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Compare ECDF and Chi-square suitability under non-normal data

ecdf_nonnormal_niche.Rd

Script to run a simulation study to compare Chi-square vs. ECDF approaches to quantify habitat suitability based on bivariate non-normal data. Bivariate data was simulated based on environmental variables (temperature and precipitation) using Gaussian copulas. Temperature followed a normal distribution while precipitation followed a Weibull distribution. The choices of the distributions were based on Haddad (2021) - Theoretical and Applied Climatology (for temperature) and on the estimation of rainfall in milimeters by Wilks (1989) - Journal of Applied Meteorology. Because the relationship between temperature and precipitation is complex across space (Rodrigo, 2022 - Theoretical and Applied Climatology), we defined five correlation values between the two variables.

temp_parameters and prec_parameters must comply to stats::qnorm or stats::qweibull, depending on the function chosen on temp_function and prec_function. For "qnorm", user can specify mean and sd, while for "qweibull"

Usage

ecdf_nonnormal_niche(
  rho_vals = c(-0.7, -0.3, 0, 0.3, 0.7),
  n_vals = c(20L, 50L, 100L, 200L, 500L),
  n_reps = 10L,
  N_ref = 1e+05,
  temp_function = "qnorm",
  temp_parameters = list(mean = 20, sd = 5),
  prec_function = "qweibull",
  prec_parameters = list(shape = 2, scale = 10),
  seed = NULL
)

Arguments

rho_vals

Numeric vector; correlations between variables.

n_vals

Integer vector; sample sizes.

n_reps

Integer; number of replicates.

N_ref

Integer; size of reference population for "true" parameters.

temp_function

Character; function used to model temperature values. One of: "qnorm" or "qweibull".

temp_parameters

List; list organizing parameters to pass to temp_function.

prec_function

Character; function used to model precipitation values. One of: "qnorm" or "qweibull".

prec_parameters

List; list organizing parameters to pass to temp_function.

seed

Optional integer for reproducibility.

Value

A list with:

  • suit_plot: ggplot of suitability vs Mahalanobis distance

  • cor_df: correlation results

  • obs_df: observation-level data

Details

Simulates bivariate environmental data using Gaussian copulas with non-normal marginals (Normal for temperature and Weibull for precipitation), and evaluates agreement between chi-squared and ECDF suitability.

Author

Matheus T. Baumgartner

Examples

# Create ECDF-niche based on personalized options:
n <- ecdf_nonnormal_niche(rho_vals = c(-0.7, -0.3, 0, 0.3, 0.7),
                          n_vals   = c(20L, 50L, 100L, 200L, 500L),
                          n_reps   = 10L,
                          N_ref    = 1e5,
                          seed     = 1991)