Vaccines Did Not Cause Rachel's Autism

Vaccines Did Not
Cause Rachel’s Autism,
by Peter Hotez.

I recently listened to an audio recording of Peter Hotez’s book Vaccines Did Not Cause Rachel’s Autism: My Journey as a Vaccine Scientist, Pediatrician, and Autism Dad. Hotez is the same author who wrote The Deadly Rise of Anti-Science, which I reviewed previously in this blog. I’m troubled by the current anti-vaccine sentiment, which is foolish and dangerous. Along with climate change denial, vaccine hesitancy is a worrisome example of an alarming anti-science movement in the United States.

Hotez’s book provides insight into the challenges faced by parents with autistic children (by the way, Peter Hotez is not the hero of this book; the hero is his wife Ann). Moreover, the book makes a compelling argument that vaccines do not cause autism. Hotez reviews much of the scientific literature relevant to the relationship of vaccines to autism. In particular, he mentions a meta-analysis of clinical studies published by a group from Australia. As much as I enjoyed and admired Hotez’s book, I probably would have led off by discussing that publication, rather than waiting until late in the book to bring it up.

“Vaccines are Not Associated With Autism:
An Evidence-Based Meta-Analysis of
Case-Control and Cohort Studies”
by Taylor, Swerdfeger, and Eslick,
Vaccine, 32:3623–3629, 2014.

Today I’ll discuss that article, titled “Vaccines are Not Associated With Autism: An Evidence-Based Meta-Analysis of Case-Control and Cohort Studies” by Luke Taylor, Amy Swerdfeger, and Guy Eslick. This paper appeared in 2014 in the journal Vaccine (Volume 32, Pages 3623–3629). The abstract appears below.

There has been enormous debate regarding the possibility of a link between childhood vaccinations and the subsequent development of autism. This has in recent times become a major public health issue with vaccine preventable diseases increasing in the community due to the fear of a ‘link’ between vaccinations and autism. We performed a meta-analysis to summarise available evidence from case-control and cohort studies on this topic (MEDLINE, PubMed, EMBASE, Google Scholar up to April, 2014). Eligible studies assessed the relationship between vaccine administration and the subsequent development of autism or autism spectrum disorders (ASD). Two reviewers extracted data on study characteristics, methods, and outcomes. Disagreement was resolved by consensus with another author. Five cohort studies involving 1,256,407 children, and five case-control studies involving 9,920 children were included in this analysis. The cohort data revealed no relationship between vaccination and autism (OR: 0.99; 95% CI: 0.92 to 1.06) or ASD (OR: 0.91; 95% CI: 0.68 to 1.20), nor was there a relationship between autism and MMR (OR: 0.84; 95% CI: 0.70 to 1.01), or thimerosal (OR: 1.00; 95% CI: 0.77 to 1.31), or mercury (Hg) (OR: 1.00; 95% CI: 0.93 to 1.07). Similarly the case-control data found no evidence for increased risk of developing autism or ASD following MMR, Hg, or thimersal exposure when grouped by condition (OR: 0.90, 95% CI: 0.83 to 0.98; p = 0.02) or grouped by exposure type (OR: 0.85, 95% CI: 0.76 to 0.95; p = 0.01). Findings of this meta-analysis suggest that vaccinations are not associated with the development of autism or autism spectrum disorder. Furthermore, the components of the vaccines (thimersal or mercury) or multiple vaccines (MMR) are not associated with the development of autism or autism spectrum disorder.

Some of the terms and concepts mentioned in the abstract may be unfamiliar, so let me explain them.

• Autism and Autism Spectrum Disorders. Autism is a disorder of the nervous system that begins during the development of a fetus. An autistic person may engage in repetitive, inflexible behaviors or have problems interacting with people. The disorder can vary in its severity and symptoms, so people with different degrees of severity are said to be on the autism spectrum.
• Vaccine. A vaccine is a biological agent that stimulates a person’s immune system to recognize and destroy a microorganism causing an infectious disease. Vaccines are often made from a weakened form of the microbe.
• The MMR Vaccine. The MMR vaccine protects children against three diseases: measles, mumps, and rubella (German measles). An initial dose of the MMR vaccine is typically given around a child’s first birthday and a second dose before entering school. It’s usually given by injection.
• Thimersal-Containing Vaccine. Thimersal is a molecule containing mercury. The element mercury, whose chemical symbol is Hg, is a known toxin. However, not all molecules containing mercury are as toxic as is mercury metal itself. Mercury compounds like thimersal are used in low doses as a preservative in some vaccines. Before 1991, thimersal was included in the childhood vaccine DPT which protects against diphtheria, tetanus (lockjaw), and pertussis (whopping cough). Now no childhood vaccines contain thimersal, although it’s still used in some flu vaccines.
• Meta-Analysis. Meta-analysis is a statistical method of analyzing and summarizing several clinical trials. A meta-analysis can increase the number of patients being analyzed, resulting a more statistical power. It can also help in resolving studies with inconsistent results.
• Case-Control Study. A case-control study is a clinical study that compares two groups: one having a disease and one not (the control). It is often retrospective, meaning it uses existing data from people known to have a disease, and therefore can be conducted quickly.
• Cohort Study. A cohort study is a clinical trial that takes a group of people and follows them through time to determine what fraction develop some disease. It is prospective, collecting data on exposure to some suspected cause. A cohort study can take a long time to complete and, for a rare disease, requires studying a large population, but it’s less susceptible to bias than a case-control study.
• Odds Ratio. The odds ratio (OR) is a statistical measure to determine if some factor has an effect. For example, suppose in a case-control study you examined the medical records of 600 people who had the MMR vaccine; 570 were healthy but 30 had autism (the odds of being healthy are 570:30, or 19:1). As a control, you examined the medical records of 400 people who did not have the MMR vaccine; 380 were healthy but 20 had autism (the odds of being healthy are 380:20, or 19:1). In that case, the odds ratio would be
  
  When the odds ratio is one, you conclude the MMR vaccine had no effect (the odds of having autism are the same whether or not you had the vaccine). If, however, among the 600 people who had the MMR vaccine 510 were healthy and 90 had autism (with the control group being unchanged from that given above) then the odds ratio would be
  
  In this case, the MMR vaccine would have a clear effect. For smoking and lung cancer, the odds ratio is quite large, about 10.
• 95% Confidence Interval. How large must the odds ratio be in order to conclude there is some effect? That depends on how much uncertainty there is. For instance, if you flip a coin four times, the most likely result is two heads and two tails. However, there is still one chance out of sixteen, about 6%, that you’ll get four heads. If you want to be more certain that a coin is fair and not biased, you would need to flip the coin more than four times. In the same spirit, to completely characterize how much confidence you have in the result of a clinical trial, you must indicate how large the uncertainty is in the result. Most clinical studies will give the odds ratio and a range of values for which—based on a statistical analysis—there is a 95% chance that the odds ratio is within that interval. The convention is that if the 95% confidence interval does not contain the value of one, then there is a statistically significant effect. If it does contain one, any effect is not statistically significant. Using a value of 95%, rather than say 98%, is arbitrary, but you have to draw the line somewhere, and 95% confidence is the usual medical criteria for significance. For example, if in one of these autism studies the odds ratio was 1.05 and the 95% confidence interval was 0.8 to 1.3, you would conclude that there is not a statistically significant effect of the vaccine. If, on the other hand, the odds ratio were 1.05 and the 95% confidence interval was 1.02 to 1.08, you would conclude there is a small but statistically significant effect of the vaccine on autism. Note that in statistics the word “significance” does not mean “important.” It means “unlikely to be due to chance.” One virtue of a meta-analysis is that by combining several studies the number of people analyzed increases, which can shrink the 95% confidence range, which provides better statistical power to say if the odds ratio is significantly different than one. 
• p-value. Whenever you have an arbitrary threshold, like saying a result is or is not statistically significant, you worry about cases that are near the threshold. To provide additional information, researchers sometimes give the p-value. It is the probability that a result at least this extreme could happen by chance. In medicine, usually p = 0.05 is the cutoff between a result being considered significant or not significant. But if the result has p = 0.03, you might say it is significant (less than 0.05) but you might think that it is still questionable and maybe you should repeat that study with a larger number of people. On the other hand, if p = 0.0002 you would say that the result almost certainly didn’t happen by chance and you would therefore have a lot of confidence in it. In this meta-analysis, the p-value is sometimes given, especially for borderline cases, to help the reader estimate the true significance of the result.
• MEDLINE, PubMed, EMBASE, Google Scholar. These databases contain information about scientific publications, including articles describing clinical trials. They can be searched using various keywords to find publications about a particular subject. MEDLINE is a database compiled by the National Library of Medicine, and covers all biomedical research. It can be searched online using a tool called PubMed, which includes MEDLINE plus a few other databases. EMBASE is an international database that focuses on the pharmaceutical industry. Google Scholar is a free web search engine that covers all scholarly publications.

Now that we understand the vocabulary, what does this meta-analysis show? It indicates that there is no evidence supporting a connection between vaccines and the development of autism. It also shows there is no risk that thimersal or mercury causes autism. In fact, some of the results suggest a weak protective effect caused by thimersal. For example, an odds ratio of 0.85 with a 95% confidence interval of 0.76 to 0.95 suggests that the odds ratio may be slightly less than one, which means the vaccine prevents people from getting autism. However, the p-value for this result was 0.01 which is small but not that small, and I wouldn’t put too much confidence in the claim that the vaccine is protective. But the results sure don’t suggest there is a health risk.

What I’ve analyzed today is one paper, albeit a meta-analysis. It’s over ten years old. There are lots of other data out there now, and Hotez describes some of it in Vaccines Did Not Cause Rachel’s Autism. He also emphasizes that autism is thought to arise from problems during the development of a fetus, long before the child receives any vaccines, so there’s no reason to suspect vaccines as a cause of autism. All this evidence, taken together, implies the probability of vaccines causing autism is extremely low.

Why do people still claim vaccines cause autism? There will certainly be cases where a child will receive a vaccine and then start showing symptoms of being on the autism spectrum. Some might point to such cases and say “see, I told you so!” The question is, how many of those children would have started showing symptoms of autism even if they didn’t get the vaccine? Homework problem 9 in Chapter 3 of Intermediate Physics for Medicine and Biology explores this type of question quantitatively. The reason you need a large, controlled statistical study is so you’re not fooled by a few such coincidences.

One thing clinical studies, such as the one that I discussed today, cannot give you is certainty. You can’t say with absolute certainty (p = 0) that vaccines don’t cause autism. Science doesn’t deal in certainties, just probabilities. All you can say is that the evidence suggests there is no connection between vaccines and autism. The best you can do is to collect enough evidence so that the probability of a relationship is very small. That is where we are today. The probability of vaccines causing autism is extremely low. That’s the best conclusion science can offer. And when the probability is vanishingly small, we often feel confident in summarizing the situation with a simple (if somewhat too simple) declarative sentence, such as Vaccines Did Not Cause Rachel’s Autism.

Outbreak News TV: Vaccines Did Not Cause Rachel's Autism.

https://www.youtube.com/watch?v=xDh3QZPx2ns&t=461s

Peter Hotez wins award for Scientific Freedom and Responsibility.

https://www.youtube.com/watch?v=WHtWmSz4cXE

Dr. Peter Hotez's mission to make a difference.

https://www.youtube.com/watch?v=xC-3ofA1hIE

The Physics of Butterflies

Marilyn Trent (the founder of
Rochester Pollinators, left), my
wife Shirley (center), and me (right).

While my wife and I like birds and bees, we love the butterflies. We’re both part of a group called Rochester Pollinators, whose mission is 

to provide education and resources to preserve the Monarch butterfly and pollinator population. We believe every citizen can help our local pollinators flourish by reintroducing Michigan native plants into local landscapes, including home gardens, businesses, and municipal landscapes. We aim to reach as many people as we can with this message!

Hooray for butterflies! Not only are they fun to see, but they illustrate a lot of physics. So now, in this last installment of my series on The Physics of Native Gardening, we turn to the physics of butterflies.

Flight

Birds, bees, and butterflies each have their own unique way of flying. Christoffer Johansson and Per Henningsson have analyzed butterfly flight. Below is the abstract of their article (Journal of the Royal Society Interface, Volume 18, Article Number 20200854, 2021).

Butterflies look like no other flying animal, with unusually short, broad and large wings relative to their body size. Previous studies have suggested butterflies use several unsteady aerodynamic mechanisms to boost force production with upstroke wing clap being a prominent feature. When the wings clap together at the end of upstroke the air between the wings is pressed out, creating a jet, pushing the animal in the opposite direction. Although viewed, for the last 50 years, as a crucial mechanism in insect flight, quantitative aerodynamic measurements of the clap in freely flying animals are lacking. Using quantitative flow measurements behind freely flying butterflies during take-off and a mechanical clapper, we provide aerodynamic performance estimates for the wing clap. We show that flexible butterfly wings, forming a cupped shape during the upstroke and clap, thrust the butterfly forwards, while the downstroke is used for weight support. We further show that flexible wings dramatically increase the useful impulse (+22%) and efficiency (+28%) of the clap compared to rigid wings. Combined, our results suggest butterflies evolved a highly effective clap, which provides a mechanistic hypothesis for their unique wing morphology. Furthermore, our findings could aid the design of man-made flapping drones, boosting propulsive performance.

Compound Eye

The Feynman Lectures on Physics,
by Richard Feynman.

Butterflies, like most insects, have a compound eye. Richard Feynman, in his famous Lectures on Physics, discusses the visual acuity of these eyes.

A compound eye… is made of a large number of special cells called ommatidia, which are arranged conically on the surface of a sphere (roughly) on the outside of the... head…

How well can such an eye see? The angle subtended by the ommatidia depends on its width on the sphere surface. The closer the ommatidia are packed, the finer the visual acuity. However, light also undergoes diffraction. When the size of the ommatidia is similar to the wavelength of the light, diffraction smears the light out, destroying your resolution. Feynman writes

If we make the [width] too small, then each ommatidium does not look in only one direction, because of diffraction! If we make them too big, each one sees in a definite direction, but there are not enough of them to get a good view of the scene. So [evolution] adjusts the [width] in order to make minimal the total effect of these two.

So the structure of the butterfly’s eye is a trade off between having a lot of small ommatidia and having fewer that are not corrupted by diffraction. I find it interesting how physics often constrains and guides evolution.

Polarization Vision

Feynman also describes another fascinating ability of butterflies and other insects: they can sense polarized light. Recall that light is an electromagnetic wave. The electric field is directed perpendicular to the direction that the wave propagates. But if the wave propagates in the z direction, then there are two possibilities for the direction of the electric field: x or y. These two, or some combination, is what we mean when we talk about the polarization of the light. Feynman writes about bees, but the same thing applies to butterflies.

Another interesting aspect of the vision of the bee is that bees can apparently tell the direction of the sun by looking at a patch of blue sky, without seeing the sun itself. We cannot easily do this. If we look out the window at the sky and see that it is blue, in which direction is the sun? The bee can tell, because the bee is quite sensitive to the polarization of light, and the scattered light of the sky is polarized.

We sometimes get Monarch butterflies visiting our gardens. We plant various types of milkweed specifically to attract them. Monarchs may use polarization to help them migrate from here in Michigan down to Mexico to spend the winter.

Wing Color

From Photon to Neuron,
by Philip Nelson.

 The color of butterfly wings is a fascinating example of optics at work. For an explanation, I quote from Philip Nelson’s book From Photon to Neuron: Light, Imaging, Vision.

Some animals display vivid colors, for purposes such as identifying potential mates. Many of these colors involve pigment molecules that selectively absorb light. But some colors, for example, those on certain butterfly wings, beetle wing cases, and bird plumage, have a very different character…

The wings of Morpho butterflies are covered with scales made mainly of a transparent substance (called cuticle)… The scales [contain] a complex structure with alternating layers of cuticle and air…

The color arises from constructive and destructive interference. Reflections off of each layer interfere constructively if the difference in path length is equal to one, two, or more integral number of wavelengths of the light. In that case, the reflected light appears bright. If the difference in path length is a half, or one and a half, etc. wavelengths, the light undergoes destructive interference and appears dark. The wavelength depends on the color of the light, so some colors will be bright and some dark. Moreover, the condition for interference depends on the angle that the light hits the wing, so the color will change with the viewing angle: iridescence.

Unfortunately, I’ve never seen a Morpho butterfly in Michigan. We have mostly monarchs and swallowtails, and a lot of those little cabbage whites. We hope this year we’ll have many more.

Before I end, I want to share with you a beautiful poster of a butterfly garden, painted by Thomas W. Ford. We purchased it at the Four Seasons Nursery in Traverse City, Michigan. Enjoy!

Butterfly Garden,
by Thomas W. Ford.

This concludes my four-part series on the physics of native gardening. It’s cold now, but spring is just a few weeks away. I can’t wait to be back at it! 

 Why Native Plants

https://www.youtube.com/watch?v=trJKZDEfvrc&t=25s

The Physics of Bees

In this third installment of The Physics of Native Gardening series, I look at the physics of bees. Each year we get more and more bees coming to our garden. I especially like the big, fat bumblebees. Some days there are so many bees that they swarm their favorite flowers. You can tell they are hard at work gathering pollen; busy as a bee.

Bumblebee Flight

Sometimes you’ll hear nonsense claiming that according to the laws of physics bumblebees can’t fly. A focus article about a 2016 Physical Review Letters paper states

Relatively small insects, like bees and house flies, have a different flying strategy than larger insects and birds. They have fairly rigid wings, which they flap as much as a hundred times per second. The flapping motion is not strictly up and down like for birds but more forward and backward… Starting with the wings “clapped” together and vertical behind the insect’s back, the wings then tilt steeply away from one another as the forward stroke begins. As they move, the wings produce low pressure in the region just behind the leading edge... The air in front of the wings curls up and over them and forms a horizontal, tornado-like vortex along the back side of the leading edge. Previous experiments and computer simulations have shown that leading edge vortices produce a suction effect that gives the necessary lift for keeping an insect aloft.

Ultraviolet Vision

An Immense World,
by Ed Yong.

Bee vision is different than human vision. The human retina has three color receptors, each sensitive to different frequencies in the visible spectrum (blue, green, and red). The bee also has three receptors, but only two are in the visible spectrum (blue and green); the other is in the ultraviolet (light with a wave length shorter than what the human eye can see). In his book An Immense World: How Animal Senses Reveal the Hidden Realms Around Us, Ed Yong wrote

Flowers use dramatic UV [ultraviolet] patterns to advertise their wares to pollinators. Sunflowers, marigolds, and black-eyed Susans all look uniformly colored to human eyes, but bees can see the UV patches at the bases of their petals, which form vivid bullseyes. Usually, these shapes are guides that indicate the position of nectar.

Oxygen Diffusion

Bees don’t have lungs. Yet, all that flying means they need a lot of oxygen to power their high metabolism. How do they supply oxygen to their muscles?

Instead of having vessels to transport blood, insects use small, air-filled pipes (trachea) that deliver oxygen. The pipes typically have a dead end, so you can’t just flow air through them. The oxygen is supplied by diffusion.

Diffusion is the movement of a molecule from a region of high concentration to low concentration. It works quickly over short distances, but takes a long time over long distances. Russ Hobbie and I discuss diffusion in Chapter 4 of Intermediate Physics for Medicine and Biology. Oxygen can diffuse through air ten thousand times faster than it can diffuse through water. Therefore, filling these insect pipes with blood would make oxygen diffusion way too slow. But having them filled with air means plenty of oxygen can diffuse in, powering flight.

One potential problem for bees would be if water was sucked into their trachea by capillary action. This would drastically lower the diffusion of oxygen. To avoid this, the trachea may be coated by a waxy substance that repels water. The pipes are so small that it is difficult to know for sure, but capillary action is so powerful there must be some way to keep water out.

Thermoregulation of Flight Muscle

Air and Water,
by Mark Denny.

In his book Air and Water, Mark Denny discusses how tiny bees stay warm. As we saw last week when describing hummingbirds, one way to produce a lot of heat is having a high metabolic rate. But it’s complicated. Denny writes

It is a tribute to the metabolic and respiratory machinery of bees and other flying insects that this magnitude of metabolism is possible. Note, however, that this high metabolic rate is closely tied to activity on the part of the bee. It must raise its metabolic rate well above that at rest (by shivering, for instance) to heat itself up. As soon as it becomes inactive, its body temperature returns to that of the ambient air.

There is a flip side to this puzzle. If a flying bee can heat its muscles to 30° C on a cold day, it seems likely that it could overheat on a hot day. Indeed this is the case, and bumblebees have evolved mechanisms that allow them to dump heat effectively from the thorax to the abdomen, from where it is shed to the air.

If you want to learn more about bees, there’s an entire website about physics for beekeepers. It’s mainly about honey bees, which are a little like cattle: non-native domesticated livestock that are commercially important. I’m not so interested in honey bees, but focus more on the many solitary, ground-nesting or cavity-nesting species of bees native to Michigan that live in our yard, such as sweat bees, carpenter bees, mason bees, and miner bees.

Many of the physical constraints faced by bees are shared by their fellow insects, the butterflies. Next week we’ll examine in more detail the physics of butterflies.

 

Native bees of Michigan with Dr. Rebecca Tonietto

https://www.youtube.com/watch?v=EICFH-DIYGU 

The Physics of Birds

In this second installment of my series on the physics of native gardening, I’ll talk about the physics of birds. We get a lot of birds in our yard. Robins visit the lawn and our crabapple tree. Too many house sparrows come to our bird feeders; they’re invasive pests. We see lots of blue jays, those big bullies, as well as goldfinches, downy woodpeckers, and black-capped chickadees. Every fall we know that winter is approaching when the dark-eyed juncos come down to Michigan from Canada. Canadian geese fly overhead, but they never stop at our house.

Flight

I often see birds high in the sky, soaring through the air without flapping their wings. I suspect many are red-tailed hawks, but I’ve never gotten close enough to one to say for sure. How does soaring work? First, it requires a thermal updraft. The sun heats the earth and the earth heats the air next to it, resulting in a temperature gradient: the air near the ground is hotter than the cooler air high above. However, hot air is lighter and therefore tends to rise. This unstable situation results in thermal updrafts. Hot air at one location will rise, and then as it cools will sink at some nearby location. The hawk can glide in the uprising air, so it slowly sinks with respect to the air but rises with respect to the ground. Once high up, it can then glide anywhere while searching for food, until it is low enough that it must seek another updraft.

Life in Moving Fluids,
by Steven Vogel.

Most birds don’t soar but instead flap their wings to fly. This flapping is complicated enough that I’ll let Steven Vogel—my favorite expert on biological fluid dynamics—explain it. The following excerpt is from his wonderful book Life in Moving Fluids.

In birds, bats, and insects, flapping wings combine the functions that airplanes divide between fixed wings and propellers—in a sense, they’re closer to helicopters than to airplanes, and it’s all too easy to be misled by our habit of calling the propulsive appendages “wings” rather than “propeller blades.” But they aren’t quite like ordinary propellers either, since flapping wings produce both thrust and lift directly, rather than producing thrust directly and getting lift by diverting some of the thrust to pay for the drag of fixed, lift-producing wings. The composite function, as well as their reciprocating rather than rotational motion, mean that the motion of flapping wings is inevitably complex… The downstroke moves a wing forward as well as downward and produces mainly upward force but usually some rearward force as well. The upstroke goes backward as well as upward, producing mainly rearward force but often some upward force.

Scaling

Scaling,
by Knut Schmidt-Nielsen.

Each summer my wife puts out a feeder filled with sugar water, and near it we plant red cardinal flowers, to attract hummingbirds. The hummingbirds are tiny and are constantly eating. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I explain how an animal’s metabolic rate scales with its size and mass. The heat produced from metabolism increases with the volume of the animal, but heat is lost by an animal at its surface. As you compare larger animals to smaller ones, the volume increases with size faster than the surface area does. This means that large animals have trouble getting rid of excess heat, while small animals find it difficult to stay warm. The tiny hummingbird is smaller than other birds, so it tends to cool down quickly (it has a large surface-to-volume ratio). To keep warm, it has to boost its metabolism, which means it must eat a lot. A high metabolic rate requires not only much food but also oxygen, which implies that the hummingbird’s heart must pump a lot of blood. The heart rate of a hummingbird can be upwards of 1000 beats per minute (a normal heart rate for a human is 60 to 100 bpm).

Scaling relationships like we just saw for the hummingbird are common in biology. If you want to learn more about this topic, I suggest Knut Schmidt-Nielsen’s fascinating book Scaling: Why is Animal Size so Important?

Drinking

My favorite bird is the mourning dove. We sometimes will have eight or more of these sweet, gentle birds around our bird feeder. I love their low-pitched coo… coo… coooooooooo song. They mate for life.

Doves are unique among birds in the way they drink. Most birds fill their bill with water and then gravity pulls it down to their stomach. Sometimes they tilt their head back to help the water flow. Mourning doves, on the other hand, suck water into their bill, like we suck water through a straw. Professor Gart Zweers, from the University of Leiden, took high-speed x-ray photos, and concluded that doves draw a partial vacuum which pulls the water up.

Singing

Bird songs are analyzed using plots of time and frequency. As discussed in Chapter 11 of Intermediate Physics for Medicine and Biology, you can resolve any function of time into its component frequencies: Fourier analysis. If you plot the instantaneous frequency versus time, you get a sonogram. The higher the frequency, the higher the pitch that we hear. The northern cardinal’s song starts on a high pitch (around 4 kilohertz, which is about the frequency of highest pitched note on a piano) and then slurs downward an octave (to 2 kilohertz) in about half a second.

Trevisan and Mindlin (Philosophical Transactions A, Volume 367, Pages 3239–3254, 2009) have modeled the bird’s vocal organ, called the syrinx. Their model might be familiar to physics students: it is Newton’s second law, force equals mass times acceleration. The important parameters that enter the model are the mass, stiffness, and a constant characterizing the dissipation or attenuation of the motion. The dissipation can be nonlinear, leading to all sorts of complex dynamics. The model predicts an oscillatory behavior (like that for a mass on a spring). Furthermore, the beak acts as a resonance tube (somewhat like an organ pipe).

We get majestic red cardinals visiting our birdfeeders all the time. Next time you hear a cardinal singing, think of all the physics going on.

Magnetoreception

Are Electromagnetic Fields
Making Me Ill?

Many birds make long migrations, and one wonders how they find their way. One method is magnetoreception: the sensing of magnetic fields. Most organisms cannot detect magnetic fields, but some birds can. Magnetoreception is possible because the birds have small particles of magnetite, called magnetosomes, which provide a magnetic moment that can interact with a magnetic field. I discussed magnetoreception in my book Are Electromagnetic Fields Making Me Ill?

In 1963, German zoologist Wolfgang Wiltschko placed European robins inside a chamber and turned on a magnetic field comparable in strength to the earth’s field. He did not expect a response, but to his surprise the birds oriented with the field… The robins proved adept at sensing magnetic signals during their annual migration.

Some researchers believe there are other mechanisms for magnetoreception besides magnetite particles. I wrote

A few animals, including the European robin, may take advantage of free radical reactions instead of magnetite for magnetoreception. Sonke Johnsen and Kenneth Lohmann [Physics Today, Volume 61, Pages 29–35, 2008], after reviewing the data, conclude that “the current evidence for the radical-pair hypothesis is maddeningly circumstantial…” The jury is still out on this issue.

To tell you the truth, I’m skeptical that free radical reactions are important.

Another animal that may detect the earth’s magnetic field and use it to navigate is the bee. Next week we will continue this series on the physics of native gardening by examining the physics of bees.

 Northern cardinal song

https://www.youtube.com/watch?v=e_b4PkcpDe0

The Physics of Native Gardening

Since my retirement, I’ve started gardening with native plants. Originally this was an interest of my wife’s, but through her I became interested too. We live in a traditional suburban neighborhood, with most of the homes having primarily turf grass lawns that are maintained with a lot of water, fertilizer, and herbicides. But whether the neighbors like it or not, we have changed. Each year, we convert more and more of our yard to native flower gardens. We have a rain garden in a low spot in the back yard, and several other gardens are back there too. In the front, under our crabapple and serviceberry trees, we have all sorts of flowers, including goldenrods and asters.

A garden in our back yard with swamp milkweed,
purple cone flowers, and black-eyed Susans.

Nature's Best Hope,
by Doug Tallamy.

The point of native gardening is not just to have pretty flowers. Our main goal is to support the native birds, butterflies, bees, and other animals. Evolution creates complex and interdependent ecosystems, where the flowers rely on the bees and butterflies for pollination, the bees and butterflies need the pollen and nectar for food, and the birds eat the caterpillars (soon to be butterflies) and flower seeds. We face a biodiversity crisis in our society that we can address, in a small way, with native gardening. One book that influenced me in this endeavor is Doug Tallamy’s Nature’s Best Hope: A New Approach to Conservation that Starts in Your Yard. I highly recommend it.

I’m still a physicist, interested in the applications of physics to medicine and biology. There’s lots of physics in native gardening, which I intend to explore. So, over the next few weeks I’ll post a series of essays about the physics of native gardening. Next week will be the physics of birds, the following week the physics of bees, and the third week the physics of butterflies. Some topics will be drawn from Intermediate Physics for Medicine and Biology, but most will come from other sources.

You might ask, why just birds, bees, and butterflies? Why not bats, beavers, and beetles? Fair question. We have many other animals visiting our yard. We’ve been trying to attract frogs and toads, but without a pond or stream it is difficult. Worms are a crucial asset for any gardener, especially if you maintain a compost heap like we do. Other insects we often see include the desirable dragonflies, moths, and lightning bugs, and some undesirable ones like wasps, flies, and mosquitoes. We have small mammals such as squirrels (who do their best to invade our bird feeders, but that’s another story), rabbits, and chipmunks. Our yard is too small to support larger predators, like foxes or coyotes, but we do occasionally have a Cooper’s hawk visit. On rare occasion, we see a raccoon, skunk, possum, or ground hog, but I don’t think they live here. One large mammal that comes a lot is white-tailed deer, which wander in from a nearby forest. They only eat plants, and act like giant rabbits as far as their ecological niche. I would enjoy having a big oak tree, but we don’t. We do have a couple maples, and a linden tree growing up in the middle of our deck. We love all these plant and animals.

It’s not my habit to do a series of postings on related topics. But biodiversity is important. Moreover, it’s cold and snowy here in Michigan right now so I can’t go out and dig, weed, water, or plant. I’ll do the next best thing and write. I hope you enjoy it.

Tune in next week as we explore the physics of birds. 

Our rain garden. A big swamp milkweed is in the center,
surrounded by nodding onions and golden Alexanders.
Blue flag irises are in the back (difficult to see in this photo).

Nature’s Best Hope: Conservation That Starts in Your Yard, with Doug Tallamy.

https://www.youtube.com/watch?v=CBWhaTbe_x0 

 

Edward O. Wilson discusses the half-earth project.

https://www.youtube.com/watch?v=lmoD-pNANWo
 

The Cyclotron Resonance Hypothesis

Want a sneak peek at one of the new homework problems tentatively included in the 6th edition of Intermediate Physics for Medicine and Biology? Today I present a problem related to the flawed “cyclotron resonance hypothesis.” A lot of nonsense has been written about the idea of extremely low frequency electromagnetic fields influencing biology and medicine, and one of the proposed mechanisms for such effects is cyclotron resonance. 

In Section 8.1 of the 5th edition of IPMB, Russ Hobbie and I discuss the cyclotron.

One important application of magnetic forces in medicine is the cyclotron. Many hospitals have a cyclotron for the production of radiopharmaceuticals, especially for generating positron-emitting nuclei for use in Positron EmissionTomography (PET) imaging (see Chap. 17).

Consider a particle of charge q and mass m, moving with speed v in a direction perpendicular to a magnetic field B. The magnetic force will bend the path of the particle into a circle. Newton’s second law states that the mass times the centripetal acceleration, v²/r, is equal to the magnetic force

      mv²/r = qvB.      (8.5)

The speed is equal to [the] circumference of the circle, 2πr, divided by the period of the orbit, T. Substituting this expression for v into Eq. (8.5) and simplifying, we find

       T = 2π m/(qB).   (8.6)

In a cyclotron particles orbit at the cyclotron frequency, f = 1/T. Because the magnetic force is perpendicular to the motion, it does not increase the particles’ speed or energy. To do that, the particles are subjected periodically to an electric field that changes direction with the cyclotron frequency so that it is always accelerating, not decelerating, the particles. This would be difficult if not for the fortuitous disappearance of both v and r from Eq. (8.6), so that the cyclotron frequency only depends on the charge-to-mass ratio of the particles and the magnetic field, but not on their energy.

This analysis of cyclotron motion works great in a vacuum. The trouble begins when you apply the cyclotron concept to ions in the conducting fluids of the body. The proposed hypothesis says that when an ion is moving about in the presence of the earth’s magnetic field, the resulting magnetic force causes it to orbit about the magnetic field lines, with an orbital period equal to the reciprocal of the cyclotron frequency. If any electric field is present at that same frequency, it could interact with the ion, increasing its energy or causing it to cross the cell membrane.

Below is a draft of the new homework problem, which I hope debunks this erroneous hypothesis.

Section 9.1

Problem 7. One mechanism for how organisms are influenced by extremely low frequency electric fields is the cyclotron resonance hypothesis. 

(a) The strength of the earth's magnetic field is about 5 × 10^–5 T. A calcium ion has a mass of 6.7 × 10^–26 kg and a charge of 3.2 × 10^–19 C. Calculate the cyclotron frequency of the calcium ion. If an electric field exists in the tissue at that frequency, the calcium ion will be in resonance with the cyclotron frequency, which could magnify any biological effect. 

(b) This mechanism seems to provide a way for an extremely low frequency electric field to interact with calcium ions, and calcium influences many cellular processes. But consider this hypothesis in more detail. Use Eq. 4.12 to calculate the root-mean-square speed of a calcium ion at body temperature. Use this speed in Eq. 8.5 to calculate the radius of the orbit. Compare this to the size of a typical cell. 

(c) Now make a similar analysis, but assume the radius of the calcium ion orbit is about the size of a cell (since it would have difficulty crossing the cell membrane). Then use this radius in Eq. 8.5 to determine the speed of the calcium ion. If this is the root-mean-square speed, what is the body temperature? 

(d) Finally, compare the period of the orbit to the time between collisions of the calcium ion with a water molecule. What does this imply for the orbit?

This analysis should convince you that the cyclotron resonance hypothesis is unlikely to be correct. Although the frequency is reasonable, the orbital radius will be huge unless the ions are traveling extraordinarily slowly. Collisions with water molecules will completely disrupt the orbit.

For those who don't have the 5th edition of IPMB handy, Eq. 4.12 says the root-mean-square speed is equal to the square root of 3 times Boltzmann's constant times the absolute temperature divided by the mass of the particle. 

I won’t give away the solution to this problem (once the 6th edition of IPMB is out, instructors can get the solution manual for free by emailing me at roth@oakland.edu). But here are some order-of-magnitude results. The cyclotron frequency is tens of hertz. The root-mean-square (thermal) speed of calcium at body temperature is hundreds of meters per second. The resulting orbital radius is about a meter. That is bigger than the body, and vastly bigger than a cell. To fit the orbit inside a cell, the speed would have to be much slower, on the order of a thousandth of a meter per second, which corresponds to a temperature of about a few nanokelvins. The orbital period is a couple hundredths of a second, but the time between collisions of the ion with a water molecule is one the order of 10^–13 seconds, so there are many billions of collisions per orbit. Any circular motion will be destroyed by collisions long before anything like an orbit is established. I’m sorry, but the hypothesis is rubbish.

Are Electromagnetic Fields
Making Me Ill?

If you want to learn more about how extremely low frequency electric fields interact with tissue, see my book Are Electromagnetic Fields Making Me Ill?

Finally, for you folks who are really on the ball, you may be wondering why this homework problem is listed as being in Chapter 9 when the discussion of the cyclotron is in Chapter 8 of the 5th edition of IPMB. (In this post I changed the equation numbers in the homework problem to match the 5th edition, so you would have them.) Hmm.. is there a new chapter in the 6th edition? More on that later…

 To be fair, I should let my late friend Abraham Liboff tell you his side of the story. In this video, Abe explains how he proposed the cyclotron resonance hypothesis. I liked Abe, but I didn’t like his hypothesis.

https://www.youtube.com/watch?v=YL-wqJ-PMAQ&list=PLCO-VktC6wofkMeEeZknT9Y4WhMnP76Ee&index=6

The Luria-Delbrück Experiment

Introduction

Today’s question is: do mutations happen randomly, or are they caused by some selective pressure? In other words, are mutations a Darwinian event where they happen by chance and then natural selection selects those that are favorable to pass on to the offspring, or are mutations Lamarckian where they happen because they help a species survive (like a giraffe constantly stretching its neck to reach the leaves at the top of the tree, thereby making its neck longer, and then passing that acquired trait to its offspring). To determine which of these two hypotheses is correct, we need an experimental test.

Let’s examine one famous experiment. To make things simple, consider a specific case. Assume we start with just one individual, who is not a mutant. Furthermore, let each parent have two offspring, and only analyze three generations. For the first two generations there is no selective pressure, and only in the third generation the selective pressure is present. To make the analysis really simple, assume the probability of a mutation, p, is very small.

The most common case is shown in the figure below. Blue circles represent the individuals in each generation, starting in the first generation with just one. Locations where lines branch represent births. (Wait, you say, each child should have two parents, not one! Okay, we are making a simple model. Assume an individual reproduces asexually by splitting into two. We should talk about “splittings” and not “births.”) The green dashed line represents when the selective pressure begins. So our picture shows one great-grandparent, two grandparents, four parents, and eight children. A mutation is indicated by changing a blue circle to red. 

Because p << 1, by far the most common result is shown below, with no mutations. 

 

Lamarckian Evolution

In the case when mutations are caused by some selective pressure (Lamarckian), you can get a more interesting situation like shown below. No one above the dashed line undergoes a mutation because there was no selective pressure then. A child below the dashed line in the bottom row might have a mutation. There are eight children, so the probability of one of the eight having a mutation is 8p. The probability of two offspring having mutations will go as p², but since we are assuming p is small the odds of having multiple mutant offspring will be negligible. We’ll ignore those cases.  

Let’s calculate some statistics for this case. Let n be the number of mutant offspring in the last generation (below the dashed line). To find the average value, or mean, of n over several experiments, which we’ll call <n>, you sum up all the possible cases, each multiplied by its probability. In general, we could have n = 0, 1, 2, …, 8, each with probability p₀, p₁, …, p₈, so <n> is 

<n> = p₀ (0) + p₁ (1) + p₂ (2) + … + p₈ (8).

But in this case p₂, p₃, …, p₈ are all negligibly small, so we have only the first two terms in the sum to worry about.

For each individual, the odds of not mutating is (1 – p). In the last generation below the dashed line there are 8 offspring, so the probability of none of them having a mutation, p₀, is (1 – 8p). The probability for one mutation (p₁) is 8p because there are 8 offspring, each with probability p of mutating. So

<n> = (1 – 8p) (0) + 8p (1) = 8p .

We will also be interested in the variation of results between different trials. For this, we need <n²>

<n²> = (1 – 8p) (0)² + 8p (1)² = 8p .

The variance is the mean of the square of the variation from the mean. In Appendix G of Intermediate Physics for Medicine and Biology, Russ Hobbie and I call the variance σ² and we prove that σ² = <n²> – <n>². In our case

σ² = <n²> – <n>² = 8p – (8p)² .

But remember, p << 1 so the last term is negligible and the variance is 8p. Therefore, the mean and variance are the same. You may have seen a probability distribution with this property before. Appendix J of IPMB states that the Poisson distribution has the same mean and variance. Basically, the Lamarckian case is a Poisson process. 

 

Darwinian Evolution

Now consider the case when mutations occur randomly (Darwinian). You still can get all the results shown earlier in the Lamarckian case, but you get others too because mutations can happen all the time, not just when the selective pressure is operating. Suppose one of the parents (just above the dashed line) mutates. Their mutation gets passed to both offspring. The odds of mutating back (changing from red to blue) are very small (p << 1), so we assume both offspring of a mutant inherit the mutation, as shown below. 

You could also have one of the two grandparents give rise to four mutant offspring below the dashed line, as shown below.

Let’s do our statistics again. As before, the vast majority of the cases have no mutations. There are now 14 cases, each of which could have the mutation in one of the offspring. All the cases are shown below.

The probability of having no mutations ever (the bottom right case) is (1 – 14p). The probability of one of the offspring having a mutation is 8p (the eight cases in the top row). The probability of any one of the parents having a mutation is p and there are 4 parents, so the probability of a mutation among the parents is 4p, and each would give rise to two mutants below the dashed line (the four cases on the left in the bottom row). Finally, one of the two grandparents could mutate (the fifth and sixth cases in the bottom row), each with probability p. If a grandparent mutates it results in 4 mutants below the dashed line. So, the mean number of mutants in the final generation is

<n> = (1 – 14p) (0) + 8p (1) + 4p (2) + 2p (4) = 24p .

The odds of a mutant appearing in the final generation is three times higher in the Darwinian case than in the Lamarckian case. What about the variance?

<n²>  = (1 – 14p) (0)² + 8p (1)² + 4p (2)² + 2p (4)² = 56p .

The variance is

σ² = <n²> – <n>²  = 56p – 24²p² = 56p

(remember, terms in p² are negligible). Now the variance (56p) is over twice the mean (24p). It is not a Poisson process. It’s something else. There is much more variation in the number of mutants because of mutations happening early in the family tree that pass the mutation to all of the subsequent offspring. 

 

Conclusion

In an experiment, p may not be easy to determine. You need to know how many individuals you start with (in our example, one) and how many generations you examine (in our example, three), as well as how many mutants you end up with. But you can easily compare the variance to the mean; just take their ratio (variance/mean). If they are the same, you suspect a Lamarckian Poisson process. If the variance is significantly more than the mean, you suspect Darwinian selection.  In our example, variance/mean = 2.3.

There are some limitations. The probability is not always very small, so you might need to extend this analysis to cases where you have more than one mutation occurring. Also, in many experiments you will want to let the number of generations be much larger than three. There is also the possibility of a mutant mutating back to its original state. Finally, during sexual reproduction you have the in-laws to worry about, and you could have more than two offspring. So, to be quantitative you have some more work to do. But even in the more general case, the qualitative conclusion remains the same: Darwinian evolution results in a larger variance in the number of mutants than does Lamarckian evolution.

I suspect you now are saying “this is an interesting result; has anyone done this experiment?” The answer is yes! Salvador Luria and Max Delbrück did the experiment using E. coli bacteria (so the asexual splitting of generations is appropriate). The selective pressure applied at the end was resistance to a bacteriophage (a virus that infects bacteria). Their result: there was a lot more variation than you would expect from a Poisson process. Evolution is Darwinian, not Lamarckian. Mutations happen all the time, regardless of if there is some evolutionary pressure present.

 

The Luria-Delbrück experiment, described by Doug Koshland of UC Berkeley. 

https://www.youtube.com/watch?v=slfLeKqE3Bg