Modelling of drug receptor interaction with birth and death processes

Stochastic modelling of drug receptor interaction at the neuromuscular junction with birth and death processes is presented. Systems with only one drug and two drugs interacting are investigated separately. The total number of receptors is assumed finite and only single receptor binding is considered. It has been possible to obtain exact analytical solutions to forward Kolmogorov equations yielding the transition probability densities and the associated probability generating functions.     

Modeling of selection processes with age-dependent birth and death rates

Two simple models for the competition and selection in age-dependent populations are developed and analyzed mathematically. Following Eigen, competition is introduced by the condition of constant overall-number of the population. In the first model this condition is satisfied by regulation of a dilution flux and in the second case by regulation of a food density. The calculation of maximal fitness is given explicitly for both situations. It is shown that fitness depends in a complicated way on the age-dependence of the birth and death rates. Therefore species have to develop special aging strategies in order to survive in a population under selection pressure. In general, early reproduction is of advantage and increases fitness.     

On the linear birth and death processes of biology as Markoff chains

Stochastic Markoff models for the linear birth and death population growth processes of biology are constructed using the Q-matrix method of Doob. The relationship of the stochastic theory to the classical deterministic foundations of these processes is stressed by showing in detail how the classical postulates are mathematically transformed via the Q-matrix elements into the basis for a stationary Markoff process with continuous time parameter and denumerably many “populations states.” It is shown that the resulting stochastic models predict that the population size will fluctuate about the deterministic time curve, the extent of fluctuation being measured by the variance functions. General formulas covering all possible transitions from one population size to another are derived.     

Reconstruction of paleodemographic characteristics from skeletal age at death distributions: perspectives from Hitotsubashi, Japan

This is a demographic exploration of the city of Edo, which reveals the changes that accompanied its urbanization and analyzes the skeletal remains of 207 individuals from a specific site in Tokyo (Hitotsubashi), using several paleodemographic approaches. A comparison of the three methods employed herein suggests that the Bayesian and maximum likelihood estimation techniques provide more plausible mortality patterns than the direct method of age estimation because the direct method of age estimation relies on published age intervals for the auricular surface and that would account for the underestimation of old people relative to the other two methods. Analyses using these new approaches indicate a short life span tendency for the people of Hitotsubashi. Although we cannot rule out methodological problems of adult-age estimation, one plausible interpretation of that life expectancy is an inadequate food supply and a poor public health situation. This study suggests that, in Tokugawa Japan, urbanization might have imposed health risks, increasing the risk of mortality. Analysis of demographic data from Hitotsubashi has refined our understanding on the impact of urbanization on the Edo period, and presents new perspectives on paleodemography in Japan.     

British National Formulary: its birth,death, and rebirth.

The British National Formulary is a direct descendant of the National War Formulary, in which the titles of the preparations were in Latin and the doses in minims and grains. The British National Formulary was born in 1948, did a good job for about 20 years, but sickened and died in 1976. It was reborn in 1981. Parturition was painful with a very hostile reception from the media and the drug industry, but it survived and has grown in stature. The 25th edition was published in February. Wish it well for the next 25 issues!     

Sex determination,longevity, and the birth and death of reptilian species

Vertebrate sex‐determining mechanisms (SDMs) are triggered by the genotype (GSD), by temperature (TSD), or occasionally, by both. The causes and consequences of SDM diversity remain enigmatic. Theory predicts SDM effects on species diversification, and life‐span effects on SDM evolutionary turnover. Yet, evidence is conflicting in clades with labile SDMs, such as reptiles. Here, we investigate whether SDM is associated with diversification in turtles and lizards, and whether alterative factors, such as lifespan's effect on transition rates, could explain the relative prevalence of SDMs in turtles and lizards (including and excluding snakes). We assembled a comprehensive dataset of SDM states for squamates and turtles and leveraged large phylogenies for these two groups. We found no evidence that SDMs affect turtle, squamate, or lizard diversification. However, SDM transition rates differ between groups. In lizards TSD‐to‐GSD surpass GSD‐to‐TSD transitions, explaining the predominance of GSD lizards in nature. SDM transitions are fewer in turtles and the rates are similar to each other (TSD‐to‐GSD equals GSD‐to‐TSD), which, coupled with TSD ancestry, could explain TSD's predominance in turtles. These contrasting patterns can be explained by differences in life history. Namely, our data support the notion that in general, shorter lizard lifespan renders TSD detrimental favoring GSD evolution in squamates, whereas turtle longevity permits TSD retention. Thus, based on the macro‐evolutionary evidence we uncovered, we hypothesize that turtles and lizards followed different evolutionary trajectories with respect to SDM, likely mediated by differences in lifespan. Combined, our findings revealed a complex evolutionary interplay between SDMs and life histories that warrants further research that should make use of expanded datasets on unexamined taxa to enable more conclusive analyses.     

Bistability versus bimodal distributions in gene regulatory processes from population balance

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.     

On birth and death in the sea

We present the first comparative study of the stage-specific patterns of mortality of Calanus and Pseudocalanus, two widely distributed genera that are representative of a relatively large-bodied, broadcast spawning calanoid copepod and a relatively small-bodied, egg-brooding calanoid. The study site is Georges Bank, a continental shelf locality in the Northwestern Atlantic with retentive circulation that renders it suitable for studies of population dynamics. Based on extensive mortality estimates from 30 cruises, we find that co-occurring Calanus finmarchicus and Pseudocalanus spp. have markedly different patterns of stage-specific mortality, the former bimodal and the latter relatively uniform with respect to developmental stage. Neither taxon exhibits a monotonic decline in mortality with developmental stage, nor are rates of mortality predictable in a useful manner by copepod body size or by ambient temperature. Young stages of the broadcast-spawning C. finmarchicus show conditional density-dependence of mortality rates, i.e. mortality rates are independent of population density when adult females are low in abundance but positively related to population density at high female abundances. This density-dependence, which is probably attributable to egg cannibalism, introduces a quadratic mortality term into population dynamic models. The egg-brooding Pseudocalanus spp., in contrast, show no evidence of density-dependent mortality. The two taxa illustrate a life history trade-off: the broadcast-spawning Calanus exhibits birth rates that are greatly elevated with respect to those of Pseudocalanus, but there is a compensatory cost in very low survivorship of the freely spawned eggs. Both the high fecundity, high mortality life history of Calanus and the low fecundity, low mortality life history of Pseudocalanus appear to have approximately equal fitness in this study site.     

Connecting geographical distributions with population processes

The geographical distribution of a species is determined by a large number of complex processes operating over spatial scales spanning 10 orders of magnitude. Patterns in population processes have been described at numerous scales. We show that two patterns, measured at different scales, jointly allow us to infer heretofore unknown patterns in the distribution of demographic patterns across the geographical range of a species. The resulting model describes three fundamentally different modes of geographical variation in vital rates of populations. One mode is characterized by a positive nonlinear relationship between the maximum rate of population growth and the intensity of intraspecific competition across a geographical range. That is, populations that grow rapidly are also those where individuals experience the greatest per capita negative effect of the presence of other individuals. The second mode of behaviour is described by a negative nonlinear relationship between maximum growth rate and density dependence. Under this scenario, populations with low capacity to grow rapidly have highest intensities of intraspecific competitive effects. A third mode of behaviour is characterized by a weak positive relationship between growth rate and intraspecific competition, with very little geographical variation in maximum growth rate. A survey of studies relating temporal means and variances in population abundance for a variety of species indicate that the second mode of geographical variation in population dynamics across species ranges is the most common, though a few species appear to be characterized by the third mode.     

A complementary note on the supercritical birth,death and catastrophe process

A central limit theorem for the population size of the super-critical linear birth and death process with a linear catastrophe component has previously been obtained under a fourth order moment condition on the increment distribution. In this note we show that this result is valid under a second order moment condition, and that no lesser condition will suffice. This is accomplished by giving a new, self-contained and simple proof of the asymptotic normality of a certain tail sum of independent variates.