This function simulates a geneology with varying population size specified by a vector of population sizes, one for each generation.

sample_geneology_varying_size(
population_sizes,
generations_full = 1L,
generations_return = 3L,
enable_gamma_variance_extension = FALSE,
gamma_parameter_shape = 5,
gamma_parameter_scale = 1/5,
progress = TRUE
)

## Arguments

population_sizes The size of the population at each generation, g. population_sizes[g] is the population size at generation g. The length of population_sizes is the number of generations being simulated. Number of full generations to be simulated. How many generations to return (pointers to) individuals for. Enable symmetric Dirichlet (and disable standard Wright-Fisher). Parameter related to symmetric Dirichlet distribution for each man's probability to be father. Refer to details. Parameter realted to symmetric Dirichlet distribution for each man's probability to be father. Refer to details. Show progress.

## 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).

## 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 $$gamma_parameter_scale = 1/\alpha$$.

sample_geneology().
sim <- sample_geneology_varying_size(10*(1:10))
#>  $population :Classes 'malan_population', 'externalptr' <externalptr> #>$ generations               : int 10
#>  $founders : int 8 #>$ growth_type               : chr "VaryingPopulationSize"
#>  $sdo_type : chr "StandardWF" #>$ end_generation_individuals:List of 100
#>  $individuals_generations :List of 199 #> - attr(*, "class")= chr [1:2] "malan_simulation" "list"sim$population#> Population with 324 individualspeds <- build_pedigrees(sim\$population)