Wright-Fisher model of evolution

This is one of the simplest models of population genetics that demonstrates the use of sample!. We implement a simple case of the model where we study haploids (cells with a single set of chromosomes) while for simplicity, focus only on one locus (a specific gene). In this example we will be dealing with a population of constant size.

It is also available from the Models module as Models.wright_fisher.

A neutral model

• Imagine a population of n haploid individuals.
• At each generation, n offsprings replace the parents.
• Each offspring chooses a parent at random and inherits its genetic material.

using Agents
numagents = 100

100

Let's define an agent. The genetic value of an agent is a number (trait field).

@agent struct Haploid(NoSpaceAgent)
    trait::Float64
end

The model can be run for many generations and we can collect the average trait value of the population. To do this we will use a model-step function (see step!) that utilizes sample!:

modelstep_neutral!(model::ABM) = sample!(model, nagents(model))

modelstep_neutral! (generic function with 1 method)

And make a model without any spatial structure:

model = StandardABM(Haploid; model_step! = modelstep_neutral!)

StandardABM with 0 agents of type Haploid
 agents container: Dict
 space: nothing (no spatial structure)
 scheduler: fastest

Create n random individuals:

for i in 1:numagents
    add_agent!(model, rand(abmrng(model)))
end

To create a new generation, we can use the sample! function. It chooses random individuals with replacement from the current individuals and updates the model. For example:

sample!(model, nagents(model))

StandardABM with 100 agents of type Haploid
 agents container: Dict
 space: nothing (no spatial structure)
 scheduler: fastest

We can now run the model and collect data. We use dummystep for the agent-step function (as the agents perform no actions).

using Statistics: mean

data, _ = run!(model, 20; adata = [(:trait, mean)])
data

As expected, the average value of the "trait" remains around 0.5.

A model with selection

We can sample individuals according to their trait values, supposing that their fitness is correlated with their trait values.

modelstep_selection!(model::ABM) = sample!(model, nagents(model), :trait)
model = StandardABM(Haploid; model_step! = modelstep_selection!)
for i in 1:numagents
    add_agent!(model, rand(abmrng(model)))
end

data, _ = run!(model, 20; adata = [(:trait, mean)])
data

Here we see that as time progresses, the trait becomes closer and closer to 1, which is expected - since agents with higher traits have higher probability of being sampled for the next "generation".