Simple mathematical models to describe the rate of mating in insect populations

Summary Simple models are constructed to describe the rate of mating in insect populations. The models are based on the assumption of random mate-searching in a closed habitat, including four parameters, i.e., population size, sex ratio, searching efficiency and male's capacity on mating frequency. The modes of effects of these parameters on the rate of mating are analyzed and some principles deduced are discussed in relation to the mating process in natural populations. This study was supported by science research fund from the Ministry of Education.     

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

Summary 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 parameterk is so stable for same species that a single value ofk is applicable for a series of counts with different means, whereas thatk differs remarkably among different species: if the reciprocal of the weighted estimate of commonk which is an adequate index measuring degree of contagiousness of the distribution, is compared among different species, it is higher in the order ofNilaparvata, Delphacodes andNephotettix. The ecological and practical implication of constancy and heterogeneity within and among species was discussed respectively as to the value of parameterk.     

Competition between laboratory populations of green leafhoppers,Nephotettix spp. (Homoptera: Cicadellidae)

Summary Intra- and interspecific competition between laboratory populations of four green leafhoppers,Nephotettix spp. was studied in the laboratory under three different temperature regimes of 24°C, 27°C and 30°C. For the single-species population of the three tropical species, the equilibrium density increased as the temperature increased. On the other hand, for the temperature speciesN. cincticeps, the highest equilibrium density was at the intermediate temperature and the lowest at high temperature. Interspecific interactions between two tropical (N. virescens vs.N. nigropictus), a tropical and a temperature (N. virescens vs.N. cincticeps) and a rice-feeding and a grass-inhabiting (N. virescens vs.N. malayanus) Nephotettix species were also studied in the laboratory at the three temperature regimes. Temperature differentially affected the outcome of competition between twoNephotettix species. BetweenN. virescens andN. nigropictus, the latter was more successful over the former at low and intermediate temperatures, while the former was more successful at high temperature. BetweenN. virescens andN. cincticeps, the temperate species inhibited the growth of the tropical species at low temperature while the tropical species inhibited the growth of the temperate species at high temperature. At intermediate temperature, the population ofN. virescens persisted at a slightly higher density over the population ofN. cincticeps. Between the rice-feedingN. virescens and the grass-inhabitingN. malayanus, regardless of temperature the population density of the latter was greatly reduced and later became extinct while the population of the former continued its growth. These consequences of competition between twoNephotettix species conformed fairly well to those predicted by theLotka-Volterra model using demographic parameters specified for each species.     

Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance

Summary An approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao, 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts. Contribution from the Entomological Laboratory, Kyoto University No. 418. Contributions from JIBP-PT No. 52. Aided in part by a grant from the Ministry of Education for the special project research, ‘Studies on the dynamic status of biosphere’.     

Ecological studies on a dragonfly,Nannophya pygmaea ramber (Odonata: Libellulidae) I. seasonal changes of adult population and its distribution in a habitat

Summary Adult population of a dragonflyNannophya pygmaea Ramber inhabited in a damp ground was investigated with mark-and-recapture method in 1975. The following results about the seasonal changes of the population size and distribution in the habitat were obtained. Adults emerged from late May to mid August. The number of the adults was most abundant in early June, but that of matured males in early July. From the recapture data, the estimate of daily survival rate was 0.82, and the length of immature stage in males was estimated as 5 days or so. Total number of post-teneral adults emerged in the habitat was estimated as about 9,000. The mean crowding-mean density regression method was applied for the analysis of the distribution pattern of the adults. Matured males showed a spaced-out distribution, while females and immatured males distributed themselves rather aggregatively. Such a distribution pattern of the matured male would be attributed to their territorial behaviour. The territorial behaviour was considered to force the matured males to extend the distribution area in July when they were most abundant. From the above-mentioned results and some observations, the meaning of the territoriality in this species was discussed.     

Competitive exclusion through reproductive interference

Summary A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficientc _ij ; (2) but, for the samec _ij -values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

Some strange properties of the logistic equation defined withr andK: Inherent defects or artifacts?

Summary In some situations the logistic equation in the usual expression, dN/dt=r(1−N/K)N, exhibits properties that are biologically unrealistic. For example, whenr≦0 the population can no longer show any normal, negative response in per-capita growth rate to increasing density. Also, when the equation is employed in the Volterra's competition model, a familiar but incredible conclusion is derived which says that the outcome of competition is entirely independent of the reproductive potentialr of each species. It is shown that all such strange properties are mere artifacts arising peculiarly in thisr-K model from its misleading implicit supposition thatK could be independent ofr, and they can be readily removed by alternative use of a plainer, classical form of the model, dN/dt=(r−hN)N.     

Modelling and analyzing density-dependent population processes: Comparison between wild and laboratory strains of the bean weevil,Callosobruchus chinensis (L.)

Three models were constructed for analyzing the population characteristics ofC. chinensis on stored beans; model A describing the whole reproductive process with a single equation, model B describing the three age-specific processes (oviposition, egg survival and larval survival) with separate equations, and model C which describes all these processes not for the whole habitat but for the individual beans comprizing it. The logit equation was employed here as a common basis to describe the density-response relationship involved. All three models showed very good fit to the experimental data obtained for both laboratory and wild strains of the weevil. The parameter values characterizing the population dynamics were, however, widely different between the two strains; the laboratory one which had been reared for some 500 generations showed significantly higher reproductive capacity, less sensitive and gentler response to crowding in both adult and egg stages, and more uniform egg distribution among individual beans, as compared with the wild strain newly introduced. Sensitivity analyses using these models suggested that these changes in population characteristics have been attained by the process of domestication or adaptation to stable laboratory conditions through a long period of time. This process seemed in effect to have optimized the population's performances in the laboratory environment. Evolutionary significance of such optimization was discussed with reference to the selection pressure which may have acted upon individuals.     

Verifying zero-infestation in pest control: A simple sequential test based on the succession of zero-samples

Summary A simple sequential test based on the succession of ‘zero's or uninfested sampling units is proposed for use in verifying zero-infestation in pest control surveys. The method is applicable efficiently to both finite and infinite populations. Problems concerning its efficiency on application are discussed.