BIO 202 — Lesson 19: Removing the family resemblance before comparing species

I survey species of earthworms around the world. For each species, I measure body size and soil pH. I get a clean negative regression. But within each clade — these three sister species, those three sister species — the relationship is positive. You can make a negative overall trend out of a bunch of positive smaller trends. The fact of stratification is inherent in all life on Earth, because we're all descended from a set of nested common ancestors. When comparing living things, relatedness will always matter.— 202_lec26_02

A — Draw the line straight across the species

Scenario

Generate a tree of N species. Simulate two traits x and y, each by Brownian motion. The traits evolve independently — the "true" slope is 0. But the naive OLS regression of y on x will often show a non-zero slope, because species in the same clade have correlated trait values.

Naive scatter of x vs y across species

N species: 30 | true slope: 0 | naive OLS slope: — | OLS P-value: —

Prediction

Q1. Two traits truly evolve independently on a tree. Across 30 species, what fraction of OLS regressions on the tip values give P < 0.05?
About 5% (the correct false-positive rate) Substantially more than 5% — phylogenetic non-independence inflates false positives Essentially 0%

Try at least 5 seeds. 0/5 seeds

Controls

seed42

N species30

R code — naive OLS

library(ape)set.seed(42); N <- 30tr <- rcoal(N)   # random coalescent treex <- rTraitCont(tr); y <- rTraitCont(tr)   # independent BMsummary(lm(y ~ x))   # naive slope

B — Subtract what the branches already share

Scenario

For each internal node of the tree, compute the contrast: (x_left − x_right) / sqrt(t_left + t_right). Do the same for y. Then regress y-contrasts on x-contrasts through the origin. For independent BM traits, this slope is centered on 0.

Naive vs phylogenetic-contrasts slope

naive OLS slope: — | PIC slope: — | PIC P-value: —

Prediction

Q1. When traits truly evolve independently on a tree, the phylogenetic-contrasts slope across many simulations will be:
Centered on 0 Systematically positive Systematically negative

Try at least 5 seeds. 0/5 seeds

Controls

seed42

true correlation0.0

R code — phylogenetic independent contrasts

library(ape)px <- pic(x, tr); py <- pic(y, tr)summary(lm(py ~ 0 + px))   # PIC slope through origin

C — How much of the resemblance is just the tree?

Scenario

Pagel's λ scales the off-diagonal elements of the phylogenetic covariance matrix. At λ=0, off-diagonals are 0 (no shared ancestry effect). At λ=1, full BM. The maximum-likelihood λ tells you how much your trait is phylogenetically conserved.

How well each setting explains the data

true setting: 1.0 | best-fit setting: — | 95% range: —

Prediction

Q1. If a trait evolves by pure Brownian motion on a tree, Pagel's λ should fit at:
0 0.5 1 Negative

Try at least 3 true λ values. 0/3 values

Controls

how much is shared ancestry1.0

seed42

R code — Pagel's λ

library(phytools)phylosig(tr, x, method = "lambda", test = TRUE)

Three ways two species could look alike

Two species' traits look correlated. Three causal stories could produce that. Build each one in the DAG below and see what the trait-vs-trait scatter looks like.

Direct effect. Trait 1 → Trait 2. Real biology happens within each lineage.
Shared ancestry. Phylogeny → Trait 1, Phylogeny → Trait 2. Both traits inherited from a common ancestor; no within-lineage link.
Both. All three arrows present.

D — AVONET birds — hand-wing index vs migration

Scenario

Hand-wing index (a wing-shape ratio) is known to correlate with dispersal ability. Naive cross-species correlation may overstate the relationship because closely related species share both. Compare naive OLS vs phylogenetic correction.

Hand-wing index vs flight ability proxy

N species shown: — | naive slope: — | corrected slope (PIC-like): —

Prediction

Q1. The PIC-corrected slope between hand-wing index and a flight-ability proxy will be:
Similar to the naive slope — phylogeny doesn't matter much here Smaller than the naive slope — phylogeny inflated the naive estimate Opposite sign — phylogeny reversed the apparent direction

Toggle between traits at least 2 times. 0/2 toggles

Controls

subsample seed42

R code — AVONET PGLS

library(ape); library(nlme)birds <- read.csv("data/clean/avonet_birds.csv")# Match to BirdTree, then PGLSm <- gls(migration ~ hand_wing_index, data = birds,         correlation = corBrownian(phy = bird_tree))summary(m)

E — The earthworm sign flip

Scenario

Synthetic earthworm data faithful to the structure in the lecture quote: 30 species in 6 clades of 5 species each. Within each clade, larger worms prefer slightly more alkaline soils (positive slope). Across clades, the bigger-bodied clades happen to occupy more acidic soils (so pooled across clades, the slope flips negative). The categorical variable is clade membership — and once it's drawn into the model, the within-clade slope is what's actually happening biologically.

Earthworm body size vs soil pH — pooled vs within-clade

pooled slope: — | median within-clade slope: —

Prediction

Q1. When you switch from pooled to within-clade view, the within-clade slopes will be:
Roughly the same as the pooled slope Weaker than the pooled slope, but the same sign Opposite sign — pooled negative; within-clade positive
Q2. Which is the right way to describe what the pooled negative slope was measuring?
"Larger body size causes worms to prefer acidic soil" "Across clades, the larger-bodied lineages happen to live in more acidic soils — that's a fact about which clade lives where, not about evolution along any single lineage" "The data are just noise"

Toggle the clade-coloring at least once. 0/1 toggles

Controls

view

R code — Simpson's paradox on a tree

worms <- read.csv("data/clean/earthworm_clades.csv")pooled  <- lm(soil_pH ~ body_size, data = worms)within  <- lm(soil_pH ~ body_size + clade, data = worms)summary(pooled)$coefficients["body_size", ]summary(within)$coefficients["body_size", ]