The effective population size of some age-structured populations

It was shown in a previous paper that if generations are discrete, then the effective population size of a large population can be derived from the theory of multitype branching processes. It turns out to be proportional to the reciprocal of a term that appears in the denominator of expressions for survival probabilities when there is a supercritical positively regular branching process for which the dominant positive eigenvalue of the first moment matrix is slightly larger than 1. If there is an age-structured population with unchanging proportions among sexes and age groups, then the effective population size is shown to be also obtainable from the theory of multitype branching processes. The expression for this parameter has the same form as in the corresponding model for discrete generations, multiplied by an appropriate measure of the average length of a generation. Results are obtained for dioecious random mating populations, populations reproducing partly by selfing, and populations reproducing partly by full-sib mating.     

Kin selection is implicated in partial sib-mating populations with constant viability differences before mating

The change in the frequency of a rare mutant allele under constant sex-differentiated viability selection in an infinite, partial full-sib mating population is studied. The diplo-diploid and haplo-diploid polygynous models are considered with a Poisson distribution for the number of offspring produced by every mated female. Reproduction is followed by weak selection among the offspring and then mating to form the next generation. It is shown that the rate of change with respect to the frequency of the mutant allele and the intensity of selection can be expressed in terms of costs or benefits of substituting the mutant type for the wild type, which correspond to average excesses in viability in females and males, multiplied by coefficients of relatedness to the individuals affected by such a substitution and reproductive values associated to the sexes of these individuals. This reveals hidden interactions between mated individuals and between males for mating, the former having positive effects on the reproductive success of related individuals and the latter having negative effects. Such interactions are the result of reproductive constraints when a fixed proportion of females must mate with a male sib and all females are fertilized as long as one mate is available. However, they affect the change in allele frequency because there is inbreeding or relatedness between mates and more generally relatedness between interacting individuals. Surprisingly, the effects of these interactions cancel out in a diploid population when the number of offspring is large enough so that the possibility for a female to have no male sib to mate with can be neglected and the viability differences are the same in both sexes.     

Fixation probabilities and effective population numbers in diploid populations with overlapping generations

A finite diploid population, observed at times t = 0, 1, 2,…, is studied. An individual is said to be in age group i at time t if its age is between i and i + 1 units at that time, where i ? 1. It is assumed that the number of individuals in a particular age-sex class is the same for every t and that the probability that a male offspring was produced by a mating of a male in age group i and a female in age group j is p_ij^m (with a corresponding probability p^f_ij for a female offspring), regardless of when the individual is born. The probability of ultimate fixation of an allele A₁ and the inbreeding effective number, for large populations, is calculated under the further assumptions that A₁ is neutral and that mating is random, given the ages of the mates.     

中国怒江片马地区怒江金丝猴种群动态及社会组织初探

2011 年10 月至2013 年10 月在云南高黎贡山自然保护区泸水县片马镇地区对一群怒江金丝猴的社会组织进行研究,基于野外实地记录与获得的视频资料统计猴群的个体数量,研究群数量初步估计为100 只。根据体型、毛色及是否携带婴猴等特征来划分所有个体的性别年龄组,依据单元内个体通过林窗时移动的时间间隔比单元间短的原则来划分不同繁殖单元及全雄群。所有视频中共发现22 个一雄多雌单元(OMU) 和1 个全雄群(AMU),因此怒江金丝猴的社会组织与其他金丝猴物种相似,由多个一雄多雌及其后代组成繁殖单元(OMUs)与雄性个体组成全雄群(AMU)组成重层社(Modular society);另外基于GPS 位点初步确定猴群活动的海拔范围为1 900 - 3 700 m,猴群生境面积约为12 km² ,初步获得猴群的密度为8 只/ km² ,比缅甸的种群密度(1 只/ km² )大得多。基于种群性别年龄计算种群动态参数,雄雌比为1∶ 2.1, 婴雌比为1∶ 4. 7,成幼比为2.5∶ 1。与滇金丝猴种群相比,该种群有很低的婴雌比和很高的成幼比。     

The effective number of a population that varies cyclically in size. II. Overlapping generations

We consider haploid and dioecious age-structured populations that vary over time in cycles of length k. Results are obtained for both autosomal and sex-linked loci if the population is dioecious. It is assumed that k is small in comparison with numbers of haploid individuals (or of numbers of males and females) in any generation of a cycle. The inbreeding effective population size N(e) is then approximately given by the expression [T summation operator (k-1)(j=0)1/[N(e)(j)T(j)]](-1), where N(e)(j) and T(j) are, respectively, the effective population size and generation interval that would hold if the population was at all times generated in the same way as at time j. The constant T, which is the effective overall generation interval, is defined to be k times the harmonic mean of the quantities T(j). Our expressions for T and N(e), in terms of N(e)(j) and T(j), are general, but the N(e)(j)s are derived under the assumption that offspring are produced according to Poisson distributions.     

Aging and nonlinear heart rate control in a healthy population

In recent years more studies are using nonlinear dynamics to describe cardiovascular control. Because of the large dispersion of physiological data, it is important to have large studies with both male and female participants to establish a range of physiological healthy values. This study investigated the effect of gender and age on nonlinear indexes. Nonlinear scaling properties were studied by using 1/f slope (where f is frequency), fractal dimension, and detrended fluctuation analysis short- and long-term correlations (DFAalpha(1) and DFAalpha(2), respectively). Nonlinear complexity was described with correlation dimension (CD), Lyapunov exponent (LE), and approximate entropy (ApEn). The population consisted of 135 women and 141 men (age, 18-71 yr). Twenty-four hour ECG recordings were obtained by using Holter monitoring. The recordings were split into daytime (8 AM-9 PM) and nighttime (11 PM-6 AM). A day-night variation was present in all nonlinear heart rate variability (HRV) indexes, except for the CD in the female population. During the night the percentage of CD values of surrogate data files differing from the CD value of the original data increased. All nonlinear indexes were significantly correlated with age. Deeper analysis per age category of 10 yr showed a stabilization in the age decline of the fractal dimension and ApEn at the age of > or =40 yr. The vagal pathways seemed to be more involved in the generation of nonlinear fluctuations. Higher nonlinear behavior was evident during the night. No clear difference between men and women was found in the nonlinear indexes. Nonlinear indexes decline with age. This can be related to the concept of decreasing autonomic modulation with advancing age.     

An age-related decrease in factor V Leiden frequency among Polish subjects

Factor V Leiden (G1691AFV mutation) is a widely acknowledged risk factor of deep vein thrombosis, including pulmonary embolism as the most serious complication. However, its high prevalence of ∼5% in the Caucasian population might be related to an unknown evolutionary advantage. It might exert a beneficial effect on the carrier, e. g. protecting women from excessive bleeding during labour or allowing increased survival in severe sepsis or with other inflammatory diseases. The aim of our study was to verify or contradict the hypothesis of a favourable association between the A allele (A1691) and longevity in the Polish population. For this purpose, the G1691A mutation was analyzed by PCR-RFLP in 1016 Poles: 400 neonates (187 female and 312 male), 184 healthy adults (129 female and 55 male), and 432 long-lived individuals (age ≥ 95 years: 343 women and 89 men). Frequencies of G1691A carriers and the A1691 allele in long-lived individuals (0.2% and 0.1%, respectively) were significantly lower than in neonates (4.2% and 2.2%, respectively) and adults (3.3% and 1.6%). The frequency of the G1691A factor V Leiden mutation decreased with age, which indicates a shorter survival time among A1691 allele carriers in the Polish population.     

Study of a single BRCA2 mutation with high carrier frequency in a small population.

Germ-line changes in the cancer-predisposition gene BRCA2 are found in a small proportion of breast cancers. Mutations in the BRCA2 gene have been studied mainly in families with high risk of breast cancer in females, and male breast cancer also has been associated with BRCA2 mutations. The importance of germ-line BRCA2 mutations in individuals without a family history of breast cancer is unknown. The same BRCA2 mutation has been found in 16/21 Icelandic breast cancer families, indicating a founder effect. We determined the frequency of this mutation, 999del5, in 1,182 Icelanders, comprising 520 randomly selected individuals from the population and a series of 632 female breast cancer patients (61.4% of patients diagnosed during the study period) and all male breast cancer patients diagnosed during the past 40 years. We detected the 999del5 germ-line mutation in 0.6% of the population, in 7.7% of female breast cancer patients, and in 40% of males with breast cancer. The mutation was strongly associated with onset of female breast cancer at age <50 years, but its penetrance and expression are varied. A number of cancers other than breast cancer were found to be increased in relatives of mutation carriers, including those with prostate and pancreatic cancer. Furthermore, germ-line BRCA2 mutation can be present without a strong family history of breast cancer. Comparison of the age at onset for mother/daughter pairs with the 999del5 mutation and breast cancer indicates that age at onset is decreasing in the younger generation. Increase in breast cancer incidence and lower age at onset suggest a possible contributing environmental factor.     

Modelling the population consequences of age- and sex-related differences in winter mortality in the oystercatcher, Haematopus ostralegus

A modelling approach is used to explore the effect of age and sex differences in oystercatcher ( Haematopus ostralegus ) winter mortality on population size, population structure and the population response to habitat loss or change. Increasing the mortality of first and second year birds reduced population size, but had very little effect on the proportion of the population that were adults. Increasing female mortality reduced population size and resulted in a male-biased population. A sex bias amongst birds of breeding age meant that there were fewer potential breeding pairs for a given population size, reducing the size of the breeding population and the breeding output. Increasing the mortality of one sex relative to the other reduced population size, even when mean adult mortality rates remained unchanged. Increasing the strength of density-dependent mortality in young birds caused a greater reduction in population size as habitat was lost. Increasing the strength of female density-dependent mortality had the same effect, even though male density-dependent mortality had been correspondingly reduced. Increasing density-independent or density-dependent winter mortality in one sex relative to another also exaggerated the disproportional effect of winter habitat loss on separate breeding subpopulations using the same overwintering area. These results suggest that any study of population dynamics should be aware of both age and sex differences in mortality. Conservationists should be particularly aware of any age or sex differences in diet or habitat use that may result in a differential response to environmental change.     

Effect of sex hormones on plasma T-kininogen in the rat

The influence of sex hormones on rat plasma T-kininogen concentration was examined. The level of T-kininogen in the post-pubertal female rat is about 3-times that of the male animal. Female rats castrated as adults or 15 days after birth, had low T-kininogen concentrations, near those of male rats. In contrast, castration of mature or immature male animals induced no change in T-kininogen. Treatment of castrated female or male rats with 17 alpha-ethinylestradiol significantly increased the T-kininogen level, whereas administration of testosterone or progesterone had no effect. The influence of estrogen was specific for T-kininogen, since plasma HMW kininogen concentration was the same in male and female rats and was not affected by castration or sex hormone treatment. T-kininogen concentration was not significantly changed in pregnant rat between the 12th and the 20th day of pregnancy, but increased after parturition. It was high in the newborn rat at birth and then decreased similarly over the next 3 weeks in males and females. It continued to decrease in the males, reaching the level of the adult rat, but it increased in the female from 3-4 weeks of age and reached the adult level at about 6-8 weeks. These data indicate that natural estrogens have a physiological influence on the plasma level of T-kininogen in female rats whereas testosterone had no effect on either male or castrated female rats. HMW kininogen is not physiologically dependent on sex hormones.     

Mate‐choice copying: A fitness‐enhancing behavior that evolves by indirect selection

A spatially explicit, individual‐based simulation model is used to study the spread of an allele for mate‐choice copying (MCC) through horizontal cultural transmission when female innate preferences do or do not coevolve with a male viability‐increasing trait. Evolution of MCC is unlikely when innate female preferences coevolve with the trait, as copier females cannot express a higher preference than noncopier females for high‐fitness males. However, if a genetic polymorphism for innate preference persists in the population, MCC can evolve by indirect selection through hitchhiking: the copying allele hitchhikes on the male trait. MCC can be an adaptive behavior—that is, a behavior that increases a population's average fitness relative to populations without MCC—even though the copying allele itself may be neutral or mildly deleterious.     

Screen detected high blood pressure under 40: a general practice population followed up for 21 years.

OBJECTIVE--To assess hypertension detected under 40 in a general practice population. DESIGN--Prospective case-control study. SETTING AND SUBJECTS--Former coal mining community in south Wales. Systematic case finding for hypertension and associated risk factors applied to a mean total population of 1945 from age 20 on a five year cycle through 21 years. Mean population aged 20-39, 227 men and 213 women. Case criteria: age < 40 and mean systolic pressure > or = 160 mm Hg or diastolic pressure > or = 100 mm Hg. Age and sex matched controls randomly sampled from the same population. MAIN OUTCOME MEASURES--Mean initial pressures and pressures at follow up in 1989 or preceding death, and all cardiovascular events. RESULTS--25 men and 16 women met criteria. Estimated five yearly inceptions were 26/1000 for men and 18/1000 for women. Male group mean initial blood pressure was 164/110 mm Hg for cases, falling to 148/89 mm Hg at follow up. Five male cases died at mean age 47.8, compared with two controls at 49.5. Female group mean initial pressure was 172/107 mm Hg for cases, falling to 145/86 mm Hg at follow up. One female case died aged 50, no controls. 10 male cases had non-fatal cardiovascular events at mean age 40.2, compared with two controls at mean age 50.5. Four female cases had non-fatal events at mean age 47.2, compared with one control aged 58. Male differences were statistically significant. CONCLUSIONS--Hypertension under 40 is dangerous, commoner in men than women, rarely secondary to classic causes, and may be controlled in general practice on a whole community basis.     

Coalescent theory for a completely random mating monoecious population

Consider a large random mating monoecious diploid population that has N individuals in each generation. Let us assume that at time 0 a random sample of ninfinity. It is then possible to obtain a generalization of coalescent theory for haploid populations if the distribution of G1 has a finite second moment and E[G(1)(3)]/N-->0 as N-->infinity.     

Sexual size dimorphism in species with asymptotic growth after maturity

If animals mature at small sizes and then grow to larger asymptotic sizes, many factors can affect male and female size distributions. Standard growth equations can be used to study the processes affecting sexual size dimorphism in species with asymptotic growth after maturity. This paper first outlines the effects of sex differences in growth and maturation patterns on the direction and degree of sexual dimorphism. The next section considers the effects of variation in age structure or growth rates on adult body sizes and sexual size dimorphism. Field data from a crustacean, fish, lizard and mammal show how information on a species' growth and maturation patterns can be used to predict the relationships between male size, female size and sexual size dimorphism expected if a series of samples from the same population simply differed with respect to their ages or growth rates. The last section considers ecological or behavioural factors with different effects on the growth, maturation, survival or movement patterns of the two sexes. This study supports earlier suggestions that information on growth and maturation patterns may be useful, if not essential, for comparative studies of sexual size dimorphism in taxa with asymptotic growth after maturity.     

Sperm competition and the dynamics of X chromosome drive: stability and extinction

Several empirical studies of sperm competition in populations polymorphic for a driving X chromosome have revealed that Sex-ratio males (those carrying a driving X) are at a disadvantage relative to Standard males. Because the frequency of the driving X chromosome determines the population-level sex ratio and thus alters male and female mating rates, the evolutionary consequences of sperm competition for sex chromosome meiotic drive are subtle. As the SR allele increases in frequency, the ratio of females to males also increases, causing an increase in the male mating rate and a decrease in the female mating rate. While the former change may exacerbate the disadvantage of Sex-ratio males during sperm competition, the latter change decreases the incidence of sperm competition within the population. We analyze a model of the effects of sperm competition on a driving X chromosome and show that these opposing trends in male and female mating rates can result in two coexisting locally stable equilibria, one corresponding to a balanced polymorphism of the SR and ST alleles and the second to fixation of the ST allele. Stochastic fluctuations of either the population sex ratio or the SR frequency can then drive the population away from the balanced polymorphism and into the basin of attraction for the second equilibrium, resulting in fixation of the SR allele and extinction of the population.     

Prevalence of coagulation factor II G20210A and factor V G1691A Leiden polymorphisms in Chechans, a genetically isolated population in Jordan

Background Coagulation factor II G20210A and coagulation factor V (Leiden) G1691A single nucleotide polymorphisms (SNPs) are major inherited risk factors of venous thromboembolism. In view of the heterogeneity in their world distribution and lack of sufficient information about their distribution among Chechans, we addressed the prevalence of these SNPs in the Chechan population in Jordan, a genetically isolated population. Methods and Results factor II G20210A and factor V Leiden SNPs were analysed by polymerase chain reaction and restriction fragment length polymorphism (PCR?CRFLP) method and Amplification refractory mutation detection system (ARMS) respectively in 120 random unrelated subjects from the Chechan population in Jordan. Among the subjects studied for factor II G20210A mutation there were three individuals carrying this mutation as heterozygous (one female and two male), giving a prevalence of 2.5?% and an allele frequency of 1.25?%. No homozygous factor II allele was found. Factor V Leiden G1691A mutation was detected as heterozygous in 22 of 120 of individuals (17 female and five male) indicating a prevalence of 18.3?% and allele frequency of 9.2?%. No homozygous allele was found. Conclusion Our results indicated that prevalence of factor II G20210A mutation in the Chechan population is similar to prevalence in Jordan and Caucasian populations (1?C6?%) while the prevalence of factor V Leiden was higher in the Chechan population compared to Jordan and Caucasian populations (2?C15?%).     

Polymorphism of trinucleotide CAG-repeats of the first exon of the androgen receptor gene in the Tomsk population

Polymorphism of the CAG repeat of exon 1 of the androgen receptor (AR) gene was analyzed in the Tomsk population. In total, 12 alleles varying in size from 285 to 318 bp (21-32 CAG units) were revealed. The allele frequency distribution did not differ from the normal one. No difference in allele frequencies was detected between men and women of the same generation. The observed heterozygosity was equal to the expected one (0.88 +/- 0.03). Compared with other populations, the Tomsk population displayed a narrower allele spectrum and a bias of the most common allele to a greater repeat number. The results obtained may reflect specific population genetic processes characteristic of young developing populations.     

Disequilibrium mapping of a quantitative-trait locus in an expanding population.

Linkage disequilibrium (LD) mapping can be successful if there is strong nonrandom association between marker alleles and an allele affecting a trait of interest. The principles of LD mapping of dichotomous traits are well understood, but less is known about LD mapping of a quantitative-trait locus (QTL). It is shown in this report that selective genotyping can increase the power to detect and map a rare allele of large effect at a QTL. Two statistical tests of the association between an allele and a quantitative character are proposed. These tests are approximately independent, so information from them can be combined. Analytic theory is developed to show that these two tests are effective in detecting the presence of a low-frequency allele with a relatively large effect on the character when the QTL is either already a candidate locus or closely linked to a marker locus that is in strong LD with the QTL. The latter situation is expected in a rapidly growing population in which the allele of large effect was present initially in one copy. Therefore, the proposed tests are useful under the same conditions as those for successful LD mapping of a dichotomous trait or disease. Simulations show that, for detection of the presence of a QTL, these tests are more powerful than a simple t-test. The tests also provide a basis for defining a measure of association, gamma, between a low-frequency allele at a putative QTL and a low-frequency allele at a marker locus.     

Pest control by genetic manipulation of sex ratio

We model the release of insects carrying an allele at multiple loci that shifts sex ratios in favor of males. We model two approaches to sex ratio alteration. In the first (denoted SD), meiotic segregation (or sperm fertility) is distorted in favor of gametes carrying the male-determining genetic element (e.g., Y-chromosome). It is assumed that any male carrying at least one copy of the SD allele produces only genotypically male offspring. In the second approach (denoted PM), the inserted allele alters sex ratio by causing genetically female individuals to become phenotypically male. It is assumed that any insect carrying at least one copy of the PM allele is phenotypically male. Both approaches reduce future population growth by reducing the number of phenotypic females. The models allow variation in the number of loci used in the release, the size of the release, and the negative fitness effect caused by insertion of each sex ratio altering allele. We show that such releases may be at least 2 orders of magnitude more effective than sterile male releases (SIT) in terms of numbers of surviving insects. For example, a single SD release with two released insects for every wild insect and a 5% fitness cost per inserted allele could reduce the target population to 1/1000th of the no-release population size, whereas a similar-sized SIT release would only reduce the population to one-fifth of its original size. We also compare these two sex ratio alteration approaches to a female-killing (FK) system and the sterile male technique when there are repeated releases over a number of generations. In these comparisons, the SD approach is the most efficient with equivalent pest suppression achieved by release of approximately 1 SD, 1.5-20 PM, 2-70 FK, and 16-3,000 SIT insects, depending on conditions. We also calculate the optimal number of SD and PM allele insertions to be used under various conditions, assuming that there is an additional genetic load incurred for each allelic insertion.     

Studies on Rhabdionvirus oryctes: III. Incidence in the Oryctes rhinoceros population of Western Samoa

The viral pathogen Rhabdionvirus oryctes [ROV] was found to be widespread in the population of Oryctes rhinoceros in Western Samoa. About 3% of the larvae and 35% of the adults were infected with ROV. Larval breeding sites more frequently contained ROV-infected insects if the sites were occupied by two broods instead of one and if there was a high density of breeding in the area. Females infected with ROV visited the breeding sites less frequently for egg-laying than healthy females. The male adults, as they increased in age, were found to be more frequently infected with ROV, but the young female adults were more frequently infected than very young or old females. The ROV-infections in adults apparently play a more important role in suppressing the O. rhinoceros population than those of larvae.