica eggs in comparison with the remaining two species (F_{2,36}= 66.36, p< 0.001) (Fig 3).
Table 2.
Estimates of the parameters attack rate (a'), handling time (Th) and consumption peak of three species of predatory mites preying upon eggs of Raoiella indica for 24 hours/ Estimaciones de los parámetros tasa de ataque (a'), tiempo de manipulación (Th) y pico de consumo de tres especies de ácaros depredadores depredando huevos de Raoiella indica por 24 horas.
a' ± SE (95% CI)  Th ± SE (95% CI)  $\left(\frac{1}{Th}\right)\left(\frac{1}{Th}\right)$ (95% CI)  

T. ornatus 



A. largoensis 



I. zuluagai 



Means followed by same letter within a column do not differ based on confidence intervals. / Las medias seguidas por la misma letra dentro de una columna no difieren según los intervalos de confianza.
The number of eggs laid by A. largoensis steadily increased with prey density, peaking at 50 R. indica eggs and decreasing afterwards (Fig 4) (Y= 0.33149 + 0.008510x  0.00081997x^{2} , r²= 0.98, P=0.0003). The oviposition of T. ornatus linearly increased with prey density (Fig 4) (y= 0.35528 + 0.01176x , r^{2}= 0.87, P =0.0022 (Fig 4). Unlike A. largoensis and T. ornatus, the oviposition of I. zuluagai was not related to R. indica egg density (p> 0.05).
Fig. 3.
Mean (± SE) variation in Raoiella indica eggs consumption by females of three species of predatory mites in relation to handling time. Equal letters do not differ significantly by Tukey tests. /Variación media (±EE) en el consumo de huevos de Raoiella indica por hembras de tres especies de ácaros depredadores con relación al tiempo de manipulación. Las letras iguales no difieren significativamente según las puebras de Tukey.
Fig. 4.
Mean (± SE) number of eggs laid by females of three species of predatory mites in relation to Raoiella indica egg density. /Número medio de huevos (±EE) depositados por hembras de tres especies de ácaros depredadores con relación a la densidad de huevos de Raoiella indica.
DISCUSSION
The predatory mites A. largoensis, I. zuluagai and T. ornatus exhibited a type II functional response to eggs of R. indica, in which there was an increase in consumption due to a greater availability of prey up to a certain density, reaching stability at high densities (19), which may be associated with satiety of the predator. These results indicate that these predators are more efficient at low to moderate prey densities.
Phytoseiid mites usually present type II functional responses to pest mites (25). For instance, type II response curves were also observed for the phytoseiids Typhlodromus pyri Scheuten preying upon protonymphs and deutonymphs of the European red mite Panonychus ulmi Koch (Acari: Tetranychidae) (26), Euseius alatus DeLeon, and Amblyseius herbicolus (Chant) feeding on larvae and nymphs of the false spider mite Brevipalpus phoenicis Geijkes (Acari: Tenuipalpidae) (27, 28). In agreement with our results, Carrillo & Peña (7) and Mendes et al (29) also found this type of functional response in A. largoensis feeding upon eggs of R. indica.
The phytoseiids A. largoensis, I. zuluagai, and T. ornatus are classified as generalist type III predatory mites. They feed upon pest mites and small arthropods as well as pollen and sugary exudates (30), which helps to sustain their populations even during scarcity. Due to their feeding habits, the populations of generalist predators tend to disperse less to new patches and are more stable than specialist predator populations in agroecossystems (31). The consumption curves were similar among predators, and only the average amount of eggs preyed by them varied. A. largoensis was more efficient, consuming around 1.5 to 2 times more eggs at the highest prey density than I. zuluagai and T. ornatus, respectively. This differential consumption among predators could be explained by the relative size of each predator species (32), since A. largoensis and I. zuluagai are larger than T. ornatus. Furthermore, A. largoensis and I. zuluagai are more active than T. ornatus, a behavior that may increase the probability of finding prey (18), as well as increasing the energy expenditure of predators leading to increasing prey consumption.
The proportion of prey consumed by A. largoensis was close to 1 up to 40 R. indica eggs, in line with Carrillo & Peña (7). In contrast, the proportion of prey consumed by I. zuluagai and T. ornatus was close to 1 only at the lowest densities (5 and 10 R. indica eggs, respectively), probably due to the difficulty of both predators in finding prey at low densities (26).
Carrillo & Peña (7) showed that A. largoensis significantly preferred and consumed more eggs of R. indica than its immatures stages or adults. Eggs of R. indica are easily accessible for predatory mites because they last for approximately 9 days, the longest developmental stage of this pest (33). In addition, R. indica eggs do not exhibit antipredator behavior. Here, the attack rate (a') did not vary among predators; however, A. largoensis consumed more R. indica eggs in shorter time compared to I. zuluagai and T. ornatus. According to Holling (19), the handling time includes the period necessary to kill and consume the prey. A longer handling time may suggest that the predator spends a longer period with one prey, taking a longer time to find and consume another prey (34). Therefore, A. largoensis needs less time to consume R. indica eggs, which may result in more time to attack and catch another prey. This can be observed by the negative relationship between variation in prey consumption and handling time, in which A. largoensis had a shorter manipulation period and a higher consumption variation when compared to T. ornatus and I. zuluagai (Fig 3). This relationship can also be altered in conspecific populations that have different times of association with the pest; for instance, native populations of A. largoensis in long association with R. indica exhibit a more aggressive behavior, a greater variation in prey consumption, and, consequently, a shorter handling time than those populations that have not been in contact with the pest (29).
The number of eggs laid by A. largoensis and T. ornatus females increased with prey density, indicating that these predators obtained nutritional benefits that promoted reproduction (35). This may indicate that the consumption of R. indica eggs by these predators may contribute to their numerical increase in the field. Similarly, females of Euseius concordis Chant (Acari: Phytoseiidae) oviposited more when fed upon eggs of the cassava green mite Mononychellus tanajoa Bondar (Acari: Tetranychidae) than when they did on immature stages or adults (35). Furthermore, A. largoensis preferred eggs over other developmental stages of R. indica and also exhibited a similar oviposition peak (7). In contrast, I. zuluagai oviposition was not related to prey density, suggesting that R. indica eggs are not an optimal developmental stage for its reproduction. However, it is possible that the consumption of mixedlife stages or other developmental stages of R. indica are more suitable for I. zuluagai as observed for other phytoseiid predators. For instance, P. persimilis, G. occidentalis, and N. californicus preferred nymphs to eggs of P. citri, suggesting that consumption of nymphs was more profitable in terms of nutritional value for these predators (18).
Our results indicate that the predatory mites A. largoensis, I. zuluagai, and T. ornatus may contribute to the control of R. indica, mainly at low to moderate densities. However, A. largoensis was the most efficient predator because it consumed the greatest number of prey with the shortest handling time and showed the highest reproductive potential when fed upon R. indica. Further field studies are needed to confirm the potential of these phytoseiids in controlling R. indica, especially A. largoensis. However, as these three predatory mites cooccur on coconut palms, further research should also focus on whether they could have an additive, neutral or negative effect on R. indica control in the field. Intraguild interactions among these predators could play a role in mediating biological control of R. indica when these predators are used. Also, augmentation or mass field releases should be evaluated as strategies for R. indica management.