In MorphoFun/psa: Phenotypic Selection Analysis tools

Install psa from GitHub

require(devtools)
install_github("MorphoFun/psa", build_vignettes = TRUE)
library(psa)

To see all of the vignettes that are available in psa, type browseVignettes("psa").

Loading the Male Bumpus data as an example

data(BumpusMales)

Check the structure of the data

str(BumpusMales)

Check the documentation to understand what each of the 13 columns represent

?BumpusMales

Define the parameters

Fitness will be represented by the relative fitness (w), which is the absolute fitness (W) of an individual divided by the mean absolute fitness for the group.

w <- BumpusMales[,1]

The phenotypic traits are stored under z:

z <- BumpusMales[,3:11]

Since Weight is a volume, and the other traits are linear measurements, we need to adjust for the dimensionality differences by taking the cube root of Weight_g. (Alternatively, one could cube all of the other phenotypic traits except Weight_g)

z$Weight_g <- z$Weight_g^(1/3)

Calculate the selection gradients, using the Lande-Arnold Method

This can be implemented by using psa::glam

The benefit of using psa::glam or psa::gradients over stats::lm or stats::glm is that the psa functions have built-in options to make the regression coefficients more directly comparable to selection gradients. There are four main benefits to using the psa functions: 1. glam and gradients will check whether the data are centered to a mean of zero and standardized to unit variance prior, and will proceed with these standardizations as a default if raw data are entered into the function.
1. Both linear and nonlinear selection are evaluated, and are output in separate lists for glam and a single data.frame for gradients. "GL" = gradients for linear selection, and "GNL" = gradients for nonlinear selection. The linear terms in GNL should be ignored because they represent biased estimates of linear selection and should be ignored. Linear selection gradients should only be evaluated in the GL, which only conducts a first order model.
1. Quadratic regression coefficients and their associated standard errors from standard statistical programs need to be doubled in order to generate appropriate quadratic selection gradients and standard errors. Such an oversight has resulted in substantial underestimation of the strength of quadratic selection (Stincombe et al. 2008). However, glam automatically accounts for this discrepancy, so that the outputted coefficients represent the selection gradients, and do not require further modification.

To demonstrate the functionality of glam, we will be using the male sparrow data from the classic Bumpus (1968) study to reproduce the results from the Lande-Arnold (1983) multiple linear regression method.

Estimating the linear and nonlinear phenotypic selection gradients

# Estimating the gradients using the matrix algebra and OLS methods
bm_all_g <- t(gradients(w, z, "all"))

# Estimate the standard errors for the matrix algebra approach, using bootstrapping
set.seed(123)
bm_booted_gMatrix <- gradients_bootstats(w,z,method = 1)

# Now, estimating phenotypic selection gradients with the OLS method, using the glam function (to get the se's)
bm_gReg <- glam(w, z, "gaussian")

# standard errors from the OLS method
bm_gReg_se <- c(summary(bm_gReg$GL)$coefficients [-1,2], summary( bm_gReg$GNL)$coefficients [-c(1:(length(z)+1)),2])

# Combining both sets of standard errors for the selection gradients
bm_all_g_se <- data.frame(cbind(gMatrix = bm_booted_gMatrix$se, gReg = bm_gReg_se), stringsAsFactors = FALSE)


# melt the results based on the method used to compute the estimates
library(reshape2)
melt_bm_g <- melt(t(bm_all_g), id = names(bm_all_g))
melt_bm_gse <- melt(t(bm_all_g_se), id = names(bm_all_g_se))

limits <- aes(ymax = melt_bm_g$value + melt_bm_gse$value, ymin = melt_bm_g$value - melt_bm_gse$value)

# plot the data
# see docs.ggplot2.org/current/geom_point.html
ggplot(melt_bm_g, aes(Var1, value, fill = Var1)) + 
  geom_point(aes(colour = factor(Var1))) + 
  geom_errorbar(limits, width = 0.2) +
  facet_wrap(~Var2) + 
  geom_abline(intercept = 0, slope = 0, colour = "gray") +
  labs(title = "Selection gradients for male Bumpus data") + 
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) + 
  theme(legend.position = "none",
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black")
    )

References
Brodie ED III, Moore AJ, Janzen FJ. 1995. Visualizing and quantifying natural selection. TREE 10(8): 313-318.
Lande SJ, Arnold R. 1983. The measurement o fselection on correlated characters. Evolution 37(6): 1210-1226.
Phillips PC, Arnold SJ. 1989. Visualizing multivariate selection. Evolution 43(6): 1209-1222.

MorphoFun/psa documentation built on Nov. 10, 2021, 7:01 a.m.