Runs a Lande-Arnold analysis and returns one table of selection differentials (S) and linear (beta), quadratic (gamma) and correlational (gamma_ij) gradients. All estimates use traits standardised to mean 0, SD 1 and relative fitness, so tables from different studies can be compared.
Arguments
- data
A data frame containing fitness and trait measurements.
- fitness_col
A string specifying the name of the fitness column.
- trait_cols
A character vector of trait column names.
- fitness_type
A string indicating the fitness type:
"auto","binary","count", or"continuous". Binary and count fitness take their p-values from a GLM (logistic, or Poisson and negative binomial) on the raw values; the gradients always come from OLS on relative fitness.- standardize
Logical indicating whether to standardize traits to mean 0 and SD 1. Default is
TRUE.- group
Optional string specifying a grouping variable (e.g., "year", "site"). Traits and relative fitness are standardised within each group, and for binary and count fitness the GLM that supplies the p-values gets a separate intercept for each group.
- use_relative_for_fit
Logical; if
TRUE(default) the gradients are estimated on relative fitness \(W / \bar{W}\) for every fitness type, as in Lande & Arnold (1983). SetFALSEonly to reproduce coefficients on the absolute fitness scale.- include_differentials
Logical; if
TRUE(default) selection differentials S are included alongside the gradients.- digits
Integer number of digits used when printing. Default is 4.
- se_type
Standard errors of the gradients:
"ols", the usual least-squares ones (the default), or"hc3", leave-one-out standard errors that allow for residual spread changing with the traits. Mitchell-Olds and Shaw (1987) suggested the jackknife for selection gradients when the residuals are not normal; HC3 (MacKinnon and White 1985) gets much the same in closed form, from how far the estimates move when each individual is left out. In the package's simulation it recovered most of the coverage beta loses when the model leaves out curvature, from 88 to 93% with normal traits, 67 to 86% with log-normal ones and 77 to 91% with heavy-tailed symmetric ones. It did nothing for the coverage lost to estimating a skewed trait's SD, and with survival and counts its intervals covered a little less, down to 91% (seecheck_selection_assumptions()). For continuous fitness the p-values follow the chosen errors; for survival and counts they come from the GLM with eitherse_type.
Value
A data frame of class "selection_report" with columns
Term, Type, Estimate, Std_Error, and
P_Value.
Details
Differentials and gradients are computed on the same individuals (those with complete fitness and trait values) and on the same trait and fitness scales. S is the population covariance (divides by n) while the OLS gradient on sd-standardised traits corresponds to the sample covariance (n - 1), so for a single trait the Differential and Linear rows differ by the factor (n - 1) / n.
Examples
selection_report(bumpus, "survival", c("total_length", "weight", "humerus"))
#> Warning: Collinear traits (VIF above 5) may inflate the standard errors
#> Selection analysis (standardised traits, relative fitness)
#> Fitness type: binary
#> p-values are from a logistic model on the same terms
#>
#> Term Type Estimate Std_Error P_Value Sig
#> total_length Differential -0.2347 NA NA
#> weight Differential -0.2024 NA NA
#> humerus Differential 0.1629 NA NA
#> total_length Linear -0.3153 0.0922 0.0016 **
#> weight Linear -0.2868 0.0952 0.0057 **
#> humerus Linear 0.4833 0.0898 0.0000 ***
#> total_length² Quadratic -0.1386 0.2088 0.3936
#> weight² Quadratic -0.0098 0.1728 0.7222
#> humerus² Quadratic 0.0056 0.1681 0.7165
#> total_length × weight Correlational -0.0334 0.1609 0.5449
#> total_length × humerus Correlational -0.0317 0.1191 0.7570
#> weight × humerus Correlational 0.0219 0.1560 0.5677
#>
#> Signif: *** 0.001 ** 0.01 * 0.05 . 0.1