Evolution of senescence: Natural increase of populations displaying gompertz- or power-law death rates and constant or age-dependent maternity rates

Several hypothetical populations which differ in degrees of senescence are compared with respect to their rates of natural increase. The rate of natural increase is employed as a measure of selective advantage. The populations are characterized by their maternity and death rates, expressed as functions of age. Maternity rates are described by constant or quasi-human, age-dependent functions. Death rates are described by constant, Gompertzian (exponential) or power functions. Longevity functions, representing the probability of survival to a specific age, are obtained by integrating the death rate functions. The degree of senescence of a population is measured by the rapidity of ascent of its death-rate function or by the rectangularity of its longevity function. The increase in death rate late in life which constitutes senescence is compensated by a decrease in death rate early in life. The balance between the two changes in rate is, by assumption, such that the mean value of the longevity function is independent of the degree of senescence. This assumption makes it possible to separate the effects produced by the evolution of senescence from those caused by changes in longevity.The rate of natural increase is obtained by numerical solution of an integral characteristic equation. The results show that senescence is advantageous in all populations except those in which the maternity function is constant and the size is declining at a rapid rate. When the parameters entering into the longevity functions have values such that the functions approximate human longevity data, the improvement in the rate of natural increase resulting from senescence closely approaches limiting values obtained with the use of a precisely rectangular longevity function. Other results support the observation that reproduction at an early age confers greater selective advantage than equivalent reproduction later in life.     

The effect of pharmaceutical innovation on longevity: Evidence from the U.S. and 26 high-income countries

This study examines the impact that pharmaceutical innovation, which accounts for most private biomedical research expenditure, has had on longevity. We perform two types of two-way fixed-effects analyses, which control for the effects of many potentially confounding variables. First, we analyze long-run (2006–2018) changes in longevity associated with different diseases in a single country: the U.S. Then, we analyze relative longevity levels associated with different diseases in 26 high-income countries during a single time period (2006–2016). The measure of longevity we analyze, mean age at time of death, is strongly positively correlated across countries with life expectancy at birth. The measure of pharmaceutical innovation we use is the mean vintage (year of initial world launch) of the drugs used to treat each disease in each country. Changes in the vintage distribution of drugs are due to both entry of new drugs and exit of old drugs. Our analysis of U.S. data indicates that the diseases for which there were larger increases in drug vintage tended to have larger increases in the longevity of Americans of all races and both sexes. In other words, the lower the mean age of the drugs, the higher the mean age at death. We test, and are unable to reject, the “parallel trends” hypothesis. We estimate that the 2006–2018 increase in drug vintage increased the mean age at death of Americans by about 6 months (66% of the observed increase). Controlling for sex, race, and education has only a small effect on the estimate of the vintage coefficient. The estimates indicate that drug vintage did not have a significant effect on the mean age at death of decedents with less than 9 years of education. Drug vintage had a positive and significant effect on the mean age at death of decedents with at least 9 years of education, and a larger effect on the mean age at death of decedents with at least 13 years of education. The finding that pharmaceutical innovation has a larger effect on the longevity of people with more education is consistent with previous evidence that more educated people are more likely to use newer drugs. Our analysis of data on 26 high-income countries indicates that the higher the vintage of drugs available to treat a disease in a country, the higher mean age at death was, controlling for fixed disease and country effects. The increase in drug vintage is estimated to have increased mean age at death in the 26 countries by 1.23 years between 2006 and 2016—73% of the observed increase. We obtain estimates of the cost of pharmaceutical innovation—its impact on drug expenditure—as well as estimates of an important benefit of pharmaceutical innovation—the number of life-years gained from it—and of their ratio, i.e., the incremental cost-effectiveness ratio. Estimates of the cost per life-year gained for the U.S. and the 26 countries are $35,817 and $13,904, respectively. Both figures are well below per capita GDP in the respective regions, suggesting that, overall, pharmaceutical innovation was highly cost-effective.     

On the role of aging in cancer incidence

All tumors classified by the Connecticut Tumor Registry which had a single peak incidence at age greater than 50 were found to have similar patterns of incidence as a function of age. The average of all such patterns was described by an equation of the form log incidence = m(age) + b, where m and b are constants. This equation suggests that the tumors in this study could all be related to a common physiological property such that the number of tumors in the population described the status of this property and the status of this property determined the number of tumors. A similar equation describes the incidence of death from all causes as a function of age. We suggest that the incidence of both cancer and death in general are related to a common physiological property and that this property is the integrity of the genome.     

延迟交配对橘小实蝇繁殖适度的影响

橘小实蝇Bactrocera dorsalis Hendel是一种世界性的入侵害虫,严重为害多种经济果蔬。本文通过响应面分析方法,研究了延迟交配对橘小实蝇交配率、产卵量、孵化率和寿命的影响。结果表明,交配率随雌虫交配日龄的延迟先增后减,雌、雄成虫均为35日龄处理组中的交配率最高,为81.00%±2.00%;而雄虫交配日龄的延迟则对其卵孵化率有明显的负面作用,在56日龄雄虫与35日龄雌虫处理组中,其卵孵化率最低,仅为27.56%±4.55%。雌成虫产卵量和寿命受到雌、雄虫双方交配日龄的的影响,产卵量（y）与雄虫日龄（x1）和雌虫日龄（x2）的回归方程为y=514.36+3.08x1-11.05x2,雌成虫寿命（y）与雄虫日龄（x1）和雌虫日龄（x2）的回归方程为y=35.85+0.23x1+0.40x2。研究结果为田间使用性信息素迷向法防治橘小实蝇提供了理论依据。     

Influences of Root Diameter, Tree Age, Soil Depth and Season on Fine Root Survivorship in Prunus avium

The rapid turnover of the fine root system is a major pathway of carbon and nutrient flow from plant to soil in forest ecosystems. In order to quantify these fluxes there is a need to understand how fine root demography is influenced by edaphic, environmental and plant ontogenetic factors. We studied the influence of four major factors (season, depth, root diameter and tree age) on the survivorship and longevity of fine roots of Prunus avium L. (wild cherry) over two years in North East Scotland. Survival analysis of data derived from minirhizotron observations showed that, for the range of root diameters studied, an increase in root diameter of 0.1 mm was associated with a 16% decrease in the risk of death. Depth was also an important factor; roots present at a depth of 10 cm had significantly lower survivorship than did roots at all lower depths studied. The effects of tree age and season on root production were more complex. Roots of old trees were more likely to die in the spring and roots of young trees were more likely to die in the autumn. Our data illustrate the complex factors that must be taken into account when scaling up information from individual observations of root longevity to model the contribution of fine roots to C and nutrient fluxes in forest ecosystems.     

Study on Age and Bunch Structure of Four Stipa Species in Inner Mongolia Plateau

The age status of four Stipa L. species, S. baicalensis Roshev., S. grandis P. Smim., S. krylovii Roshev., and S. klemenzii Roshev. in Inner Mongolia plateau was analyzed using a transect sampling method. The ontogeny of Stipa species was divided into five stages: the seedling, juvenile, reproductive, presenile, and senile. Dynamics of the population age speetra were determined mainly by the appearance of new individuals and their death rate. The survival rate of the seedlings was very low while that of file adults was high. The considerable longevity of bunch life allowed the old individuals to accumulate in the population. Both S. grandis and S. krylovii had higher proportion of seedlings than others. The proportion of the juveniles and the reproductives in the population decreased from S. baicalensis community to S. klemenzii community, but the old individuals including the preseniles and the seniles showed a reverse pattern. The aging process occurred in bunch level was characterized by the fragmentation of bunch and the within-bunch- self-thinning of the tillers. The process of within-bunch-self-thinning can be described by power equation Y: aXb. Meanwhile as a response to enviroument changes especially to the fluctuation of annual precipitation and its seasonal distribution both the numbers of reproductive shoots and vegetative shoot mass within a bunch were variable.     

内蒙古高原四种针茅种群年龄与株丛结构的研究

用样带法调查了内蒙古高原4种针茅(StipaL.)的年龄结构,并将其年龄划分为5个阶段:幼苗、幼龄、成年、老龄前期和老龄期。结果表明:幼苗对种群年龄结构和动态有较大的影响,针茅幼苗的存活率通常很低,而成年株丛的存活率较高,株丛的实际寿命很长,老龄株丛在种群中占有较大的比例。4种针茅中大针茅(S.grandisP.Smirn.)和克氏针茅(S.kryloviiRoshev.)的幼苗比例较高,从贝加尔针茅(S.baicalensisRoshev.)群落到小针茅(S.klemenziiRoshev.)群落种群中幼龄和成年株丛比例呈下降的趋势,而老龄株丛比例呈增加的趋势;针茅属植物在株丛水平上的动态主要表现为株丛的破碎与枝条自疏过程,以及株丛生殖枝数量和营养枝生物量的波动,幂函数模型Y=aXb可以对株丛的枝条自疏过程进行定量描述     

Genetics of healthy aging and longevity

Longevity and healthy aging are among the most complex phenotypes studied to date. The heritability of age at death in adulthood is approximately 25 %. Studies of exceptionally long-lived individuals show that heritability is greatest at the oldest ages. Linkage studies of exceptionally long-lived families now support a longevity locus on chromosome 3; other putative longevity loci differ between studies. Candidate gene studies have identified variants at APOE and FOXO3A associated with longevity; other genes show inconsistent results. Genome-wide association scans (GWAS) of centenarians vs. younger controls reveal only APOE as achieving genome-wide significance (GWS); however, analyses of combinations of SNPs or genes represented among associations that do not reach GWS have identified pathways and signatures that converge upon genes and biological processes related to aging. The impact of these SNPs, which may exert joint effects, may be obscured by gene-environment interactions or inter-ethnic differences. GWAS and whole genome sequencing data both show that the risk alleles defined by GWAS of common complex diseases are, perhaps surprisingly, found in long-lived individuals, who may tolerate them by means of protective genetic factors. Such protective factors may ‘buffer’ the effects of specific risk alleles. Rare alleles are also likely to contribute to healthy aging and longevity. Epigenetics is quickly emerging as a critical aspect of aging and longevity. Centenarians delay age-related methylation changes, and they can pass this methylation preservation ability on to their offspring. Non-genetic factors, particularly lifestyle, clearly affect the development of age-related diseases and affect health and lifespan in the general population. To fully understand the desirable phenotypes of healthy aging and longevity, it will be necessary to examine whole genome data from large numbers of healthy long-lived individuals to look simultaneously at both common and rare alleles, with impeccable control for population stratification and consideration of non-genetic factors such as environment.     

Exploring mechanisms of sex differences in longevity: lifetime ovary exposure and exceptional longevity in dogs

To move closer to understanding the mechanistic underpinnings of sex differences in human longevity, we studied pet dogs to determine whether lifetime duration of ovary exposure was associated with exceptional longevity. This hypothesis was tested by collecting and analyzing lifetime medical histories, age at death, and cause of death for a cohort of canine ‘centenarians’– exceptionally long‐lived Rottweiler dogs that lived more than 30% longer than average life expectancy for the breed. Sex and lifetime ovary exposure in the oldest‐old Rottweilers (age at death, ≥ 13 years) were compared to a cohort of Rottweilers that had usual longevity (age at death, 8.0–10.8 years). Like women, female dogs were more likely than males to achieve exceptional longevity (OR, 95% CI = 2.0, 1.2–3.3; P = 0.006). However, removal of ovaries during the first 4 years of life erased the female survival advantage. In females, a strong positive association between ovaries and longevity persisted in multivariate analysis that considered other factors, such as height, body weight, and mother with exceptional longevity. A beneficial effect of ovaries on longevity in females could not be attributed to resistance against a particular disease or major cause of death. Our results document in dogs a female sex advantage for achieving exceptional longevity and show that lifetime ovary exposure, a factor not previously evaluated in women, is associated with exceptional longevity. This work introduces a conceptual framework for designing additional studies in pet dogs to define the ovary‐sensitive biological processes that promote healthy human longevity.     

Intergenerational and Genealogical Approaches for the Study of Longevity in the Saguenay-Lac-St-Jean Population

The mechanisms of longevity have been the subject of investigations for a number of years. Although the role of genetic factors is generally acknowledged, important questions persist regarding the relative impact of environmental exposures, lifestyle characteristics, and genes. The BALSAC population register offers a unique opportunity to study longevity from an intergenerational and genealogical point of view. Individuals from the Saguenay-Lac-St-Jean population who died at age 90 or older between 1950 and 1974 were selected from this database (n?=?576), along with a control group of individuals born in the same period who died between 50 and 75 years of age. For these subjects and controls, spouses’ ages at death and parental ages at death and at their birth were investigated using regression analysis. Genealogical reconstructions were carried out for each individual, and various analyses were performed on both groups. Both fathers’ and mothers’ mean ages at death were significantly higher among the longer-lived cases than among controls whereas spouses’ ages at death and parental ages at birth had no effect. Regression analysis confirmed the positive effect of both fathers’ and mothers’ age at death. Mean kinship coefficients for the parents’ generations displayed significant differences, indicating that kinship was higher among subjects than controls (this effect was stronger among the oldest 10% of the subjects). Frequencies and genetic contributions of ancestors were very similar for the two groups, and none of these ancestors appeared more likely to have introduced genetic variants involved in longevity patterns in this French Canadian population.     

Protein and nitrate content of lemna sp. As a function of developmental stage and incubation temperature

Lemna protein per frond and per root increases with developmental stage until plants are at least two generations old. Protein per frond, per root, and per unit dry weight is greater in plants grown at 23.9 C than at 18.3 C. More protein is found in fronds than in roots, and more nitrate occurs in roots than in fronds. Nitrate per root increases with developmental stage and is higher (per root) in plants grown at 23.9 C than in those grown at 18.3 C. The distribution of generations within a growing population is constant for at least eight doubling times. Whether populations multiply slowly at 15.6 C or more rapidly at 23.9 C, fronds which have not yet produced progeny form 62% of the population; fronds which are one generation old form 24% of the population; and fronds which are two generations old form 9% of the population.     

Reproductive Trade-Offs May Moderate the Impact of Gyrodactylus salaris in Warmer Climates

Gyrodactylus salaris is a notifiable freshwater ectoparasite of salmonids. Its primary host is Atlantic salmon (Salmo salar), upon which infections can cause death, and have led to massive declines in salmon numbers in Norway, where the parasite is widespread. Different strains of S. salar vary in their susceptibility, with Atlantic strains (such as those found in Norway) exhibiting no resistance to the parasite, and Baltic strains demonstrating an innate resistance sufficient to regulate parasite numbers on the host causing it to either die out or persist at a low level. In this study, Leslie matrix and compartmental models were used to generate data that demonstrated the population growth of G. salaris on an individual host is dependent on the total number of offspring per parasite, its longevity and the timing of its births. The data demonstrated that the key factor determining the rate of G. salaris population growth is the time at which the parasite first gives birth, with rapid birth rate giving rise to large population size. Furthermore, it was shown that though the parasite can give birth up to four times, only two births are required for the population to persist as long as the first birth occurs before a parasite is three days old. As temperature is known to influence the timing of the parasite''s first birth, greater impact may be predicted if introduced to countries with warmer climates than Norway, such as the UK and Ireland which are currently recognised to be free of G. salaris. However, the outputs from the models developed in this study suggest that temperature induced trade-offs between the total number of offspring the parasite gives birth to and the first birth timing may prevent increased population growth rates over those observed in Norway.     

Field studies on the population dynamics of Biomphalaria glabrata, intermediate host of Schistosoma mansoni on the West Indian Island of St. Lucia

Growth curves, calculated for field populations of B. glabrata, were not materially affected by habitat, altitude or season. A mean growth curve was therefore used to estimate the age-frequency distribution of snails in successive field samples. These data permitted the construction of ecological life tables and the estimation of r, the intrinsic rate of natural increase (or decrease) of the different populations. The calculated values of r were inserted in a simple model of unlimited population growth but the resultant curves poorly represented the observed data. A model for unlimited growth was more satisfactory for pond and marsh populations but, apparently, immigration made it less satisfactory for stream and banana drain populations. Nevertheless, r may still be of value in predicting repopulation rates in certain habitats after a mollusciciding which does not kill the entire snail population.     

Age‐ and temperature‐dependent oviposition model of Neoseiulus californicus (McGregor) (Acari: Phytoseiidae) with Tetranychus urticae as prey

In this study, we developed an oviposition model of Neoseiulus californicus (McGregor) with Tetranychus urticae Koch as prey. To obtain data for the model, we investigated the longevity, fecundity and survivorship of adult female N. californicus at six constant temperatures (16, 20, 24, 28, 32 and 36°C), 60–70% RH and a photoperiod of 16 : 8 (L : D) h. Longevity (average ± SE) decreased as temperature increased and was longest at 16°C (46.7 ± 5.25 days) and shortest at 36°C (12.8 ± 0.75 days). Adult developmental rate (1/average longevity) was described by the Lactin 1 model (r² = 0.95). The oviposition period (average±SE) was also longest at 16°C (29.8 ± 2.93 days) and shortest at 36°C (6.7 ± 0.54 days). Fecundity (average±SE) was greatest at 24°C (43.8 ± 3.23 eggs) and lowest at 36°C (15.9 ± 1.50 eggs). The oviposition model comprised temperature‐dependent fecundity, age‐specific cumulative oviposition rate and age‐specific survival rate functions. The temperature‐dependent fecundity was best described by an exponential equation (r² = 0.81). The age‐specific cumulative oviposition rate was best described by the three‐parameter Weibull function (r² = 0.96). The age‐specific survival rate was best described by a reverse sigmoid function (r² = 0.85).     

沣西新城曹家寨清代墓地古人口学初步研究

曹家寨墓地是一处位于陕西西咸新区沣西新城的清代平民墓地,文章通过体质人类学和古人口学研究方法,结合历史文献,对曹家寨墓地的人口结构进行了初步分析。结果表明,沣西新城曹家寨清代居民的性别比为117.5,男性远多于女性,可能与清代盛行的“溺女婴”风俗有关。两性的死亡高峰皆在中年期,但生育行为使得女性壮年期的死亡率是男性的2倍多,有更多的男性居民活到了老年期,表明男性个体有相对更长的寿命。墓地人骨的埋葬方式和迁葬行为,反映了清代一夫一妻多妾的婚姻形式以及平民阶层个体家庭为主的家庭结构。     

The dynamics of hierarchical age-structured populations

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.     

Use of a serum-based glomerular filtration rate prediction equation to assess renal function by age, sex, fasting, and health status in bottlenose dolphins (Tursiops truncatus)

Glomerular filtration rate (GFR) is a direct measurement of renal function. Although clearance tests using 24‐h urine collection or blood sample series are gold standards for measuring GFR, serum‐based prediction of GFR based upon the Modification of Diet in Renal Disease (MDRD) Study equation is acceptable for routine use in human adults. The purpose of our study was to assess the ability for a modified MDRD Study equation to predict expected changes in GFR in bottlenose dolphins (Tursiops truncatus) using a healthy dolphin population represented by 1,103 routine serum samples collected from 50 dolphins of all age groups, years 1998–2005. Predicted GFR was also calculated from serum collected from a 32‐yr‐old male dolphin with end‐stage renal disease. The dolphin‐adjusted MDRD equation predicted GFR changes in our population that paralleled what has previously been reported in other mammals, including decreasing predicted GFR with age (P < 0.01), higher predicted GFR in dolphins that had recently eaten (P < 0.01), and rapidly decreasing predicted GFR in the animal with end‐stage renal disease. We conclude that a serum‐based GFR prediction equation may be a feasible means of detecting and tracking renal function in bottlenose dolphins.