Main wrapper function for selection analysis following Lande & Arnold (1983). Extracts linear (beta), quadratic (gamma), and correlational selection gradients.
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.- return_grouped
Logical indicating whether to return results grouped if a
groupis specified.- 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 containing selection coefficients (Term, Type,
Beta_Coefficient, Standard_Error, P_Value, Variance), with the standard
errors used in the attribute "se_type".
References
MacKinnon, J. G. and White, H. (1985) Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 29, 305-325. Mitchell-Olds, T. and Shaw, R. G. (1987) Regression analysis of natural selection: statistical inference and biological interpretation. Evolution 41, 1149-1161.
Examples
selection_coefficients(bumpus, "survival", c("total_length", "weight"), fitness_type = "binary")
#> there are higher-order terms (interactions) in this model
#> consider setting type = 'predictor'; see ?vif
#> Warning: Collinear traits (VIF above 5) may inflate the standard errors
#> Term Type Beta_Coefficient Standard_Error
#> 1 total_length Linear -0.17811220 0.0974800
#> 2 weight Linear -0.09992466 0.0974800
#> 3 total_length² Quadratic -0.23342057 0.2111590
#> 4 weight² Quadratic 0.02096490 0.1628337
#> 5 total_length × weight Correlational -0.06949785 0.1585041
#> P_Value Variance
#> 1 0.07276336 0.009502351
#> 2 0.30287778 0.009502351
#> 3 0.24402273 0.044588139
#> 4 0.93873420 0.026514809
#> 5 0.57236384 0.025123549
# one set of gradients per sex, each sex standardised on its own
selection_coefficients(bumpus, "survival", c("total_length", "weight"),
group = "sex", return_grouped = TRUE)
#> there are higher-order terms (interactions) in this model
#> consider setting type = 'predictor'; see ?vif
#> there are higher-order terms (interactions) in this model
#> consider setting type = 'predictor'; see ?vif
#> Term Type Beta_Coefficient Standard_Error
#> male.1 total_length Linear -0.3407483627 0.09731904
#> male.2 weight Linear -0.0545617939 0.09731904
#> male.3 total_length² Quadratic -0.0273816426 0.19241802
#> male.4 weight² Quadratic 0.0462210677 0.17271044
#> male.5 total_length × weight Correlational -0.0762079316 0.15832913
#> female.1 total_length Linear 0.0004585805 0.20517997
#> female.2 weight Linear -0.2876716237 0.20517997
#> female.3 total_length² Quadratic -0.2985821975 0.48947090
#> female.4 weight² Quadratic 0.0333986785 0.32247945
#> female.5 total_length × weight Correlational -0.0520198090 0.33611268
#> P_Value Variance Group
#> male.1 0.001978417 0.009470995 male
#> male.2 0.606430455 0.009470995 male
#> male.3 0.832288575 0.037024693 male
#> male.4 0.751956548 0.029828895 male
#> male.5 0.544449522 0.025068112 male
#> female.1 0.962802935 0.042098822 female
#> female.2 0.159163810 0.042098822 female
#> female.3 0.478153622 0.239581761 female
#> female.4 0.599203577 0.103992995 female
#> female.5 0.968497077 0.112971735 female