Eizi Kuno

COMPETITIVE EXCLUSION THROUGH REPRODUCTIVE INTERFERENCE

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 Volterras 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.

A new method of sequential sampling to obtain the population estimates with a fixed level of precision

A simple method of sequential sampling is developed which would make it automatically possible to secure, without excess sampling, a predetermined level of precision for a series of population estimates being required. It appears to have wide application to sampling field populations under various situations since it is simply based upon the relationship of variance to mean for which a comprehensive formula deduced for biological populations from the linearity in the regression of mean crowding on mean density could be adopted. Some problems that may arise in practical application of the method are also discussed.

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

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.

Dispersal and the Persistence of Populations in Unstable Habitats: A Theoretical Note

SummaryIt is illustrated theoretically that in a heterogeneous habitat the dispersal of individuals, even when it is random and density-independent, may have a pronounced effect of raising the average reproductive rate of the whole population, in addition to the effect of stabilization in the usual sense of reducing its variance. This implies that in such a population the habitat instability has been converted by dispersal into a condition profitable for the population. The role played by dispersal here is therefore regarded as much more positive than that which the expression ‘spreading of risk’ usually means.

Sampling error as a misleading artifact in “key factor analysis”

The influences of sampling error in key factor analysis are investigated statistically. The error involved in the data distorts the results in various misleading ways. In the course of detecting key factors by correlation analysis, the distortion arises in the following two ways: (1) the contributions made by the first and the last components of population trend index (logI orK) to the total variation are overrated as compared with the others; and (2) spurious negative correlation arises between successive two components. The risk of misinterpretation due to such disturbance is usually increased further if the error is concentrated on any particular developmental stages. In the tests to detect density-dependence by using regression analysis, the error consistently acts as if it were a density-dependent factor: under the effect of sampling error, the slopeb for the regression of logN i+1 on logN i , for example, is expected to become<1 even where there is no density-dependent factor at all. A set of formulas are derived which may serve to check and correct these misleading distortions caused by the error. It is also shown that such undesirable influences can be avoided, at least to a considerable extent, if appropriate sampling plans are adopted for the study. The validity of key factor analysis is discussed in reference to this and some related problems.

Comparative analysis of the population dynamics of rice leafhoppers,Nephotettix cincticepsUhler andNilaparvata lugensStål, with special reference to natural regulation of their numbers

In southwestern districts of Japan, four species of rice leafhoppers, Nephotettix cincticeps, Nilaparvata lugens, Sogatella furcifera and Laodelphax striatellus, often cause serious damage to the cultivated rice either directly by sap-sucking or indirectly as the vector of some virus diseases. Since 1961, a long-term population study on these four species has been conducted in this station to reveal the basic features of the dynamics of their populations in paddy fields and thereby to prepare an ecological basis for the effective control of these important insect pests which had not yet been established. On the basis of the 8-year results of this study, we describe here the outline of the population properties of the first two species of the above four, Nephotettix and Nilaparvata, that are predominant in abundance. The description covers the two aspects of population dynamics, temporal changes and spatial structure; and the results are discussed with particular reference to the comparison of the situation as to natural population regulation between these two species. Our main conclusions in this paper are fundamentally consistent with those that were derived from the 6-year results (1961-1966) in a previous paper (KUNO 1968) dealing with all the four species, but they have become more confirmative by addition of the data for both 1967 and 1968. The general methods of sampling and data-analysis for this study have also been described in detail in the previous paper, so that they will be mentioned here only briefly.

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model,p=1−(1+m/k) −k, and the empirical model,p=1−exp(−am b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.

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

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 Volterras 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.

Some notes on population estimation by sequential sampling

In a previous paper (KUNO 1969), I proposed a sequential sampling technique for population estimation which makes it possible to secure, without excess sampling, a desired precision level for individual estimates. There may be no doubt about the potential usefulness of such a technique for field studies of animal populations, because the census work in these studies is very laborious usually and yet standardization of the data with respect to the precision level is a desirable condition for avoiding misleading disturbance due to sampling error (e. g. KuNo 1971). I t was also suggested that the method would be applicable to a wide variety of species under different conditions, since it is based upon a comprehensive formula describing the relationship of variance to mean in biological populations: a2= ( ~ + l ) m + ( # l ) m z. (1) In this method, however, the following problems have yet been left for closer examination. (1) The bias in estimation resulting from the specific sampling procedure involved in sequential plans. (2) The practical validity of formula (1) as a general basis of the plans for field populations. (3) The development of modified techniques applicable to the cases where the original method cannot easily be applied. The purpose of the present paper is to present solutions to these three problems which may affect the validity of this type of sampling technique for practical application to population studies.

Aggregation pattern of individuals and the outcomes of competition within and between species: Differential equation models

The influence of spatial distribution pattern on the outcomes of intra- and interspecific competition is studied theoretically. The models developed are the generalized logistic andVolterra equations, whereLloyd’s indices of intra- and interspecies mean crowding were incorporated with their assumed linear relationship to mean density in order to express the intensity of crowding which is really effective to the existing individuals. It is shown that while the increasing patchiness of distribution has a pronounced effect of promoting the intraspecific competition and lowering the equilibrium density for individual populations, it generally relaxes the interspecific competition, making it easy for different species sharing the same niche, which would otherwise be incompatible, to coexist stably. These models thus provide a simplest theoretical basis to explain why many insect populations in nature are kept relatively rare in number and why a number of allied species often coexist freely sharing the same resource, against the “competitive exclusion principle” deduced from the originalVolterra equations.