Binary Stellar Population Synthesis Model

Using Yunnan evolutionary population synthesis (EPS) models, we present integrated colours, integrated spectral energy distributions (ISEDs) and absorption-line indices defined by the Lick Observatory image dissector scanner (Lick/IDS) system, for an extensive set of instantaneous-burst binary stellar populations (BSPs) with interactions. By comparing the results for populations with and without interactions we show that the inclusion of binary interactions makes the appearance of the population substantially bluer. This effect raises the derived age and metallicity of the population. To be used in the studies of modern spectroscopic galaxy surveys at intermediate/high spectral resolution, we also present intermediate- (3A) and high-resolution (~0.3A) ISEDs and Lick/IDS absorption-line indices for BSPs. To directly compare with observations the Lick/IDS absorption indices are also presented by measuring them directly from the ISEDs.Comment: 2 pages 2 figure

A nonsmooth two-sex population model

This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose parameters are the secondary sex ratio (the ratio of males to females at time of birth), inter-, intra- and outer-gender competitions, fertility and mortality rates and a mating function. For the case where there is no inter-gender competition and the mortality rates are negligible with respect to the density-dependent mortality, using geometrical techniques, we analyze the singularities and the basin of attraction of the system, determining the relationships between the parameters for which the system presents an equilibrium point. In particular, we describe conditions on the secondary sex ratio and discuss the role of the average number of female sexual partners of each male for the conservation of a two-sex species.Comment: 18 pages, 6 figures. Section 2, in which the model is presented, was rewritten to better explain the elements of the proposed model. The description of parameter "r" was correcte

The nk model and population genetics

The nk model of fitness interactions is examined. This model has been used by previous authors to investigate the effects of fitness epistasis on substitution dynamics in molecular evolution, and to make broader claims about the importance of epistasis. To examine these claims, an infinite-allele approximation is introduced. In this limit, it is shown that the nk model is, at an appropriate level of description, formally identical to the non-epistatic House-of-Cards model--a well-studied model in theoretical population genetics. It is further shown that in many parameter regimes, the analytical results obtained from this infinite-allele approximation are very close to results from the full nk model (with a finite number of alleles per locus). The findings presented shed light on a number of previous results

Population Dynamics in the Penna Model

We build upon the recent steady-state Penna model solution, Phys.Rev.Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes each of which decay exponentially with its respective time constant. The long time behaviour of population is therefore likely to be dominated by the modes with the largest time constants. We confirm our analytical approach with simulation data.Comment: 6 figure

Gravity model explained by the radiation model on a population landscape

Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.Comment: 14 pages, 4 figure

A scale-invariant model of marine population dynamics

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence that the population dynamics in the ocean is approximately scale-invariant. We use this invariance in the construction and solution of a size-structured dynamical population model. Starting from a Markov model encoding the basic processes of predation, reproduction, maintenance respiration and intrinsic mortality, we derive a partial integro-differential equation describing the dependence of abundance on weight and time. Our model represents an extension of the jump-growth model and hence also of earlier models based on the McKendrick--von Foerster equation. The model is scale-invariant provided the rate functions of the stochastic processes have certain scaling properties. We determine the steady-state power law solution, whose exponent is determined by the relative scaling between the rates of the density-dependent processes (predation) and the rates of the density-independent processes (reproduction, maintenance, mortality). We study the stability of the steady-state against small perturbations and find that inclusion of maintenance respiration and reproduction in the model has astrong stabilising effect. Furthermore, the steady state is unstable against a change in the overall population density unless the reproduction rate exceeds a certain threshold.Comment: Same as published version in Phys.Rev.E. except for a correction in the appendix of the coefficients in the Fokker-Planck equation (A8). 18 pages, 8 figure

SOC in a population model with global control

We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic', `directed percolation'), but instead of using an infection or recovery rate as control parameter, the population size is controlled directly and globally by removing excess plants. We show that the model is very closely related to directed percolation (DP). Anomalous scaling laws appear in the limit of large populations, small densities, and long times. These laws, associated critical exponents, and even some non-universal parameters, can be related to those of DP. As in invasion percolation and in other models where the r\^oles of control and order parameters are interchanged, the critical value $p_c$ of the wetting probability $p$ is obtained in the scaling limit as singular point in the distribution of infection rates. We show that a mean field type approximation leads to a model studied by Y.C. Zhang et al. [J. Stat. Phys. {\bf 58}, 849 (1990)]. Finally, we verify the claim of Wallinga that family extinction in a marginally surviving population is governed by DP scaling laws, and speculate on applications to human mitochondrial DNA.Comment: 19 pages, with 10 ps-figured include