Populations genetics and dynamics of bacteria on a Graph

Disclaimer:

I’m a physicist and I’m fairly new to Bioinformatics therefore somethings below may not make sense.

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My purpose:

I would like to simulate genetic evolution of bacterial populations, implementing interactions among different bacterial strains on a graph.

My starting point is to generate a graph with a certain topology.

Each vertex $V_i$ should contain a population of $N_i$ individuals for which I choose a certain allelic profile from an MLST database. Population numerosity and allelic profile is assigned by random choice.
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At starting time each vertex is populated with a "pure" strain of $N_i$ clones, identified with a randomly choosen allelic profile.

Dynamics assumptions

I will assume that:

• Topology does not change with time

• Vertex dynamic flows as a Moran process:
  At time $t$ , one individual is chosen randomly to reproduce and one
  individual is chosen to die. The same individual can be chosen to reproduce and
  then die. Thus, an individual has either zero, one, or two descendants. Zero and
  two with equal probability $p_0 = p_2 = (N_i -1 )/N_i^2$ , and one with probability $p_1 = 1 − 2 p_2$.

• Migration from one Vertex to one another is possible for nearest neighborhood with some fixed probability depending on choosen topology. I will assume that when migration occurs $I$ new individuals enters into $V_i$ and $O$ individuals exits from $V_i$, with $I$ and $O$ depending on origin vertex numerosity. Migrants carry allelic frequencies according to population they came from. When migration occurs a new population is established: allelic profile frequencies changes according to that.

• Migration and Moran process evolution does not happen simultaneously; This allows me to guarantee that each population performs at least one evolution.

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Questions:

(1) Is there something fundamental that I’m missing?

(2) Moran model ensures that the population size remains constant (apart from migration effects obviously). Is this appropriate in order to simulate dynamic in stationary growing phase or should I introduce some demographic effects?

(3) Which could be a proper "timing" for migration and evolution steps?