1. Within-Plant Distribution of Twospotted Spider Mite, Tetranychus urticae Koch (Acari: Tetranychidae), on Impatiens : Development of a Presence-Absence Sampling Plan F. J. ALATAWI, G. P. OPIT, D. C. MARGOLIES, AND J. R. NECHOLS Department of Entomology, Kansas State University, Manhattan, Kansas, 66506-4004, fkhalid98@hotmail.com ABSTRACT The twospotted spider mite, Tetranychus urticae Koch, is an important pest of impatiens, a floricultural crop of increasing economic importance in the USA. Because of the large amount of foliage on individual impatiens plants, the small size of twospotted spider mites and the mite’s ability to build high populations quickly on impatiens, a reliable sampling method for T. urticae is required to develop a management program. We were particularly interested in spider mite counts as the basis for release of biological control agents. Within-plant mite distribution data from greenhouse experiments were used to identify the sampling unit that should be used. Leaves were divided into three categories; inner, intermediate, and other. On average, 40, 33, and 27% of the leaves belonged to the inner, intermediate, and other leaves categories, respectively. We found that 60% of the mites on a plant were on the intermediate leaves. These results lead to development of a presence-absence (=binomial) sampling method for T. urticae using generic Taylor coefficients for this pest. By determining numerical or binomial sample sizes for accurately estimating twospotted spider mite populations, growers will be able to estimate the number of predatory mites that should be released to control twospotted spider mite on impatiens. INTRODUCTION Developing integrated control of twospotted spider mite, Tetranychus urticae Koch (TSM), on any crop involves assessing pest distribution and developing a sampling program for the crop in question. Major drawbacks of conventional monitoring procedures for mites are the tedium, inaccuracy, and time involved with counting tiny individual mites. Sampling methods that are easy to use and provide estimates of reasonable accuracy within a short time are likely to be more successful. This particularly is important on impatiens, which have a large amount of foliage. Presence-absence sampling is ideally suited for mites because instead of counting the individual mites, the number of units (leaves) with mite is recorded. This is a relatively simple approach and, therefore, one that growers may be willing to adopt. Developing a presence-absence sampling plan for TSM on impatiens requires: 1) knowing the within-plant distribution of TSM, 2) specifying the sampling unit, as well as 3) the relationship between the proportion of TSM- infested sampling units and the mean number of TSM on each sampling unit. OBJECTIVES Determine the within-plant distribution of TSM on impatiens. Use numerical relationships to develop a binomial sampling plan that could substitute for the more laborious and difficult direct counting method. STEPS 1 Within-plant TSM distribution  Intermediate (INT) leaves were chosen as the sampling unit (Fig. 1). At each sampling time, the leaves on each plant were divided into three categories: Inner (IN), Intermediate (INT), and Other (OT) (Fig. 1) On each leaf, TSM in all stages of development but eggs were counted. The average percentage of total leaves in IN, INT and OT categories was 40, 33, and 27%, respectively. The average percentage of total TSM was 31, 60, and 9%, respectively. For each week, the scatter plot of the total number of mites on each plant against the mean number of mites on the INT category showed a linear relationship and the value of R 2 was 0.72. 0.88, 0.91, and 0.87. This conclusion is supported by the finding that the total number of mites on a plant can be predicted using mean TSM on the INT category. Using the INT leaf as the sampling unit improves the: 1) efficiency and ease of sampling because the sampling units are similar and easily recognized, and 2) detection of TSM at low population densities because INT leaves are the most infested.. STEPS 2 Binomial sampling model  Taylor’s Power Law describes the distribution of TSM in the INT category (Fig 2). Taylor’s Power Law (Taylor 1961): S 2 = am b, where S 2 = variance, m = mean, and “a” and “b” are coefficients; “a” is largely a sampling factor and “b” an index of aggregation. If a regression of ln S 2 on ln m yields a significant p-value and a high coefficient of determination, Taylor’s Power Law can be used to describe the distribution of TSM in a sample unit category. The relationship between the mean number of TSM per INT leaf and the variance, predicted by Taylor’s power law was highly significant (F = 1027.3; df = 1, 22; P < 0.0001) (Fig. 2). ln S 2 = 1.21 + 1.32 ln m (R 2 = 0.94) The value of “b”, the slope, is 1.32 and is significantly different from the mean value of 1.49 found by Jones (1990) This difference may be attributed to the small sample size used to derive the value of “b” in this study  At a tally threshold of 0 mites/leaf, the relationship between mean number of pests per sampling unit m and pest-infested sampling units PI was well described by the binomial model and showed that generic Taylor coefficients provide good prediction of mean TSM population levels in impatiens (Fig. 3). A binomial model developed by Wilson and Room (1983) shows the relationship between the proportion of pest-infested sampling units (PI) and the mean number of pests per sampling unit (m). It uses the variance-mean relationship that incorporates Taylor's equation which, in simplified form, can be expressed as: In (1-PI) = -m ln (am b-1 )/ (am b-1 – 1) {1} The fit of the binomial model was evaluated by regressing the right hand side of equation 1 against the left using our data (Wilson and Morton 1993). Jones (1990) verified generic values of a = 3.3 and b = 1.49 for spider mites under many situations. If the binomial model, with Jones’ generic values of a and b, describes the relationship between mean number of TSM on INT leaves and the proportion of these leaves that are infested, we can use the binomial model to develop a sampling method. Tally thresholds of 0, 2 and 5 mites/leaf were tested to determine which resulted in the best fit. If the model fits well, the intercept should be zero and the slope equal to one. At a tally threshold of 0 mites/leaf, the relationship between m and PI was described by the binomial model (F =280.8, df = 1, 27; P < 0.0001) The intercept was not significantly different from zero (t = 1.41; 27 df; SEM =0.98; P =0.17). However, the slope was significantly different from 1 (t = 16.7; 27 df; SEM =0.07; P < 0.0001), indicating that the model (equation 1) could be improved (Fig. 3) by incorporation of only the regression slope. 1.7 ln (1 - PI) = -m ln (am b-1 )/ (am b-1 - 1) Which can be rewritten as : PI = 1 - e ^ {(-m ln (3.3m 0.49 )/ (3.3m 0.49 - 1)/1.7} (R 2 = 0.91) Tally thresholds of 2 and 5 also had high R 2 values, 0.89 and 0.84, respectively, indicating they could be used as well. Fig. 1. The three categories of leaves: inner, intermediate, and other Fig.2. Relationship between variance and the mean for TSM on impatiens leaves. Fig. 3. Mean number TSM/leaf vs. proportion of leaves infested with TSM (points). Solid line represents predicted values from modified model of Wilson et al. (1983) using generic Taylor’s coefficients. STEPS 3 Optimal sample size  Binomial samples are highly recommend to be used for accurately estimating TSM populations (Fig. 4) Optimal numerical sample size, when using presence-absence sampling is represented by: n = Z a/2 D -2 p -1 q {2} where n = sample size, Z a/2 is the upper a/2 of the standard normal distribution, D is a proportion of m, m is expressed in terms of the number of TSM on the leaves, p is the proportion of the sampling units infested, q is the proportion not infested, D = CI/2p is the level of precision, CI is the confidence interval, and "a" and "b" are Taylor coefficients (Gutierrez 1996, Karandinos 1976). From results above, we can now estimate binomial and numerical sample sizes for accurately estimating TSM populations (Fig. 4 and Fig. 5) At a threshold TSM density of 0, when binomial sampling is used, only 23 leaves would have to be checked ( Fig. 3), while 60 leaves should be observed when numerical sample is applied. However, because the maximum number of TSM per leaf that would have to be counted is 1 and only 23 leaves are required to estimate density, Binomial samples would save growers considerable time and could increase adoption. Fig 5. Optimal numerical sample size for TSM on impatiens; D = 0.25 (broken line) and D = 0.5 (continuous line); α = 0.05. REFERENCES Gutierrez, A. P. 1996. Sampling in applied population ecology. Pp. 9-26 In Applied Population Ecology: A Supply-Demand Approach. John Wiley and Sons, Inc. New York. Jones, V. P. 1990. Developing sampling plans for spider mites (Acari: Tetranychidae): Those who don’t remember the past may have to repeat it. J. Econ. Entomol. 83:1656-1664. Karandinos, M. G. 1976. Optimum sample size and comments on some published formulae. Entomol. Soc. Am. Bull. 22: 417-421. Wilson, L. T., and P. M. Room. 1983. Clumping patterns of fruit and arthropods in cotton with implications for binomial sampling. Environ. Entomol. 12:50-54. Wilson, L. T. and R. Morton. 1993. Seasonal abundance and distribution of Tetranychus urticae (Acari: Tetranychidae), the twospotted spider mite, on cotton in Australia and implications for management. Bull. Entomol. Res. 83:291-303. EXPERIMENTAL DESIGN Impatiens cultivar ‘Impulse Orange’. Randomized complete block design (RCBD) with two treatments – low and high TSM densities. Four-week-old plants were inoculated with 7 or 13 adult female TSM. Weekly after inoculation, 8 plants were destructively sampled. Intermediate Inner Other ACKNOWLEDGMENT We thank the following individuals from Kansas State University for their contributions: Kimberly Williams, Kiffnie Holt, Yan Chen, and Xiaoli Wu. Fig 4. Optimal binomial sample size for TSM on impatiens; D = 0.5; α = 0.05