Dispersal of Trichogramma ostriniae (Hymenoptera: Trichogrammatidae)

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(Hymenoptera: Trichogrammatidae) in Potato Fields. ANNA V. CHAPMAN,1 THOMAS P. KUHAR,2 PETER B. SCHULTZ,3. AND CARLYLE C. BREWSTER1.
QUANTITATIVE ECOLOGY

Dispersal of Trichogramma ostriniae (Hymenoptera: Trichogrammatidae) in Potato Fields ANNA V. CHAPMAN,1 THOMAS P. KUHAR,2 PETER B. SCHULTZ,3

AND

CARLYLE C. BREWSTER1

Environ. Entomol. 38(3): 677Ð685 (2009)

ABSTRACT The dispersal ability of Trichogramma ostriniae Pang and Chen, a biological control agent of Ostrinia nubilalis Hu¨ bner, was studied in commercial potato Þelds on the Eastern Shore of Virginia. The purpose was to quantify dispersal of T. ostriniae after an inundative release to aid in determining the number of release points needed per unit area for effective biological control of O. nubilalis in solanaceous crops. A single release of ⬇0.5 million wasps was made in two spatially separate potato Þelds in summer 2005 and 2006. Each release area contained 25 monitoring points at distances from 5 to 45 m from the release point bearing a yellow sticky card and O. nubilalis egg sentinels to observe for adult parasitoids and parasitism, respectively. Results showed that movement of T. ostriniae adults from the release point was rapid with individuals captured at 45 m within 1 d of emergence. High rates of parasitization (20 Ð50%) also were observed at this distance, but the levels decreased with increasing distance from the release point. The distances that encompassed 98% recaptured T. ostriniae adults (x98) were 27.5 and 12.9 m from the release point in 2005 and 2006, respectively. The (x98) distances for parasitization of O. nubilalis were 21Ð26 m in 2005 and 8 Ð10 m in 2006. However, the highest levels of parasitization in both years occurred nearest the release point. T. ostriniae showed uniform dispersal within an area of ⬇0.1 ha, indicating that multiple release points should be used for effective dispersal of T. ostriniae and control of O. nubilalis in solanaceous crops. Based on the assumption that a distance of 16 m represents the radius around a release point in which T. ostriniae activity was at its maximum, we estimate that ⬇12 release points/ha would be required in potato Þelds. KEY WORDS Trichogramma, European corn borer, dispersal, integrated pest management, biological control

Understanding the dispersal behavior of natural enemies is important for developing effective augmentative release strategies and for assessing the spread and potential nontarget effects of an introduced natural enemy (Smith 1996, Orr et al. 2000). Trichogramma ostriniae (Pang and Chen) (Hymenoptera: Trichogrammatidae) is a lepidopteran egg parasitoid endemic to China. Because of its effectiveness as a natural enemy of the Asian corn borer, Ostrinia furnicalis Guene´ e (Lepidoptera: Crambidae), the parasitoid was introduced into the United States in the early 1990s as a biological control agent of the European corn borer, O. nubilalis Hu¨ bner (Lepidoptera: Crambidae) (Hassan and Guo 1991, Hoffmann et al. 1995). Augmentative releases of the parasitoid have resulted in signiÞcantly reduced damage by O. nubilalis in sweet corn (Wang et al. 1999, Wright et al. 2002, Hoffmann et al. 2002, Kuhar et al. 2002, 2003), peppers, 1 Department of Entomology, Virginia Tech, 216 Price Hall, Blacksburg, VA 24601. 2 Corresponding author: Department of Entomology, Virginia Tech Eastern Shore AREC, 33446 Research Dr., Painter, VA 23420 (e-mail: [email protected]). 3 Department of Entomology, Virginia Tech, Hampton Roads Agriculture Research and Extension Center 1444, Diamond Springs Rd., Virginia Beach, VA 23455.

and potatoes (Kuhar et al. 2004). O. nubilalis is an established and economically important pest in potato in the eastern United States (Kennedy 1983, Nault et al. 2001). Larvae tunnel into and within stems damaging tissue and leaving plants susceptible to breakage. Tunneling larvae also create openings for stem rot pathogens such as Erwinia carotova (Kennedy 1983). Growers in North Carolina and Virginia routinely apply one to two foliar sprays of insecticides to potato each year for O. nubilalis control (Nault and Kennedy 1996, Nault et al. 2001). Kuhar et al. (2004) showed a signiÞcant reduction of O. nubilalis larvae and larval tunnels in potato stems after innundative releases of T. ostriniae in small plots. Understanding the dispersal and searching abilities of T. ostriniae can assist in the optimization of releases of the parasitoid in solanaceous crops. In sweet corn, Wright et al. (2001) observed rapid dispersal of T. ostriniae over distances of 35Ð230 m after an inoculative release of ⬇ 1 million wasps from a central release point. In addition, they also found that uniform parasitism of O. nubilalis egg masses occurred up to 1Ð2 ha around a central release point. Similar observations were made in Þeld corn (M. G. Wright, personal communication). Crop habitat can have a major impact on the searching ability and

0046-225X/09/0677Ð0685$04.00/0 䉷 2009 Entomological Society of America

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dispersal behavior of a parasitoid (Gingras and Boivin 2002). T. ostriniae, in particular, has a tendency to search for host eggs preferentially and/or more efÞciently in corn compared with broadleaf vegetable crops such as bean, pepper, or potato (Kuhar et al. 2004) or wooded habitats (Wright et al. 2005). The objective of this study was to assess the dispersal of T. ostriniae adults and parasitism of O. nubilalis after inundative releases of the parasitoid in potato (Solanum tuberosum L.) Þelds. An understanding of dispersal and searching abilities of the parasitoid can assist in the optimization of releases of the parasitoid in solanaceous crops. Materials and Methods Experiments were conducted in May and June 2005 and 2006, within two commercial potato Þelds each year located in Northampton County, VA. In each Þeld, growers planted ÔAtlanticÕ potatoes in early March on rows spaced 0.9 m apart with plants seeded ⬇0.28 m within rows. At the time the studies were conducted in each year, potato plants were in bloom, with a dense canopy within rows and a plant height of 0.5Ð 0.9 m. Field Plot Design. A square plot measuring 4,096 m2 or ⬇0.4 ha was marked off within each of the potato Þelds. Within each of the plots, 25 sampling stations were marked off in a grid pattern at varying distances from a central location that would serve as a release point for T. ostriniae. In 2005, sampling stations were placed at 1, 16, 23, 32, and 45 m from the central release point (Fig. 1A), and in 2006, stations were placed 1, 5, 7, 9, 13, 18, 26, and 45 m from the central release point (Fig. 1B). At each sampling station, a wooden tomato stake bearing a 15 by 15-cm yellow sticky card (Olson Products, Medina, OH) was placed at the height of the plant canopy. In the row adjacent to and within 1 m of the stake, O. nubilalis egg mass sentinels were pinned to the undersides of leaves on Þve individual potato plants. The egg masses were obtained from an established laboratory colony of O. nubilalis moths in cages and allowing them to oviposit on sheets of wax paper. A sentinel egg mass strip was made by cutting around one or two egg masses containing ⬇15Ð30 eggs and gluing these to a small (⬇10 cm2) strip of wax paper; moth scales were not brushed onto sentinels (Wright et al. 2001, 2002). Sentinel egg masses and sticky cards were placed in the Þelds the day before release in addition to a few days before T. ostriniae releases to assess background populations of naturally occurring Trichogramma. In 2005, Þve sticky cards and 10 sentinel egg masses were placed in an adjacent Þeld and collected 3 d later. In 2006, a full Þeld plot was set up before releasing wasps with 25 sticky cards and Þve sentinel egg masses around each card and collected 3 d later. Parasitoid Releases. Trichogramma ostriniae, originally collected from northern China, were obtained from a colony maintained by M. P. Hoffmann at Cornell University, Ithaca, NY. At the Cornell University

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laboratory, parasitoids were maintained on sterilized eggs of Ephestia kuehniella (Zeller) (Lepidoptera: Pyralidae) under conditions of 16 L:8 D, 25:23⬚C, and ⬇80% RH with access to undiluted honey for adults (Hoffmann et al. 1995). Before Þeld releases were made, T. ostriniae were reared for four generations on O. nubilalis eggs and subsequently mass-reared using E. kuehniella eggs following the methods of Morrison (1985). Approximately 500,000 T. ostriniae females were released in each Þeld using cardboard release containers with parasitized E. kuehniella eggs inside (Wright et al. 2001). Release cartons were perforated to allow T. ostriniae emergence and were fastened to a wooden stake bearing a small (30 by 30 cm) plywood roof to shelter the release cartons from the weather. One central release point per study plot was used. Data Collection. Sticky cards and egg mass sentinels were collected at each sampling station and replaced at 1- to 3-d intervals for up to 10 d, which is approximately the life span of the adult parasitoid (Hoffmann et al. 1995). Sticky cards were examined, and the numbers of T. ostriniae recaptured were counted using a stereoscopic zoom microscope with ⫻100 Ð 400 magniÞcation. Sentinels were also collected, removed from wax paper, placed in gelatin capsules (size 00), and held at room temperature in the laboratory until eclosion or emergence of adult parasitoids (Kuhar et al. 2002). A characteristic blackening of the vitelline membranes of host eggs is manifested during Trichogramma prepupal and pupal stages (Flanders 1937); thus, “black” eggs were considered to be parasitized. Analysis of Dispersal and Parasitism. The method described in Rudd and Gandour (1985) for Þtting release-recapture data to the diffusion model was used to characterize the dispersal patterns of T. ostriniae adults from a central release point within each of the study plots in the four potato Þelds. It is well known that the solution to the diffusion model is a normal distribution (Taylor 1978) and that any transect through a two-dimensional normal distribution is a normal distribution in one dimension (Allen and Gonzalez 1974). Therefore, for simplicity in using the diffusion model to characterize the dispersal pattern of T. ostriniae adults in two-dimensional space (the potato plots), it was only necessary to describe the process for the one-dimensional case. The diffusion model for the movement of the parasitoid in onedimensional space (such as along a row of the potatoes), may be written as ⭸y/⭸t ⫽

D⭸ 2y ⫺ ␮y ⭸x2

[1]

This model describes the change in the number of parasitoids, y, at a distance, x, from a release point at time, t. The constant D is the diffusion coefÞcient, and ␮ is a removal constant for individuals as a result of emigration and/or mortality. The solution to equation 1 is

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A. 2005 9m

12 m

7m

10 m

16 m 23 m Release point

B. 2006

19 m

9m

13 m

4m

6m 7m

5m

Release point

Fig. 1. Field plot design for T. ostriniae dispersal and parasitism study conducted in commercial potatoes in Virginia in 2005 and 2006. Each symbol represents the location of a yellow sticky card and sentinel egg masses of O. nubilalis.

e ␮te ⫺共x /4Dt兲 y共 x,t兲 ⫽ y 0 2 冑␲ Dt 2

[2]

where y0 is the initial population of parasitoid released at the central location. For a Þxed time t, the distribution is normal with variance 2Dt (Rudd and Gandour 1985). The diffusion models outlined in equations 1 and 2 assume that individual adult parasitoids move at random and show no preferential directional movement in any one direction from the point of release point. That is, the model assumes there are no external forces (e.g., wind) acting to inßuence the movement of individuals and resulting in drift or displacement in their movement (Rudd and Gandour 1985, Turchin and Thoeny 1993, Blackmer et al. 2004, Bancroft 2005,

Puche et al. 2005). In the case where drift is thought to have occurred, equation 2 can be modiÞed to include this effect, so that e ␮te ⫺共x⫺vt兲 /4Dt) y共 x,t兲 ⫽ y 0 2 冑␲ Dt 2

[3]

where v is a parameter of constant velocity that moves the center of the distribution (Rudd and Gandour 1985). As a Þrst step in estimating the diffusion coefÞcient, D, for T. ostriniae, a least squares method was used to Þt the sticky trap data to a model that represents the parametric form of half of the normal distribution (Rudd and Gandour 1985). The model 2

y i ⫽ Ae ⫺Bxi

[4]

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describes the relationship between the numbers of individuals dispersing, yi, and distances, xi. The constants A and B are estimates of the number of individuals at the release point (x ⫽ 0) and the proportional reduction in the number of individuals with distance, respectively. After the data were Þtted to equation 4, we used the value of the parameter B to estimate D (Rudd and Gandour 1985), based on the equation D⫽

1 4Bt

[5]

In addition, we calculated the distances that encompassed 98% of the T. ostriniae adult activity as inßuenced by diffusion (Bancroft 2005) by x 98 ⫽ 2 冑4Dt

[6]

Following from the above analyses, a one-dimensional redistribution kernel, K(x), for T. ostriniae adult dispersal was derived for each sampling time point within each of the four study plots. A redistribution kernel describes the distribution of dispersal distances for an organism (Neubert et al. 1995, Brewster and Allen 1997). Several methods are available for estimating the redistribution kernels from observed (Neubert et al. 1995). We used the method described in Kot et al. (1996) to develop dispersal kernels for T. ostriniae from the observed release-recapture data. After obtaining the curve of the relationship of T. ostriniae trap catches with distance using equation 4, the curve was mirrored about the origin and divided by the total area underneath the resulting curve to generate the probability density function with an area equal to 1. All of the above curve Þtting analyses were carried out using TableCurve 5.01 (SYSTAT Software, Richmond, CA). We examined the relationship between the distribution of T. ostriniae trap catches and parasitization of O. nubilalis sentinel egg masses using a two-sample Crame´ r-von Mises test (Syrjala 1996). The two-sample Crame´ r-von Mises test has the advantage of being insensitive to differences in total values of the samples in each of the two distributions to be compared. The null hypothesis for the test was that there was no statistical difference between the spatial distributions of T. ostriniae sticky trap catches and parasitization of O. nubilalis in a study plot. The test was carried out by the method outlined in Syrjala (1996), which is brießy described here. An overall test statistic (⌿1) for the comparison of the two original spatial distributions was derived after the data in each of the distributions were normalized. After this, 999 pseudo-random permutations of the normalized data in the two distributions were examined where, for each permutation, one of the observations from corresponding locations in the two spatial distributions was randomly assigned to the Þrst distribution and the other to the second distribution. A new test statistic, ⌿n (n ⫽ 1É999) was calculated after each permutation. The signiÞcance level (P value) for the comparison was the proportion of the 1,000 test statistics (⌿n ⫹ ⌿1) that was ⱖ⌿1. The

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Crame´ r-von Mises analysis was carried out only on the data collected in 2005 using a program written in MATLAB (Mathworks, Natwick, MA). Results 2005 Study. No evidence of background activity for Trichogramma was detected in the study areas based on yellow sticky card catches and parasitization of O. nubilalis egg mass sentinels placed out before T. ostriniae releases were made. The relationship between the number of T. ostriniae adults on yellow sticky cards and distances from the release point at different days after release are shown in Fig. 2A and C for plots 1 and 2, respectively. The Þt of the sticky card data to the model in equation 4 was exceptionally good (r2 ⬎ 0.90) for all of the data and for those collected in plot 2 at 10 d after T. ostriniae release was made (r2 ⫽ 0.78; Table 1). The diffusion coefÞcients for the dispersal of T. ostriniae adults captured on sticky card data on each of the sampling dates in the two study plots are also shown in Table 1. As expected, D was relatively high at 1 d after release (67.31 m/d) but decreased thereafter to a mean of 7.78 ⫾ 0.84 (SE) m/d between days 4 and 8 after T. ostriniae adults release. At 1 d after release in plot 1, T. ostriniae were recaptured on sticky cards at 16, 23, and 32 m from the release point. Within 4 d after release, T. ostriniae adults traveled up to 45 m and persisted at this distance through the eighth day of sampling. Despite differences in D with sampling time, the distance from the release point that encompassed 98% of recaptured T. ostriniae females (x98) was similar for the different sampling dates, except in plot 2 at 10 d after release (Table 1). Mean x98 across both Þelds on all sampling dates, except in plot 2 at day 10, was 27.53 ⫾ 2.39 (SE) m. The mean value for x98 is reßected in the shape of the redistribution curves shown in Fig. 2B and D for plots 1 and 2. The curves ßatten out at the tail near the mean x98 distance. The mean proportion of parasitized sentinels was 100% at the release point on all sampling dates in plots 1 and 2, except on day 10 in plot 2, when no parasitism was observed (Fig. 3A and B). The mean proportion of parasitized sentinels was 10% at 16 and 23 m from the central release point. In both Þelds, parasitization peaked at 4 d after release with ⬇40% of O. nubilalis egg sentinels parasitized at 30 m from the release point. Using analysis similar to that carried out on the sticky card data, estimates of the distance from the release point that encompassed 98% of the parasitism (x98), were ⬇21 and 26 m in plots 1 and 2, respectively. The results of the two-sample Crame´ r-von Mises analysis indicated that there was no statistically significant difference (P ⬎ 0.05) in the distribution of sticky card captures of T. ostriniae adults and the distribution of parasitism of O. nubilalis sentinel egg masses (Table 2). 2006 Study. As in 2005, sticky cards and O. nubilalis sentinel eggs placed in the plots before T. ostriniae adults were released detected no evidence of back-

CHAPMAN ET AL.: DISPERSAL OF T. ostriniae Redistribution Kernels

Dispersal Curves

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Distance from Release (m) Fig. 2. Dispersal of T. ostriniae in potato in 2005. Recapture-with-distance curves and corresponding redistribution kernels for the parasitoid are shown for (A and B) Þeld 1 and (C and D) Þeld 2.

ground activity for Trichogramma in the study areas. The relationships between the number of adults and distance from the release point at different days after release are shown in Fig. 4A and C for plots 1 and 2, respectively. The Þt of the sticky card data to the model in equation 4 was reasonably good (r2 ⱖ 0.77) in most cases, except for the data collected in plot 1 at day 6 (r2 ⫽ 0.03) and in plot 2 at day 1 (r2 ⫽ 0.44) after release of T. ostriniae, respectively (Table 1). Because of the poor Þt to the model, no useful assessment could be made of the diffusion coefÞcient D for these sampling dates. Table 1.

For the sampling dates where the diffusion coefÞcient for the sticky card data were calculated, the values were much lower than those estimated for the study conducted in 2005. The highest level achieved was at 1 d after release in plot 1 (12.39 m/d). For all the other sampling dates, D ⬍ 3 m/d. As such, the mean of D in the 2006 study, excluding dates for which the Þt to equation 4 was poor, was 4.15 ⫾ 2.07. Nevertheless, as was observed for the 2005 study, the distance from the release point that encompassed 98% of the T. ostriniae females (x98) recaptured was similar for the different sampling data for which equation 4

Variables and coefficients determined by fitting T. ostriniae release-recapture data to a diffusion model

Year

Plot no.

ta

A

B

r2

D (m2/d)

x98 (m)

2005

1

1 4 8 Cumulative 4 7 10 Cumulative 1 3 6 Cumulative 1 3 6 9 Cumulative

29.0780 152.9375 48.8095 231.2914 201.6155 18.9083 1.8759 231.8831 108.8268 134.5224 1.3679 243.2545 5.8448 54.2935 64.2217 17.9958 142.6592

0.00371 0.0088 0.0036 0.0062 0.0066 0.0062 0.0014 0.0095 0.0202 0.0329 — 0.0253 0.0015 0.0384 0.0200 0.0179 0.0236

0.98 0.99 0.95 0.98 0.93 0.98 0.78 0.96 0.92 0.90 — 0.90 — 0.95 0.87 0.77 0.88

67.31 7.11 8.75 5.05 9.49 5.76 17.74 2.64 12.39 2.54 — 1.65 — 2.17 2.06 1.556 1.17

32.82 21.33 33.47 25.42 24.64 25.40 53.28 20.54 14.08 11.03 — 12.58 — 10.21 14.14 14.94 13.01

2

2006

1

2

a Days after release of T. ostriniae; cumulative represents analysis done on the total no. of parasitoids recaptured over all sampling days. A, no. of T. ostriniae at the release point t days after release (equation 4 in text); B, proportional reduction in the no. of T. ostriniae with distance from the release point (equation 4 in text); D, diffusion coefÞcient (equation 5 in text); x98, distance that encompases 98% of activity (equation 6 in text).

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Mean Proportion of Eggs Parasitized

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Distance from Release (m) Fig. 3. Relationship of mean proportion of O. nubilalis egg masses parasitized and distance from release point on different sampling dates after release of T. ostriniae. (A and B) Relationships observed in 2005 in Þelds 1 and 2, respectively. (C and D) Relationships observed in 2006 in Þelds 1 and 2, respectively.

could be Þtted (Table 1). Mean x98 across both Þelds on all sampling dates was 12.88 ⫾ 0.94 m. As expected, this value is much lower than was obtained for the 2005 study. However, again, the mean value for x98 is reßected in the shape of the redistribution curves shown in Fig. 4B and D for plots 1 and 2, respectively. The curves again tended to ßatten out at the tail near the mean distance. The mean proportion of parasitized sentinels was 100% at the release point on all sampling dates after release in plots 1 and 2, except on day 6 in plot 1 (Fig. 3C and D). On that date, no parasitism was observed at any distance. In both plots, parasitization was still relatively high at 3 d after release, with just ⬎40% of sentinels parasitized at 7 m from the release point.

Estimates of the distance from the release point that encompassed 98% of the parasitism (x98) were ⬇8 and 10 m for plot 1 and plot 2, respectively. When the data for each year were combined, a negative relationship was found between distance and sticky card catch of T. ostriniae adults. Moreover, sentinel egg mass parasitism was negative for both years. The regressions of distance to egg mass parasitism had very similar slopes and intercepts for both years [2005: y ⫽ ⫺0.2776 ln(x) ⫹ 1.5290; 2006: y ⫽ ⫺0.2608 ln(x) ⫹ 1.3779], showing similar dispersal behavior after releases in 2005 and 2006. There was no signiÞcant interaction between distance and time for all Þelds (P ⬎ 0.05). Discussion

Table 2. Cramer von Mises two-sample analysis of T. ostriniae release-recapture data and parasitism of O. nubilalis egg masses in 2005 Field

ta

⌿1

P value

1

1 4 8 Overall 4 7 10 Overall

0.0102 0.1630 0.0327 0.0076 0.3172 0.0032 Ñ 0.0073

0.1990 0.5250 0.1260 0.2510 0.2140 0.2770 Ñ 0.2330

2

a Numbers are days after release of T. ostriniae; overall represents per-sampling day for the parasitoid density and average level of parasitism.

The results of this study showed the positive behavior characteristics of T. ostriniae as a biological control agent in solanaceous crops. In keeping with similar results from Wright et al. (2001) in sweet corn, we found that T. ostriniae dispersed rapidly over large distances within the commercial potato Þelds used in our studies. Despite a preference of T. ostriniae for corn over dicotyledonous plants (Kuhar et al. 2004), the parasitoid successfully moved throughout a 0.4-ha area of potatoes and reproduced within 45 m of a central release point. At 45 m, ⬇20% parasitism was observed within 4 d after release in 2005, and 33% was observed within 1 d after release in 2006. However, although signiÞcant levels of parasitism were recorded

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Distance from Release (m) Fig. 4. Dispersal of T. ostriniae in potato in 2006. Recapture-with-distance curves and corresponding redistribution kernels for the parasitoid are shown for (A and B) Þeld 1 and (C and D) Þeld 2.

at these distances, parasitism greatly decreased with increasing distance. With the exception of plot 1 in 2005, correlations between sticky card catch of T. ostriniae and parasitism were not signiÞcant for distances ⱖ26 m. Despite a decrease in parasitism with distance, sticky card catch was comparatively similar across distances. This suggests that the decrease in parasitism with distance may not be the result of a lack of presence of T. ostriniae, but perhaps the inability of wasps to locate hosts in a much larger Þeld area. The analysis supports this idea. In the 2005 study, for example, the mean distance in which 98% of the trapped parasitoids were found was 27.53 ⫾ 2.39 m. Thus, the majority of parasitoids were trapped in an area equivalent to ⬇18% of the entire 4,096-m2 (64 by 64 m) study area. This value was lower in the 2006 study. Trichogramma are thought to disperse randomly or through phoresy on the host moth, although this is largely undocumented (Smith 1996). Natural O. nubialis pressure was low in our study sites in 2005 and 2006 and, most likely, the majority of the wasps dispersed on their own. As T. ostriniae dispersed further away from the central release, host egg density (on sentinels) decreased. Wajnberg et al. (2003) found a signiÞcant increase in patch leaving tendency for Trichogramma females that successfully oviposit in a host and/or reject a previously attacked host. The low abundance of native O. nubialis egg masses and the low density of sentinel egg masses at greater distances may have increased localized searching or patch residence time of T. ostriniae and decreased their ability to Þnd sentinel hosts. Nonetheless, having the majority of parasitism contained within the release site

might tend to minimize potential nontarget effects of the parasitoid (Orr et al. 2000). Weather conditions such as wind and rain can affect the movement of parasitoids and their subsequent levels of parasitism. Although the Þt of the data to equation 3 showed the effect of drift (as measured by the parameter v) to be negligible in describing the dispersal of the T. ostriniae, wind could have played a role in T. ostriniae movement based on trends in dispersal direction. In both years of study, cumulative parasitism was observed to be greater in the direction of prevailing winds for the area. Numerous studies have shown parasitism signiÞcantly decreases in the upwind direction (Hsiao 1981, Smith 1988, Greatti and Zandigiacomo 1995, Fournier and Boivin 2000). Precipitation also likely affected the dispersal of the T. ostriniae in our study. In Þeld 2 in 2005 and Þeld 1 in 2006, wasps dispersed quickly within 3Ð 4 d after release. After which, heavy rain and thunderstorm conditions occurred in both years, and no parasitism was found on subsequent sample dates. However, without more precise data on environmental conditions, it is difÞcult to determine whether wind was the primary factor in directional dispersal. In a study of attack by T. pretiosum Riley on eggs of the cabbage looper, Tricoplusiani (Hu¨ bner), Allen and Gonzalez (1974) implied that the spatial pattern of attack could be used to infer the dispersal pattern of the parasitoid. This study provides some evidence to support this position by Allen and Gonzalez (1974). The two-sample Crame´ r-von Mises analyses of the distribution of sticky card catch of T. ostriniae and the distribution of parasitism of O. nubilalis sentinel egg masses found no statistically signiÞcant difference be-

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tween the pairwise distribution (Table 2). Thus, the two distributions were highly correlated in all of the cases examined so that high trap catches were usually obtained at locations where there were high levels of parasitism and vice versa. As such, the spatial distribution of attack of T. ostriniae on O. nubilalis eggs could have been used to study the dispersal pattern of the parasitoid. The data from our study also may provide us a way to predict the distribution of the parasitoid some time after a release. This can be done using the method described in Brewster and Allen (1997) that requires information on the initial number of parasitoids at time, t, and the redistribution kernel (K) for the insect at time t. These two pieces of information can be used to develop an integrodifference equation model (Neubert et al. 1995, Kot et al. 1996, Brewster and Allen 1997) such as

冘 n

Y t⫹1共 x兲 ⫽

K共 x ⫺ u兲Y t共u兲

[7]

u⫽1

to estimate the number of parasitoids at each location in a one-dimensional spatial system at time t ⫹ 1. In equation 9, Yt and Yt⫹1 are the populations of parasitoid at time t and t⫹1, respectively, and K(x ⫺ u) is the dispersal or redistribution kernel seen in Figs. 2B, 3B, 5, and 6B that describes the probability density of individuals moving from point u to x in the spatial system. The model for two-dimensional dispersal is the logical extension to equation 7 (Brewster and Allen 1997). Population simulations with integrodifference equations can be done using the method described in Allen et al. (2001). When applying our results for augmentative control of O. nublialis, it is important to consider dispersal and parasitism in conjunction with pest suppression. Inundative releases rely on rapid dispersal and uniform coverage of the target area. Although T. ostriniae were found throughout ⬇0.4 ha and showed high rates of parasitism out to 45 m, the distance that encompassed 98% of the total parasitism from the release point averaged 16 m based on the four experimental plots. This average represents a conservative estimate for the radius around a release point in which T. ostriniae activity was at its maximum. This would translate to 12 release points per hectare for uniform coverage of T. ostriniae. Based on our release numbers, this would amount to nearly six million wasps per hectare, which is a serious economic constraint for Þeld adoption. Additional research is needed to evaluate the density of T. ostriniae needed per unit area for effective control of O. nubilalis as well as timing of releases throughout the growing season to manage multiple generations of the pest. Acknowledgments The research presented in this paper was sponsored by grants from the National Science Foundation Center for IPM and the Environmental Protection Agency Strategic Agricultural InitiativeÑRegion III. The authors sincerely thank

Vol. 38, no. 3

E. Hitchner, M. Cassell, H. Doughty, R. Bradley, K. Peoples, R. Horner, A. Windsor, and J. Blodgett, who assisted with the Þeld data collection.

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