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lande

Stroud lab’s Lande-Arnold toolkit for measuring phenotypic selection.

The package estimates selection differentials and linear (beta), quadratic (gamma) and correlational (gamma_ij) selection gradients, fits spline fitness functions and two-trait fitness surfaces, and computes the adaptive landscape of mean fitness against the population mean. Each of these can be repeated by year, and several groups can sit on one surface.

Traits are standardised to mean 0 and SD 1 and fitness is relativised (w / mean w) before fitting. Quadratic gradients and their standard errors are doubled (Stinchcombe et al. 2008); correlational gradients are not. For binary fitness the gradients come from OLS on relative fitness and the p-values from a logistic GLM; count fitness gets its p-values from a Poisson GLM, or a negative binomial one when the counts are overdispersed.

Installation

# install.packages("remotes")
remotes::install_github("Human-Augment-Analytics/lande")

Gradients

library(lande)

traits <- c("weight", "total_length", "humerus")

# Standardise traits and add relative fitness
prepared <- prepare_selection_data(bumpus, "survival", traits)

# Selection gradients
selection_coefficients(bumpus, "survival", traits, fitness_type = "binary")

# Differentials and gradients in one table
selection_report(bumpus, "survival", traits, fitness_type = "binary")

# Bootstrap standard errors and intervals
bootstrap_selection(bumpus, "survival", traits, fitness_type = "binary")

# Assumption checks: normality of the traits, VIF, rows per term, residuals
check_selection_assumptions(bumpus, "survival", traits)

# One set of gradients per sex, each sex standardised on its own
selection_coefficients(bumpus, "survival", traits, group = "sex", return_grouped = TRUE)

# Canonical axes of the gamma matrix
canonical_analysis(bumpus, "survival", traits)

Fitness functions and surfaces

# cubic spline, Wald band by default, bootstrap band with bootstrap = TRUE
uni <- univariate_spline(prepared, "survival", "weight")
plot_univariate_fitness(uni, "weight")

# two-trait surface, blank outside the convex hull of the data
surf <- correlated_fitness_surface(prepared, "survival", c("weight", "total_length"))
plot_correlated_fitness(surf, c("weight", "total_length"), show_points = TRUE)

too_far also blanks cells farther than a share of the axis range from any individual, as in Beausoleil et al. (2023). With group set and group_effect = FALSE one surface is fitted to everyone and each group’s mean and highest point are marked, which puts several species on one surface. The highest point is filled for a peak and open otherwise.

A GAM surface carries its standard error and a band. uncertainty = "se" or "band" in the plots draws them, and peak_difference() compares the fitted fitness at two points, or each with the pass between them.

Adaptive landscapes

land <- adaptive_landscape(prepared, surf$model, c("weight", "total_length"))
plot_adaptive_landscape(land, c("weight", "total_length"))

# one trait, from the spline
land1 <- adaptive_landscape(prepared, uni$model, "weight")
plot_adaptive_landscape(land1, "weight")

Over time

finch <- prepare_selection_data(finch_yearly, "survived", "beak_pc1")
years <- temporal_landscape(finch, "survived", "beak_pc1", "year")
years$summary
plot_temporal_landscape(years)
plot_temporal_landscape(years, type = "heatmap")

App

run_app() opens the analysis in a browser: bundled or uploaded data, gradients, fitness functions, surface, landscape and per-group results, with the fitting options in Advanced settings. Needs shiny; plotly adds the rotatable 3D landscape. The app lives in inst/app; see its README there.

Data

• bumpus: Bumpus’s 1898 house sparrows, 136 birds, nine traits and survival.
• crescent_pond_pupfish and little_lake_pupfish: the pupfish of Martin (2016), F2 hybrids in field enclosures in two lakes and laboratory-reared fish of the three parental species. Martin’s analyses use the high-density enclosures, density == "H", and so do the examples and the app.
• finch_yearly: the yearly medium ground finch data of Beausoleil et al. (2019), with survival as being seen again in any later year.
• finch_community: the five-group finch community of Beausoleil et al. (2023), with apparent lifespan as fitness and the year each bird was first caught.

Each has a help page with its columns and source. The pupfish and finch data are also in inst/extdata as CSV files.

Notes

detect_family() classifies fitness as binary, count or continuous and picks the model used for the p-values; the gradients themselves always come from OLS on relative fitness. The spline uses a cubic regression basis with the smoothing chosen by GCV (UBRE for survival and Poisson counts) and the surface a thin-plate basis chosen by REML; both can be changed with bs and smoothing.

See vignette("evolutionary-selection-analysis") for the maths and worked examples.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.