This function simulates a geneology where the last generation has population_size individuals.

sample_geneology(
  population_size,
  generations,
  generations_full = 1L,
  generations_return = 3L,
  enable_gamma_variance_extension = FALSE,
  gamma_parameter_shape = 5,
  gamma_parameter_scale = 1/5,
  progress = TRUE,
  verbose_result = FALSE
)

Arguments

population_size

The size of the population.

generations

The number of generations to simulate:

  • -1 for simulate to 1 founder

  • else simulate this number of generations.

generations_full

Number of full generations to be simulated.

generations_return

How many generations to return (pointers to) individuals for.

enable_gamma_variance_extension

Enable symmetric Dirichlet (and disable standard Wright-Fisher).

gamma_parameter_shape

Parameter related to symmetric Dirichlet distribution for each man's probability to be father. Refer to details.

gamma_parameter_scale

Parameter realted to symmetric Dirichlet distribution for each man's probability to be father. Refer to details.

progress

Show progress.

verbose_result

Verbose result.

Value

A malan_simulation / list with the following entries:

  • population. An external pointer to the population.

  • generations. Generations actually simulated, mostly useful when parameter generations = -1.

  • founders. Number of founders after the simulated generations.

  • growth_type. Growth type model.

  • sdo_type. Standard deviation in a man's number of male offspring. StandardWF or GammaVariation depending on enable_gamma_variance_extension.

  • end_generation_individuals. Pointers to individuals in end generation.

  • individuals_generations. Pointers to individuals in last generations_return generation (if generations_return = 3, then individuals in the last three generations are returned).

If verbose_result is true, then these additional components are also returned:

  • individual_pids. A matrix with pid (person id) for each individual.

  • father_pids. A matrix with pid (person id) for each individual's father.

  • father_indices. A matrix with indices for fathers.

Details

By the backwards simulating process of the Wright-Fisher model, individuals with no descendants in the end population are not simulated. If for some reason additional full generations should be simulated, the number can be specified via the generations_full parameter. This can for example be useful if one wants to simulate the final 3 generations although some of these may not get (male) children.

Let \(\alpha\) be the parameter of a symmetric Dirichlet distribution specifying each man's probability to be the father of an arbitrary male in the next generation. When \(\alpha = 5\), a man's relative probability to be the father has 95\ constant 1 under the standard Wright-Fisher model and the standard deviation in the number of male offspring per man is 1.10 (standard Wright-Fisher = 1).

This symmetric Dirichlet distribution is implemented by drawing father (unscaled) probabilities from a Gamma distribution with parameters gamma_parameter_shape and gamma_parameter_scale that are then normalised to sum to 1. To obtain a symmetric Dirichlet distribution with parameter \(\alpha\), the following must be used: \(`gamma_parameter_shape` = \alpha\) and \(`gamma_parameter_scale` = 1/\alpha\).

See also

Examples

sim <- sample_geneology(100, 10) str(sim, 1)
#> List of 7 #> $ population :Classes 'malan_population', 'externalptr' <externalptr> #> $ generations : num 10 #> $ founders : int 19 #> $ growth_type : chr "ConstantPopulationSize" #> $ sdo_type : chr "StandardWF" #> $ end_generation_individuals:List of 100 #> $ individuals_generations :List of 210 #> - attr(*, "class")= chr [1:2] "malan_simulation" "list"
sim$population
#> Population with 388 individuals
peds <- build_pedigrees(sim$population) peds
#> List of 19 pedigrees (of size 48, 36, 30, 28, 27, 26, ...)