Lec 13 Teaching Prep: Part 1 — Pavo vocab + Miyazawa labyrinths
2026-05-11 18:00:35 • 20:52
Lecture 13 Teaching Prep.
Part 1.
The Vocabricap.
The Conceptual Map.
And the Miyazawa Labyrinths.
Hey Michael.
Welcome to your prep for Lecture 13.
This is Tuesday, May 12th, Week 7, the second half of the Color Patterns Unit.
There are three things to hold in your head as you walk in.
First, this is a bridge lecture, not a fresh start.
Thursday you ended with the Walpert Versus Touring Dicotomy and the 4-cell Pallet.
Today you pick up exactly where you left off and push two ways at once.
You push deeper into the math with the Miyazawa Labyrinths and Murray Scaling Rule.
And you push wider into the genetics with the Master Regulator Toolkit and the ALX3 Stripe
Story.
The synthesis at the end is what makes the lecture work, three knobs of pattern evolution,
cell palette and patterning rule and master regulators.
The lecture earns that three knob pay off if you defend the pace through the middle and
don't lose ten minutes on touring math.
Second, Wednesday is demo seven.
The students show up to lab the next day and run pavo on real fish images.
The opening twelve minutes of today's lecture are explicit demo seven prep.
You are reactivating the metrics they need, K and JC and JT and M and A and M underscore
DS and M underscore DL.
Don't skip this.
If a student walks into the demo Wednesday without those abbreviations in their head, they
will spend forty minutes confused.
The pavo vocab block is a service you are providing to your own Wednesday lab.
Third, the deck is long.
Thirty-six slides.
You will not deliver every slide at full pace.
The two natural cut targets if you are running long are the Murray geometry slide, the one
about curved surfaces and effective diffusion, and the second mammalus slide on the guideless
gene.
Both are good but neither is the spine.
Cut them silently.
Don't apologize for skipping.
Part one of your prep covers the opening through the pufferfish pattern blending story.
About thirty-five minutes of class time.
Part two covers reaction diffusion math through the exit ticket.
Let's start.
Your title slide is up.
Lecture 13.
Color patterns two.
The subtitle, math evolution and the rules that scale is the spine of the lecture.
Hold the slide for three seconds.
Then advance.
Slide one is announcements.
Demo seven prep URL.
Office hours, Tuesday, two to four.
This is thirty seconds.
Point at the URL.
Say the line.
If you show up Wednesday without a working you will spend the first twenty minutes installing
instead of doing science.
Do it tonight.
Then advance.
Slide two is the color vocabulary slide.
Hue saturation luminance.
The big hue will SVG is the visual anchor on the right.
The three definitions are on the left.
This is ninety seconds of clean vocabulary.
Walk it briskly.
Hue is what color the wavelength identity.
Saturation is how pure.
Vivid magenta high.
Washed out pink low.
Gray zero.
Luminance is how bright.
Regardless of hue.
Then the key pavo move at the bottom.
Chromatic boundaries change hue or saturation.
Acromatic boundaries change brightness only.
A black and white striped fish has high luminance contrast, but zero chromatic contrast.
A rainbow fish can have huge chromatic contrast at moderate brightness contrast.
Plant this distinction firmly.
It is the conceptual basis for M underscore DS versus M underscore DL three slides from
now.
Slide three is the first TPS.
Pavo pattern metrics review.
Terminal phase.
Rass on the left.
Three questions on the right.
Ninety seconds discussion.
Sixty seconds cold call.
The three questions are how many color classes define JC and JT in your own words.
And would you expect JC and JT to be high or low for this fish?
Walk among them.
Listen.
The most common error is over splitting.
Students see six or seven colors because they treat shading variations as distinct color
classes.
Push them to group similar hues.
The right answer is three to four colors.
Magenta body, cyan chin and tail, yellow pectoral patch, maybe a dark eye.
JC is moderate because three bold colors cover large areas.
Not low because there are multiple colors.
Not high because three is not a lot.
JT is low to moderate because with three colors in big patches there are only a few boundary
types.
Cold call two pairs.
Validate the moderate answers visibly.
Then advance.
!
Slide four is the answer reveal for K, JC and JT.
Don't dwell.
Sixty seconds.
The key intuition to land is that JT depends on both how many colors and how they are arranged.
Few colors in big patches means few transition types.
A mosaic with the same colors would have higher JT.
Then advance.
Slide five is the second TPS.
The harder one.
Compare two fish.
The colorful terminal phase ross on the left.
The juvenile thalasoma with horizontal stripes on the right.
Ninety seconds discussion.
Two questions.
Define m and a.
For fish b, predict whether a is greater than, less than or roughly equal to one.
Then define m underscore ds and m underscore dl.
Which fish has higher m underscore ds.
Which has higher m underscore dl.
This is where students need the most help.
M is transition density, total boundary complexity.
The striped thalasoma has more boundaries per unit area because the stripes are fine.
So fish b is higher m.
A is aspect ratio, vertical over horizontal.
The thalasoma has strong horizontal stripes, so vertical transitions outnumber horizontal
ones, which means A is less than one.
The ross has large patches with no strong directional bias, so A is roughly equal to one.
The harder pair is m underscore ds versus m underscore dl.
M underscore ds is mean chromatic boundary strength.
How much hue changes at a boundary?
Fish A, the rainbow ross, has magenta to yellow to cyan transitions, dramatic hue shifts.
High m underscore ds.
Fish b is stripes, but the stripes are mostly dark to light transitions with less hue change.
Lower m underscore ds.
M underscore dl is mean luminance boundary strength.
How much brightness changes?
Fish b is sharp dark stripe light interest stripe boundaries.
High m underscore dl.
Fish A also has brightness contrasts, but they're more gradual.
Moderate m underscore dl.
Cool cool.
Then advance.
Slide 6 is the answer reveal for m.
A m underscore ds.
M underscore dl.
About 2 minutes.
The right column has the abbreviations nomenic table.
M is mean.
A is aspect.
D is delta.
S is saturation, the chromatic term.
L is luminance, the brightness term.
So m underscore ds is mean delta saturation at boundaries, chromatic strength.
M underscore dl is mean delta luminance at boundaries, brightness strength.
Walk that table once.
Once a student sees that D means delta and S means saturation and L means luminance.
The rest of the abbreviations stop being mysterious.
Then deliver the bridge line.
These are the metrics you will compute on Wednesday with Pavo.
Now let's get back to the Turing answer from Thursday.
Advance.
You are about 12 minutes in.
The vocab recap is done.
The lecture pivots now.
Slide 7 is the four ways to make a pattern.
The conceptual map for everything that follows.
For boxed mechanism cards.
Turing self organization.
Global information.
Hybrid blending.
Regulatory switches.
Walk each box.
Turing is local activation plus long range inhibition.
Examples are zebrafish stripes and pufferfish labyrinths.
Positional information is cells reading where they are on a tissue.
Examples are mimulus nectar guides and butterfly wing modules.
Hybrid blending is two parameter sets meeting in the same skin.
Examples are salmoned hybrids and a wroth-ron pufferfish.
Turing switches are small changes in when or where master regulators are expressed.
Examples are W and T A. Optics.
ALX3.
Connects in 41.8.
The teaching move here is not that these boxes are mutually exclusive.
The teaching move is that real pattern biology often combines them.
Butterfly wing modules are positional information at the developmental level, but their evolution
is dominated by regulatory switches.
Walk the room rhetorically.
Where would you put the rest we just scored?
Don't take answers.
Just plant the question.
Total time on this slide is about four minutes.
Slide 8 is the Thursday TPS callback.
Two cyclic photos.
The striped melanocromisoratus.
The Bard pseudotrophius demisoni.
The cross prediction.
Most of you predicted intermediate stripes.
Some stripes some bars of blend.
Thirty seconds.
Flash the images and ask who remembers what they predicted.
Don't answer yet.
Advance.
Slide 9 is the answer.
Labyrinths.
This is the dramatic reveal slide.
The big white photo card at the top has the Miyazawa Ellen model figure.
The spots to labyrinth to inverse spot sequence on a sphere.
The fragments below add the second figure with three different Turing models, all showing
the same path.
Start with only the first figure visible.
Say something close to this.
Imagine the patterning rule running on the surface of a sphere.
We are not drawing spots by hand.
We are changing one tuning parameter in the activator inhibitor system.
Walk left to right.
Initially local activator peaks stabilize the spots.
As the activation inhibition balance shifts, the spots connect into a labyrinth.
Farther along the sweep, the polarity flips and the background becomes the spot.
And advance the fragment to show all three rows.
The key teaching beat is that this is not a quirk of one model.
Three different Turing models, the linear Ellen model, the Giror-Mine heart model, the
Grayscott model, all show the same spots to labyrinth to inverse spot sequence.
The labyrinth zone is a generic property of reaction diffusion systems.
Then the biological logic.
Turing parameters are quantitative traits.
If they are determined by multiple loci, hybrids inherit intermediate values.
Intermediate values land in the labyrinth zone.
The hybrid pattern is predicted to be labyrinthin, not a blend of spots and stripes.
Something genuinely new.
Two minutes on this slide.
Then the bridge.
That's the prediction from math.
Can we test it with real fish?
Advance.
Slide 10 is Miyazawa 2010 the setup.
Salmoned hybrids.
Mark four panel figure on the left.
Story pros on the right.
Tell it as a story.
Two salmoned species live in the same Japanese rivers.
One has light spots on a dark background.
The white spotted char.
The other has dark spots on a light background.
The misuse salmon.
In Turing terms, these are on opposite sides of parameter space.
They occasionally hybridize naturally, and Miyazawa also made artificial crosses.
The hybrid, both natural and artificial, shows a labyrinthin pattern that neither parent
has.
Sinois worm-like markings.
Exactly what the simulation predicted.
Two minutes.
Slide 11 is the four by four hybrid grid.
Miyazawa 2010 figure four.
The full proof.
For salmoned species.
Within group crosses, light by light or dark by dark, produce parent-like patterns.
Across group crosses, light by dark, produce labyrinths every time.
Eight intergeneric combinations.
All labyrinthin.
Panel E is the scatter plot.
Hybrids sit at intermediate color tone, but higher pattern complexity than either parent.
Transgressive.
More complex than both parents.
This is the signature of nonlinear blending.
The punchline.
This is not one lucky cross.
It is a systematic repeatable result.
Two minutes.
Then the bridge.
So the 2010 paper proved it in salmoneds.
Ten years later Miyazawa asked, does pattern blending explain color diversity across all
fishes?
Advance.
Slide 12 is the bigger question slide.
Miyazawa 2020 figure one.
Bridge slide.
Ninety seconds.
Don't go deep here.
Just establish two facts.
One.
Color patterns are more similar across, distantly related species than among close ones.
Most relatives.
Massive homoplacee.
Two.
Miyazawa tested pattern blending across 18,114 fish species from 559 families.
The strongest association is between labyrinthin patterns and spot patterns.
Exactly what blending predicts.
Counterintuitive because labyrinths look like stripes, but the data say labyrinth co-occurs
with spots.
Then the teaser.
Can we catch it in the act?
Pufferfish coming up after the cell biology block.
Advance.
Slide 13 is the student question slide.
Why can small fish pattern but small mammals can't?
Two photos on the left, the house mouse uniform and the zebrafish bold striped at similar
body size.
This was an actual student question from Thursday.
Don't blow past it.
The setup.
Both use touring dynamics, but different implementations.
Two differences that matter.
When and how?
Again, mammals pattern the embryo when the skin domain is tiny.
Fish pattern post-embranically on growing skin.
So a mouse embryo can't fit even one wavelength and ends up uniform.
A zebrafish larva is already several millimeters and growing, so even a small adult fish has
many wavelengths of pattern.
How?
Mammals use molecular activator inhibitor pairs, WNT and DKK for hair follicle spacing,
and interpath way for skin appendages.
Molecular diffusion gives a long wavelength.
Fish use cell cell interactions, melanophoresanthophore repulsion plus gap junction support.
Cell contact and gap junction reach give a shorter wavelength.
Shorter wavelength means finer pattern.
The important caveat.
Don't say mammals can't do touring.
They can.
The Murray slide later will show that they do.
The question is why size constrains them more severely than fish.
Two minutes on this slide.
Then advance.
Slide 14 is the zebrafish three cell system slide.
Gertwein 2020 figure 1A on the left.
The Hebrew University a Doddy-Lad paper.
The big idea is that a stripe is not made by one pigment cell.
Three cell types.
Melanophores, black, light absorbing.
Santafores, yellow orange.
Iridophores, reflective with guanine crystal stacks.
The dark stripe and the light in terstripe are local neighborhoods.
Each neighborhood gives cells different signals.
And with the question.
Are stripe and terstripe Iridophores the same cells in different places or different cell
states?
That is the question Gertwein answered.
Two minutes.
Slide 15 is the old model slide.
Two panel figures showing model 1 respsification versus model 2 differentiation in Cetero.
The old model said Iridophores start in the interstripe, then some cells move into the
stripe and transform.
More phagenetic respsification.
The new model says precursors settle in each neighborhood and differentiate there.
Differentiation in Cetero.
The analogy I want you to use is not people moving and changing jobs.
The analogy is new arrivals in each neighborhood training for different jobs because the local
environment tells them what to become.
After it all did time lapse imaging and fate mapping.
They watched thousands of cells.
Dense and terstripe Iridophores did not migrate out and become loose stripe Iridophores.
So model 2 wins.
Three minutes.
Slide 16 is the new model slide.
Two Iridophore crystallotypes.
Crystalotype is the word to teach.
A cell type distinguished by the architecture of its guanine crystals.
Ritophore is our loose stellate cells with more ordered crystal arrays and blue shifted
reflection.
Interstripe Iridophores are dense cuboidal cells with different crystal organization and
silvery yellowish appearance.
Both use guanine.
The crystal architecture differs.
Why it matters for patterning.
The reflective layer is itself patterned.
Fish are not just arranging black and yellow pigment cells.
They are also locally building different structural color cells.
This is the clean bridge back to Tuesday's lecture.
Fish can make fine adult patterns because their chromatophore palette is richer than mammalian
melanocytes.
Three minutes.
Slide 17 is the pattern blending hypothesis slide.
Miizawa 2020 figure one again.
This time with the framework on the right.
The teaching move.
Cross two simple patterns and you get a labyrinth.
The strongest association in the 18,000 species data set is labyrinth and plus spot patterns.
This is the pufferfish on the next slide.
Two minutes.
Slide 18 is the pufferfish slide.
Pattern blending caught in the act.
Miizawa 2020 figure three.
The arothron pufferfish vertical panel on the left.
This is the centerpiece of the Miizawa vignette.
Walk through carefully.
The spotted parents.
A. Firmamentum and A. Stelaedis on opposite sides of parameter space.
The labyrinthin species.
A. Multilineatus.
A. Cardiose.
A. Mappa.
Then the genomic proof.
Whole genome sequencing of 12 arothron species.
The labyrinthin species are hybrids of spotted parents.
PCA on 28 million SNPs put them between the parents.
Admixture analysis estimated 50-50 ancestry.
Interclass hetero-segosity was 97 to 99%.
They are early generation hybrids.
The punchline.
A. Multilineatus and A.
Cardiose were originally described as distinct species based on their peculiar skin patterns.
They are not distinct species.
They are hybrids.
Pattern blending created camouflage phenotypes that fooled taxonomists for over 100 years.
78% of possible trios among spotted and labyrinthin arothron species
showed significant patterns in D, indicating widespread hybridization.
3 minutes.
Slide 19 is the 18,000 species quantification.
Figure 4A.
Simulations match real pufferfish.
Blue dots are R.D. predictions.
Colored symbols are real arothron species.
Spotted at the extremes.
Labyrinthin in the middle.
Intermediate tone, but higher complexity.
Transgressive.
Across all fishes, Bayesian phylogenetic analysis found correlated evolution of labyrinthin
and spot motifs in 8 of 10 major fish orders.
Over 900 fish species with labyrinthin patterns across over 160 families.
Two minutes.
Slide 20 is the pattern blending framework synthesis.
Two coupled fields same skin.
Different wavelengths.
Different cell systems.
Additive in the final phenotype.
The big idea.
Pattern diversity is cheap to generate.
Reformation makes new patterns with no new genes needed.
This makes plain explosive cycloid radiations.
Same logic across fish butterflies and snakes.
Land the punchline.
The cell does the math.
Selection picks the winners.
End of part 1.
You are about 35 minutes into the lecture.
Have done.
Take a breath.
Part 2 starts with the reaction diffusion math and Murray's scaling rule.
In the master regulator toolkit, the ALX 3 stripe story, plants and the 3 knob synthesis.