A standardized two-sex stable population

The “problem of the sexes” has been one of trying to reconcile inconsistent male and female demographic rates. The present paper deals with that question in the context of a two-sex stable population. A “rectangular” population, with equal numbers of persons in each age-sex group, is introduced as a standard, and a standardization relationship expressed in Eq. (3) relates changes in rectangular population rates to changes in age-sex composition. The standardization relationship is shown to satisfy a number of desirable properties and produce a realistic two-sex model. The standardization approach is then applied to data from Sweden 1973 and the United States 1963, and the results and their implications are discussed. In particular, it is seen that the intrinsic growth rate in a two-sex stable population is not necessarily bounded by the growth rate of the associated male and female one-sex stable populations.     

On two-sex models leading to stable populations

A mathematical, 2-sex, stable-population model that treats sex and age simultaneously was developed. The birth function is expressed in the form of an integral formula which when solved yields the intrinsic growth rate. Some of the concepts involved include the intrinsic sex ratio, the intrinsic age-specific birthrates, and the gross and net reproduction rates for both sexes. The new model demonstrates that both sexes can coexist in a stable population, whereas in the 1-sex model the intrinsic rates are internally inconsistent in regard to sex. 7 forms of the model are discussed and applied to data for the United States from 1963.     

A note on Das Gupta's two-sex population model

Some critical comments are made on the two-sex deterministic population model recently put forward by P. Das Gupta in this Journal, both in its interpretation and relation to any possible stochastic version of the model, and in regard to the validity of solutions other than the asymptotic limiting case.     

A generalized two-sex logistic model

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.     

From homogeneous eigenvalue problems to two-sex population dynamics

Journal of Mathematical Biology - Enclosure theorems are derived for homogeneous bounded order-preserving operators and illustrated for operators involving pair-formation functions introduced by...     

A two-sex demographic model with single-dependent divorce rate

Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.     

A two-sex life history model of handicap signaling

The males of many species (such as peacocks) develop excessively large traits, which appear to interfere with their agility and hence survival probability. Moreover, it is also observed that females seem to prefer mating males with such clumsy traits. Zahavi (1975) proposed a handicap theory to explain this phenomenon, suggesting that this trait/preference interaction is a way in which strong males can signal their viability by yielding a handicap in terms of a clumsy trait size. This paper presents a two-sex model of selfish genes that generates this particular male-female interaction, and characterizes the conditions behind a handicap equilibrium. We first show the female dominance result of Bateman (1948) in this two-sex model, and then specify the relevant equilibrium conditions, including the incentive compatibility condition for females, the individual rationality condition for males, and the stability condition of population composition. Identifying these conditions helps us understand the various features of the searching/signaling of sex selection in evolution.     

Relationships in a simple harmonic mean two-sex fertility model

A continuous time two-sex stable population model that does not recognize age is examined under the “harmonic mean” consistency condition of equation (2). Solutions for the stable population intrinsic growth rate r and the sex composition 5 are presented in equations (5) and (6). The process of stabilization is examined, and it is shown that, given two basic constraints, any initial population sex composition will eventually converge to the stable population value. An algebraic solution for the discrete case where the sex ratio at birth is unity is presented and used to describe the trajectory to stability of several hypothetical populations. A closed form algebraic expression for the trajectory to stability is presented for the continuous model in the special case of no mortality.     

Blood group and height in a multiethnic population

In a sample of 4,472 boys, aged 17-18 years, resident in Jerusalem, those with blood groups B or AB tended to be slightly shorter than groups O and A (p = 0.011). Participants were classified into 8 groups according to father's country of origin: Israel, Southern Europe/Balkans, rest of Europe, North Africa, Iraq, Iran, Yemen and the rest of Asia. The association of ABO blood group, classified according to the presence of the B antigen (groups B and AB) or its absence (O and A), with height differed in the 8 origin groups (p = 0.026 for interaction). In 7 of the 8 groups, subjects with the B allele were either shorter or of equal height to groups O and A and in only one instance were they taller. These findings do not support the generalizability of a positive association of the presence of the B antigen with height suggested by Borecki et al. [1985].     

The two-sex problem with persistent unions: a generalization of the birth matrix-mating rule model

The birth matrix-mating rule (BMMR) model solves the two-sex problem of classical stable population theory by allowing births to adjust to changes in a population's age-sex composition. To avoid complications the BMMR model assumes that unions last for only a single period. This paper drops that assumption and presents the BMMRPU (BMMR persistent unions) model. To establish the existence of equilibrium in the BMMRPU model, the existence proof used in the BMMR model is supplemented by a fixed-point argument.     

Generalized stable population theory

In generalizing stable population theory we give sufficient, then necessary conditions under which a population subject to time dependent vital rates reaches an asymptotic stable exponential equilibrium (as if mortality and fertility were constant). If x ₀(t) is the positive solution of the characteristic equation associated with the linear birth process at time t, then rapid convergence of x ₀(t) to x ₀ and convergence of mortality rates produce a stable exponential equilibrium with asymptotic growth rate x ₀–1. Convergence of x ₀(t) to x ₀ and convergence of mortality rates are necessary. Therefore the two sets of conditions are very close. Various implications of these results are discussed and a conjecture is made in the continuous case.     

Y-chromosomal diversity in the population of Guinea-Bissau: a multiethnic perspective

Background  

The geographic and ethnolinguistic differentiation of many African Y-chromosomal lineages provides an opportunity to evaluate human migration episodes and admixture processes, in a pan-continental context. The analysis of the paternal genetic structure of Equatorial West Africans carried out to date leaves their origins and relationships unclear, and raises questions about the existence of major demographic phenomena analogous to the large-scale Bantu expansions. To address this, we have analysed the variation of 31 binary and 11 microsatellite markers on the non-recombining portion of the Y chromosome in Guinea-Bissau samples of diverse ethnic affiliations, some not studied before.     

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

年龄-龄期两性生命表及其在种群生态学与害虫综合治理中的应用

生命表是种群生态学与害虫治理的重要工具,由于传统雌性生命表无法正确描述昆虫的变态且忽略雄性个体,近年来国内外学者普遍采用年龄-龄期两性生命表。本文首先从昆虫种群的龄期分化、性比对种群增长的影响、总产卵前期与成虫产卵前期的差异、产卵期与产卵日数的差异4个方面概述了年龄-龄期两性生命表(age-stage, two-sex life table)的基本原理,进而阐明了基于bootstrap技术的生命表分析技术及其主要优点,然后介绍了年龄-龄期两性生命表各软件(TWOSEX-MSChart, CONSUME-MSChart, TIMING-MSChart)的主要用途,即预测种群的增长与防治适期、正确分析天敌的捕食率与害虫的取食量、预测天敌的种群增长与捕食潜能以及指导天敌的大量繁育。昆虫生命表作为一种强有力的分析技术,不仅在研究种群生态学和害虫治理方面已有广泛的应用,展望未来,这项技术还可以用于昆虫生理、抗药性、亚致死剂量、共生菌等方面的研究。     

Trends and dietary determinants of overweight and obesity in a multiethnic population

Objectives : To describe trends in BMI among different ethnic groups in Hawaii and to explore the relation of nutrient and food intake with excess weight. Research Methods and Procedures : We pooled demographic, anthropometric, and nutritional data derived from a detailed diet history for 159, 683 participants of 18 population‐based epidemiological studies conducted in Hawaii over a 25‐year period. The age‐adjusted prevalence of excess weight (BMI ≥ 25 kg/m²) was estimated for 5‐year intervals. To explore dietary determinants of excess weight, we computed odds ratios using logistic regression. Results : During the study period, the prevalence of excess weight increased considerably among all ethnic groups. Native Hawaiians had the highest and Asian Americans had the lowest prevalence of excess weight at all times. Although the percentage of calories consumed from carbohydrates increased, the percentage of calories from fat decreased over time. On an individual level, fat and protein consumption predicted a higher BMI, and dietary fiber intake predicted a lower BMI. Similarly, a higher consumption of meat, poultry, and fish was related to excess weight, whereas fruit and vegetable intake were inversely associated with excess weight. After stratification by ethnicity, the associations were not materially altered among women, but carbohydrates seemed to have a stronger association with excess weight among Native Hawaiian and Japanese men than among white men. Discussion : In this large ethnically diverse population, plant‐based foods and dietary fiber emerged as a potential protective factor against excess weight regardless of ethnicity.     

An interactive nonrandom-mating two-sex model whose intrinsic growth rate lies between one-sex rates.

In a recent paper, the author has presented an interactive two-sex model and applied it to the U.S. population, 1940–1971. While the model has removed many inconsistencies in the one-sex models for males and females, it has two major limitations. First, the model assumes random mating of men and women within their reproductive ages. Second, it gives an intrinsic growth rate that is not necessarily intermediate between the male and the female intrinsic growth rates, as obtained from the one-sex models. A new two-sex model is provided in this paper that removes both these limitations. The new model is applied to the U.S. population for the years 1940–1974.     

Exponential growth in age-structured two-sex populations

We consider a continuous age-structured two-sex population model which is given by a semilinear system of partial differential equations with nonlocal boundary conditions and is a simpler case of Fredrickson-Hoppensteadt model. The non-linearity is introduced by a source term, called from its physical meaning, the marriage function. The explicit form of the marriage function is not known; however, there is an understanding among the demographers about the properties it should satisfy. We have shown that the homogeneity property of the non-linearity leads to the fact that the system supports exponentially growing persistent solutions using a general form of the marriage function and its properties. This suggests that the model can be viewed as a possible extension of the one-sex stable population theory to monogamously mating two-sex populations.