Dispersive behaviour of larvae of the common cabbage butterflyPieris rapae crucivora

Summary To investigate the aggregative nature of the larvae ofPieris rapae crucivora, each 50 individuals of the 4th and 5th instar larvae collected from cabbage farms and reared under crowded and solitary conditions were released on an experimental arena and their dispersive behaviour was observed with the lapse of time. Both the 4th and 5th instar larvae showed the trend to approach toward random distribution when they were released under clumped condition, and they maintained random distribution when they were released at random. Therefore, it may be concluded that the larvae have not any aggregative nature caused by the mutual attraction among individuals. However, as the larvae reared in crowds sometimes showed the slight aggregative behaviour, it seems that the larval dispersal is different between densely and sparsely populated plants in field.     

Rectangularization revisited: Variability of age at death within human populations*

Rectangularization of human survival curves is associated with decreasing variability in the distribution of ages at death. This variability, as measured by the interquartile range of life table ages at death, has decreased from about 65 years to 15 years since 1751 in Sweden. Most of this decline occurred between the 1870s and the 1950s. Since then, variability in age at death has been nearly constant in Sweden, Japan, and the United States, defying predictions of a continuing rectangularization. The United States is characterized by a relatively high degree of variability, compared with both Sweden and Japan. We suggest that the historical compression of mortality may have had significant psychological and behavioral impacts.     

A decomposition method based on a model of continuous change

A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations. We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifies the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function. A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied flexibly to a wide variety of decomposition problems. This study also suggests that when data are available at multiple time points over a long interval, it is more accurate to compute an aggregated decomposition based on multiple subintervals than to compute a single decomposition for the entire study period.     

A model of the species rank-abundance relation for a community in an open habitat

Summary A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi, 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders’s (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.     

Age patterns of mortality for older women: An analysis using the age‐specific rate of mortality change with age

The age‐specific rate of mortality change with age, defined by k(x) = d Inμ(x)/dx, where μ(x) is the age‐specific death rate at exact age x, is estimated for middle and old ages in ten selected populations that are considered to have relatively accurate age data. For females in each of the study populations, k(x) follows a bell‐shaped curve that usually peaks around age 75. In some of the populations, the age pattern of k(x) for males is confounded with substantial cohort variations, which seem to reflect long‐term impacts of their World War I experiences.

Among the mathematical models proposed by Gompertz, Makeham, Perks and Beard, only the Perks model is consistent with the bell‐shaped pattern of k(x). It is shown that, if the risk of death for every individual follows the Makeham equation and if the individual frailty is gamma‐distributed, then the age‐specific death rate follows the Perks equation.     

Age-specific growth rates: The legacy of past population dynamics

Recent developments in population mathematics have focused attention on a function that is widely available but rarely examined: the set of age-specific growth rates in a population. In particular, this set of rates is sufficient for translating the current birth rate and age-specific mortality rates into the current age distribution. This growth-rate function contains all of the pertinent features of a population's demographic history that are required to relate major demographic functions for a particular period to one another. This article presents an expression for the age-specific growth rate and uses it to derive an equation for age distribution. We show how the value of the age-specific growth rate is determined by a population's demographic past and present various sets of growth rates corresponding to stylized demographic scenarios. Several noteworthy sets of growth rates observed in human populations are discussed. Finally, we explain why age-specific growth rates make it possible to determine the age distribution solely from information on current demographic conditions.     

The narrowing sex differential in life expectancy in high-income populations: effects of differences in the age pattern of mortality

Using data from the Human Mortality Database for 29 high-income national populations (1751-2004), we review trends in the sex differential in e(0). The widening of this gap during most of the 1900s was due largely to a slower mortality decline for males than females, which previous studies attributed to behavioural factors (e.g., smoking). More recently, the gap began to narrow in most countries, and researchers tried to explain this reversal with the same factors. However, our decomposition analysis reveals that, for the majority of countries, the recent narrowing is due primarily to sex differences in the age pattern of mortality rather than declining sex ratios in mortality: the same rate of mortality decline produces smaller gains in e(0) for women than for men because women's deaths are less dispersed across age (i.e., survivorship is more rectangular).     

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

Summary 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. Aided by a grant from Scientific Research Expenditure of the Ministry of Education.     

The species-area relation III. A third model for a delimited community

A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed.