Computer simulation of sympatric speciation with Penna ageing model

Abstract

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...

The penna model for biological aging and speciation

“…16 Each individual has n = 0, 1, or 2 bits set at this position. A female with n such bits at position 11 selects only males with the same number n of such speciation bits.…”

“…If the birth rate changes from 1 to 1 + n, the new species ends up with a larger population than the original, but both may still coexist. 16 …”

“…17 The intention was to mimic rainfall's seasonal effect on the availability of different-sized seeds in the Galapagos Islands and this availability's impact on beak size in the population of ground finches feeding on those seeds. 18 Beak size is encoded by a single pair of bit strings added to the genome of each individual by counting the number of recessive bit positions (chosen as 16), where both bits are set to 1, plus the number of dominant positions with at least one of the two bits set. It will therefore be a number k between 0 (meaning a very small beak) and 32 (a very large one).…”

“…When the fitness function F(k) is single-peaked, there is no selective pressure for mating selectiveness, and the population is panmictic. After F(k) becomes double-peaked, females that mutate into selectiveness will choose mating partners that have beak sizes similar to their own: if a female has k <(>) 16 and is selective, she will only mate with a partner that also has k <(>) 16. Figure 5 shows the distribution of phenotypes-in this case, beak size-of the population at time step N step = 12,000 (up to which the fitness function was single-peaked) and at time step 50,000 (after it has been double-peaked for 30,000 time steps).…”

Evolution, ageing and speciation: Monte Carlo simulations of biological systems

“…Both a simpler and a more elaborated model (with two phenotypic traits) using the Penna bit-string strategy to simulate sympatric speciation can be found in [33].…”