get_mean_var_shifts: Estimate Shifts in Optimal Trait Values and Variance

Description

Estimates shifts in both the optimal trait values (mean) and evolutionary variance along a phylogeny under an Ornstein-Uhlenbeck (OU) process, using an \(\ell_1\)-penalized optimization procedure. Optionally accounts for measurement error in the observed trait data.

Usage

get_mean_var_shifts(
  Y,
  tree,
  alpha,
  lambda1,
  lambda2,
  max.steps = 1000,
  t = 0.01,
  penalty = "L1",
  thres = 0.01,
  sigma2 = NULL,
  measurement_error = FALSE
)

Value

A list containing:

shifts_mean: Indices of branches with detected shifts in optimal trait values (\(\beta \neq 0\)).
shifts_var: Indices of branches with detected shifts in evolutionary variance (\(\gamma \neq 0\)).
beta: Estimated shift coefficients for optimal trait values.
gamma: Estimated shift coefficients for evolutionary variance.
sigma2: Estimated base variance (\(\sigma^2\)) of the OU process.
b0: Estimated intercept (root state).
sigma2_error: Estimated measurement error variance (only returned if measurement_error = TRUE).

Arguments

Y: A numeric vector of continuous trait values for the species at the tips of the tree.
tree: A phylogenetic tree of class phylo.
alpha: The selection strength parameter in the OU process.
lambda1: Non-negative penalty for \(\beta\) (shifts in optimal trait values).
lambda2: Non-negative penalty for \(\gamma\) (shifts in evolutionary variance).
max.steps: Maximum number of optimization steps. Default is 1000.
t: Step size for the gradient-based updates. Default is 0.01.
penalty: Type of penalty to apply. Options are "L1" (default) or "None".
thres: Convergence threshold for the change in loss between steps. Default is 0.01.
sigma2: Optional initial value for the base evolutionary variance. If NULL, it is initialized to 1.
measurement_error: Logical. If TRUE, the method estimates additional measurement error variance.