Spatial Patterns of freeborni and Culex tarsalis (Diptera: Culicidae) Larvae in California Rice Fields

MICHAEL J. PITCAIRN.1 LLOYD T. WILSON.2 ROBERT K. WASHINO, AND ELISKA RE JMANKOVA3 Department of Entomology, University of California, Davis, CA 95616

J. Med. Entoniol. 31(4): 545-553 (1994) ABSTRACT Spatial patterns ofAnophelesfreeborni Aitken and Culex tarsalis Coquillett larvae were studied during summer by sampling with a standard dipper in 104 rice fields in northern California. Culex tarsalis larval abundance was highest initially, then decreased and remained low through late summer. An. freeborni larval abundance was low initially, increased steadily, and peaked in mid-August. The degree of aggregation for both species as measured using Taylor's power law and Iwao's Patchiness Regression was highest among the first instars and then decreased as the larvae aged. Seasonal peaks in the degree of aggregation were observed. Analysis of covariance showed that for Taylor's model both instar and time effects were statistically significant, with instar show- ing the largest effect. In comparison, all slopes resulting from Iwao's model were signifi- cantly different, indicating that this model was affected by specific combinations of instar, week, and location and, thus, was less useful in developing an area-wide sampling plan. Optimal sample size was estimated using two methods. One method calculated the num- ber of dips needed to estimate population abundance at three fixed-precision levels. The second calculated the minimum number of dips needed to collect at least one . The latter requires a substantially smaller sample size and may provide an effective method for monitoring larval niosquito abundance for control purposes.

KEY WORDS Anopheles freeborni, Culex tarsalis, spatial pattern

COMMERCIALRICE PRODUCTION in northern Cal- level of accuracy, has not been studied for An. ifornia provides an optimal habitat for the devel- freeborni. Mackey & Hoy (1978) and Stewart et opment and reproduction of the mosquitoes al. (1983) examined the dispersion of Cx. tarsalis Anopheles freeborni Aitken, a vector of in central California rice fields and compared and canine heartworm (Bohart & Washino 1978), dip-sample data to the Poisson and negative bi- and Culex tarsalis Coquillett, the primary vector nomial statistical distributions. Their objective of western equine encephalomyelitis and St. was to develop sequential sampling plans for this Louis encephalitis viruses (Hardy et al. 1980). species, and both studies reported that the neg- Both species attain high adult numbers during ative binomial distribution provided a good fit to the summer months and require control by local their data. abatement districts. Larval abundance in any one rice field, however, is low, and this has hin- Other attempts to fit statistical distributions to dered the development of adequate sampling larval mosquito sample data have not produced plans. Accurate population estimates are time consistent results. Service (1985) presented dip- consuming and, for control purposes, are eco- sample data on Aedes cantons (Meigen), Anoph- nomically prohibitive and possibly unnecessary. eles arabiensis Patton, and Anopheles gambiue A standard mosquito dipper (Service 1976) pro- Giles populations and found that none of several vides a rapid estimate of relative abundance and distributions, including the Poisson and the neg- is used commonly to monitor larval abundance. ative binomial, consistently fit all of the data. However, the distribution of larvae among sam- The problem lies in the fact that various statisti- ples, or larval dispersion, which directly affects cal parameters (e.g., k of the negative binomial) the number of samples required for any desired vary with density. Recently, Taylor's power law (Taylor 1961) and Iwao's Patchiness Regression (Iwao 1968) have been used to analyze the spa- 1 California Department of Food and Agriculture, Biological Control Program, 3288 Meadowview Road, Sacramento, CA tial patterns in larval mosquito populations. The 95832. advantage of these models is that they account 2 Department of Entomology, Texas A&M University, Col- for the increase in variance with increasing den- lege Station, TX 77843. 3 Department of Environn~entalStudies, University of Cali- sity and indicate the amount of aggregation in- fornia, Davis, CA 95616. dependent of density effects.

0022-258519410545-0553$02.00/0 0 1994 Entomological Society of America 546 JOURNALOF MEDICALENTOMOLOGY Vol. 31, no. 4

Andis & Meek (1984) used Iwao's model to nia rice fields during July through September analyze the larval distribution of Psoropora co- (Washino 1980); no other species were collected. lumbiae (Dyar & Knab) and Anopheles crucians Models of Dispersion. Taylor's power law Wiedemann in Louisiana rice fields and reported (Taylor 1961) and Iwao's Patchiness Regression that, for Ps. columbiae, the early instars were the (Iwao 1968) were used to quantify the relation- most aggregated. In contrast, An. crucians larvae ship between the sample variance and mean. were weakly aggregated, and the degree of ag- Taylor's power law states that the variance of a gregation did not change with age. Service population is related to its mean density as fol- (1985) reviewed studies that used Taylor's and lows: Iwao's models to analyze sample data on Anoph- eles sinensis Wiedemann, Culex tritaer~iorhyn- chus Giles, and An. arabiensis in rice fields. He The parameters, a and b, were estimated by re- concluded that larvae of all three species showed gressing logio (variance, s2) against logio (mean, consistent but weak aggregation, except for the Z). Wilson (1985) pointed out that both the inter- first instars, which were strongly aggregated. cept, a, and the slope, b, contribute to describing Sandoski et al. (1987) used Taylor's model to aggregation; b generally contributes more when analyze dip samples of Anopheles quadrimacu- mean density is high, but a becomes important latus Say larvae (all instars combined) in Arkan- when the density is low (e.g., 2 < 1). sas rice fields and found no aggregation. Walker Iwao (1968) found that the change in Lloyd's et al. (1988), using Taylor's and Iwao's models, estimate of mean crowding (x, the mean number reported that An. quadrimaculatus larvae in a of other individuals per individual in the same Michigan marsh were aggregated and attributed dip) with mean density (2) could be fitted to a this to the heterogeneity of the habitat. linear regression, termed Iwao's Patchiness Re- In an earlier study in California rice fields gression (Southwood 1978): (Christensen & R.K.W., unpublished data) in which dip-sample data were analyzed using Iwao's model, it was estimated that, for Cx. tar- salis, at least 250 dips would be required to es- The intercept, a, indicates the tendency of indi- timate the larval population in a single rice field viduals to be found in groups. It is >0 when at a precision level of 0.25 for a population of 0.5 individuals are found together more often than larvae per dip. For An. freeborni, at least 360 expected by chance alone, =0 when found to- dips would be required to achieve the same level gether at random, and <0 when found together of precision. less often than expected by chance alone. The Here we report a detailed analysis of the larval slope, & equals unity when the larvae are dis- dispersion of An. reeborni and Cx. tarsalis in tributed at random and greater than unity when commercial rice ftelds in northern California. aggregated. Our objectives were to document the phenology The effects of instar, time (sample week), and of mosquito abundance and, using Taylor's location (density) were investigated using analy- power law and Iwao's Patchiness Regression, to sis of covariance (SAS Institute 1985) with logio characterize the spatial pattern of larvae within a (mean) and the sample mean as the covariate for field. The effect of age (instar), time, and density Taylor's and Iwao's models, respectively. This on the spatial pattern also was investigated. procedure was used to identify significant differ- ences in slope and intercept among instar, week, and location. Model parameters were estimated and reported for individual instars. A t test was Materials and Methods used to determine if b or p were statistically Sampling Procedure. Sample sites of ==3,000 significantly different from one and if a and a m2 were established in 104 commercial rice were statistically significantly different from fields in Sutter County in northern California zero. before or immediately after flooding in early The optimal sample size for monitoring larval May. Sampling began on 29 June 1987 and con- abundance was investigated in two ways. One tinued weekly for 10 wks. Three individuals method examined the number of dips needed to spaced "10 m apart took three dips using a stan- estimate population abundance with a fixed level dard mosquito dipper (=400 ml) at 10 stops along of precision given specified amounts of aggrega- linear transects into the field. The first stop was tion in the sampled population. Wilson & Room 3-5 m from the edge of the field; subsequent (1983) incorporated Taylor's power law into stops were spaced 3-5 m apart. Observations for Karandinos's (1976) model for estimating optimal each dip were recorded separately. For each dip, sample size as follows: all mosquito larvae were identified to species and instar, counted, and returned to the field. One sample consisted of 90 dips. Only Cx. tar- where n is the number of samples, Zda is the salis and An. freeborni occur in northern Califor- upper d2 part of the standard normal distribu- July 1994 PITCAIRNET AL.: SPATIALPATTERNS OF An. freeborni AND Cx. tarsalis LARVAE 547 tion, a is the confidence level, and D is a fixed proportion of the mean. The other parameters are 1 Anopheles freeborn1 0 - I as defined in equation 1. For a 95% confidence interval, a = 0.05 for which Zo,02s = 1.96 when n > 30. Optimal sample size also was examined by cal- culating the minimum number of dips necessary to ensure collection of at least one mosquito larva in 95 out of 100 samples. When larval abundance is low, it can be difficult to collect any larvae, even when larvae are present. The number of dips necessary to collect at least one larva in 95 out of 100 samples was estimated as

where P(o) is the probability of collecting no lar- July August Sept. vae in a dip and n is the sample size. Solving for n gives Fig. 1. Seasonal abundance of An. freeborni and Cx. tarsalis larvae in northern California rice fields; n = 104 fields. where loge is the natural logarithm. We esti- mated Pie) using the Poisson and the negative fields), and Bobbins (35 fields). Larval abun- binomial probability distributions. For the Pois- dance was highest in East Nicolas and lowest in son Bobbins (Fig. 2). By grouping fields, the effect of density levels on the parameters of Taylor's and Iwao's models was investigated. Because the lar- For the negative binomial distribution val abundance of Cx. tarsalis was low through most of this study, regional differences were not examined for this species. where k is the dispersion pattern of the sampled The frequency distribution of larvae per dip population. Wilson & Room (1983) used Taylor's for samples taken during the week of highest model to relate k to the sample mean as k = x2/ abundance (Cx. tarsalis, 29 June-2 July; An. (s2 - 2). Substituting for k gives freeborni, 10-13 August, East Nicolas) is pre- sented in Fig. 3. Even at peak abundance, most dips contained no larvae. The frequency distri- bution of samples (1 sample = 90 dips, n = 1,040 Using Taylor's model, s2 = axb, and substituting samples) as a function of abundance is shown in for s2 produces Fig. 4 for both mosquito species. Most samples had collected less than nine larvae (i.e., 2 < 0.1 larva per dip). The minimum number of dips necessary to col- lect at least one larva, given a 5% error rate, was estimated using P described by equation 6 for the Poisson distrithion and equation 9 for the Anopheles freeborni negative binomial distribution. -East Nicolaa

Results and Discussion The mean number of larvae per dip (all instars) from late June through early September is shown in Fig. 1. The mean abundance of Cx. tarsalis larvae was highest the first week, then declined, and remained low during late summer. In con- trast, the number of An. freeborni larvae was initially low, increased steadily, and reached peak abundance in mid-August. 1 8 15 22 29 5 12 19 26 2 9 For An. freeborni, mean larval abundance ap- July August Sept peared to vary regionally. The 104 study fields Fig. 2. Seasonal abundance of An. freeborni in were spread over 400 km2 and located in three three geographic regions within the study area; n = 34 somewhat distinct geographical areas identified fields in East Nicolas, 34 fields in Pleasant Grove, 35 as East Nicolas (34 fields), Pleasant Grove (35 fields in Bobbins. 548 JOURNALOF MEDICALENTOMOLOGY Vol. 31, no. 4

Anopheles freeborn1

Sample VMRzl.0 Sample VMR>I.O

- Culex tarsa~~s - - m Sample VMRsl.0 -n Culex tarsalis 5 100-3 Sample VMR>1.0 >> w 60- 0 in s- 3 0- Â - U- 40-

à 0) 10 0 b. 20- 0 4 8 12 16 20 24 28 32 36 40 44 46 52 56 I < Number of Larvae per Sample (90 ~ips) Fig. 4. Distribution of samples as a function of 0 number of larvae collected in 90 dips in northern Cal- ifornia rice fields; n = 1,040 samples. Number of Larvae per Dip

Fig. 3. Frequency of larvae collected in 90 dips for investigated for all samples (except zeros) using the week of highest abundance (An. freeborni: 10-13 Taylor's and Iwao's regression models. For An. August at East Nicolas, n = 33 fields; Cx. tarsalis: 29 June-2 July, n = 65). freeborni, Taylor's model showed that the level of aggregation was highest among the first instars and then decreased (Fig. 5A). This was seen in One index of dispersion is the variance to the decrease in both a and b values. Plotting the mean ratio (VMR), which is equal to 1-0if larvae regression coefficients over time showed that are distributed randomly (i.e., as a Poisson) and the degree of aggregation tended to decrease B1.0 when aggregated (Elliott 1977). The VMR through the season, being highest in early July of individual samples were compared indepen- and lowest in August (Fig. 5B). However, three dently to 1.0 using the chi-square test described peaks in aggregation were evident, occurring in in Elliott (1977). For An. freeborni, 831 out of early July, early August, and late August. Aggre- 1,040 samples contained at least one larva; of gation was highest in the area of lowest density these, 39% had a VMR statistically significantly (Bobbins, Fig. 5C); however, the differences greater than 1.0 (for a sample size of 90 dips, the among locations were not significant (Table 1). VMR must exceed 1.31 [df = 89, P < 0.051 in a Using Taylor's model to analyze the spatial two-tailed test). No samples were significantly distribution of Cx. tarsalis larvae showed that less than 1.0. At densities of <0.05 larva per dip, aggregation was highest among the first instars the VMR of most samples did not differ signifi- and then declined, in a manner similar to that cantly from 1.0; however, sample variance in- exhibited by An. freeborni (Fig. 6A). Plotting the creased with increasing mosquito density, and regression coefficients over time showed two the VMR usually exceeded 1.0 for samples with peaks in aggregation, one in mid-July and one in B0.05 larva per dip (Fig. 4). For Cx. tarsalis, 328 mid-August. Aggregation was lowest in late Au- out of 1,040 samples contained at least one larva, gust and early September (Fig. 6B). and of these, 32% had a VMR significantly Iwao's Measure of Aggregation. Analysis using greater than 1.0; no samples had a VMR signifi- Iwao's model also showed that An. freeborni lar- cantly less than 1.0. As with An. freeborni, a vae were more aggregated among the early in- greater proportion of Cx. tarsalis samples with a stars and less aggregated for the older instars VMR greater than 1.0 were associated mostly (Fig. 5D) as indicated by the decline in 6 with with higher densities (Fig. 4). age. The value of a was significantly different Taylor's Measure of Aggregation. The relation- from 0 for the first instar only (Table I), suggest- ship between variance and mean density was ing that first instars were commonly collected in July 1994 PITCAIRNET AL.: SPATIALPATTERNS OF An. freeborni AND Cx. tursulis LARVAE 549

July August July August Date Date

-a 2.3 - n b ¥Ç - n 0) 2 2.2 - 0) ..c w- 2.1 - m -

1.9 I I I - East Pleasant Robbins East Pleasant Robbins Nicolas Grove Nicolas Grove

Location Location Fig. 5. Plot of parameters from Taylor's power law (A-C) and Iwao's Patchiness Regression (D-F) for An. freebumi larvae collected in 104 rice fields on 10 dates: parameters are plotted against instar (A&D), sample date (B&E), and location (C&F).

groups. The change in Q across weeks showed quito density (Bobbins) and the lowest value, at the same trend as Taylor's model: high initial the location of highest density (East Nicolas). aggregation followed by a general decline (Fig. Again, a was always close to 0. 5E). The value of a did not deviate from 0 across For Cx. tursulis, Q was highest among the first weeks. The effect of location on the regression instars and lowest among the third and fourth coefficients is shown in Fig. 5F. The highest instars (Fig. 6C). The regression intercept did aggregation was at the location of lowest mos- not deviate from 0 and did not vary among instars 550 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 31, no. 4

Table 1. Significance levels for factorial analysis of covariance and effects of instar, sample week, and location on the relationship between sample variance and mean of Anopheles freeborni larvae in commercial rice fields

Taylor's model Iwao's model Source of df Homogeneity Homogeneity Homogeneity Homogeneity variation of slopes of intercepts of slopes of intercepts F P F P F P 17 P Instar 3 46.95 0.01 29.84 0.01 4.31 0.01 12.74 0.01 Week 9 4.42 0.01 2.60 0.01 5.57 0.01 1.11 >0.05 Location 2 2.44 >0.05 2.31 >0.05 7.18 0.01 0.79 >0.05 Instar x week 27 0.75 >0.05 0.95 >0.05 3.99 0.01 1.00 >0.05 Instar X location 6 0.32 >0.05 0.43 >0.05 2.63 0.02 0.30 >0.05 Week x location 18 0.77 >0.05 1.52 >0.05 1.85 0.02 0.76 >0.05 Instar x week x location 54 0.51 >0.05 0.67 X.05 2.94 0.01 0.58 30.05 Error 2,212

(Table 2). The slope, B, was variable over time, females who deposit a clutch of eggs in one spot. but no consistent trend was observed (Fig. 6D); For both species, the abundance of first instars the highest value occurred in early August. would be concentrated around the spot of ovipo- Interpretation of the Spatial Pattern. Both Tay- sition immediately after hatching. As the larvae lor's and Iwao's models indicated that the larval age, movement would displace individuals in all populations of An. freeborni and Cx. tarsalis directions from the oviposition spot and, coupled were more aggregated in the early stadia and with losses from mortality, result in the later in- then became less aggregated with age. These stars being less aggregated than the early instars. results were consistent with the oviposition be- Shortly after flooding, a rice field is colonized havior of Cx. tarsalis females who deposit a by invading female mosquitoes. If we assume clutch of eggs as a floating raft and An. freeborni that there is no preference by female mosquitoes

- 1 I I I I - 5 I 11 Ill I V

July August July August

Fig. 6. Plot of parameters from Taylor's power law (A-B) and Iwao's Patchiness Regression (C-D) for Cx. tarsalis larvae collected in 104 rice fields on 10 dates: for parameters are plotted against instar (A&C)and sample date (B&D). July 1994 PITCAIRNET AL.: SPATIALPATTERNS OF An. freeborni AND Cx. tarsalis LARVAE 551

Table 2. Significance levels for factorial analysis of covariance and effects of instar, sample week, and location on the relationship between sample variance and mean of Culex tarsalis larvae in commercial rice fields

-- -- Taylor's model Iwao's model Source of d f Homogeneity Homogeneity Homogeneity Homogeneity variation of slopes of intercepts of slopes of intercepts F P F P F P F P Instar 3 23.78 0.01 5.18 0.01 0.23 >0.05 3.47 0.02 Week 9 1.45 >0.05 0.76 >0.05 0.68 >0.05 0.59 >0.05 Instar x week 27 0.41 >0.05 0.92 >0.05 0.77 >0.05 0.95 >0.05 Error 725 for locating their oviposition within a field, then cause it indicates that this model was not affected these spots would be randomly distributed by specific combinations of instar, week, and lo- throughout the field. At that time, the spatial cation. In this way, the parameters estimated distribution of larvae would appear as distinct with these data appear to represent all fields re- clusters with many larvae interspersed with ar- gardless of location. In contrast, there was no eas with few larvae. As the season progresses, homogeneity among slopes for the main effects the rate of oviposition in the field will increase or the interaction terms in Iwao's model. Thus, and result in a decrease in distance between this model was affected by specific combinations oviposition spots. Consequently, we would ex- of instar, week, and location, and its parameters pect the larval population to become more were less useful in developing an area-wide sam- evenly distributed throughout the field and the pling plan. aggregation of larvae less distinct. This is what Parameter Estimates. Estimating a and b pa- may have been observed for An. freeborni, rameters by regressing logio(s2) against logio(?) which showed a steady increase in larval abun- can produce a biased estimate. An unbiased es- dance and a concomitant decrease in the degree timate was calculated by using a nonlinear re- of aggregation through the course of this study gression procedure on the untransformed mean (see Figs. 1, 5B and E). In contrast, the abun- and variance data. To compare the results from dance of Cx. tarsalis larvae was high initially, these two regression methods, the amount of ex- decreased, and remained low throughout the plained variance was calculated by plotting the study. The degree of aggregation of Cx. tarsalis observed and predicted s2 against ? in the origi- larvae varied over the course of this study, but no nal scale. The explained variance, 3,was esti- trend was observed (see Figs. 1, 6B and D). mated as A factorial analysis of covariance showed that for Taylor's model, both instar and week effects 2(observed s2 - predicted s2)2 were significant, with instar exhibiting the stron- 1 - (10) gest effect (Table 1). No interaction term was ^(observed s2 - average s2)2 significant. In contrast, all slopes resulting from Iwao's model were significant, The fits of Taylor's and Iwao's models are pre- Analysis of covariance tests for homogeneity of sented in Table 3. In general, the amount of the regression coefficients within treatment ef- explained variance was higher for the third and fects. For Taylor's model, the lack of significance fourth instars than for the early instars. This was among the interaction terms is important be- observed for both Taylor's and Iwao's models.

Table 3. Parameter estimates for Taylor's power law and Iwao's Patchiness Regression models (n = sample size)

Taylor's model Iwao's model Species Instar n Linear Nonlinear a b r2 a h r2 a P r2 Anopheles freehorni 1st 666 2.659" 1.222" 0.541 3.088" 1.193" 0.606 0.281' 3.928" 0.454 2nd 621 1.748Â 1.133" 0.585 2.341" 1.194" 0.683 0.007 3.863& 0.570 3rd 501 1.439" 1.081" 0.852 1.869" 1.173" 0.906 0.036 2.728'' 0.868 4th 425 1.209O 1.042" 0.887 1.194" 1.029 0,933 0.021 1.948" 0.884 All instars 831 2.071" 1.174b 0.648 2.825" 1.374b 0.765 0.220" 2.611" 0.712 Culex tarsalis 1st 215 2,948" 1.244" 0.750 3.296" 1.247" 0.801 0.252' 4.086" 0.744 2nd 203 1.612" 1.112,*' 0.659 2.651" 1.403" 0.756 0.022 2.904" 0.710 3rd 171 1.289" 1.052 0.919 1.220" 1.022 0.950 0.069" 1.718 0.917 4th 177 1.220" 1.043" 0.866 1.157" 1.013 0.925 0.026 2.058 0.861 Alliristars 328 2.037" 1.168" 0.725 2.382" 1.132" 0.782 0.155 2.355 0.692

Significantly different from 0 (P < 0.05, t-test). lJ Significantly different from 1.0 (P < 0.05, t-test). 552 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 31, no. 4

estimate the larval population of a field with a Anopheles freeborni density of 0.5 larva per dip. These sample sizes are very high and are impractical for routine sur- veillance, yet these densities were common in this study (see Fig. 2). If the objective of a sampling program is to determine if the population of larvae in a rice field exceeds some treatment threshold, an alter- native plan may be to take enough dips to collect at least one mosquito larva. Failure to collect any larvae in a series of dips does not mean that no larvae are present. Rather, there is a direct rela- tionship between larval density and the proba- Density (Larvae per Dip) bility of collecting larvae. When larval popula- tions are high, few dips would be necessary to collect at least one larva. Conversely, as popula- tion abundance decreases, more dips would be necessary. The probability of a sample protocol to find larvae is affected by both larval density and sample size (number of dips). For a given sample size, there exists a high probability of finding no larvae despite the existence of a bio- logically meaningful population of mosquito lar- vae. It may be possible to use this phenomenon to determine if the larval density in a rice field exceeds a treatment threshold as would exist in a monitoring program. Given an arbitrary density and an assumed de- gree of aggregation in the larval population, the Density (Larvae per Dip) minimum number of dips necessary to collect at Fig. 7. Number of dips required to estimate the least one larva in 95 out of 100 samples (a series mean number of An. freeborni and Cx. tarsalis larvae of dips is one sample) can be estimated. For An, at three fixed-precision (D) levels. freeborni and Cx. tarsalis, 61% and 68%, respec- tively, of field samples did not have a VMR sig- nificantly greater than 1.0 and the greatest pro- The fit of Taylor's model was consistently better portion of these occurred at low population using the nonlinear regression method. densities. The Poisson distribution, then, may Optimal Sample Sizes. We used two methods provide an adequate description of the larval to determine the sample size necessary to assess spatial pattern, especially when populations are the density of mosquito larvae in a single rice increasing early in the season. field. One method used a fixed-precision sam- We estimated the number of dips required to pling model (Ruesink 1980). The other method collect at least one larva given an error rate of 5% estimated the minimum number of dips needed using both the Poisson and negative binomial to collect at least one larva. probability distributions. For the Poisson distri- Optimal sample size is dependent on the spa- bution, the variance is assumed to be equal to the tial pattern of the sampled population. As re- mean, so the probability of finding a larva de- ported earlier, we found age and temporal differ- pends only on density, For the negative bino- ences in Taylor's and Iwao's parameter values mial, the degree of aggregation of the sampled for both mosquito species. Jones (1990), how- population, k, was estimated using Taylor's a and ever, suggested that Taylor's a and b values are b values for "All Instars" in Table 3. merely samples from a large population of val- The estimated sample sizes are reported for ues. We suggest that if one sampling protocol is densities between 0 and 0.3 larva per dip (Fig. to be used, pooled estimates of the model param- 8). The minimum number of samples increased eters should provide the best estimate of a and b. with decreasing densities, but sample sizes were The values reported for "All Instars" in Table 3 substantially lower than those required for a were used for both species in the analyses of fixed-precision estimate. For example, for a den- optimal sample sizes. sity of 0.05 An. freeborni larvae per dip, 461 dips The number of samples required to estimate are required to obtain a sample value within 20% An. freeborni and Cx. tarsalis larval numbers at of the population mean; only 60 samples are re- three levels of i recision are shown in Fig. 7. For quired to ensure collection of at least one larva in fixed-precision levels of 10% and 20%, at least 95 out of 100 samples. This may provide an effi- 1,800 and 461 dips, respectively, are necessary to cient and cost-effective method for monitoring July 1994 PITCAIRNET AL.: SPATIALPATTERNS OF An. freeborni AND Cx. tarsalis LARVAE 553

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. nophetes freeborn1 Karandinos, M. G. 1976. Optimum sample size and comments on some published formulae. Bull. En- tomol. Soc. Am. 22: 417-421. Mackey, B. E. & J. B. Hoy. 1978. Culex tarsaUs; lex tarsalls sequential sampling as a means of estimating pop- illations in California rice fields. J. Econ. Entomol. 71: 329-334. Ruesink, W. G. 1980. Introduction to sampling the- ory, pp. 61-78. In M. Kogan & D. E. Herzog [eds.], Sampling methods in soybean entomology. Springer, New York. Density (Larvae per Dip) Sandoski, C. A., T. J. Kring, W. C. Yearian & M. V. Meisch. 1987. Sampling and distribution of Fig. 8. Estimated minimum number of dips re- Anopheles quadrimaculatus immatures in rice quired to collect at least one n~osquitolarva given an fields. J. Am. Mosq. Control Assoc. 3: 611-615. error rate of An. freeborni negative binomial, Cx, 5%; SAS Institute. 1985. SAS users guide: statistics. SAS tarsalis negative binomial, both species Poisson. Institute, Gary, NC. Service, M. W. 1976. Mosquito ecology. Applied larval mosquito abundance for control purposes Science Publishers, London. in northern California rice fields. 1985. Population dynamics and mortalities of mos- quito preadults, pp. 185-201. In L. P. Lounibos, J. R. Rey & J. H.Frank [eds.], Ecology of mosqui- Acknowledgments toes: proceedings of a workshop. Florida Medical Entomology Laboratory, Vero Beach. We thank Gene Kaufman, manager of the Sutter- Southwood, T.R.E. 1978. Ecological methods, with Yuba Mosquito Abatement District, for his cooperation particular reference to the study of popula- during this project. We also thank Steve Schoenig and tions, 2nd ed. Chapman & Hall, London. Charles Pickett for their comments on the manuscript. Stewart, R. J., C. H. Schaefer & T. Miura. 1983. This work was supported in part by the USDA Re- Sampling Culex tarsalis (Diptera: Culicidae) imnia- search Grant CR 806771-02, RF-4148A; the NASA tures on rice fields treated with combinations of Ames Research Center/University of California, Davis mosquitofish and Bacillus thuringiensis H-14 toxin. Consortiunl (NASA 2-428); and the Special Mosquito J. Econ. Entomol. 76: 91-95. Augmentation Fund, University of California. Taylor, L. R. 1961. Aggregation, variance, and the mean. Nature (Lond.) 189: 732-735. References Cited Walker, E. D., R. W. Merritt & R. S. Wotton. 1988. Analysis of the distribution and abundance of Andis, M. D, & C. L. Meek. 1984. Bionomics of Anopheles quadrimaculatus (Diptera: Culicidae) Louisiana riceland mosquito larvae. 11. Spatial dis- larvae in a marsh. Environ. Entomol. 17: 992-999. persion patterns. Mosq. News 44: 371-376. Washino, R. K. 1980. Mosquitoes-a by-product of Bohart, R. M. & R. K. Washino. 1978. Mosquitoes of rice culture. Calif. Agric. 34: 11-12. California, 3rd ed. Univ. Calif. Div. Agric. Sci. Puhl. Wilson, L. T. 1985. Estimating the abundance and 4084. impact of natural enemies in IPM sys- Elliott, J. M. 1977. Some methods for the statistical tems, pp. 303-322. In M. A. Hoy & D. C. Herzog analysis of samples of benthic invertebrates, 2nd [eds.], Biological control in IPM systems. Aca- ed. Freshwater Biol. Assoc. Sci. Publ. 25. demic, Orlando, FL. Hardy, J, L., E. J. Houk, L. D. Kramer & R. P. Meyer. Wilson, L. T. & P. M. Room. 1983. Clumping pat- 1980. Mosquitoes as carriers of viral diseases. Ca- terns of fruit and in cotton, with impli- lif. Agric. 34: 8. cations for binomial sampling. Environ. Entomol. Iwao, S. 1968. A new regression method for analyz- 12: 50-54. ing the aggregation pattern of populations. Res. Popul. Ecol. (Kyoto) 10: 1-20. Received 23 June 1993; accepted 24 January 1994.