Basic unit of population observed in the distribution of the rice-stem borer,Chilo simplex,in a paddy field. Pattern of the spatial distribution of insect. 4th report

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Contributions from the Entomological Laboratory, Kyoto University, No. 231.     

A comparative analysis on the distribution of nymphal populations of some leaf- and planthoppers on rice plant

The frequency distribution of the number of nymphs per hill of rice plant were analyzed for three species of rice leaf- and planthoppers, Nilaparvata lugens, Delphacodes striatella and Nephotettix cincticeps, based on the sampling data obtained during their last generations in the paddy field. For every species concerned, individual distributions were proved to be contagious and to fit well to the negative binomial distribution. Further, it was found that the value of negative binomial parameter k is so stable for same species that a single value of k is applicable for a series of counts with different means, whereas that k differs remarkably among different species: if the reciprocal of the weighted estimate of common k which is an adequate index measuring degree of contagiousness of the distribution, is compared among different species, it is higher in the order of Nilaparvata, Delphacodes and Nephotettix. The ecological and practical implication of constancy and heterogeneity within and among species was discussed respectively as to the value of parameter k.     

An index of spatial distribution

The index , which takes the value of −1 for a perfectly regular distribution, +1 for a highly aggregated distribution and 0 for the distribution implied by the theoretical varianceσ², is proposed and a significance table provided.     

The spatial distribution of the wheat-bulb fly,Leptohylemyia coarctata (fall.) (Diptera: Anthomyiidae)

The spatial distribution of the eggs, larvae, pupae and adults of the wheat-bulb fly was investigated by fitting 42 sets of data comprising 1334 samples to the Poisson and negative binomial distributions, and by using the power law (S²=am^b). In general, the tests indicated that all stages were aggregated and fitted the negative binomial model.     

Influence of parental density on the distribution pattern of eggs in the common cabbage butterfly,Pieris rapae crucivora

To investigate the relation between the distribution pattern of eggs and the parental density in the common cabbage butterfly, Pieris rapae crucivora, the countings of egg number per plant were made on both cabbage plants cultivated in the farm and planted in the net house in which the female butterflies were released at various densities. The frequency distribution of eggs fits well to the negative binomial excepting the cases where they agree withPoisson series, and the degree of aggregation expressed as the reciprocal of the parameter, 1/k, tends to decrease as the egg or parental density increases. At the same parental density, however, the distribution of eggs can be described by the negative binomial with a common parameter, k_c, regardless of the difference in the density of laid eggs. In the case where a single female butterfly lays eggs, the spatial pattern of egg distribution is always lean, while its frequencies conform toPoisson or the negative binomial series. This lean changes toward patchy with increasing the parental density. From these results, it is concluded that the degree of aggregation in the distribution of eggs decreases with the increase of the parental density.     

Measurement of non-randomness in spatial distributions

The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficient C_x is proposed for use with positively contagious distributions and tests of significance are given. When C_x and another index (S²/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.     

Population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus Yasumatsu (Hymenoptera: Cynipidae)

Summary As a part of serial study on population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus, analyses of the distribution of eggs, gall-cells and emergent holes were made from the statistical point of view. Many of distributions of the eggs per bud could be described by the truncated Poisson, but some cases showed slight overdispersion than expected by chance. Because of no linear increase of with increasing (expected mean for complete sample), however, the truncated negative binomial seemed to be not so available for whole series. Distributions of the gall-cells and the emergent holes were, on the other hand, well described by the truncated Poisson distribution when the observed frequency was calculated for respective trees. Negative-binomial tendency found in distributions from some stations consisted of a certain number of trees would be resulted from mixture of Poisson populations with different means. Random or slightly concentrated oviposition and random mortality within galls was thus supposed for future study unless the proof favouring other distribution models would appear.     

Process generating the ditribution pattern of eggs of the common cabbage butterfly,Pieris rapae crucivora

The process generating the negative binomial in the distribution pattern of eggs of the common cabbage butterfly, Pieris rapae crucivora, was investigated by releasing the female adults in a net house where cabbages were planted. The distribution of butterflies visited and laid an egg or more per plant followed thePoisson series under the uniform light condition, while that of eggs laid per visit conformed to the logarithmic distribution. From these results, it may be concluded that the negative binomial arises from compounding of thePoisson and the logarithmic distribution. The observed frequency of eggs found per plant fitted to the negative binomial with parameter thus computed theoretically. The change in the degree of aggregation with the increase of the parental density was considered in connection with the above results.     

An analysis of the predator-prey system in the paddy field

A predator-prey system involving Lycosa pseudoannulata as predators and both the green rice leafhopper, Nephotettix cincticeps and the brown planthopper, Nilaparvata lugens as prey was studied in an experimental paddy field. Daily predation rates on the prey and weekly disappearance rates of Lycosa females were related to densities of both predators and prey by multiple regression. During the off-season of reproduction for predators and prey, it proved possible to simulate the interaction between Lycosa and its prey.     

A distance measure of spatial pattern in a biological population

Suppose that n individuals locate independently and randomly on a segment of line of finite length (habitat). Let the theoretical and observed ranges of the sites of the individuals on the segment be μ_n-1 and r_n-1, respectively. Then, the degree of dispersion of the individual sites is measured by the ratio, T_n=n_n-1/μ_n-1, as follows: A random spatial pattern for I_r−1=1 An aggregated spatial pattern for 0≤I_r<1 A uniform spatial pattern for (n+1)/(n−1)≥I_r>1. Another method was derived. Let the probability that an observed range is less than r_n−1 be I_p, under the hypothesis of a Beta distribution. Then indicates A random spatial pattern for I_p=1/2 An aggregated spatial pattern for I_p<1/2 A uniform spatial pattern for I_p>1/2. The first index can be used for comparing populations having the same number of individuals, whereas the second one can be used for comparing populations with different numbers of individuals.     

Life table studies on the paddy field population of the green rice leafhopper,Nephotettix cincticeps Uhler (Hemiptera: Cicadellidae), with special reference to the mechanism of population regulation

The population growth of the green rice leafhopper, Nephotettix cincticeps, in the paddy field was analyzed based on the life table data accumulated for six years. The paddy field population, which stems from the invading adults of the first generation (G-I), repeats two complete generations, and the hatchlings of the fourth generation (G-IV) enter diapause and overwinter as the fourth instar nymphs in fallow paddy fields. It was clarified that the density dependent reduction in the mean longevity and oviposition rate of adult females in G-II and III played a primary role in stabilizing the annual population densities. The annual average of the mean longevity of G-II females (3.9 days) was much shorter than that of G-III ones (7.7 days) and thus the density dependent reduction in the mean longevity induced a more prompt regulatory effect on the oviposition of G-II females compared with G-III ones. As the result, two equilibrium densities of eggs were obtained, e.g., ca 100 and 700 eggs per hill in G-III and IV, respectively. Density dependent decrease in the proportion of mature females in the adult population was especially conspicuous in G-II, and this was closely associated with the density dependent reduction in the mean longevity and fecundity. Thus, the density dependent dispersal (emigration) of the adult females by flight in G-II and III was the most convincing factor in the process of population regulation. The density dependent dispersal of the adult females is effective in avoiding the deleterious effects of nymphal crowding in a breeding habitat unit (a paddy field), and may result in a more even distribution of the population over a continuous habitat units in a locality than otherwise.     

The estimation of population density of the green rice leafhopper,Nephotettix cinticeps Uhler,in spring field by the capture recapture method

The population parameters of green rice leafhopper, Nephotettix cincticeps in hibernated generation was estimated by the capture-recapture method on the gramineous weeds of resting paddy field from late in April to mid-May, 1962–1965. The difficulty of applying the capture-recapture method to this insect is caused from the low density and the low activity of the leafhopper, so that it is necessary to make the suitable plan of capture-recapture series and to construct the special method to detect the population parameters. The number of adults differed greatly among the years and among the plots in the same year. But, in general, the density was relatively high late in April, and decreased rapidly in May. The number of males was higher than that of females late in April, but decreased rapidly to become lower in May. The sampling efficiency with sweep-net depends upon the many factors, such as weather and floristic conditions; especially the atmospheric temperature and the force of wind are considered to affect greatly to the efficiency. In general, low temperature and strong wind are the cause of low sampling efficiency.     

Experimental studies on the distribution of the aphid counts

The present paper dealt with the sequential changes of the distribution pattern of apterous females aphid populations, that were artificially settled at the beginning on the experimental barley ‘field'. The aphids were settled at random or even with a fixed denisty per plant. For five or six days after the settling, the number of individuals followed the negative binomial distributions in all cases while the parameters k and p were varying. The estimated values of k were rather small for the first one week after the settling, which may suggest that the number of moving aphids between plants was relatively small and the degree of concentration expressing the intrinsic increase was high. After that, as the number of individuals increased, the number of moving aphids between plants would be considered to be increased. It was found that with the lapse of time the degree of concentration decreased or k became larger. The distribution of aphids per blade in a plant was also described briefly.     

Spatial distribution of the green peach aphid used in estimating the populations of gynoparae

Summary In 2 years, during the initial invasion of peach leaves by the green peach aphid,Myzus persicae (Sulzer), the number of gynoparae was low, and the distribution on leaves was random. Then as the mean number increased, the distribution became intermediate and could not be distinguished from either a Poisson or a negative binomial. Finally, as the mean continued to increase, the variance increased rapidly, and the population was found to fit a negative binomial distribution. Thus the aggregation response was verified because the dispersion pattern fitted a contagious distribution. A sampling plan was devised by which the dispersion parameterk was used to estimate the density of aphids per leaf based on the percentage of leaves infested. Sampling the third year of the study confirmed the validity of the sampling parameter that had been calculated from data for the 2 previous years.     

Population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus Yasumatsu (Hymenoptera: Cynipidae) IV. Further analysis of the distribution of eggs and young larvae in buds using the truncated negative binomial series

Distribution pattern of eggs and the first instar larvae of the chestnut gall-wasp, Dryocosmus kuriphilus, per bud of the chestnut tree was re-examined using the truncatedPoisson and the truncated negative binomial series. The results are as follows:

1. About sixty percent of the distribution are approximated by the truncated negative binomial and another thirty percent by the truncatedPoisson . When the distribution has been approximated by the truncated negative binomial, the show scattered values, some of which are near thePoisson , but the mean value of is about 4 both in eggs and in the first instar larvae.
2. The number of buds which have not been infested by gall-wasps is resulted from various factors as follows: (a) Buds formed after the laying activity of gall-wasps has ceased; (b) Old and shrunk buds which were avoided in laying; (c) Buds in which eggs have died by the time of sampling; and (d) Buds escaping ovipositions by chance. Most of the gall-wasp-free buds located in the middle part of the shoot are accounted for the zero-class expected by the negative binomial series.
3. Brass (1958) moment method for estimating parameters of the truncated negative binomial give good precision within the range of from 1 to 10 and of from 1 to 6.
4. It is concluded that the truncated distributions used are useful for the purpose of analysis of the distribution pattern of the chestnut gall-wasp.