A stochastic computer model for simulating population growth

Summary A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model’s behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka’s Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values orr _m andK. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetleTribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

A computer model of family building based on expected values

A computerized probability model of family building is described. Called FERMOD, the model is designed to follow the changing distribution of children ever born and birth intervals of a large homogeneous population as it moves through the reproductive period. Use of the model presupposes assumptions about such factors as risks of fetal wastage, lengths of pregnancy, and postdelivery amenorrhea conditional to outcome of pregnancy, length of reproductive period, fecundability, desired family size, preferred birth spacing!, and effectiveness of contraception. Use of FERMOD is illustrated in a limited application to United States fertility. Relations to other models are briefly discussed.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.     

A simple endogenous growth model with endogenous fertility: indeterminacy and uniqueness

This paper studies the equilibrium dynamics and indeterminacy of equilibria in an endogenous growth model with endogenous fertility choice. We characterize the conditions that give rise to an unique equilibrium as well as multiple equilibria. Whenever there exists a unique equilibrium, it will be globally determinate; when multiple equilibria arise, indeterminacy occurs. In particular, we find that two equilibria occur – one is associated with high fertility and low growth, while the other is associated with low fertility and high growth. A parameterized example is given to assess the empirical feasibility of our results. The validity of the neo-Malthusian relation between fertility and growth is then re-examined. Finally, we study the relation between growth and welfare and compare different balanced growth equilibria in terms of their lifetime-attained utility. JEL classifications: O41, J13 Received December 11, 1995 / Accepted October 20, 1996     

A simple in-host model for Mycobacterium tuberculosis that captures all infection outcomes

ABSTRACT

Tuberculosis infection can result in clearance, latent infection, or active disease, with slow or fast progression. A four-dimensional model of in-host tuberculosis infection includes macrophages, T lymphocytes, tuberculosis bacteria, and their interactions. Changes in the infection rate, cell-mediated immunity rate, macrophage loss rate, and bacteria killing rate most affect disease outcomes. Simulations show that a periodic solution can occur. When the infected macrophage killing rate is constant, a backward bifurcation exists and the system is globally stable.     

A systems model and computer simulation of the green rice leafhopper populations in control programmes

Summary A simulation model of the green rice leafhopper-spiders system was presented. The validity of this model for simulation purpose was tested by comparing the calculated values with observed ones (Fig. 4). The effectiveness of various control measures against leafhoppers was evaluated by computer simulations. The computer simulation demonstrated that the wrong use of selective insecticide, contrary to expectation, brought an increase in the pest density, i. e., that the egg densities of leafhoppers in the 2nd and 3rd generations are increased by the insecticidal application in February, while they are decreased by the July application (Table 2). To obtain satisfactory control by sterile-male release, 320,000 sterile-male per square kilometer should be released even in the combined use with insecticides (Fig. 5). The escape of leafhoppers from predation by spiders was demonstrated by the simulation. It is suggested that spiders are able to suppress the leafhopper populations at a low density when there is a very favorable balance between spiders and leafhoppers, and this condition may be realized by sophisticated use of selective insecticides (Fig. 6). Factors and/or processes which have to be involved in a more improved systems model are discussed. A part of this research was supported by science research fund from the Ministry of Education.     

A simple measure of fertility control

We describe a simple measure of fertility control: the proportion of all births from the age-specific fertility schedule that occurs among women by age 35. This measure has broad applicability because it does not require information on marital fertility rates. When both the proportion of births by age 35 and the most commonly used measure of fertility control, m, are calculated for a population over time, they are correlated very highly. Because of increasing levels of nonmarital fertility in several developed countries, measures of fertility control that are based on marital fertility are less appropriate now than in the past.     

The impact of child mortality on spacing by parity: A Cox-regression analysis

Child mortality may affect spacing through biological and behavioral channels. The death of a child may elicit a desire to have another one soon; further, it may interrupt breastfeeding and shorten the sterile period following childbirth. The hypothesis that the child mortality-spacing linkage varies across parities, being strongest in the middle parities, is examined using microdata from Malaysia and the Cox-regression technique. The empirical results lend support to the hypothesis.     

The influence of child spacing on child survival

Summary This study evaluates the strength of the influence of spacing on child survival. Data related to a traditional culture (Punjab) in which almost all children are breast-fed up to the age of 17 months. An initial pregnancy history survey, subsequent four years updating through continuous monitoring of vital events and a second cross-sectional pregnancy history survey at the mid-point provided a file containing information on pregnancies and survival of children of 5,018 women. The analysis first looks at the correlation between the lengths of the preceding and subsequent intervals of index children, then examines whether this correlation was related to the repeated pattern of child death or survival. Next, the influence of the duration of the preceding interval on the survival of the index child in general and after accounting for the fate of the preceding child were considered. Then the influence of the length of the subsequent interval on the survival of the index child after conception and after the birth of the next child were studied. Lastly, regression analyses with preceding and subsequent intervals as independent variables and age-specific survival or death as the dependent variable were performed.     

The pattern of birth spacing during Taiwan's demographic transition

This paper considers the impact of an extended family structure on the fertility behavior of married women in Taiwan. A sequential duration model is applied to identify the differences in fertility behavior during the early and latter stages of a woman's reproductive period. Heterogeneity adjustments which correct the respondent-specific characteristics are also implemented. It is found that living with the husband's parents has an impact on the wife's fertility only at the early stage of her childbearing period, and that the subjective son preferences together with the objective fact of no son in the previous 2 births do force a wife to expedite her third birth. These results are robust across different cohorts during the demographic transition and under different specifications of hazard functions. We thank an anonymous referee for his or her valuable comments and suggestions. Responsible editor: Junsen Zhang.     

A computer simulation of the epidemiology of the rice dwarf virus

Summary An epidemiological system model was developed to evaluate the role of factors which were responsible for the prevalence of rice dwarf virus (RDV) transmitted by the green rice leafhopper,Nephotettix cincticeps. Simulation tests were conducted by varying values of the following three parameters: the vector density, the coefficient of the efficiency of feeding acquisition of RDV of the vector, and that of efficiency of RDV transmission by the vector. The effect of each parameter was assessed in terms of changes in percentages of infected insects and of infected rice hills. Both the percentages of infected insects and of infected rice hills increased rapidly with increasing vector density within a range of low vector density. The former increased linearly when the acquisitive coefficient was increased. But the percentage of infected rice hills was affected to a lesser extent. The percentage of infected insects and that of infected rice hills increased exponentially with increasing values of the transmission coefficient. The results obtained from the simulation tests were discussed in relation to the ecological factors which caused the recent prevalence of RDV. A part of this research was supported by science research fund from the Ministry of Education.     

The Effect of birth spacing on childhood mortality in Pakistan

Summary In this study retrospective data from the 1975 Pakistan Fertility Survey are used to examine the effects of birth spacing on infant and child mortality. The length of the preceding interval between live births emerges as a major determinant of mortality. The effect persists for rural and urban families, for children of uneducated and educated mothers, for both boys and girls, and for large and small families. The possibility that this relationship is the spurious consequence of data defects or of a common cause, such as early weaning, is examined but rejected. Once the length of the preceding interval is controlled, the average spacing of earlier births is found to be unrelated to survivorship. However, the length of the succeeding interval is significantly related to survivorship during the second year of life.     

A simple evolutionary model of dormancy and dispersal in heterogeneous patches with special reference to phytophagous lady beetles: I. Stable environments

Summary A simple evolutionary model of dormancy and dispersal is presented with special reference to phytophagous lady beetles. In order to investigate spatially heterogeneous environments, we assume the simplest patch structure, that is, there are only two patches, main and sub. Environments are also assumed to be temporally constant. The main patch is superior to the sub patch, but density effect at the main patch is higher than at the sub patch. Optimal dormancy and dispersal are obtained at the same time by the method of evolutionarily stable strategy (ESS). In the univoltine life cycle, dormancy strategy vanishes because dormant individuals do not reproduce at all but suffer from a certain mortality rate during winter hibernation. In the bivoltine life cycle, the dormancy and dispersal rates constitute a trade-off: the rates change together with a negative correlation when the mortality rate during dispersal or during winter hibernation changes. When suitability of the main patch gradually deteriorates, the optimal strategy changes as follows: neither dormancy nor dispersal is adopted at the most suitable condition, the dispersal rate is increased without dormancy in the intermediate condition, and then the dormancy rate is increased with a constant dispersal rate. We discuss the field observation data of lady beetles in the light of results of our model.     

The effect of female education on fertility: A simple explanation

This paper investigates the structure of the relationship between female education and fertility. It is based on data published in First Country Reports of the World Fertility Surveys for eleven countries—Costa Rica, Colombia, Dominican Republic, Panama, Fiji, Korea, Malaysia, Pakistan, Sri Lanka, Thailand, and Indonesia. The cumulative marital fertility of educated women is shown to be similar in different settings. A lack of uniformity in the education and fertility relationship including the curvilinear nature of this relationship observed across countries is shown to be attributable to marked differences between countries in the average fertility of women with no education rather than to the presumed differences in the average fertility of the educated women. The structure of the relationship is shown to be similar across several developing countries. This analysis suggests that advancement in female education can be expected to influence fertility behavior even without simultaneous changes in other factors such as increasing opportunity for participation in the paid labor force in the modem sector.     

A model of voluntary childlessness

Demographers and sociologists have studied why women remain childless for more than two decades; however, this specific choice of zero fertility has not interested economists. Permanent childlessness, in developed countries, can concern up to 30 % of the women in a cohort. Childlessness rates can be positively related to average fertility for some cohorts of women. This paper provides an explanation for this using an endogenous fertility model where individuals have different preferences for children. The main mechanism considered goes through the intergenerational evolution of preferences: I show that a reduction in the gender wage gap, or an increase in the fixed cost of becoming a parent, has a negative effect on both fertility and childlessness. The reduction of childlessness is due to a composition effect: small families shrink more than larger families, and this reduces childlessness.     

A magical model of happiness

A model of happiness is described that is based on nonlinear mathematics. Happiness at timet+1 is given by:Hnext=M(1–H)H+I, whereH is happiness at timet, M is a person parameter, andI is an environmental impact term comprised of a prevailing component (Ip) and an episodic component (dI). Eight properties of the model are detailed and its utility illustrated for reconciling problematic issues in the literature that include the positive skew in the distribution of psychological well being (PWB) scores, the stability and change in PWB, and the relationships of emotionality with global PWB and its indicators. The operationalization of the model is described from the population level down to that of the single case.