One species is simulated to split into two separate species via random mutations, even if both populations live together in the same environment. This speciation is achieved in the Penna bitstring model of biological ageing, with modified Verhulst factors, and in part by additional bitstrings regulating phenotype and mate selection. I IntroductionThe common ancestors of today's humans and today's chimpanzees presumably lived several million years ago. Then, due to genetic mutations and/or changes in the environment, the population split into the ancestors of humans and the ancestors of chimpanzees. Such a separation of one species into two is called "speciation". It is easily explained if the two populations live in separate environments, like one on an island and the other on a continent, making the mating of males from one population with females from the other population impossible. This effect is called allopatric speciation. More difficult to explain is sympatric speciation, where the two populations continue to live in the same environment but nevertheless cease to mate each other [1]. A recent computer model [2] in the physics literature also cites biological examples, serving as a background also for our paper. We concentrate here on models with age-structured populations [3,4,5] and in particular use the Penna bitstring model [6,7], which is the presently most widespread model to simulate biological ageing. We deal only with sexual reproduction where two populations are defined as being different species if the mating from different populations produces no viable offspring.The next section shortly explains this Penna model and then presents the minimal modifications which we found necessary to get sympatric speciation. A more realistic model involving three pairs of bitstrings instead of only one is discussed in the following section. We end with a short summary. II Simple Model II.1 Penna ModelThe Penna bitstring model for biological ageing [6,7] simulates the mutation accumulation by storing bad mutations (= hereditary diseases) in a string of (usually) 32 bits. The position of the bit corresponds to the age of the individual; its value corresponds to health (zero) or sickness (one). Sick bits act from the age to which their positions belong up to the death of the individual. Three active sicknesses kill the animal; in addition all animals are killed at each time step t = 1, 2, . . . with the Verhulst probability V (t) = N (t)/N max where N (t) is the current population and N max is often called the carrying capacity describing the limitation of food and space. After reaching an age of eight "years" (= bit positions or iterations), each individual gives birth to one child per year until its death; the child inherits the same bitstring as the mother except for one possible mutation at a randomly selected position where the mutated bit is set to one irrespective of its previous value. Initially, all bit strings are zero.For the sexual Penna model used here, each individual has two bitstrings inherited f...

We investigate the macroscopic effects of the ingredients that drive the origin of species through sympatric speciation. In our model, sympatric speciation is obtained as we tune up the strength of competition between individuals with different phenotypes. As a function of this control parameter, we can characterize, through the behavior of a macroscopic order parameter, a phase transition from a non-speciation to a speciation state of the system. The behavior of the first derivative of the order parameter with respect to the control parameter is consistent with a phase transition and exhibits a sharp peak at the transition point. For different resources distribution, the transition point is shifted, an effect similar to pressure in PVT system. The inverse of the parameter related to sexual selection strength behaves like an external field in the system and, as thus, is also a control parameter. The macroscopic effects of the biological parameters used in our model reveal thus fingerprints typical of thermodynamic quantities in a phase transition of an equilibrium physical system.The branching of a single population into two or more species without prevention of gene flow through geographic segregation is known as sympatric speciation [1,2,3,4]. Herbivorous insects have long been considered prime candidates for sympatric speciation because of an intimate and frequently highly specialized relationship with their host plants, which serve as habitat, food resource, and, often, mating location [5]. The apple maggot fly Rhagoletis pomonella has been considered, since 1966, as the classical example of sympatric speciation in progress [3]. R. pomonella shifted from feeding on the unabscised fruit of its native host hawthorn (Crataegus spp.) to utilizing the introduced, domesticated apple (Malus pumila) sometime in the mid-1800s in the Hudson River Valley region of the state of New York. Genetic evidence suggests that the species is in the process of shifting and adapting to this new host plant [6,7].Two ingredients are important for sympatric speciation to happen in a population [8,9,10]: The competition caused by fluctuations in ecology [11,12] and assortative mating caused by selective mating [13,14]. Ecological and sexual selection models have addressed these two aspects of sympatric speciation separately [9]. The starting point of ecological models is the assumption that sympatric speciation results from disruptive selection. That is, competition for diverse resources leads to separation in a population, if individuals with intermediate phenotypes are losers when they compete with those with extreme ones. Such selection can cause sympatric speciation because it provides an advantage for reproductive isolation between opposite, well-adapted, extreme phenotypes, and reproductive isolation can be achieved due to evolution of nonrandom mating [15]. Sympatric speciation can also be driven by selective mating, or sexual selection, that is, nonrandom mating leading to differential reproductive successes of different pheno...

namely, the order-disorder conflict. Order, represented by a minimum of the free energy in physical systems, is related to the Darwinian principle of survival of the fittest; disorder, or entropy maximization, is driven by temperature in physical systems and genetic mutations in biological systems.The Penna model for biological aging 2 is based entirely on Darwinian evolution with mutations and is a representation of the Darwinian conflict particularly well suited for computer simulations. It has played a role similar to the Ising model for magnetic systems in the sense that it is a minimal model that retains only the essentials of Darwinian dynamics. Like the Ising model, it uses binary variables to represent genes: zero for ordinary genes and ones for harmful ones. Originally focused on problems of biological aging, application to several different evolutionary problems substantially increased its scope. Our purpose here is to provide an updated review of recent results researchers have obtained with this model. 74Copublished by the IEEE CS and the AIP

Galapagos finches, have motivated much theoretical research aimed at understanding the processes associated with the formation of the species. Inspired by them, in this paper we investigate the process of sympatric speciation in a simple food web model. For that we modify the individual-based Penna model that has been widely used to study aging as well as other evolutionary processes. Initially, our web consists of a primary food source and a single herbivore species that feeds on this resource. Subsequently we introduce a predator that feeds on the herbivore. In both instances we manipulate directly a basal resource distribution and monitor the changes in the populations. Sympatric speciation is obtained for the top species in both cases, and our results suggest that the speciation velocity depends on how far up, in the food chain, the focus population is feeding. Simulations are done with three different sexual imprinting-like mechanisms, in order to discuss adaptation by natural selection.

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.

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