Iwao's Model Research Articles

A model of temporal distribution of Aphis gossypii (Glover) (Hem., Aphididae) on cotton

Abstract:The spatio‐temporal distribution of Aphis gossypii (Glover) was studied for a 4‐year period in a plot of Gossypium hirsutum located in Bangui, Central African Republic. A study of the temporal evolution of the number of aphids by means of non‐linear regression indicated a rapid population increase during the first 8 weeks of cotton cultivation. The overdispersion of the aphids was found to be significant during most of the season. We tested three population dispersion models; Iwao's model and Taylor's power law describe the relationship between the mean m and variance σ2 for the number of aphids, and the Nachman's model describes the functional dependence between m and the proportion p of non‐infested cotton plants. The results of these statistical tests indicate that only the Taylor's model was not rejected. The aphids’ aggregation increases with population density. The regression parameter confidence intervals for each of the 4 years of observation prove the stability of the Taylor's model. The model σ2 = 45m1.3 is recommended when the environmental and cultural conditions are similar to those of our study.

Sampling of Diaphorina citri (Homoptera: Psyllidae) on Orange Jessamine in Southern Florida

Dispersion indices and related statistics of Asian citrus psyllid, Diaphorina citri Kuwayama, on orange jessamine [Murraya paniculata (L.) Jack] shoots in southern Florida from 1998 to 1999 were determined with 235 data sets and used to develop sampling plans. Three regression models, Taylor's power law, Iwao's patchiness regression, and k = c +dm [k = m2 / (S2 - m)] (where k is the parameter for the negative binomial distribution) were used to analyze the data. Taylor's power law (a = 0.3407 0.03, b = 1.2971 0.03, r2 = 0.88) fit the data better than Iwao's model (a = -0.3217 0.12, = 1.6979 0.06, r2 = 0.76). Taylor's b and Iwao's were both significantly > 1, indicating that D. citri populations were aggregated. Iwao's a was significantly

Distribution Pattern and Sampling of Eggs of the Western Hemlock Looper (Lepidoptera: Geometridae) in Mature Western Hemlock Stands

An egg sampling study of the western hemlock looper, Lambdina fiscellaria lugubrosa (Hulst), was conducted in mature western hemlock stands from 1992 to 1994 in British Columbia, Canada. Egg density of the looper was homogenous within a tree crown, Suggesting that lower-crown sampling is effective for egg density estimation on the entire tree. Both the Taylor power law and the Iwao patchiness regression described egg distribution as aggregated. This aggregated distribution was further delineated as negative binomial distribution by chi-square test. Based on the Iwao model, the optimal sample size required to reach a predetermined precision level was calculated. To reduce egg-counting time, the relationship between mean egg density and proportion of lichen samples containing a specified number of eggs was established. The effect of tree height, diameter at breast height, crown width, crown length, and presence of heartrot on egg density was also examined. The results indicated no significant effect on egg density of these variables.

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

Spatial patterns of Anopheles freeborni Aitken and Culex tarsalis Coquillett larvae were studied during summer by sampling with a standard mosquito 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 showing the largest effect. In comparison, all slopes resulting from Iwao's model were significantly 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 number 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 larva. The latter requires a substantially smaller sample size and may provide an effective method for monitoring larval mosquito abundance for control purposes.

Variation in Spatial Patterns of the Russian Wheat Aphid (Homoptera: Aphididae) Among Small Grains in the Northwestern United States

Field sampling of the Russian wheat aphid, Diuraphis noxia (Mordvilko), infesting spring wheat, spring barley, and winter wheat in the northwestern United States from 1988 to 1991 generated a data set of 117 mean aphid density (m) and variance (S2) estimates, based on individual tillers, with an average sampling error level of 0.172. This provided a data set desired for use in spatial analysis and the development of sampling plans. Three regression models-ln(s2) = ln(a) + bln(m) (Taylor's power law), m* = α + βm (Iwao's model), and k = c + dm [k = m2/(s2 − m) (a parameter for the negative binomial distribution)—were fit to the data pooled by crop type or growing season. Taylor's power law generally fit the data better than Iwao's model. Taylor's b and Iwao's β were significantly ≤1 for all cases (single crop, season, or pooled together), indicating that D. noxia populations were aggregated. The slope d for the summer populations on winter wheat was indistinguishable from 0, indicating the existence of a common k (estimated as 0.003). However, a common k was not detected for the summer populations on spring wheat and barley and the fall populations on winter wheat because their d values were Significantly ≤0, indicating the dependence of k on m. Based on comparisons of intercepts and slopes from the three models, the counts of the summer populations on all three grains could be pooled effectively to generate a more representative data set covering a wide range of variation. However, the fall populations on winter wheat should be treated separately because their spatial pattern apparently is distinct from those of the summer populations. Finally, temporal changes in spatial pattern (represented by the estimates of 1/k) on spring and winter grains are discussed with respect to crop stages and aphid densities.

THE INFLUENCE OF COMPANION HERBS ON EGG DISTRIBUTION OF THE IMPORTED CABBAGEWORM, PIERIS RAPAE (LEPIDOPTERA: PIERIDAE), ON COLLARD PLANTS

AbstractThe effect of interplanting collards with a mixture of herbs on oviposition of the imported cabbageworm, Pieris rapae (L.), was investigated at Chesterfield Co., Virginia during 1981 and 1982. Analysis of the dispersion indices of the insect using Taylor's power law and Iwao's model revealed that P. rapae eggs were significantly — m (P < 0.001) clumped (b > 1) on collards interplanted with herbs. However, insect counts on control collards conformed to the Poisson distribution (b = 1, P > 0.05). Pieris rapae laid significantly (P < 0.01) more eggs on collards hidden between sage than on collards hidden between other companion plants. Also, P. rapae laid significantly (P < 0.005) more eggs on collards bordered by companion plants than on non-bordered control. These data suggest that companion herbs did not repel P. rapae but instead significantly encouraged colonization of the insect and produced an aggregated distribution.