Simulate Dail-Madsen open N-mixture data

Latent N_1 ~ Poisson(lambda); for t >= 2, N_t = Binomial(N_(t-1), omega_{t-1}) + Poisson(gamma_{t-1}); observed via Binomial(N_t, p) over J secondary visits in each of T primary seasons. Returns a 3D array N x J x T suitable for tobs() with dyn_abun().

Usage

simulate_dyn_abun(
  N = 150,
  T = 4,
  J = 3,
  n_abund_covs = 1,
  beta_lambda = NULL,
  p = 0.5,
  omega = 0.6,
  gamma = 1,
  beta_omega = NULL,
  beta_gamma = NULL,
  mixture = c("poisson", "negbin"),
  r = 2,
  zi = 0,
  seed = NULL
)

Arguments

N

Number of sites (default 150).

T

Number of primary seasons (default 4).

J

Number of secondary visits per season (default 3).

n_abund_covs

Number of initial-abundance covariates (default 1).

beta_lambda

Initial-abundance coefficients (log). Default c(log(5), runif(n_abund_covs, -0.4, 0.4)).

p, omega, gamma

Detection, apparent-survival, and recruitment parameters (scalars; defaults 0.5, 0.6, 1.0). omega / gamma set the constant rate used when beta_omega / beta_gamma are NULL.

beta_omega, beta_gamma

Optional length-2 coefficients c(intercept, slope) for a season-varying survival (logit link) or recruitment (log link) rate driven by a per-(site, interval) season covariate. NULL (default) keeps the constant omega / gamma.

mixture

Initial-abundance distribution: "poisson" (default) or "negbin" (negative-binomial N_1 ~ NB(mean = lambda, size = r)).

r

Negative-binomial size for mixture = "negbin" (default 2).

zi

Structural-zero share for a zero-inflated model (default 0). With probability zi a site is never occupied (N_t = 0 for all seasons), so all its counts are zero; fit such data with dyn_abun(mixture = "zip") / "zinb".

seed

Optional random seed.

Value

A list with y (N x J x T count array), data (covariates, including the [N x (T-1)] season_cov matrix column when a season-varying rate is used), and truth (coefficients, per-site lambda, the realised omega / gamma rates, and r under "negbin").

Details

Survival and recruitment are constant across seasons by default. Supplying beta_omega (logit-scale) or beta_gamma (log-scale) instead makes the rate depend on a per-(site, interval) season covariate z: omega_{i,t} = plogis(beta_omega[1] + beta_omega[2] * z_{i,t}), gamma_{i,t} = exp(beta_gamma[1] + beta_gamma[2] * z_{i,t}). The covariate is returned as a [N x (T-1)] matrix column season_cov of data, ready for omega = ~ season_cov.

Examples

sim <- simulate_dyn_abun(N = 40, T = 3, J = 3, seed = 1)
dim(sim$y)