Sex ratio evolution through group selection using diffusion approximation

We consider a haploid, hermaphrodite population subdivided into an infinite number of demes of finite size N. Assuming recurrent mutation, random union of gametes, partial dispersal, genetic drift, and incorporating group competition, a diffusion approximation is used to describe the evolution of sex ratio, corresponding to sex allocation to male versus female functions. The stationary distribution is deduced. In presence of group selection, a female-biased sex ratio in the whole population is found to be optimal in the sense that an allele coding for this sex ratio is always more frequent at equilibrium when segregating with another allele coding for a different sex ratio than for the same sex ratio. Numerical studies are presented to check the validity and accuracy of this prediction.Research supported in part by grants from NSERC of Canada and FCAR of Quebec. This work is part of the first authors Ph.D. thesis at the Université de Montréal under the supervision of the second author.Send offprint requests to: Sabin Lessard     

Threshold behaviour of a SIR epidemic model with age structure and immigration

We consider a SIR age-structured model with immigration of infectives in all epidemiological compartments; the population is assumed to be in demographic equilibrium between below-replacement fertility and immigration; the spread of the infection occurs through a general age-dependent kernel. We analyse the equations for steady states; because of immigration of infectives a steady state with a positive density of infectives always exists; however, a quasi-threshold theorem is proved, in the sense that, below the threshold, the density of infectives is close to 0, while it is away from 0, above the threshold; furthermore, conditions that guarantee uniqueness of steady states are obtained. Finally, we present some numerical examples, inspired by the Italian demographic situation, that illustrate the threshold-like behaviour, and other features of the stationary solutions and of the transient. Supported in part by FIRB project RBAU01K7M2 “Metodi dell’Analisi Matematica in Biologia, Medicina e Ambiente” of the Italian Ministero Istruzione Università e Ricerca     

Factors that affect fertility in a feral population of sheep

Feral livestock offer an excellent opportunity lo study factors affecting fertility as the physiology of their husbanded relatives is well known and social and environmental influences can be studied free of man's interference. This is so in the population of about 1250 sheep of the primitive Soay breed on the islands of St Kilda, Scotland. There is a high coincidence of oestrus amongst the ewes in mid November, and the breeding season is constant within a few days, from year to year. The breeding season in other British breeds of sheep demonstrates a strong correlation with latitude. On St Kilda, mortality rates in male sheep are higher than in females so that the ratio of rams to ewes at mating time is about 1:5. Competition amongst rams is intense. The optimal time for mating and the place of ram lambs in the social system are discussed.     

Effect of immigration on a chaotic insect population

Recently, the most convincing evidence of complex dynamics and chaos in biological populations has been presented for Tribolium castaneaum, a classic laboratory model insect. In this note, the robustness of this system is investigated and a constant immigration term is added to the adult population equation. It has been found that such perturbation to the model can either have a complicating effect (when the isolated system is periodic) or a simplifying one (when the system is chaotic in isolation).     

Branching stochastic processes with immigration in analysis of renewing cell populations

This paper considers the utility of a new class of stochastic branching processes with non-homogeneous immigration in modeling complex renewing cell systems. Such systems typically include the population of stem cells that provides an inexhaustible supply of cells necessary for maintaining the cellular composition of a tissue. A stem cell may be induced to transform (differentiate) into a progenitor cell. Progenitor cells retain the ability to proliferate and their function is believed to provide a quick proliferative response to an increased demand for cells in the population. There may be several sub-types of progenitor cells. Terminally differentiated cells do not divide under normal conditions; they are responsible for maintaining tissue-specific functions. Recent advancements in experimental techniques offer considerable scope for quantitative studies of in vivo cell kinetics based on stochastic modeling of renewing cell populations. However, no ready-made theory is currently available to take full advantage of these advancements. This paper introduces such a theory with a special focus on its feasibility in biological applications.     

Low fertility in humans as the evolutionary outcome of snowballing resource games

For decades, evolutionary biologists and anthropologists havepuzzled over the negative relationship that exists between wealthand fertility in humans. Particularly mystifying have been that(1) humans do not appear to translate their reproductive resourcesinto additional offspring, and (2) attempts to model naturalselection resulting in a negative relationship between amountof economic resources and fertility have all predicted the oppositerelationship. In this article, we use game theory to derivethe evolutionarily stable ratio of offspring investment versusresource generation when the continuing survival of offspringlineages is strongly affected by long-term resource accumulation.The model generates the prediction that fertility should belower when there are more resources available and when moreintensive investment in resource generation has the potentialto acutely increase the survival probability of descendant offspringlineages. This prediction provides a simple and general evolutionaryexplanation for why fertility negatively correlates with wealthboth within and between human populations. Indeed, this mayprovide a new understanding of low fertility in contemporaryhuman groups in addition to furthering our understanding thedemographic transition in general.     

Low twinning rate and seasonal effects on twinning in a fertile population,the Hutterites

This paper analyzes from the mid 18th century to 1987 the birth records of the Dariusleut, one of the three subgroups of the Hutterite population. The aim of this study is to describe several aspects of the twinning rate in a fertile population. The overall rate of twinning was 0.90%:103 twins among all 11492 maternities. The rate peaked at the 7th birth order and at the maternal age of 40 years and over. Until the mid 19th century when the Hutterites lived in Russia, the twinning rate was higher (1.5%), and it decreased during the migration period in the second half of the 19th century (0.7%). After the group had settled in the USA and Canada, the population maintained a twinning rate of 1.0% until 1965. After 1965 the rate decreased to 0.7%, partly due to a decline in fertility among women aged 30 years and over. There was a significant seasonal variation: the twinning rate decreased to 0.5% in May–July compared to 1.2% for the other three seasons during the years up to 1965 (P<0.01), while more recent mothers did not show such a seasonal variation. The incidence of twin births in this population seems to have been influenced by environmental factors, which would change their effect seasonally and secularly.     

Selection on floral traits through male fertility in a natural plant population

Most studies on selection in plants estimate female fitness components and neglect male mating success, although the latter might also be fundamental to understand adaptive evolution. Information from molecular genetic markers can be used to assess determinants of male mating success through parentage analyses. We estimated paternal selection gradients on floral traits in a large natural population of the herb Mimulus guttatus using a paternity probability model and maximum likelihood methods. This analysis revealed more significant selection gradients than a previous analysis based on regression of estimated male fertilities on floral traits. There were differences between results of univariate and multivariate analyses most likely due to the underlying covariance structure of the traits. Multivariate analysis, which corrects for the covariance structure of the traits, indicated that male mating success declined with distance from and depended on the direction to the mother plants. Moreover, there was directional selection for plants with fewer open flowers which have smaller corollas, a smaller anther–stigma separation, more red dots on the corolla and a larger fluctuating asymmetry therein. For most of these traits, however, there was also stabilizing selection indicating that there are intermediate optima for these traits. The large number of significant selection gradients in this study shows that even in relatively large natural populations where not all males can be sampled, it is possible to detect significant paternal selection gradients, and that such studies can give us valuable information required to better understand adaptive plant evolution. Second affiliation for Mark Van Kleunen is temporary until February 2007.     

Changing household composition,labor patterns,and fertility in a highland New Guinea population

The European demographic transition of the nineteenth century is often proposed as a model for demographic change in twentieth century developing nations, and economic development is seen as leading to an inevitable reduction in total fertility in these nations. This paper examines data from the Gainj of Papua New Guinea, a natural fertility population with very low reproductive output, and suggests that the effects of development on fertility change are much more complex than a simple demographic transition model would suggest. Looking at two variables known to contribute significantly to low total fertility among the Gainj, late age at first birth for women and long interbirth intervals, the paper suggests that households, in their recruitment and allocation of labor, may exert a mediating influence in the relationship between economic development and fertility.     

The Trojan female technique: a novel,effective and humane approach for pest population control

Humankind''s ongoing battle with pest species spans millennia. Pests cause or carry disease, damage or consume food crops and other resources, and drive global environmental change. Conventional approaches to pest management usually involve lethal control, but such approaches are costly, of varying efficiency and often have ethical issues. Thus, pest management via control of reproductive output is increasingly considered an optimal solution. One of the most successful such ‘fertility control’ strategies developed to date is the sterile male technique (SMT), in which large numbers of sterile males are released into a population each generation. However, this approach is time-consuming, labour-intensive and costly. We use mathematical models to test a new twist on the SMT, using maternally inherited mitochondrial (mtDNA) mutations that affect male, but not female reproductive fitness. ‘Trojan females’ carrying such mutations, and their female descendants, produce ‘sterile-male’-equivalents under natural conditions over multiple generations. We find that the Trojan female technique (TFT) has the potential to be a novel humane approach for pest control. Single large releases and relatively few small repeat releases of Trojan females both provided effective and persistent control within relatively few generations. Although greatest efficacy was predicted for high-turnover species, the additive nature of multiple releases made the TFT applicable to the full range of life histories modelled. The extensive conservation of mtDNA among eukaryotes suggests this approach could have broad utility for pest control.     

The impact of immigration on unemployment and earnings among racial minorities in the United States

The existing immigration literature presents inconsistencies and contradictions. Some studies suggest that immigration has no effect on the earnings and employment levels of native‐born minorities, while others offer contrary evidence. In an effort to make more progress, a study was done to examine the impact of immigration on unemployment and earnings among racial minorities in the US. Employing United States census data covering 1940 to 1980, and using states and a sample of metropolitan statistical areas as units of analysis, this study found that increases in immigration in some periods of US history had significant negative effects on employment levels among racial minorities in the United States. Specifically, results of the regression analysis showed that, in 1970, a standard deviation change in immigration increased unemployment among minorities by nearly 14 per cent, while in 1980 unemployment increased by nearly 10 per cent, given a standard deviation increase in immigration. With regard to earnings, the study found that immigration decreases minority income. In 1980 a one per cent increase in immigration reduced racial minority earnings, on average, by nearly $25.32. Analysis also showed that low skill levels among minorities, as well as family breakdown may in part be responsible for high minority unemployment and low earnings. For example, in 1980 a one per cent increase in divorce reduced minority earnings, on average, by $65.89. Low minority skill levels reduced earnings by $104 on average. However, the deleterious effects of immigration on racial minority unemployment and earnings remain even after adjusting for the potentially confounding effects of skill levels and divorce. Policy implications of the findings are discussed at length, and suggestions are proposed for future research.     

Surnames in Argentina: a population study through isonymy

In order to study the isonymic structure of Argentina, the surname distributions of 22.6 million electors registered for the year 2001 were analyzed in the 24 districts (distritos) and 541 municipalities (municipios) of the country. The number of different surnames found was 414,441. Matrices of isonymic distances between districts were constructed and tested for correlation with the geographic distance between the capital towns of the districts. We found that, for the whole of Argentina, Euclidean distance was correlated with the log of geographic distance (r=0.480+/- 0.067). A dendrogram of the 24 regions was built from the matrix of Euclidean distances, using the UPGMA method. The clusters identified by the dendrogram are coincident with conterminous geographical regions of the country. Random inbreeding calculated from isonymy, F(ST), was highest in La Rioja, Corrientes, and Santiago del Estero. It was lowest in the area of Buenos Aires and in the north-central region of Santa Fé. Average Fisher's alpha for municipalities was 358; for districts, it was 422; and for Argentina as a unit, it was 602. The geographical distribution of alpha in 541 municipalities, high in the east and lower in the west of the country, is compatible with the settlement in the 20th century of subsequent waves of immigrants moving from the North Atlantic coast toward the foot of the Andes and toward the south. The present structure of Argentina indicates that migration dominates over drift.     

Stability of stationary distributions in a space-dependent population growth process

We consider a spatial population growth process which is described by a reaction-diffusion equation c(x)u _t = (a ²(x)u _x ) _x +f(u), c(x) >0, a(x) > 0, defined on an interval [0, 1] of the spatial variable x. First we study the stability of nonconstant stationary solutions of this equation under Neumann boundary conditions. It is shown that any nonconstant stationary solution (if it exists) is unstable if a _xx0 for all x[0, 1], and conversely ifa _xx>0 for some x[0, 1], there exists a stable nonconstant stationary solution. Next we study the stability of stationary solutions under Dirichlet boundary conditions. We consider two types of stationary solutions, i.e., a solution u ₀(x) which satisfies u ₀ x0 for all x[0, 1] (type I) and a solution u ₀(x) which satisfies u _0x = 0 at two or more points in [0, 1] (type II). It is shown that any stationary solution of type I [type II] is stable [unstable] if a _xx 0 [a _xx 0] for all x[0, 1]. Conversely, there exists an unstable [a stable] stationary solution of type I [type II] if a _xx <0 [a _xx >0] for some x[0, 1].     

Intermediate variables in the explanation of differential fertility: Results of a village study in rural Java

A tendency for fertility to be higher among middle-class women than among lower-class women has been found in all the recent sources of data on fertility levels and patterns in Indonesia. After briefly reviewing these findings, this article presents the results of a community study in rural Java which systematically investigates the positive relation between fertility and socioeconomic status, focusing on the so- called intermediate variables (first inventoried by Davis and Blake in 1956) which directly determine fertility. Differential patterns of marital stability, secondary sterility, and the practice of postpartum abstinence in particular were found to contribute to the contrasts in fertility levels observed. The use of modern contraceptives, a recent innovation at the time of the study, was found to a greater extent among middle-class women, and may prove to be an important determinant of future patterns of fertility and fertility differentials.This article is based on a study of fertility patterns undertaken in Yogyakarta during 1972–1973. The research was funded by the Australian National University. A complete account of the research findings is contained in Hull (1975), and a detailed analysis of the topics discussed here can be found in Hull (1976).     

Regulation of differentiation in a population of cells interacting through a common pool

We consider a model of a suspension of a cell population in a well-mixed medium. There are two chemical substances, say A and H, reacting in each cell of the population and the substance H can only diffuse from the inside of cell to the medium or vice versa across the cell membrane. The medium is well mixed that the concentration of H is kept uniform over the medium. Cells interact indirectly with each other through the medium. The differential equations governing the dynamics of the suspension are analyzed using standard techniques for differential equations. It is shown that the cell population divides into several groups in respect of the chemical concentrations as time elapses. It is also shown how the fraction of the number of cells belonging to each subgroup to the total number of cells is regulated. The results may be used to explain the mechanism for differentiation of multi-cellular organisms.     

High fertility in a Peruvian Amazon Indian village

The relation between fertility and cultural change in a Peruvian Amazon Indian village was studied initially in 1964 and in more detail in 1969. The 1969 study included observations concerning social, economic, environmental, cultural, and health changes. Population growth in the village is nearly 5% per year, and fertility appears to exceed that previously recorded for other groups. The factors that may be contributing to the high fertility are explored. They are thought to include early and prolonged parity, nearly universal marriage and fertility, high reproductive efficiency, short birth intervals, Western health intervention lowering both infant and maternal mortality rates, and a decline in the prevalence of polygyny.Presented at the 99th annual meeting of the American Public Health Association, Minneapolis, Minnesota, October 13, 1971. The project upon which this publication is based is supported by Bureau of Health Services Training Grant #8-TO1OHSOO17-04.