Scaling up from individual behaviour of Orius sauteri foraging on Thrips palmi to its daily functional response
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DOI: 10.1007/s10144-011-0270-9
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- Hemerik, L. & Yano, E. Popul Ecol (2011) 53: 563. doi:10.1007/s10144-011-0270-9
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Abstract
Functional responses of predators are generally measured under laboratory conditions at rather high prey densities. This is also true for the predation capability of the anthocorid predatory bug Orius sauteri (Poppius). To quantify the daily impact of one female Orius predator on its prey Thrips palmi Karny on greenhouse eggplants where the prey is present below the economic threshold density, we use its patch-leaving and feeding behaviour on eggplant leaves with different prey numbers and scale up to the larger spatio-temporal scale of the greenhouse and one foraging day by means of a simulation model. For this, we also use literature data on the distribution of T. palmi over eggplant leaves. The simulation results in a typical type II functional response for O. sauteri as a function of average T. palmi density: O. sauteri can find and eat approximately 10 prey items per day if T. palmi is present around its economic injury level. The daily mean number of prey eaten per O. sauteri predator, i.e., its predation capability, is highly sensitive to the actual baseline leaving tendency, the effect size of the presence of prey on the baseline leaving tendency and the effect size of the encounter rate with prey thereon.
Keywords
Holling type II functional responseSimulationSurvival analysisIntroduction
Functional response is defined as the temporal rate at which an individual predator kills prey, namely the average number of prey eaten per individual predator per unit of time as a function of prey density. In models, the functional response is either assumed to be (1) linear, increasing with increasing prey density (Holling 1959; type I functional response), (2) reaching a plateau after a linear increase with increasing prey density (Holling 1959; type II functional response) or (3) increasing after an initial slow start up, levelling off to a plateau with increasing prey density (Holling 1959; type III functional response with sigmoid shape). The basis of Holling’s disc equation (type II) is that the time budget of a predator is divided between searching for prey and handling prey (chasing, eating and digesting it). In this formulation, the search activity of the predator is constant irrespective of the density of prey. For the sigmoid functional response the predator intensifies its searching activity when prey densities increase.
The predacious anthocorid O. sauteri is well known to be one of the important indigenous natural enemies of T. palmi on eggplants in the field in Japan (Yano 1996). If field populations of Orius spp. including O. sauteri are conserved by using selective pesticides that do not affect Orius spp., then Orius populations suppress outbreak of T. palmi on eggplants in the field (Nagai 1993; Takemoto and Ohno 1996; Ohno and Takemoto 1997). Orius sauteri has also been demonstrated to suppress the population of T. palmi around the economic injury level on eggplants in greenhouses (Kawai 1995). Orius sauteri was registered in Japan in 1998 as a biopesticide of T. palmi and Frankliniella occidentalis (Pergande) in greenhouses.
The effectiveness of O. sauteri as a biological control agent of T. palmi mainly depends on its reproductive capacity and its predation capability. The intrinsic growth rate is generally used to indicate the reproductive capacity (Birch 1948). For T. palmi without predators around, this relative growth rate amounts to 0.102 per day (Kawai 1986), while that of O. sauteri fed with T. palmi is 0.128 per day (Nagai and Yano 1999). The reproductive capacities of these two species show no large differences. Therefore, the effectiveness of O. sauteri is mainly expected to depend on its predation capability. In this study, its functional response has been used to measure its predation capability.
The functional response of single Orius predators of different species are investigated frequently (e.g., McCaffrey and Horsburgh 1986; Isenhour et al. 1989, 1990; Coll and Ridgway 1995; Nagai and Yano 2000; Gitonga et al. 2002). As the experimental arena in most of the functional response studies in the laboratory were very small homogeneous spaces such as a Petri dish or a plastic vial to which the Orius individual was confined (McCaffrey and Horsburgh 1986; Isenhour et al. 1989, 1990; Coll and Ridgway 1995; Nagai and Yano 2000; Gitonga et al. 2002), the number of prey attacked in a given time period was over-estimated. In addition, the predator experienced higher prey densities than actual prey densities in greenhouses or in fields, where prey occur at densities around the economic injury level. In the experiments of Nagai and Yano (2000), the lowest density of thrips that could be used was three individuals per leaf, which is about five times higher than the economic injury level (of 0.55 per leaf). From such experiments it is impossible to directly extrapolate and obtain a reliable estimate of the predation capability of one Orius individual during one foraging day in a greenhouse where prey density is around the economic injury level. An estimate for this daily predation capability can be obtained in two ways (1) in a semi-field set-up where an Orius female could exploit many patches, and (2) by using results from observations on the foraging behaviour of the predator in a spatial simulation model.
The main objective of this work is to assess the number of T. palmi prey that an individual adult female O. sauteri consumes on average per day when foraging on eggplants. When O. sauteri females are used as a biological control agent in greenhouses, they visit numerous patches in 1 day. Thus, for one female, the foraging day consists of a sequence of patch visits. Because we have experimental data on the behaviour of one individual predator foraging for prey on one egg-plant leaf with different numbers of prey items present, we have a good starting point from which to scale up. Our earlier findings concerning the foraging process and the patch-leaving behaviour of O. sauteri are that, irrespective of the actual density of prey items on a patch, the leaving tendency only decreased by a factor of about 3 on average because prey were present (Yano et al. 2005). Moreover, the leaving tendency increases when patch exploitation lasts longer. To assess the number of T. palmi consumed per day by O. sauteri, we scale up from these earlier findings on how its foraging process and its patch-leaving behaviour are affected. We have developed a simulation model in which the simulated individual encounters a realistic distribution of prey over eggplant leaves (extracted from mean crowding estimations in Kawai 1986). This crowded distribution is simulated with a negative binomial distribution of prey over leaves, because insects are often found to have a clumped distribution (Harcourt 1961; Atkinson and Shorrocks 1984). The simulation model is first validated in two ways, and its results are discussed against the background of earlier experimental findings on a (simulated) functional response by Van Roermund et al. (1997).
Methods
The structure of the simulation model
Parameter values
As we want to determine the number of 2nd instar larvae of T. palmi that one female adult of the species O. sauteri consumes in one foraging day, we have based our simulation model on studies where the patch-leaving behaviour was studied (Yano et al. 2005; see “Patch-leaving rate” and “Other rate parameters” below) and where the distribution of thrips larvae is determined in greenhouses (Kawai 1986; see “Parameterizing the clumped distribution of thrips over leaves” below).
Description of the parameters in the model
Parameter | Description | Unit | Mean value |
---|---|---|---|
β_{pres} | Regression coefficient of proportional hazards model giving the effect on the baseline hazard rate when prey are present | – | −1.30 |
β_{time} | Regression coefficient of proportional hazards model giving the effect on the baseline hazard rate per minute since patch entry at the latest encounter with prey | min^{−1} | 0.012 |
h_{0} | Baseline hazard rate on empty patch | s^{−1} | 1/875 |
r_{enc} | Encounter rate with prey items | s^{−1} | 1/709 |
r_{h} | Handling rate of prey items | s^{−1} | 1/200 |
r_{travel} | Travelling rate between patches | s^{−1} | 1/100 |
m | Mean of the negative binomial distribution of thrips over eggplant leaves | number leaf^{−1} | Number of values^{a} |
k | Aggregation parameter of the negative binomial distribution of thrips over eggplant leaves | – | Number of values^{a} |
T | Total foraging time in 1 day (14 h) | s | 50400 |
Orius sauteri is active and forages only during daytime (K. Nagai, personal observation). For the simulation of 1 day we use the total average time in one foraging day of O. sauteri in central Japan, where the mean day length in spring to autumn is 14 h.
Patch-leaving rate
The parameter estimates for the β (β_{pres} = −1.30, β_{time} = 0.012, h_{0} = 1.143E−03) are only slightly different from those reported as the estimates in the Cox proportional hazards model (Yano et al. 2005).
To be able to scale up from eggplant leaf level to greenhouse level, the distribution of the GUTs on empty patches as parameterized by the baseline hazard h_{0} has to be known, otherwise the realizations of the stochastic process cannot be simulated. On empty patches the mean GUT is estimated as 875 s (=1/h_{0}). The value for the regression parameter β_{pres} indicates that the average GUT on patches with prey is 3.7 [=exp(1.30)] times larger than on empty patches. Both of these average times are influenced by the time (in minutes) since patch entry: each minute reduces the average time by a factor 0.988 [=exp (−0.012)].
Other rate parameters
As stated above, both the handling time and the travel time are stochastic and are assumed to follow an exponential distribution. The average handling time of prey is 200 s (Yano et al. 2005), and the travelling time between patches is set at 100 s based on the data of walking speed (=0.2967 cm/s), walking activity, i.e., the fraction of the total time that the bug is active (=0.6933), and the mean distance between adjacent leaves (=20 cm) (K. Ohno and E. Yano, unpublished data). It was assumed that O. sauteri individuals travel by walking between patches based on observation of patch-leaving behaviour (E. Yano, personal observation).
For the encounter rate of prey items, the same approach is used as in the appendix of Vos and Hemerik (2003). Those authors assume that both the IBEs and the GUTs result from an exponential distribution with parameters r_{enc} and h_{0}, respectively. From our data set on O. sauteri foraging on T. palmi, we calculated the overall mean g for all observed IBEs and GUTs together on prey-infested patches. This equals g = 1/(r_{enc} + h_{0}). The calculated value was 539 s, and the number of realized IBE intervals and GUT intervals in our data were 162 and 52 (fractions 0.76 and 0.24). Under the assumption of exponentially distributed encounters and GUTs, we know from the appendix of Vos and Hemerik (2003) that the fraction of realized encounters with prey (f_{enc}) and the fraction of realized GUTs (1 − f_{enc}) are derived as, respectively, f_{enc} = r_{enc}/(r_{enc} + h_{0}) and 1 − f_{enc} = h_{0}/(r_{enc} + h_{0}). Therefore, the mean duration of IBE and GUT in all experiments are, respectively, 709 s (=g/f_{enc}) and 2246 s (=g/(1 − f_{enc})). In the simulation we only use the mean value for the IBEs explicitly [r_{enc} = (1/709) s^{−1}, see Table 1], because the other estimate is already simulated with the leaving rate and the effects (β_{pres} and β_{time}) as estimated with the parameterized survival model given in Eq. 1.
Parameterizing the clumped distribution of thrips over leaves
For T. palmi, Kawai (1986) estimated the functional relationship between the mean crowding m* and the mean m (number of thrip larvae per leaf). He did not compute the clumping parameter of the negative binomial distribution explicitly. Therefore, we have to look into the details of his estimated relationship: The mean crowding m* is defined as the mean number of neighbouring individuals per individual per quadrate. Its relation to the mean m and variance σ^{2} is known to be m* = m − 1 + (σ^{2}/m) (formula a from Iwao and Kuno 1968). In general, the relation between the mean and the mean crowding can be described with a simple linear regression as m* = α + βm (formula b from Iwao 1977). For larvae of the species T. palmi, Kawai (1986) reported two different estimates for α and β in such a linear regression equation, namely (α, β) = (4.11, 1.34) or (4.84, 3.54), respectively. The former estimates were obtained from the survey in a greenhouse where the eggplants were just planted, and the latter estimates were for a later cropping period of eggplants. Combining regression values α and β with the two formulas a and b for mean crowding and the mean and variance of the negative binomial distribution (just above Eq. 2) results in two different relationships between k and m, namely k = f_{1}(m) = m/(4.11 + 0.34 m) and k = f_{2}(m) = m/(4.84 + 2.54 m). For our simulation study we used these two different functions to describe the relationship between the mean m and the clumping parameter k to be able to simulate numbers of prey items in a patch as a random draw from the negative binomial distribution with mean m and clumping parameter k.
Model validation
Ideally, the model could be compared with data for one predator that could explore a semi-field set-up with, say, eight eggplant plants during 14 h. Such data are not available, thus we have only tested the prey consumption and the patch-leaving part of our model. Additional data were collected on the number of prey eaten and the patch residence time for patches with 20 prey items as initial density (N. Jiang and E. Yano, unpublished data) in a set-up as described in Yano et al. (2005). There were 24 replicates. It should be noted that this data set (used for testing the model) has been obtained independently from the data used by Yano et al. (2005). To test our model, we simulated the numbers eaten and the patch residence times on 1000 patches with initial prey density set to 20. We compared the data and the simulation results for the number of prey eaten using a non-parametric Wilcoxon rank-sum test (for all 1000 simulations and for the same simulations divided into 40 subsets of 25 patches). For the patch residence times a Kaplan–Meier survivor plot was drawn and the samples were compared with a log-rank test (Klein and Moeschberger 1997). All analyses were done in the R language version 2.8.0 (R Development Core Team 2008).
Simulation scenarios
We have performed simulations of the searching behaviour of O. sauteri at densities below or around the economic injury level of 0.55 second instar larvae of T. palmi per eggplant leaf to estimate the number of prey eaten by this predator during one foraging day. We also included mean densities of 1, 2 or 3 per leaf, which are far above the normal levels encountered in a greenhouse, to acquire knowledge on how much one adult Orius predator is able to eat at such high densities in case one wants to start biological control after having measured these mean number of thrips per eggplant leaf. For each combination of m and k, 1000 individual predators were simulated, essentially having access to an unlimited number of leaves with and without prey, because the number of prey on each leaf was drawn from a negative binomial distribution (which is clumped and therefore represents an over-representation of empty patches).
Statistical methods
For the different values of k of the negative binomial distribution we tested with the Wilcoxon rank-sum test at each mean number of thrips per leaf whether there was a difference between the differently clumped distributions. These analyses were done in the R language version 2.8.0 (R Development Core Team 2008).
We also fitted three different Holling-type functions (\( {({\text{I}})\;y = a_{1} \, m,\;({\text{II}})\;y = {\frac{{a_{2} \, m}}{{b_{2} \, + \, m}}}\;{\text{and}}\;({\text{III}})\;y \, = \, {\frac{{a_{3} \, m^{2} }}{{b_{3}^{2} \, + \, m^{2} }}}} \), where y is the number of prey eaten and m is the mean prey density) to the functional responses and made a selection between these models using Akaike’s information criterion (AIC, Akaike 1974). The model with minimum AIC is the best (the analysis was performed in the R language version 2.8.0 by non-linear regression).
Sensitivity analysis
We are quite sure that the parameter values that describe the searching and decision process of the predator are correctly estimated from our data (with low variance). However, we would still like to know how the parameters included in the model affect the functional response of O. sauteri. Therefore, we performed a sensitivity analysis on each of the 6 following parameters: h_{0}, r_{enc}, r_{h}, r_{travel}, β_{pres} and β_{time}. To get a good view of whether parameter changes cause large variations we varied the parameter values by –50% and +50% at mean prey densities of m = 0.1, 0.3, 0.5, 1 or 2 prey per leaf with their corresponding k values of the more clumped distribution described by the relation k = f_{2}(m) = m/(4.84 + 2.54 m).
Results
Model validation
Simulation
Sensitivity analysis
Results of sensitivity analysis for the number of prey eaten in one foraging day
h_{0} | r_{enc} | β_{pres} | ||||
---|---|---|---|---|---|---|
−50% | +50% | −50% | +50% | −50% | +50% | |
m = 0.1 | −30% | +24% | −31% | +23% | −19% | +25% |
m = 0.3 | −32% | +17% | −30% | +20% | −18% | +9% |
m = 0.5 | −32% | +15% | −30% | +16% | −18% | +3% |
m = 1 | −28% | +13% | −32% | +19% | −11% | −3% |
m = 2 | −24% | +10% | −34% | +18% | −9% | −6% |
Results of sensitivity analysis for the fraction eaten of the total number of prey encountered in one foraging day
h_{0} | r_{enc} | β_{pres} | ||||
---|---|---|---|---|---|---|
−50% | +50% | −50% | +50% | −50% | +50% | |
m = 0.1 | +19% | −13% | −24% | +12% | −25% | +18% |
m = 0.3 | +28% | −19% | −27% | +14% | −25% | +22% |
m = 0.5 | +35% | −17% | −29% | +17% | −27% | +28% |
m = 1 | +36% | −17% | −30% | +20% | −28% | +30% |
m = 2 | +40% | −20% | −34% | +22% | −32% | +37% |
Discussion
First we take a critical look at the assumptions of the model. As we have pointed out above, our simulation model is not spatially explicit. Therefore, we have not included a preference for detecting prey-infested patches, although it is known that predatory bugs of the genus Orius are preferentially attracted to herbivore-infested patches (Venzon et al. 1999; Mochizuki and Yano 2007). It is also not quantitatively known whether and to what extent arrival tendencies to prey-infested plants differ. Including such a preference when choosing between neighbouring patches would have increased the predation capability slightly, because a clumped distribution of hosts implies also a lot of empty patches that are neighbouring each other. The exponentially distributed handling times and arrival times represent the best and simplest distributions for such variable times that are not quantified in detail.
The simulation results of the model depicted in Fig. 1 show that one female adult of O. sauteri can find and eat approximately 10 prey individuals per day at a level of infestation around the economic injury level of T. palmi (an average of 0.55 individuals per leaf). Since the intrinsic rate of natural increase of T. palmi at 25°C is estimated at 0.102 per day (Kawai 1986), it is calculated that the T. palmi population increases only by approximately 11% per day. For a not too small ratio of the number of O. sauteri to T. palmi, O sauteri has great potential to suppress the T. palmi population. Since the functional response is the individual predator response to the prey density, we have not included interference or competition between predators, because no visual response was observed when two individuals met each other. When predators compete with each other, this might reduce the number of prey eaten per day per individual. However, densities of the predator in biological control are generally not so high; for example, in the study by Kawai (1995), the maximum density of the total of nymphs and adults of O. sauteri per eggplant leaf in five greenhouses was 0.21 in about 60 days after 0.5 or 1.0 nymphs per leaf were released once in each greenhouse.
Most experimental studies in very small homogeneous spaces such as a Petri dish or a plastic vial have shown a type II functional response by Orius spp. to densities of different types of prey (McCaffrey and Horsburgh 1986; Isenhour et al. 1989, 1990; Coll and Ridgway 1995; Nagai and Yano 2000; Gitonga et al. 2002). Among them, Nagai and Yano (2000) studied the functional response of O. sauteri to densities of T. palmi and found at 25°C a type II response for a female adult for aging at different densities of the second instar larvae. The current simulation study also results in a type II response of O. sauteri foraging at low densities of T. palmi around its economic injury level. It was also shown that the distribution of T. palmi among patches has a great influence on the shape of the functional response (a homogeneous distribution leads to a type I functional response). This kind of effect of the distribution of prey on the functional response is not found often. We know of one occasion where in a simulation study the distribution of hosts had a similar effect: When modelling the foraging behaviour of Encarsia formosa Gahan (Hymenoptera, Aphelinidae) attacking immature greenhouse whitefly Trialeurodes vaporariorum (Westwood) (Homoptera, Aleyrodidae), functional responses of E. formosa to immature whitefly densities were greatly affected by host distribution over leaflets, as those of O. sauteri to densities of thrip larvae (Van Roermund and Van Lenteren 1994; Van Roermund et al. 1997).
The results of the model validation strengthen our opinion that the details of the simulation model resemble the behaviour of O. sauteri foraging on eggplant leaves at ambient temperature of 25°C as explained at the end of the “Introduction”. In addition to this fact, it is no surprise that the model outcomes are highly sensitive to the values of the baseline patch-leaving rate h_{0} and the encounter rate r_{enc}. When the encounter rate is higher at the same baseline patch-leaving rate, more prey can be encountered and both the number of prey eaten and the fraction of the total prey population on the visited patches increase. If, alternatively, the baseline patch-leaving rate is higher at the same value of the encounter rate, then a patch is left earlier. Thus, the number of patches that are visited in the same amount of time and the total number of prey eaten both increase, but the consumed fraction of the total prey population on the visited patches decreases. How the number of prey eaten is influenced by the value of β_{pres} is not so clear. The encounter rate with prey is only defined on prey-infested patches, and the behavioural parameter β_{pres} influences the leaving tendency on such patches. Therefore, the resulting effect on the number of prey eaten in 1 day after having visited prey-infested and empty patches is not straightforward. This is also obscured by the fact that, in clumped distributions, there are some patches with high prey densities but also a lot of empty patches. The consumed fraction of prey is higher when β_{pres} is higher because an increase in the negative value by 50% means that initially the GUT on patches with prey is multiplied by seven [=exp(1.5 × 1.3)]. For low mean prey densities this results in higher numbers eaten per day, but for high mean prey densities more time is wasted after some time on an eggplant leaf, because the predator prolongs its GUT on prey-infested patches.
In the simulation study of Van Roermund et al. (1997) at high host densities with a clustered distribution of hosts over leaflets, the GUT on a leaflet was the most essential parameter influencing the parasitoid–host dynamics. Outcomes of our study are also highly sensitive to the value of the baseline patch-leaving rate h_{0}. Other parameters could not be compared with the results of Van Roermund et al. (1997) because of differences in model structures and in foraging behaviour between E. formosa and O. sauteri.
With this simulation study we have quantified the daily value of the functional response for a general predatory anthocorid bug, suggesting that this value allows for effective control of thrips by such a predator. The previously performed behavioural analysis (Yano et al. 2005) served as a starting point for the quantification of the impact that one individual O. sauteri has on its prey population at ambient temperature of 25°C. If the predator–prey dynamics of O. sauteri on T. palmi are investigated in future studies, the most appropriate functional response to use is Holling type II.
Acknowledgment
Most of this work was performed in Japan, during L.H.’s stay that was subsidized by the Japanese Society for the Promotion of Science (JSPS ID S-08116). We thank Wopke Van Der Werf and Herman Van Roermund for constructive comments upon an earlier version of the manuscript, and Elizabeth Van Ast for correction of the English.
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