Pheromone trapping models for pest control: Effects of mating patterns and immigration

Summary Several models are presented which examine pest population behaviour with the release of female sex pheromones for the attraction and annihilation of males. These models include male polygamy and female monogamy, various mating frequencies, delayed mating of females, immigration of one or all individual types, and differential survivorship of males and females. In all the models there are two steady states, a stable s.s. at the origin and an unstable s.s. in the positive domain for a given value of pheromone release rate. In all the models, control relies on the reduced ability of males to fertilize virgin females following trapping and male annihilation. As such, control is very sensitive to mating frequency, being very difficult when males mate frequently. Control is also very difficult with the immigration of even a moderate number of fertilized females. Control is much easier when mating is delayed, especially if survivorship is low, or with density dependent population regulation.     

Model life tables: An empirical test of their applicability to less developed countries

Model life tables are commonly used for estimating various parameters of mortality of populations in developing countries with limited data. The application of the models is based on the assumption that the agemortality pattern of the population under consideration resembles one of the life tables in the models. The analysis in this paper tests the validity of this assumption for developing countries with data usable for the purpose. The major conclusion is that infant mortality in the populations analyzed is higher than predicted by the models corresponding to the levels of adult mortality of these populations. The observed discrepancy is ascribed to the selectivity involved in the construction of model life tables, which are primarily derived from the historical experience of Western countries. Populations in the currently developing countries apparently differ in the process of mortality change from those used in the models. Though the analysis is limited to a few countries and may not necessarily be true for all the less developed countries, it suggests the need for caution in the use of conventional model life tables.     

Lek mating system and its impact on male annihilation technique

Summary Simulation models were presented which describe the matings inside a lek. The size of the lek was assumed to follow a poisson distribution, the dominance factor of each of the males was drawn from a gamma distribution, and the mating probability for each male was determined by its mating effectiveness raised to female mating factor divided by the sum of all the mating effectivenesses raised to this power. The mating probatility for each male and the actual matings were determined by Monte Carlo simulation. Based on the simulation data, the effects of female mating factor and size of the lek on the frequency of actual matings accomplished by the males inside the lek were discussed. In the case of male annihilation, the mean number of effective matings per male in the lek, calculated from the frequency of actual matings weighted by the effective mating ratio, was used to evaluate the efficiency of male annihilation method.     

HIV and population dynamics: A general model and maximum-likelihood standards for East Africa

In high-prevalence populations, the HIV epidemic undermines the validity of past empirical models and related demographic techniques. A parsimonious model of HIV and population dynamics is presented here and fit to 46,000 observations, gathered from 11 East African populations. The fitted model simulates HIV and population dynamics with standard demographic inputs and only two additional parameters for the onset and scale of the epidemic. The underestimation of the general prevalence of HIV in samples of pregnant women and the fertility impact of HIV are examples of the dynamic interactions that demographic models must reproduce and are shown here to increase over time even with constant prevalence levels. As a result, the impact of HIV on population growth appears to have been underestimated by current population projections that ignore this dynamic.     

Intrinsically Dynamic Multistate Models

Multistate life table models, which follow persons through more than one living state, have found increasing use in demographic analyses. Multistate stable populations, however, are infrequently used because the constant rate assumption is quite strong and such populations can take centuries to approach stability. Dynamic models, that is models where the rates can change over time, are examined to derive a new solution for the size and composition of a multistate population in terms of the sequence of underlying population projection matrices (PPMs). Constraints on the subordinate eigenvalues and the subordinate eigenvectors of the time-varying PPMs produce a model population that grows according to the dominant eigenvalues of each time-specific PPM and has a state composition that depends only on the most recent PPM. The two living state model is examined in detail, relationships between the PPM elements and the size and composition of the model are explored, and two illustrative applications of the model are presented.     

Impact of lek mating on the sterile insect technique: A modeling study

Summary Modelling studies are presented which describe the effect of lek mating on the control of a wild population by sterile male release. The mixed leks are assumed to follow a Poisson-binomial distribution and the system includes three parts: territory defense, matings inside a lek and matings outside a lek. The effects of parameters on the hatchability are discussed. Among the parameters, sterile type effect (W _s ), female choice (f _s ) and mating competitiveness (C _m ) are the most important. The application to determining the effects of sterile male release and on the proportion of sterile males required for eradication are also discussed.     

Impact of developmental variance on behavior of models for insect populations II. Models for populations with density dependent restrictions on growth

Summary The impact of variation in developmental times on behavior of models for insect populations is investigated with special reference to models which include various types of intraspecific competition. At low densities, increases in developmental variation led to decreases in reproductive rate. At high densities, increases in developmental variation led to increases in reproductive rate. There was little change in the relationship between developmental variance and generation time as density increased.     

Heterogeneous sexual mixing in populations with arbitrarily connected multiple groups

"A simple procedure for constructing [social/sexual] mixing models for arbitrarily classified (e.g. by sex, age, geographical location, sexual preference) populations is outlined, including a scheme for finding the number of independent mixing parameters required, and a simple (linear algebra) means for finding the values of the dependent mixing parameters. Various worked examples are presented, including the two-sex problem and structured and selective mixing." The use of the models for analyzing mixing structures for AIDS transmission is assessed. (SUMMARY IN FRE)     

Modeling and forecasting populations by time series: The Swedish case

Time series analysis techniques are used to model and to forecast populations. An autoregressive (AR) and a moving average (MA) model, which seem to fit the population of Sweden very well, are found. Forecasts are calculated using both models and are compared with the forecasts obtained by other methods. This comparison is very favorable for the time series models. Although our study is confined to the mid-year population of Sweden, there are good reasons to expect that the technique can be successfully applied to other population parameters.     

Problems and solutions in forecasting geographical populations

This paper asks the question: how does the multistate population model need to be adjusted to provide forecasts of geographical populations? Following an exposition of the standard model, ossible solutions to the problems posed by excessive number of parameters are discussed. ecomposition, aggregation and parameterization are described, drawing on some new results. ssues in the temporal forecasting of model components are outlined and the alternative approach of using a spatial interaction model is considered. The paper concludes by arguing that the design of forecasting models is a powerful learning device for both designers and users.     

Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.     

Age structure and capital dilution effects in neo-classical growth models

This paper reexamines the problem of the relationship between demographic growth and per capita income in neo-classical growth models with age-structured populations. It is suggested that, when they assume a constant rate of capital depreciation, such models overestimate the negative impact of population growth through capital dilution effects. With more realistic depreciation schedules, the ageing of the capital stock which results from lower growth implies a higher overall depreciation rate, which reduces benefits from lower capital dilution. The implications of this observation are examined for the existence of an optimum population growth rate, for models with heterogeneous capital, and for models where capital obsolescence is not fixed but is allowed to vary.This article is a modified version of a paper presented at the First Annual Meeting of the European Society for Population Economics, Rotterdam, September 1987. I am indebted to the anonymous referees for helpful comments and suggestions and to Linda Sergent for revising the English text.     

Relations between demographic parameters

The mean life-expectancy e describes the average prospective life-time of an individual aged zero. This parameter can be explicitly described in terms of the survivorship distribution of the population. The Malthusian parameter r represents the asymptotic growth rate of a population. This parameter can be implicitly expressed in terms of the net-maternity distribution. The parameters e and r incompletely incorporate the age-specific fertility and mortality pattern of a population; distinct populations may have the same growth rate but different net-maternity functions; distinct populations may be characterized by the same mean life expectation but may have different survivorship distributions. This article analyzes a class of parameters called the entropy of a population (Demetrius, 1974a) which distinguishes between net-maternity functions with the same growth rate and also mortality distributions with the same mean life expectation. This class of parameters measures the convexity of the fertility and mortality distributions. This paper analyzes the relations between the entropy parameter and the standard demographic parameters.     

利用小普查数据对“随机婚配”假定的再检验--兼论Logistic回归系数的可比性问题

使用2005年人口小普查数据研究了独生子女之间的婚配选择问题,发现独生子女更可能与独生子女结婚,且非独生子女也更可能与非独生子女结婚,所以认为独生子女与非独生子女之间“随机婚配”的假定并不符合实际。然而,以往有关生育政策调整的人口预测大都基于这一假定之上,这导致预测结果一方面低估了“双独”和“双非”夫妇的数量,另一方面高估了“单独”夫妇的数量。同时,本文还以独生子女的婚配选择问题为例讨论了嵌套模型中Logistic回归系数的可比性问题。直接比较Logistic回归系数可能导致错误的结论,借助“y?标准化”法和“KHB分解法”可以在一定程度上解决Logistic回归系数不可比的问题。     

人口结构失衡与犯罪研究：回顾、借鉴与展望

通过对现有东西方人口结构与犯罪关系文献的梳理和总结,笔者提出了适合研究性别比偏高亚洲国家的假设框架,以及可婚配男（女）性比例与犯罪率的u型假说。对中国1982—2008年人口年龄一性别结构与犯罪率数据探索性分析显示：反映人口年龄一性别结构的青年男性比例与可婚配男性比例的波动与犯罪率的波动高度一致,未来婚姻市场可婚配男性比例的不断升高将成为影响犯罪的主要人口结构因素。     

Simplified birth rate estimates under nonstable conditions

Coale's robust birth rate estimate, obtained by adjusting the birth rate of a stable population selected by matching the observed population of both sexes under the age of 15, C(15), and the probability of survival of births to age 5, l5, is shown to be equal to the birth rate obtainable by reverse surviving the proportion under the age of 15. Variations of matching the criterion of Coale's method to the rate of increase and C(15) or l5 are shown to lead to variants of Coale's birth rate estimate that are also nearly equal to the reverse survival birth rate based on C(15). A simplified birth rate estimate that does not require reference to models of life tables or stable populations is suggested and some of its applications are illustrated.     

A reformulation of the two-sex problem

The ability of classical stable population theory to determine the equilibrium growth rate and age structure of a population from its vital rates in a single period depends on assuming that the observed maternity rates are equilibrium rates. This paper resolves the two-sex problem by replacing the fixed, age-specific fertility schedule of classical stable population theory by two basic relationships: a “birth matrix” and a “mating rule.” Placing certain restrictions on the birth matrix and the mating rule (BMMR), I establish that under certain plausible conditions, the BMMR model solves the two-sex problem by allowing matings and births to adjust to changes in population structure. The BMMR model thus provides an equilibrating mechanism in place of a fixed maternity schedule of classical stable population theory.     

Union Instability as an Engine of Fertility? A Microsimulation Model for France

Opportunities for conceiving and bearing children are fewer when unions are not formed or are dissolved during the childbearing years. At the same time, union instability produces a pool of persons who may enter new partnerships and have additional children in stepfamilies. The balance between these two opposing forces and their implications for fertility may depend on the timing of union formation and parenthood. In this article, we estimate models of childbearing, union formation, and union dissolution for female respondents to the 1999 French Etude de l’Histoire Familiale. Model parameters are applied in microsimulations of completed family size. We find that a population of women whose first unions dissolve during the childbearing years will end up with smaller families, on average, than a population in which all unions remain intact. Because new partnerships encourage higher parity progressions, repartnering minimizes the fertility gap between populations with and those without union dissolution. Differences between the two populations are much smaller when family formation is postponed—that is, when union formation and dissolution or first birth occurs after age 30, or when couples delay childbearing after union formation.     

The development and use of demographic models

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.     

Male mating behavior in relation to spermatophore transfer in the white cabbage butterfly

The lifetime mating frequency of female butterflies is believed tobe dependent on the reproductive status of the males which they have mated. This report assesses those status usingPieris rapae L. Multiple mating females mated males with a short time interval after the last mating or males with many mating records. Such males, like small ones, produced small spermatophores during copulation, which may have resulted in high mating frequency of those females. The males with short time interval after the last mating or those with many mating records also showed a long mating duration. Alternative interpretations of the adaptive significance of this behavior for males are discussed.