Abstract
Sympatric speciation, i.e. the evolutionary split of one species intotwo in the same environment, has been a highly troublesomeconcept. It has been a questioned if it is actually possible. Eventhough there have been a number of reported results both in the wildand from controlled experiments in laboratories, those findings areboth hard to get and hard to analyze, or even repeat. In the current studywe propose a mathematical model which addresses the question ofsympatric speciation and the evolution of reinforcement.Our aim has been to capture some of theessential features such as: phenotype, resources, competition,heritage, mutation, and reinforcement, in as simple a way aspossible. Still, the resulting model is not too easy to grasp withpurely analytical tools, so we have also complemented those studieswith stochastic simulations. We present a few results that bothillustrates the usefulness of such a model, but also rises newbiological questions about sympatric speciation and reinforcement inparticular.
Highlights
In the year 1707 two boys were born who both turned out to ponder on the concept of species
This paper addresses the question of sympatric speciation in combination with reinforcement dynamics
By sympatric speciation we mean that a population of one species through mutations, competition, mating etc. may break up into two or more distinct species sharing the same habitat
Summary
In the year 1707 two boys were born who both turned out to ponder on the concept of species. The competition between the individuals, which determines the variables cj, is deterministic, and expressed uniquely in terms of the population phenotype at time t This means that the total size of the population at time t + 1 is the sum of N independent Poisson distributed random variables, and is Poisson distributed. Two candidates are E c(z) log ( Zt, 1 c(z)) Zt(dz) and E[ Zt, 1 ] The first of these is, the expected population size, and the second is the relative entropy of the food distribution with respect to the probability measure Zt/|Zt|. The mechanism for reproduction in our model is very simple: choose two parents, compute the number of their offspring, and generate children with a phenotype that is the average of the parent’s phenotype plus a random noise term. The analysis is carried out in detail in [9] (see [4])
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