Related papers: Predictive implications of Gompertz's law
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component…
Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According…
We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
In many cohorts (such as the UK Biobank) on which Mendelian Randomization studies are routinely performed, data on participants' longevity is inadequate as the majority of participants are still living. To nevertheless estimate effects on…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…
Since laws of physics exist in nature, their possible relationship to terrestial growth is introduced. By considering the human body as a dynamic system of variable mass (and volume), growing under a gravity field, it is shown how natural…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
In this paper we examine some relative orderings of upper and lower records. It is shown that if m > n, the mth upper record ages faster than the nth upper record, where the data sets come from a sequence of independent and identically…
This paper is an attempt to formalize analytically the question raised in "World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?" Huffington Post, \cite{HJ}. We start developing simple deterministic Malthusian growth…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and…
Hundreds of millions of people live in countries that do not have complete death registration systems, meaning that most deaths are not recorded and critical quantities like life expectancy cannot be directly measured. The sibling survival…
Suppose, contrary to fact, in 1950, we had put the cohort of 18 year old non-smoking American men on a stringent mandatory diet that guaranteed that no one would ever weigh more than their baseline weight established at age 18. How would…
We introduce a population-age-time (PAT) model which describes the temporal evolution of the population distribution in age. The surprising result is that the qualitative nature of the population distribution dynamics is robust with respect…
Growth of the world population and the world economic growth were hyperbolic in the past 2,000,000 years. Recently, from around 1950, they started to be diverted to slower trajectories but they are still close to the historical hyperbolic…