ABMEv.jl is a package aimed at simulating the eco-evolutionary dynamics of a population in a multidimensional space, at the individual level.

ABMEv.jl is a package aimed at simulating the eco-evolutionary dynamics of a population in a multidimensional space, at the individual level.

Individuals are characterised by a set of traits in some combination of evolutionary spaces. An evolutionary space can represent for example a geographical landscape, a trait space, or genetic structure. Individuals experience three elementary events : **birth, death, mutation (or migration)**.

Individuals are characterised by **a set of traits** in some **combination of evolutionary spaces**. An evolutionary space can represent for example a geographical landscape, a trait space, or genetic structure. Individuals give birth at a rate given by the birth function `b`, and die at a rate given by the death function `d`. When an individual give birth, its offspring can move on the underlying evolutionary spaces. The movement can capture whether migration or mutation processes, and is characterised by a probability `m` and movement range `D`.

The user can provide **any birth and death functions**, which should depend on the system state and the individuals' trait. Together with the mutation process, this defines the dynamics of the system.

The user can provide **any birth and death functions**, which should depend on the system state and the individuals' trait. Together with the **movement rate and movement range**, this defines the dynamics of the system.

ABMEv.jl provides a **numerical laboratory** for eco-evolutionary dynamics, supplying

- flexible types for **individuals**, which can

- evolve over any combination of space,

- flexible types for **individuals**, which can

- evolve over any combination of space,

- store ancestors trait,

- flexible types for **evolutionary spaces**, that can consist of multidimensional **discrete or continuous domains**, as well as **graphs**,

- the possibility to use **callback functions** to save the state of the system at any time step

- several **algorithms** for the simulations (Gillepsie, CFM),

- several **algorithms** for the simulations (Gillepsie, Wright Fisher, etc...),

-**utility functions** to analyse simulation results.

## Installation

Open Julia in your favorite REPL and type the following

Open Julia in your favorite REPL and type the following

This will download latest version from git repo and download all dependencies.

## Getting started

Check out the great documentation if you want to use the advance features of ABMEv.jl. Otherwise, you can content yourself with the simple tutorial prodived below

Check out the documentation if you want to use the advanced features of ABMEv.jl. Otherwise, you can content yourself with the simple tutorial prodived below.

## Similar packages

[Agents.jl](https://juliadynamics.github.io/Agents.jl/) is a library oriented towards general ABM modelling, and thus is not as easy to deploy as ABMEv.jl for simulating stochastic models of structured populations.

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## A first tutorial

We provide here a tutorial a simple scenario, where the population is structured over the vertices of a graph, where each vertex selects for an optimal trait value $`\theta_i \in \{-1,1\}`$.

We provide here a tutorial that sums up the 5 steps necessary to launch a simulation. For the sake of the tutorial, we propose to model a population that is structured over the vertices of a graph and characterised by a trait under selection.

### 0. Import the relevant libraries

Let's import ABMEv.jl, and LightGraphs.jl

```julia

usingABMEv

usingLightGraphs.jl

```

Now define the trait space, and the graph (i.e. the abstraction of the landscape). We choose a star graph with 7 vertices.

### 1. Define the evolutionary spaces

We define the geographical space as star graph with 7 vertices (i.e. the abstraction of the landscape), and a continuous trait space.

```julia

nodes=7

g=star_graph(nodes)

landscape=GraphSpace(g)

θ=[rand([-1,1])foriin1:nodes]

traitspace=RealSpace(1)

evolspace=(landscape,traitspace)

```

Now let's define the birth and death functions. Individuals are characterised by their position on the graph and the adaptive trait.

### 2. Define birth and death function

Birth and death functions depend on agents position in the combination of spaces defined above, i.e. position on the graph and the adaptive trait.

We decide that each vertex selects for an optimal trait value $`\theta_i \in \{-1,1\}`$.

> :warning: birth and death functions should have the same number of

arguments as above.

### 3. Define how individuals move over the evolutionary space

Individual movements correspond to migration and mutation processes. On continuous spaces, one should specify a migration range and a migration rate. On discrete spaces, only a migration rate is needed (one assumes that indivuals can migrate only to neighbour patches).

```julia

K=1000

b(X,t)=1-0.5*(θ[X[1]]-X[1])^2

d(X,Y,t)=(X[1]≈Y[1])/K

D=[nothing,5e-1]# movement ranges

mu=[1.,1.]# movement rates

```

Define the mutation processes. Assuming a random walk of length 1, you should specify `nothing`.

### 4. Define the initial population state

```julia

D=[nothing,5e-1]

mu=[1.,1.]

myagents=[]# array containing the founder individuals

With a few more tricks, one can also plot the population trait density over time, for example the local trait density for individuals living on vertex 1.