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The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as…
The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
We examine the complete dataset of baby name popularity collected by U.S. Social Security Administration for the last 131 years (1880-2010). The ranked baby name popularity can be fitted empirically by a piecewise function consisting of…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor,…
We analyze mathematical models of the global human population growth and compare them to actual dynamics of the world population and of the world surplus product. We consider a possibility that the so-called world's demographic transition…
Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is…
The composition of cellular metabolism is different across species. Empirical data reveal that bacterial species contain similar numbers of metabolic reactions but that the cross-species popularity of reactions is so heterogenous that some…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Inequality in human success may emerge through endogenous success-breeds-success dynamics but may also originate in pre-existing differences in talent. It is widely recognized that the skew in static frequency distributions of success…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
Recent studies have revealed that for the majority of species the length distributions of duplicated sequences in natural DNA follow a power-law tail. We study duplication-mutation models for processes in natural DNA sequences and the…
The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…
We investigate the distribution of flavonoids, a major category of plant secondary metabolites, across species. Flavonoids are known to show high species specificity, and were once considered as chemical markers for understanding adaptive…