Estimating the distribution of probable age-at-death from dental remains of immature human fossils

In two historic longitudinal growth studies, Moorrees et al. (Am J Phys Anthropol 21 (1963) 99-108; J Dent Res 42 (1963) 1490-1502) presented the "mean attainment age" for stages of tooth development for 10 permanent tooth types and three deciduous tooth types. These findings were presented graphically to assess the rate of tooth formation in living children and to age immature skeletal remains. Despite being widely cited, these graphical data are difficult to implement because there are no accompanying numerical values for the parameters underlying the growth data. This analysis generates numerical parameters from the data reported by Moorrees et al. by digitizing 358 points from these tooth formation graphs using DataThief III, version 1.5. Following the original methods, the digitized points for each age transition were conception-corrected and converted to the logarithmic scale to determine a median attainment age for each dental formation stage. These values are subsequently used to estimate age-at-death distributions for immature individuals using a single tooth or multiple teeth, including estimates for 41 immature early modern humans and 25 immature Neandertals. Within-tooth variance is calculated for each age estimate based on a single tooth, and a between-tooth component of variance is calculated for age estimates based on two or more teeth to account for the increase in precision that comes from using additional teeth. Finally, we calculate the relative probability of observing a particular dental formation sequence given known-age reference information and demonstrate its value in estimating age for immature fossil specimens.     

A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms

This paper advances a unified approach to the modeling of sigmoid organismal growth. There are numerous studies on growth, and there have been several proposals and applications of candidate models. Still, a lack of interpretation of the parameter values persists and, consequently, differences in growth patterns have riddled this field. A candidate regression model as a tool should be able to assess and compare growth-curve shapes, systematically and precisely. The Richards models constitute a useful family of growth models that amongst a multitude of parameterizations, re-parameterizations and special cases, include familiar models such as the negative exponential, the logistic, the Bertalanffy and the Gompertz. We have reviewed and systemized this family of models. We demonstrate that two specific parameterizations (or re-parameterizations) of the Richards model are able to substitute, and thus to unify all other forms and models. This unified-Richards model (with its two forms) constitutes a powerful tool for an interpretation of important characteristics of observed growth patterns, namely, [I] maximum (relative) growth rate (i.e., slope at inflection), [II] age at maximum growth rate (i.e., time at inflection), [III] relative mass or length at maximum growth rate (i.e., relative value at an inflection), [IV] value at age zero (i.e., birth, hatching or germination), and [V] asymptotic value (i.e., adult weight or length). These five parameters can characterize uniquely any sigmoid-growth data. To date most studies only compare what is referred to as the “growth-rate constant” or simply “growth rate” (k). This parameter can be interpreted as neither relative nor actual growth rate, but only as a parameter that affects the slope at inflection. We fitted the unified-Richards and five other candidate models to six artificial data sets, generated from the same models, and made a comparison based on the corrected Akaike’s Information Criterion (AICc). The outcome may in part be the result of the random generation of data points. Still, in conclusion, the unified-Richards model performed consistently well for all data sets, despite the penalty imposed by the AICc.     

Body mass and growth rates in a wild primate population

Summary We obtined data on body mass and growth rates for the immature members of two groups of wild baboons in Amboseli National Park, Kenya. Data were collected without feeding, trapping, or handling. The data were separated into cross-sectional and longitudinal components, allowing both the examination of body mass-age relationships and the calculation of growth rates for individuals. For animals less than three years old, body mass was wellperedicted from age by a linear model. Differences based on social group membership were small but consistent, and their origins are discussed. We detected no differences in body mass based on sex or on maternal dominance rank. For older juveniles, those three to seven years of age, a better fit was obtained from log of mass than by mass in a linear model. This was also true for the cross-sectional data set over the whole age range (zero to seven years). For older juveniles, samples were too small for quantitative analysis of differences based on sex, rank, or group membership, but trends in the data are indicated. Growth rates derived from repeat measures of body mass for 38 animals are presented and discussed.The growth rate values obtained in this study are consistent with data from cross-sectional studies of other wild baboon populations; these values for wild baboons are consistently one-half to one-third lower than growth rate values for well-provisioned captive baboons and equivalent to captive baboons fed a low-protein diet. Comparisons between primates and other mammals in the primate size range raise questions concerning ecological and behavioral constraints on primate growth rates; some possible mechanisms of constraint are suggested.     

Elasticity Analysis of Green Sturgeon Life History

I provide an analysis of a simplified life history model for green sturgeon, Acipenser medirostris, based on published and recent estimates of reproduction and growth rates and survival rates from life history theory. The deterministic life cycle models serve as a tool for qualitative analysis of the impacts of perturbations on green sturgeon, including harvest regulations based on minimum and maximum size limits (“slot limits”). Elasticity analysis of models with two alternative age–length relationships give similar results, with a high sensitivity of population growth rate to changes in the survival rate of subadult and adult fish. A dramatic increase in the survival of young of the year sturgeon or annual egg production is required to compensate for relatively low levels of fishing mortality. Peak reproductive values occur from ages 25 to 40. An increase or decrease in the maximum and minimum size limits can have a profound effect on the elasticity of population growth to changes in the annual survival rate of age classes specified by the slot, due to changes in the number of age classes of subadults and adults that are available for harvest. This analysis provides managers with a simple tool to assess the relative impacts of alternative harvest regulations. In general, green sturgeon follow life history patterns similar to other sturgeon, but species-specific demographic information is needed to produce more complex assessment and viability analysis models.     

Changes in the rate of growth in a stunted roach Rutilu rutilus population

Data is presented concerning the growth of roach in a South Lancashire lake. Results from a sample of roach in May 1969 indicate the slowest growth rate for which published records are available. A comparison of the length/age and weight/age relationships between data for May 1969 and May/June 1971 yields significant between-year differences indicating an increase in the growth rate during that period. A study of the growth history of individual year classes using back-calculated values from operculum measurements suggests that for both sexes the observed increase in the rate of growth commenced after the 1965–67 period during which very weak year classes were produced. The mean length of females appears to have been larger than that of males from the age of four onwards but the 95% confidence intervals are almost totally overlapping for each pair of values and a statistical comparison of growth rates between the sexes indicates no significant differences. Data for the sexes combined is compared with published results from other British and Continental waters.     

A hierarchical Bayesian model for calibrating estimates of species divergence times

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account.     

Reference data for evaluating the growth of common riverine fishes in the UK

Comparative assessments of population mean growth rates in length remain important aspects of stock assessment in river fisheries. To facilitate these assessments, for 15 fish species encountered in UK rivers reference data are provided on their expected lengths at age, maximum theoretical lengths (L_∞), growth coefficient (K) and instantaneous mortality rate (Z). These data are also transferable to fish populations outside of the UK that experience a similar growth season (approximately April to October, mean water temperatures 12–22°C). Considerable plasticity was observed in the growth of all species examined, with length at age values revealing growth rates from very slow to very fast. Populations considered fast growing against reference data were coincident with a relatively low ultimate length, a high growth coefficient and a high instantaneous mortality rate, suggesting a trade‐off exists between growth rate, ultimate length and life span.     

The relationship between the relative growth rates of the shoot system, number of tillers and mean tiller size in Lolium perenne

The relative growth rate of the shoot system of Lolium perenne may be considered as being made up of two components, the relative growth rate of the increase in the number of tillers and the relative growth rate of the mean tiller. These three relative growth rates were calculated for twenty-two clones of Lolium perenne growing in twenty-eight environments. Analyses of variance showed that differences in the environment were responsible for a greater amount of variation than either differences between clones or the interaction between clonal and environmental influences.
For each clone it was possible to calculate relationships between the relative growth rate of the shoot and its two components as they varied with the environments. The relationships held irrespective of the environmental factor(s) which altered to cause the difference in relative growth rates. In all clones an increase in the relative growth rate of the shoot was found to be due to an increase in the relative growth rates of both components. In seventeen clones the relationship between the increments of the two components was constant. In five of the clones an increase in the relative growth rate of the shoot at low values was due more to an increase in the relative growth rate of the number of tillers than to an increase in the relative growth rate of the mean tiller. At high values the opposite occurred.
These results are discussed in relation to the theory of 'nutritive diversion' and in relation to the proportion of lateral buds which produce tillers.     

Partial life cycle analysis: a model for pre-breeding census data

Matrix population models have become popular tools in research areas as diverse as population dynamics, life history theory, wildlife management, and conservation biology. Two classes of matrix models are commonly used for demographic analysis of age‐structured populations: age‐structured (Leslie) matrix models, which require age‐specific demographic data, and partial life cycle models, which can be parameterized with partial demographic data. Partial life cycle models are easier to parameterize because data needed to estimate parameters for these models are collected much more easily than those needed to estimate age‐specific demographic parameters. Partial life cycle models also allow evaluation of the sensitivity of population growth rate to changes in ages at first and last reproduction, which cannot be done with age‐structured models. Timing of censuses relative to the birth‐pulse is an important consideration in discrete‐time population models but most existing partial life cycle models do not address this issue, nor do they allow fractional values of variables such as ages at first and last reproduction. Here, we fully develop a partial life cycle model appropriate for situations in which demographic data are collected immediately before the birth‐pulse (pre‐breeding census). Our pre‐breeding census partial life cycle model can be fully parameterized with five variables (age at maturity, age at last reproduction, juvenile survival rate, adult survival rate, and fertility), and it has some important applications even when age‐specific demographic data are available (e.g., perturbation analysis involving ages at first and last reproduction). We have extended the model to allow non‐integer values of ages at first and last reproduction, derived formulae for sensitivity analyses, and presented methods for estimating parameters for our pre‐breeding census partial life cycle model. We applied the age‐structured Leslie matrix model and our pre‐breeding census partial life cycle model to demographic data for several species of mammals. Our results suggest that dynamical properties of the age‐structured model are generally retained in our partial life cycle model, and that our pre‐breeding census partial life cycle model is an excellent proxy for the age‐structured Leslie matrix model.     

一种获得非线性生长函数参数初始值的新方法:杂种遗传算法

本研究旨在杂种遗传算法应用于非线性生长函数的参数估计.提出了杂种遗传算法估计非线性生长函数参数的数学模型.5种非线性生长函数Gompertz、Logistic、von Bertalanffy、Richards、Brody分别拟合一个较大型的、群体类型差异大的番鸭体重生长资料,利用杂种遗传算法获得了有效初始值,在lsqcurvefit与proc nlin中获得了一致最优解的结果.表明杂种遗传算法估计非线性函数参数的实际可行性.     

Growth, protein-turnover rates and nucleic-acid concentrations in the white muscle of rainbow trout during development

We have studied the growth rate, nucleic-acid concentration, protein-accumulation rate (K_G), and several other parameters relating to protein turnover, such as the protein-synthesis (K_S), and protein-degradation rates (K_D), protein-synthesis capacity (C_S), protein-synthesis efficiency (K_RNA), protein-synthesis rate per DNA unit (K_DNA) and protein-retention efficiency (PRE), in the white muscle of rainbow trout during development. Both growth rate and relative food intake decreased significantly with age and weight, as did the food-efficiency ratio (FER) and protein-efficiency ratio (PER). Although absolute RNA and DNA contents increased with age, their relative concentrations decreased. The RNA/DNA ratio increased sharply from 14 to 28 weeks but afterwards decreased towards initial values. Hypertrophy increased rapidly to the 28-week stage but thenceforth increased much more slowly. Hyperplasia, on the other hand, continued to increase linearly, resulting in a significant four- to fivefold predominance in this type of growth at the end of the 96-week experimental period. K_G decreased significantly with age, as did K_S, and C_S, whereas at the 14-week stage, K_D was significantly lower than at other ages. K_RNA increased until 28 weeks. K_DNA increased significantly in juvenile fish compared to both fingerlings and adults, where it showed similar lower values. PRE remained high at all ages.     

The mechanic state of "inner tissue" in the growing zone of sunflower hypocotyls and the regulation of its growth rate following excision

Spontaneous growth of isolated inner tissue from the etiolated sunflower (Helianthus annuus L.) hypocotyl growing zone was investigated. A new preparation technique allowed measurements starting 3 s after excision. Elongation with respect to the turgescent and plasmolized state was quantified in terms of relative growth rates, facilitating comparison to growth in situ. Turgor and turgor-induced strain were determined. Overall longitudinal strain in inner tissues in situ was positive, indicating that compressive forces exerted by peripheral tissues are outweighed by turgor-dependent tensile stress. Inner tissue expansion following isolation depended on water uptake. Extreme plastic extension rates occurred immediately after excision, suggesting that mechanical parameters of inner tissue in situ cannot be extrapolated from the mechanics of excised sections. In the long term, excised inner tissue autonomously established values of turgor, turgor-induced strain, and relative growth rates similar to values in the living plant. These results support historic models of tissue cooperation during organ growth, in which inner tissues actively participate in the control of growth rates.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Evaluation of different approaches for modelling individual tree seedling height growth

We compared different approaches for modelling height growth of individual beech seedlings in a controlled factorial experiment as well as in field data from naturally regenerated beech seedlings under the canopy of overstorey mature beech trees. Several competition indices, a model of overstorey fine root density, relative photosynthetically active radiation (PAR) values, and soil water values were used in these approaches. In the factorial experiment relative PAR and soil water content were measured and used for the prediction of seedlings height growth. In the field experiment this was done by using relative PAR and estimated fine root biomass as a surrogate for below ground resource availability. The latter approach was compared with a model where we used various competition indices representing the impact of overstorey trees on beech seedlings. Our results suggested that (1) models which combine resource based growth functions are suitable for the prediction of individual height growth of beech seedlings. Resource based models offer the opportunity to investigate on the independent multiplicative effect of irradiance and water supply and their interactions on tree seedlings. It was (2) shown that a combined model could be used not only to predict individual height growth of beech seedlings in a controlled experiment but also in the field. The model parameters of a pure light response function for the controlled factorial experiment are comparable to those obtained in the field study. The results showed (3) that the precision of predicting beech seedlings height growth is comparable between the model types tested within this study. Approximately half of the observed variation in seedlings relative height growth rate could be explained. However, the simple competition index approach provides no information on the environmental factors constraining tree seedlings growth; whereas the multiplicative combined models can be used to get a better understanding of growth dynamics in the field.     

Effect of water temperature and density of juvenile salmonids on growth of young-of-the-year Atlantic salmon Salmo salar

A von Bertalanffy growth model for young-of the-year Atlantic salmon Salmo salar in a small French coastal stream was fitted using water temperatures and densities of juvenile salmonids (S. salar and brown trout Salmo trutta) as covariates influencing daily growth rate. The Bayesian framework was used as a template to integrate prior information from external data sets. The relative influence of the covariates on parr growth was quantified and results showed that growth of S. salar juveniles depended on both water temperatures and densities, but that most of the spatiotemporal variability of growth resulted from local spatiotemporal variations of 0+ age salmonid (S. salar and S. trutta) densities. Further analysis revealed that the fluctuations in young-of-the-year salmonid densities are likely to dominate the effects of potential future warming of water temperature due to climate change. It is concluded that factors that could affect salmonid densities might well have a greater effect on S. salar population dynamics than factors influencing water temperatures.     

Kunze-Murken growth-specific approximations of somatograms

Tables for human height at age values by Kunze and Murken are submitted to mathematical approximations applying the 2-step-model introduced by Sager (1981). The basic term reflects growth as expected when a growth spurt is lacking which may be the case for children with chromosomal aberrations. The 2nd term comprises an expression for the growth spurt proper thus allowing an evaluation for the intensity of the spurt. The approximations as gained with nonlinear regressions show very close agreement with the measurements. Besides the growth curve its first derivative--the growth velocity or increase--is calculated and represented graphically. Moreover the results and their relative amounts against the final values at adulthood are compared for nine height at age tables treated hitherto with the same growth model.     

甘肃鼠兔幼子生长的初步研究

根据3 窝14只甘肃鼠兔幼子56 天的生长发育资料初步分析了甘肃鼠兔的生长发育规律。依据逻辑斯蒂曲线的拐点,甘肃鼠兔的体重生长可划分为加速增长相（0～0.5日龄）和减速增长相（20.5日龄以后）。按照瞬时生长率曲线的拐点,体重增长过程可分为3个时期,即缓慢生长期（0～6.5 日龄）、快速生长期（6.5～34.5 日龄）和渐进生长期（34.5 日龄以后）。文章对使用逻辑斯蒂方程和其它“S”形曲线描述动物生长过程存在的一些问题进行了讨论,认为：如果只用1条“S”形曲线描述动物的整个生长过程,就有可能会因为成年期动物生长规律的变化而破坏模型参数的生物学意义,同时引起模型拟合精度的降低。为克服这一问题,作者建议：在使用“S”形曲线拟合动物生长模型时,生长过程的资料最好不要覆盖体重波动较大的成年阶段。     

Age-dependence of metabolism in mussels Mytilus edulis (L.) from the White Sea

Age structure, natural mortality and growth, as well as age- and size-dependent changes in parameters of energy metabolism were studied in blue mussels Mytilus edulis (L.) from the White Sea. Mussels were sampled in August (Summer sample, SS) and October (Autumn sample, AS) and contained animals of three size groups, 2-9 years old. Field data showed an increase of mortality of mussels and strong decrease in growth rates after 6 years of age. Absolute tissue growth increment (AI) reconstructed from winter growth marks on the shells decreased with age and was strongly size-dependent, while relative tissue growth increment (RI) did not depend on size of the animals. Respiration rates and citrate synthase activity demonstrated power regression versus tissue weight with regression coefficients -0.231 and -0.170, respectively. After weight correction both parameters showed a decrease with increasing age. ATP and phosphagen levels also showed a pronounced decrease in animals older than 5-6 years despite considerable differences in the absolute values of both parameters in SS and AS. pH(i) in mussels was also age-dependent and decreased with increasing age after 5 years. In air exposed mussels, pH(i) was reduced only at young age such that pH(i) was low and constant within the whole age range. Our data give evidence that aerobic metabolic rate in M. edulis from the studied population declines when animals reach an age of about 6 years. The decrease in oxygen consumption reflects the drop in mitochondrial respiration, which is mirrored by the decrease in CS activity. A concomitant fall in ATP turnover may include a downregulation of the mechanisms of acid-base regulation. pH(i) will then approach equilibrium indicated by lower pH(i) values in older animals. Our data suggest that intrapopulational comparisons of physiological parameters in mussels should take into account age composition of compared samples.     

Systems approaches to understanding cell signaling and gene regulation

The age of 'omics' is upon us, and scientific papers that reflect this are starting to appear at an ever-increasing rate. The amount of information generated in any 'omics' program is daunting and often overwhelms plant scientists whose main interests relate to cell or developmental biology. For this revolution in data generation to have any impact in plant signaling studies, we must have great confidence in both the quality of the data and our ability to represent it in ways that are meaningful to general plant biologists. Systems biology has begun to address these issues and to provide examples in which the analysis of large data sets has led to biological insights into cell signaling and gene regulation.