The Penna model for biological ageing on a lattice: spatial consequences of child-care

We introduce a square lattice into the Penna bit-string model for biological ageing and study the evolution of the spatial distribution of the population considering different strategies of child-care. Two of the strategies are related to the movements of a whole family on the lattice: in one case the mother cannot move if she has any child younger than a given age, and in the other case if she moves, she brings these young children with her. A stronger condition has also been added to the second case, considering that young children die with a higher probability if their mothers die, this probability decreasing with age. We show that a highly non uniform occupation can be obtained when child-care is considered, even for an uniform initial occupation per site. We also compare the standard survival rate of the model with that obtained when the spacial lattice is considered (without any kind of child-care).Comment: 8 pages, 6 Postscript figure

Phase transition in a mean-field model for sympatric speciation

We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field approximation may be decoupled. We find a phase transition leading to sympatric speciation as a parameter that quantifies competition strength is varied. This transition, previously found in a computational model, occurs to be of first order.Comment: accepted for Physica

Applications and Sexual Version of a Simple Model for Biological Ageing

We use a simple model for biological ageing to study the mortality of the population, obtaining a good agreement with the Gompertz law. We also simulate the same model on a square lattice, considering different strategies of parental care. The results are in agreement with those obtained earlier with the more complicated Penna model for biological ageing. Finally, we present the sexual version of this simple model.Comment: For Int.J.Mod.Phys.C Dec. 2001; 11 pages including 6 fig

Computer simulations on the sympatric speciation modes for the Midas cichlid species complex

Cichlid fishes are one of the best model system for the study of evolution of the species. Inspired by them, in this paper we simulated the splitting of a single species into two separate ones via random mutations, with both populations living together in sympatry, sharing the same habitat. We study the ecological, mating and genetic conditions needed to reproduce the polychromatism and polymorphism of three species of the Midas Cichlid species complex. Our results show two scenarios for the A. Citrinellus speciation process, one with and the other without disruptive natural selection. 
In the first scenario, the ecological and genetic conditions are sufficient to create two new species, while in the second the mating and genetic conditions must be synchronized in order to control the velocity of genetic drift

Simulations of a mortality plateau in the sexual Penna model for biological ageing

The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individuals genomes are represented by bit-strings. It provides a simple metaphor for the evolutionary process in terms of the mutation accumulation theory. In its original version, an individual dies due to inherited diseases when its current number of accumulated mutations, n, reaches a threshold value, T. Since the number of accumulated diseases increases with age, the probability to die is zero for very young ages (n = T). Here, instead of using a step function to determine the genetic death age, we test several other functions that may or may not slightly increase the death probability at young ages (n < T), but that decreases this probability at old ones. Our purpose is to study the oldest old effect, that is, a plateau in the mortality curves at advanced ages. Imposing certain conditions, it has been possible to obtain a clear plateau using the Penna model. However, a more realistic one appears when a modified version, that keeps the population size fixed without fluctuations, is used. We also find a relation between the birth rate, the age-structure of the population and the death probability.Comment: submitted to Phys. Rev.