# API Documentation¶

This is the API documentation for msprime, and provides detailed information on the Python programming interface. See the Tutorial for an introduction to using this API to run simulations. See the tskit documentation for information on how to use the tskit Python API to analyse simulation results.

## Simulation model¶

The simulation model in msprime closely follows the classical ms program. Unlike ms, however, time is measured in generations rather than in units of $$4 N_e$$ generations, i.e., “coalescent units”. This means that when simulating a population with diploid effective size $$N_e$$, the mean time to coalescence between two samples in an msprime simulation will be around $$2 N_e$$, while in an ms simulation, the mean time will be around $$0.5$$. Internally, msprime uses the same algorithm as ms, and so the Ne parameter to the simulate() function still acts as a time scaling, and can be set to 0.5 to match many theoretical results, or to 0.25 to match ms. Population sizes for each subpopulation and for past demographic events are also defined as absolute values, not scaled by Ne. All migration rates and growth rates are also per generation.

When running simulations we define the length $$L$$ of the sequence in question using the length parameter. This defines the coordinate space within which trees and mutations are defined. $$L$$ is a continuous value, so units are arbitrary, and coordinates can take any value from $$0$$ to $$L$$. (So, although we recommend setting the units of length to be analogous to “bases”, events can occur at fractional positions.) Mutations occur in an infinite sites process along this sequence, and mutation rates are specified per generation, per unit of sequence length. Thus, given the per-generation mutation rate $$\mu$$, the rate of mutation over the entire sequence in coalescent time units is $$\theta = 4 N_e \mu L$$. It is important to remember these scaling factors when comparing with analytical results!

Similarly, recombination rates are per unit of sequence length and per generation in msprime. Thus, given the per generation crossover rate $$r$$, the overall rate of recombination between the ends of the sequence in coalescent time units is $$\rho = 4 N_e r L$$. Although breakpoints do not necessarily occur at integer locations, the underlying recombination model is finite, and the behaviour of a small number of loci can be modelled using the RecombinationMap class. However, this is considered an advanced feature and the majority of cases should be well served with the default recombination model and number of loci.

Population structure is modelled by specifying a fixed number of subpopulations $$d$$, and a $$d \times d$$ matrix $$M$$ of per generation migration rates. Each element of the matrix $$M_{j,k}$$ defines the fraction of population $$j$$ that consists of migrants from population $$k$$ in each generation. Each subpopulation has an initial absolute population size $$s$$ and a per generation exponential growth rate $$\alpha$$. The size of a given population at time $$t$$ in the past (measured in generations) is therefore given by $$s e^{-\alpha t}$$. Demographic events that occur in the history of the simulated population alter some aspect of this population configuration at a particular time in the past.

Warning

This parameterisation of recombination, mutation and migration rates is different to ms, which states these rates over the entire region and in coalescent time units. The motivation for this is to allow the user change the size of the simulated region without having to rescale the recombination and mutation rates, and to also allow users directly state times and rates in units of generations. However, the mspms command line application is fully ms compatible.

## Running simulations¶

The simulate() function provides the primary interface to running coalescent simulations in msprime.

## Population structure¶

Population structure is modelled in msprime by specifying a fixed number of subpopulations, with the migration rates between those subpopulations defined by a migration matrix. Each subpopulation has an initial_size that defines its absolute diploid size at time zero and a per-generation growth_rate which specifies the exponential growth rate of the sub-population. We must also define the number of genomes to sample from each subpopulation. The number of populations and their initial configuration is defined using the population_configurations parameter to simulate(), which takes a list of PopulationConfiguration instances. Population IDs are zero indexed, and correspond to their position in the list.

Samples are drawn sequentially from populations in increasing order of population ID. For example, if we specified an overall sample size of 6, and specify that 2 samples are drawn from population 0 and 4 from population 1, then samples 0 and 1 will be initially located in population 0, and samples 2, 3, 4, and 5 will be drawn from population 2.

Given $$N$$ populations, migration matrices are specified using an $$N \times N$$ matrix of between-subpopulation migration rates. See the documentation for simulate() and the Simulation model section for more details on the migration rates.

## Demographic Events¶

Demographic events change some aspect of the population configuration at some time in the past, and are specified using the demographic_events parameter to simulate(). Each element of this list must be an instance of one of the following demographic events that are currently supported. Note that all times are measured in generations, all sizes are absolute (i.e., not relative to $$N_e$$), and all rates are per-generation.

### Debugging demographic models¶

Warning

The DemographyDebugger class is preliminary, and the API is likely to change in the future.

## Initialising simulations from a tree sequence¶

By default msprime simulations are initialised by specifying a set of samples, using the sample_size or samples parameters to simulate(). This initialises the simulation with segments of ancestral material covering the whole sequence. Simulation then proceeds backwards in time until a most recent common ancestor has been found at all points along this sequence. We can also start simulations from different initial conditions by using the from_ts argument to simulate(). Informally, we take an ‘unfinished’ tree sequence as a parameter to simulate, initialise the simulation from the state of this tree sequence and then run the simulation until coalescence. The returned tree sequence is then the result of taking the input tree sequence and completing the trees using the coalescent.

This is useful for forwards-time simulators such as SLiM that can output tree sequences. By running forward-time simulation for a certain number of generations we obtain a tree sequence, but these trees may not have had sufficient time to reach a most recent common ancestor. By using the from_ts argument to simulate() we can combine the best of both forwards- and backwards-time simulators. The recent past can be simulated forwards in time and the ancient past by the coalescent. The coalescent simulation is initialised by the root segments of the input tree sequence, ensuring that the minimal amount of ancestral material possible is simulated.

Please see the tutorial for an example of how to use this feature with a simple forwards-time Wright-Fisher simulator

### Input requirements¶

Any tree sequence can be provided as input to this process, but there is a specific topological requirement that must be met for the simulations to be statistically correct. To ensure that ancestral segments are correctly associated within chromosomes when constructing the initial conditions for the coalescent simulation, forward-time simulators must retain the nodes corresponding to the initial generation. Furthermore, for every sample in the final generation (i.e. the extant population at the present time) there must be a path to one of the founder population nodes. (Please see the tutorial for further explanation of this point and an example.)

### Recombination map limitations¶

Because of the way that msprime handles recombination internally, care must be taken when specifying recombination when using the from_ts argument. If recombination positions are generated in the same way in both the initial tree sequence and the coalescent simulation, then everything should work. However, the fine scale details of the underlying recombination model matter, so matching nonuniform recombination maps between simulators may not be possible at present. (To make it work, we must ensure that every recombination breakpoint in from_ts matches exactly to a possible recombination breakpoint in msprime’s recombination map, which is not guaranteed because of msprime’s discrete recombination model.)

One case in which it is guaranteed to work is if from_ts has integer coordinates, and we want to simulate a coalescent with a uniform recombination rate. In this case, to have a uniform recombination rate r use:

L = int(from_ts.sequence_length)
recomb_map = msprime.RecombinationMap.uniform_map(L, r, L)
final_ts = mpsrime.simulate(from_ts=from_ts, recomb_map=recomb_map)


## Simulating mutations¶

When running coalescent simulations it’s usually most convenient to use the mutation_rate argument to the simulate() function to throw neutral mutations down on the trees. However, sometimes we wish to throw mutations down on an existing tree sequence: for example, if we want to see the outcome of different random mutational processes on top of a single simulated topology, or if we have obtained the tree sequence from another program and wish to overlay neutral mutations on this tree sequence.

msprime.BINARY == 0

The binary mutation alphabet where ancestral states are always “0” and derived states “1”.

msprime.NUCLEOTIDES == 1

The nucleotides mutation alphabet in which ancestral and derived states are chosen from the characters “A”, “C”, “G” and “T”.