Social security policy with public debt in an aging economy

This paper analyzes a social security policy with public debt in an overlapping generations growth model. In particular, the paper considers a situation in which population aging causes a heavy burden of social security payments where public debt is issued by the government to finance the payment. In the model presented below, an economy with an aging population may achieve two dynamically inefficient equilibria. Under certain conditions, the effects of pension reform and population aging on capital accumulation are entirely different between the two equilibria. Received: 23 July 2001/Accepted: 22 August 2002 I am deeply grateful to an anonymous referee and Professor A. Cigno, the Editor of this journal, for their valuable comments and suggestions. I am also grateful to Kazuyo Tanimoto and Kiheiji Nishida for their research assistance. Any remaining errors are my own. The research reported here was conducted as part of a larger study, the “Project on Intergenerational Equity” at the Institute of Economic Research, Hitotsubashi University. Financial support from Kani Hoken Bunka Zaidan is also gratefully acknowledged. Responsible editor: Alessandro Cigno.     

Niche modification and stability of competitive systems. II. Persistence of interspecific competitive systems with parasitoid wasps

Summary Effects of niche shift in ecological time scale on the population dynamics of competing species were studied in the experimental populations of two parasitoid wasp species,Anisopteromalus calandrae andHeterospilus prosopidis (both are solitary parasites), on a host, the azuki bean weevil,Callosobruchus chinensis. Four resource conditions were set up with combination of kind of bean (azuki or black eye), and host distribution (uniform or clumped). In each resource condition, four developmental stages of hosts were provided as a resource spectrum for parasitoid wasps. Population dynamics of the two wasp populations were investigated in each resource condition in Multi-Generation Competitive Systems (MGCS), in which fresh hosts of four developmental stages were periodically introduced and were parasitized competitively by the two wasp species. Competitive coexistence of both wasps occurred in the azuki-clumped condition, where the peaks of the resource utilization curves separated in the two species; pupae inA. calandrae and the early or late fourth instar inH. prosopidis, A. calandrae was eliminated in the azuki-uniform condition andH. prosopidis went extinct in two black eye conditions irrespective of host distributions. The degrees of overlap of the resource utilization patterns of the two wasp species during population dynamics were not significantly different among resource conditions irrespective of the results of coexistence or extinction. Even in the azuki-clumped condition, however, extinction ofA. calandrae was observed when resource partitioning could not be realized with only the late fourth instar larvae available to wasps. Further analytical experiments showed that parasitizing ability ofA. calandrae increased with host density per bean with azuki beans, butA. calandrae could express higher parasitizing ability with black eye beans thanH. prosopidis irrespective of host density per bean. The flexibility in parasitizing ability byA. calandrae for various host stages under different resource conditions was thought to be the major factor in determining the competitive coexistence or the extinction of either species under different resource conditions. The present experiments also suggested that different second-best host stages between competitors could be a major contributing factor to competitive coexistence.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

Lattice population dynamics for plants with dispersing seeds and Vegetative propagation

The population dynamics of plants in a lattice structured habitat are studied theoretically. Plants are assumed to propagate both by producing seeds that scatter over the population and by vegetative reproduction by extending runners, rhizomes, or roots, to neighboring vacant sites. In addtion, the seed production rate may be dependent on the local density in the neighborhood, indicating beneficial or harmful crowding effects. Two sets of population dynamical equation(s) are derived: one based onmean-field approximation and the other based onpair approximation (tracing both global and local densities simultaneously). We examine the accuracy of these approximate dynamics by comparing them with direct computer simulation of the stochastic lattice model. Pair approximation is much more accurate than mean-field approximation. Mean-field approximation overestimates the parameter range for persistence if crowding effects on seed production are harmful or weakly beneficial, but underestimates it if crowding effects are highly beneficial. Dynamics may show bistability (both population persistence and extinction) if the effect of crowding is strongly beneficial. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximised by a mixture of seed production and vegetative reproduction, rather than by pure seed production or by pure vegetative reproduction. This result is correctly predicted by pair approximation but not by mean-field approximation.     

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.     

Population fluctuation and persistence of one-host–two-parasitoid systems depending on resource distribution: from parasitizing behavior to population dynamics

Population dynamics and variability were examined in one-host–two-parasitoid experimental systems with different resource distributions: resource-clumped and resource-sparse conditions. The system consists of a seed beetle host, Callosobruchus chinensis, and two parasitoid wasps, Anisopteromalus calandrae (Pteromalidae) and Heterospilus prosopidis (Braconidae). In the resource-clumped condition, suitable hosts for parasitism (the late fourth-instar larvae and pupae) were clumped in 1 large resource patch, but they were scattered evenly among 16 small patches in the resource-sparse condition. Population censuses were conducted at 10-day intervals in long-term cultures, renewing 10 g of azuki beans (Vigna angularis). In both resource conditions, the first period was a single-species system of C. chinensis only, and A. calandrae was added in the second period. The one-host–one-parasitoid system with C. chinensis and A. calandrae showed stable population dynamics with small fluctuations. After addition of H. prosopidis in the third period, two of three replicates persisted to day 800 in each resource condition, although one replicate in each went to extinction at an immediate outbreak of the H. prosopidis population after the introduction. Population variabilities of C. chinensis and H. prosopidis were significantly higher and the mean population size of A. calandrae was significantly smaller in the resource-sparse condition than that in the resource-clumped one. A short-term experiment on parasitism efficiencies revealed that H. prosopidis parasitized significantly more at a low host density in the resource-sparse condition than in the resource-clumped one. Mutual interference of H. prosopidis was weak enough at low parasitoid densities but became abruptly stronger with high densities. Providing fresh hosts in a mixture of already parasitized ones, host-searching behaviors of a parasitoid were recorded by video for 3 h and were compared between the two wasp species. H. prosopidis could parasitize fresh hosts more efficiently than A. calandrae through frequent long-distance walks (walking to distant beans at one bout or outside a clump of beans with hosts and back soon on a distant bean of the clump) after reencounters with parasitized hosts. Considering all the experimental results, populations were judged to be more fragile and more likely to go to extinction in the resource-sparse condition than in the resource-clumped one. A higher attacking efficiency of H. prosopidis destabilized population dynamics more in the resource-sparse condition. Received: December 23, 1998 / Accepted: January 20, 1999     

Human capital,technological progress and the demographic transition*

We emphasize the importance to consider components of population growth — fertility and mortality ‐ separately, when modeling the mutual interaction between population and economic growth. Our model implies that two countries with the same population growth will not converge towards the same level of per capita income. The country with the lower level of birth and death rates will be better off in the long run. Introducing a spill over effect of average human capital on total productivity our model implies multiple equilibria as illustrated in Becker el al. (1990) and Strulik (1999). Besides the existence of a low and high level equilibrium ‐ as characterized by low and high levels of per capita output respectively ‐ we show the existence of multiple low level (Malthusian) equilibria. Initial conditions and parameters of technological progress and human capital investment determine whether an economy is capable to escape the low level equilibrium trap and to enjoy sustained economic growth.     

A management policy for sika deer based on sex-specific hunting

We consider here a management policy for a sika deer (Cervus nippon) population in the eastern part of Hokkaido. Deer populations are characterized by a large intrinsic rate of population increase, no significant density effects on population growth before population crash, and a relatively simple life history. Our goals of management for the deer population are (1) to avoid irruption with severe damage to agriculture and forestry, (2) to avoid the risk of extinction of the deer population, and (3) to maintain a sustainable yield of deer. To make a robust program on the basis of uncertain information about the deer population, we consider three levels of relative population size and four levels of hunting pressures. We also take into consideration a critical level for extinction, an optimal level, and an irruption level. The hunting pressure for females is set to increase with the population size. We also recommend catching males if the population size is between the critical and optimal levels and catching females and males if the population size is larger than the optimal level. We must avoid cases of irruption or threatened population under various sets of uncertain parameter values. The simulation results suggest that management based on sex-specific hunting is effective to diminish the annual variation in hunting yield. Received: April 8, 1998 / Accepted: December 25, 1998     

Stabilization of the population of a parasite on fruit by the population of a cleptoparasite

Summary When there exist two species such that one is a parasite on fruit and the other exploits the parasitized fruits, they must compete for a limited resource with each other. The relation betweenDacus cucurbitae andAtherigona orientalis is an example of such a situation. We raise a question whether the population of a parasite on fruit can be stabilized by the existence of the cleptoparasite of the parasite on fruit. The changes in their population densities are represented as a differential equation with time delayed parameters, which is deduced from the context of life histories of the two species. An index representing degree of overlapping of generations (g) is defined as an average oviposition period devided by the average preoviposition period, and the value is assumed to be the same in the two species. The stability of the system is classified by three parameters: the reproductive rate of the parasite on fruits (R), the survival probability of it through competition against the cleptoparasite (p), and the generation overlapping index (g). For small values ofg, e.g. less than some 0.5, the stability is determined mainly by a product ofRp: the values larger than 1 result in no equilibrium and infinite increase of both species, the values near 0 lead to large amplitude oscillations, and the intermediate values make stable equilibria or regular small oscillations. Asg takes the larger values, the stability region in the space (p, R) occupies the larger area. The model presented here is well adjusted to the fluctuating pattern of the population ofD. cucurbitae on Okinawa Is., and would also be applied to analysis of both hyperparasitisms and inquilin. This study was supported partly by Science Research Fund (No. 574092) from the Ministry of Education, Japan.     

Theoretical aspects of extinction by inbreeding depression

Populational extinction due to inbreeding depression is analyzed with simple population genetic and population ecological models. Two alternative genetic mechanisms of inbreeding depression, i.e. recessive deleterious genes and overdominant genes, are assumed in separate analyses in order to examine their relative importance. With both mechanisms the population size and the coefficient of inbreeding are maintained at stable equilibria if there is no non-genetic demographic disturbance or stress. With a certain amount of demographic disturbance the population declines rapidly due to interaction between the decrease of population size and the increase of inbreeding coefficient. Such rapid extinction occurs with both genetic mechanisms. However, in the case of overdominant genes extinction happens only if the equilibrium population size is small and the selection coefficient is large such that segregation load is large. In nature, extinction due to overdominant genes is considered to be much less likely than extinction due to recessive deleterious genes.     

The population dynamics of the large pine aphid,Cinara pinea (Mordv.)

Summary The large pine aphid,Cinara pinea lives exclusively onPinus species, where it feeds on the foliated shoots of the current and previous year. The paper describes the development of a computer model designed to simulate the aphid’s population dynamics on saplings in the controlled environment of the laboratory, i.e. in the absence of natural enemies. The model was able to account for about 80% of the variation in aphid numbers within and between trees over a three month period. Sensitivity analysis revealed that the number of pine aphids is limited primarily by nymphal emigration, the operation of which is sensitive both to density and to plant quality as reflected in aphid growth rates. Of secondary importance are changes in reproduction acting through increased reproductive delay, again a result of altered growth rates and adult size. Development, too, has an important secondary influence. Contrary to expectation and conventional belief, however, alate production proved to be of negligible importance, either in limiting or regulating population numbers. Alatae are produced in too few numbers and for too short a period to significantly alter the pattern of population change.     

Comparative analysis of population characteristics of the brown planthopper,Nilaparvata lugens st?l, between wet and dry rice cropping seasons in West Java, Indonesia

Summary Population dynamics of the brown planthopper (BPH),Nilaparvata lugens St?l, were investigated in paddy fields in the coastal lowland of West Java, Indonesia, where rice is cultivated twice a year, in the wet and dry cropping seasons. Distinct differences in the basic features of population dynamics were detected between the two rice cropping seasons: (1) In the wet season, BPH populations multiplied rapidly in the period from initial to peak generation, reaching quite often the destructive level despite the low density of initial immigrants. However, in the dry season, the population growth rate and the peak population density were much lower than those in the wet season. The abundance of natural enemies such as arthropod predators played a major role in determining such a difference in seasonal population development. (2) The density at the peak generation or the occurrence of outbreaks in each field was predictable in the wet season with fairly high accuracy on the basis of the density at the initial or previous seasonal generations. In the dry season, however, the rate of population growth and the peak population density widely varied among the fields depending on the water status in each field. (3) Density-dependent processes to regulate the population density were detected in both cropping seasons. In the wet season, the regulatory processes were only detected in such high densities as cause the considerable deterioration of host plants, which suggested that the processes were largely attributable to intra-specific competition. In the dry season, however, the regulatory processes operated at a much lower density in the earlier stages of the crops. The results of an analysis of adult longevity or residence period suggested that the density-dependent dispersal of macropterous adults played an important role in stabilizing the population fluctuation among the fields in the early dry season.     

Ethnic population projections for the UK, 2001–2051

This paper reports on projections of the United Kingdom’s ethnic group populations for 2001–2051. For the years 2001–2007 we estimate fertility rates, survival probabilities, internal migration probabilities and international migration flows for 16 ethnic groups and 355 UK areas. We make assumptions about future component rates, probabilities and flows and feed these into our projection model. This model is a cohort-component model specified for single years of age to 100+. To handle this large state space, we employed a bi-regional model. We implement four projections: (1) a benchmark projection that uses the component inputs for 2001; (2) a trend projection where assumptions beyond 2007 are adjusted to those in the UK 2008-based National Population Projections (NPP); (3) a projection that modifies the NPP assumptions and (4) a projection that uses a different emigration assumption. The projected UK population ranges between a low of 63 millions in 2051 under the first projection to a high of 79 million in the third projection. Under all projections ethnic composition continues to change: the White British, White Irish and Black Caribbean groups experience the slowest growth and lose population share; the Other White and Mixed groups to experience relative increases in share; South Asian groups grow strongly as do the Chinese and Other Ethnic groups. The ethnic minority share of the population increases from 13% (2001) to 25% in the trend projection but to only 20% under our modified emigration projection. However, what is certain is that the UK can look forward to be becoming a more diverse nation by mid-century.     

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.     

The sterile release method for population control with interspecific competition

Summary A differential equations model of competing species with the release of sterile individuals of one of the species is examined. The system is found to have two positive steady states for certain parameter values; one of these is stable and the other is unstable. The system is quite resilient around the stable steady state. The release of steriles causes the nontarget species to increase in numbers. There exists a value of the release rate above which the pest species collapses to extinction. The existence of the competitor species assists the sterile release program since the pest equilibrium at any release rate is lower with the competitor species present than without it; in addition the release rate required to cause collapse of the pest species is lower with the competitor species present than without it. The effects of the parameters on the ease of eradication were examined. It was found that the ideal competitor species should have a high rate of increase, a large carrying capacity and exert strong competitive depression on the pests. The ideal pest would have a low rate of increase, a low carrying capacity and be a poor competitor.     

Human Carrying Capacity Is Determined by Food Availability

Simple mathematical models have illustrated the relationship between human carrying capacity and population growth. In this study, food supply is proposed as the variable which best accounts for the human carrying capacity. The logistic equation, using food supply data as a variable carrying capacity, yields population estimates which are in accord with actual population numbers. That food supply data adequately fits the logistic model of human population dynamics provides evidence that, consistent with ecological notions typically applied only to nonhuman species, human population increases are a function of increased food availability.     

The sterile insect release method on species with two-stage life cycles

Summary A continuous-time density dependent model was constructed of a species with a two stage life cycle. This model has a unique stable equilibrium. With the introduction of steriles at constant rate a second positive unstable steady state appears; this condition does not depend on the mode of action within the life cycle of the density dependence or its relative strength. A comparison was made of the effects of having the density dependence in each of larval and adult recruitment and larval and adult losses. It was found that if only adult recruitment is denisty dependent, then adult numbers can actually increase with the release of steriles provided density independent recruitment greatly exceeds density independent losses. Sterile releases were often more effective against larvae than against adults, although in some cases not importantly so. Density dependence in recruitment gives much lower equilibrium values than when density dependence of comparable strength is in the mortality. The release rates needed to cause extinction were generally between 0.1 and 0.5 of the larval equilibrium with no sterile releases except when the density dependence is predominantly in adult recruitment, in which case much higher release rates are required.     

Toward a general analysis of endogenous Easterlin cycles

Easterlin believed that there were two features associated with the birth cycles he observed: the cycles were related to the labor market, and they might be self-generating. This paper tries to set up a model that contains both of these two features. We suppose that the welfare of various age-specific cohorts are determined by their respective marginal productivity, and that the underlying technology which puts together labor force of various age-specific cohorts can be characterized by a general production function. Under these weak assumptions, we show that the well-analyzed cohort and period models along the lines of Lee (1974) are restricted versions of our general setting. Given that both the cohort model and the period model were rejected by statistical tests, we adopt the coefficient values obtained from the estimation of the unrestricted version to perform the bifurcation analysis. We go beyond the previous study which focused upon the possible existence of limit cycles, and show that the U. S. fertility limit cycle solution is unstable. Therefore the population trajectory will never converge to that limit cycle.We thank Professors Kenneth Wachter, Shripad Tuljapurkar, and two anonymous referees for their valuable help, comments and suggestions.     

Modelling the effects of population aggregation on the efficiency of insect pest control

Summary A methodology is developed to assess the effects of spatial distribution on the efficiency of insect pest control. This methodology is especially applicable to pest control methods whose efficiency of action depends either positively or negatively on pest density It is applied here to the sterile insect technique and pheromone trapping for male annihilation, which both depend negatively on density. This methodology relies on quantifying clumps of various size and then relating this to efficiency of control and predicting the total pest production given the information on clump sizes and efficiency of control for each clump size. It is found that control is about four times as difficult for a population that is highly clumped (k of the negative binomial distribution=0.25) as for a regularly dispersed population.     

Population dynamics of the whitebacked planthopper,Sogatella furcifera (Hemiptera: Delphacidae) with special reference to the relationship between its population growth and the growth stage of rice plants

A population census was conducted to describe the effects of the growth stage of rice on the population dynamics ofS. furcifera, in particular, on immigration, seasonal abundance, population growth rate, and wing-form expression. The number of immigrants was highest on rice plants 17 to 30 days after transplanting (DAT), which suggested that immigrants prefer to settle or remain more on rice plants at the tillering stage (approximately 20–30 DAT). Population growth rate from immigration to the 1st generation decreased with an increase in rice plant age. In contrast, population growth rate from the 1st to 2nd generation was not influenced by rice plant age and was negatively density-dependent. The percentage of macropters (flyers) was positively related to the growth stage of rice when rice was in the vegetative or early part of the reproductive stage, and reached 100% at about 10 days before heading (booting stage). Threafter, most adult females molted into macropters regardless of population density. The roles of host plant age and crowding effect on the population dynamics ofS. furcifera are discussed.