A good test of the fit of your secsse model, is to verify found parameter estimates using simulations. In other words: we want to know if the recovered model will also be recovered when the true model is really the focal model. If it is not, then although you found the best fitting model, this model does not explain the data well. Alternatively, you might want to create some artificial data to test your pipeline on. In either case, simulating a tree under the secsse model can come in very handy!

Tree simulation in secsse takes a very similar form to performing a Maximum Likelihood analysis, e.g. again we need to formulate our Lambda List, Mu vector and Q matrix, and this time we also need to populate these with actual values.

For a more detailed description of how the Lambda List, Mu vector and Q matrix
work, we refer to the vignette
`vignette("starting_secsse", package = "secsse")`

. We will here first simulate
using the CR model:

spec_matrix <- c(0, 0, 0, 1) spec_matrix <- rbind(spec_matrix, c(1, 1, 1, 1)) lambda_list <- secsse::create_lambda_list(state_names = c(0, 1), num_concealed_states = 2, transition_matrix = spec_matrix, model = "CR") mu_vector <- secsse::create_mu_vector(state_names = c(0, 1), num_concealed_states = 2, model = "CR", lambda_list = lambda_list) shift_matrix <- c(0, 1, 3) shift_matrix <- rbind(shift_matrix, c(1, 0, 4)) q_matrix <- secsse::create_q_matrix(state_names = c(0, 1), num_concealed_states = 2, shift_matrix = shift_matrix, diff.conceal = FALSE)

In order for secsse to be able to use these to simulate a tree, we need to
provide actual starting parameters. secsse has a helping function (`fil_in()`

)
for that as well!

speciation_rate <- 0.5 extinction_rate <- 0.05 q_ab <- 0.1 q_ba <- 0.1 used_params <- c(speciation_rate, extinction_rate, q_ab, q_ba) sim_lambda_list <- secsse::fill_in(lambda_list, used_params) sim_mu_vector <- secsse::fill_in(mu_vector, used_params) sim_q_matrix <- secsse::fill_in(q_matrix, used_params)

The function `fill_in()`

will go over the different objects and fill in the
appropriate parameter value from the `used_params`

vector, e.g. when it finds a
`1`

as rate indicator, it enters the value at position `used_params[1]`

, when
it encounters a `2`

as rate indicator, it enters the value at position
`used_params[2]`

etc.

sim_tree <- secsse::secsse_sim(lambdas = sim_lambda_list, mus = sim_mu_vector, qs = sim_q_matrix, crown_age = 5, num_concealed_states = 2, seed = 5) if (requireNamespace("diversitree")) { traits_for_plot <- data.frame(trait = as.numeric(sim_tree$obs_traits), row.names = sim_tree$phy$tip.label) diversitree::trait.plot(tree = sim_tree$phy, dat = traits_for_plot, cols = list("trait" = c("blue", "red")), type = "p") } else { plot(sim_tree$phy) }

Notice that `secsse_sim()`

can simulate a tree conditioning on different
tip-states: either it uses the conditioning `obs_states`

, in which case secsse
will keep simulating until it simulates a tree that has all observed states.
This is usually advised, as typically the observed states are the starting point
of the analysis, and not having observed all of them seems unrealistic.
Alternatively, secsse can also condition on `true_states`

- in this case secsse
will try to simulate until all possible combinations of observed and concealed
states are present at the tips:

sim_tree <- secsse::secsse_sim(lambdas = sim_lambda_list, mus = sim_mu_vector, qs = sim_q_matrix, crown_age = 5, num_concealed_states = 2, conditioning = "obs_states", seed = 6) sim_tree$obs_traits sim_tree$true_traits sim_tree <- secsse::secsse_sim(lambdas = sim_lambda_list, mus = sim_mu_vector, qs = sim_q_matrix, crown_age = 5, num_concealed_states = 2, conditioning = "true_states", seed = 6) sim_tree$obs_traits sim_tree$true_traits

Here, we have only explored a two-state system and the differences may not be very large, but for large numbers of states, such conditioning might yield very different trees.

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