In the next few lectures, we are going to discuss the genetics of populations or populational genetics. Populational genetics is dealing with changes which happens in populations under the influence of evolutionary factors. Populational genetics is actually one of the most mathematical fields of biology and genetics, and therefore, it makes sense to also redefine the subject of populational genetics in a little bit more mathematical terms. Then we can define this subject as studying the question that, given a set of initial conditions, a set of certain parameters, what we expect about allelic frequencies dynamics in space and time. Before this definition becomes any operational, we first need to define what are these evolutionary factors which I have mentioned, and we also will need to define what is genetic population. So, if we think of evolutionary factors, the first thing which comes to mind is mutation. A mutation is a process of random change in DNA sequence, and this mutation may be inherited by future generations. So, in that mutation process, provides the material for genetic diversity. Then we need to define selection, and we define it as a process of differential reproduction. And differential here means that it is genotype-dependent. So selection is acting upon on the material which is provided by the mutation process. Next, a very important set of factors which need to be considered, are factors which are putting constraints and certain structure on potential gene flow. So, these are such factors as migration, isolation, or presence of specific breeding structures. And finally last but not the least, we need not forget that natural populations have finite size, therefore, in these populations, random events are also playing important role in the dynamics of allele and genotypic frequencies. So, we need to also keep in mind the presence of genetic drift. Now, let us define what is a genetic population. Here, we are interested in what is going to happen with these populations, so this means we are going to use prospective definition, and our definition is going to be also relative. You will understand what I mean by these just in few minutes. So, we will call two individuals, say A and B, to be belonging to the same genetic population if there is some non-zero chance for these two individuals to have a common offspring. And here by having common offspring, I don't mean that they should have common offspring immediately, but this is to denote a possibility that these two individuals may have a common offspring in potentially number of generations. However, we cannot stop here, because this definition is now coming too close to the definition of species, and we are interested in genetic populations which exist within the species. So, we miss something important in our definition. So, we are going to extend it as follows. We will tell that two individuals, A and B, belong to the same genetic population if they have non-zero chance to have an offspring in common, and this chance is much higher than the chance for this individual to have an offspring in common with some third individual C, which we will say is belonging to a different genetic population. To give a little bit more of practical flavor to this definition, I'm going to consider relatively simple example, an example of a population of individuals which live on the islands scattered across the sea. So, let's consider to start with two islands which are separated by the sea. And then, of course, if we consider a group of individuals which live within the island, and we assume that the major factor which isolates the populations and which sets the boundary on the gene flow is isolation by distance, then, naturally, we can assume that within the island, the chance for two individuals to have common offspring is much higher than the chance for two individuals coming from different islands. So, in this context, we can speak about genetic population of island A and separate genetic population of island B. However, our definition is relative. So, if we introduce another island, say C, which is more remote than islands A and B, then we can think of genetic populations, joined genetic populations of islands A and B are relative to the population of island C. We can even take this one step further, because A, B, and C, despite the fact that they may be quite isolated by the scene between, still may have some gene flow between them, and the possibility for individuals from these three islands to have a progeny in common may still be much higher than chances of these individuals to have common progeny with individuals from some way remote continental population.