Lesson 20 — Measuring rates across sliding intervals
Measure how fast something changed. Then measure the same change over a longer stretch, and get a different number.
Siccar Point plays a big role in the history of geology — which means it has a big role in the history of the Industrial Revolution and economics in general. It also has a huge role in biology. This is where deep time was discovered. Charles Darwin, trained as a geologist, learned about this and studied with Adam Sedgwick. He understood the geological principles of Siccar Point, and that led him to understand deep time — which led to the theory of evolution.
— 312_lec_strat2_01
A — Rate = distance / time
If I told you a car was driving at 50 mph and has gone 100 miles, how long ago did it leave? You have a distance and a speed — distance divided by speed gives you time. Number of mutations is your distance. The slope of mutations versus time is your speed. Number of mutations divided by slope gives you time to most recent common ancestor.
— 202_lec20_02
10,000 generations of a Brownian-motion trait. Slide the interval length and watch the median measured rate (per generation) fall as the interval grows. This is the Gingerich decline, from one simulated lineage.
median rate at this L:—
Top: the simulated trait trajectory with two endpoints L apart highlighted. Bottom: rate distribution across all non-overlapping L-windows. As L grows, the rate distribution slides toward zero — the Brownian-motion lineage's apparent speed drops as you ask about it over longer windows.
B — Gingerich's decline
A lot of solids can flow more than you'd expect. You see this with windows in really old buildings — sometimes there's a thickening at the bottom. Some of it is just because they used to make windows thicker at the bottom. Some of it is that non-crystalline solids can flow a bit more than people realize. There's still motion.
— 312_lec02_03
Every pair of measurements in 1,400 real time series — fossils, museum skins, field studies — plotted as how fast the trait changed against how long the gap was. Both axes step by powers of ten.
slope:—
| interval span:—
C — Why does the rate decline?
A lot of Permian things we have fossils of were burrowers. That's not necessarily because Permian things burrowed more than things today. Maybe they did, maybe they didn't. But think about how a fossil is made — something dies and gets buried. If you die in your burrow, you've skipped a step. You're already buried. So burrowers fossilize more easily. All else being equal, if you live underground, you have an easier time ending up underground when you're dead.
— 440_lec11_04
Predict first. Three ways a trait might behave over time. Which one, measured the way Stage B measures, produces the steepest decline?
this process gives slope:—
| the real fossils give:—
D — The PETS time series — Hyopsodus across the Eocene
We don't know about the alpine dinosaurs. We don't know about the rainforest dinosaurs. Those are not environments where sediments get preserved. We know about river delta dinosaurs. We know about swamp dinosaurs. We know about coastline dinosaurs.
— 312_lec22_03
One real series at a time. Slide the window and read the rate it gives you.